# Mathematical Sciences

The oldest known science, mathematics is the language of numbers, logic, reasoning, structure, space and shape. The Infosys Prize has awarded work in number theory, mathematical physics, complex geometry, theoretical computer science, and applied mathematics among others.

## Laureates

##### Mathematical Sciences 2023

### Bhargav Bhatt

Fernholz Joint Professor, Institute for Advanced Study and Princeton University Gehring Professor, University of Michigan

Read More##### Mathematical Sciences 2022

### Mahesh Kakde

Professor, Department of Mathematics, Indian Institute of Science, Bengaluru

Read More##### Mathematical Sciences 2020

### Sourav Chatterjee

Professor of Mathematics and Statistics, Department of Statistics, Stanford University, USA

Read More##### Mathematical Sciences 2019

### Siddhartha Mishra

Professor, Department of Mathematics, ETH Zürich

Read More##### Mathematical Sciences 2018

### Nalini Anantharaman

Professor and Chair of Mathematics, Institute for Advanced Study, University of Strasbourg

Read More##### Mathematical Sciences 2017

### Ritabrata Munshi

Professor, School of Mathematics, Tata Institute of Fundamental Research, Mumbai and Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata

Read More##### Mathematical Sciences 2016

### Akshay Venkatesh

Professor, Department of Mathematics, Stanford University, US

Read More##### Mathematical Sciences 2015

### Mahan Mj

Professor, School of Mathematics, Tata Institute of Fundamental Research, Mumbai

Read More##### Mathematical Sciences 2014

### Madhu Sudan

Principal Researcher, Microsoft Research New England, and Adjunct Professor, Electrical Engineering and Computer Science department, and Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, USA

Read More##### Mathematical Sciences 2013

### Rahul Pandharipande

Professor, Department of Mathematics, Eidgenössische Technische Hochschule (ETH), Zurich

Read More##### Mathematical Sciences 2012

### Manjul Bhargava

Professor of Mathematics, Princeton University, USA

Read More##### Mathematical Sciences 2011

### Kannan Soundararajan

Professor of Mathematics and Director, Mathematics Research Center, Stanford University, USA

Read More##### Mathematical Sciences 2010

### Chandrashekhar Khare

Professor, Mathematics, University of California, Los Angeles

Read More##### Mathematical Sciences 2009

### Ashoke Sen

Professor, Department of Physics,Harish-Chandra Research Institute, Allahabad

Read More##### Mathematical Sciences 2008

### Manindra Agrawal

Professor & Dean of Faculty Affairs, Department of Computer Science & Engineering , Indian Institute of Technology, Kanpur

Read More## Jury

### Chandrashekhar Khare

Professor, University of California, Los Angeles

View More### Chandrashekhar Khare

Professor, University of California, Los Angeles

View More### Prof. Chandrashekhar Khare

Professor, University of California, Los Angeles

View More### Prof. Chandrashekhar Khare

Professor & David Saxon Presidential Term Chair in Mathematics, University of California, Los Angeles

View More### Prof. Chandrashekhar Khare

Professor & David Saxon Presidential Term Chair in Mathematics, University of California, Los Angeles

View More### Prof. Srinivasa S. R. Varadhan

Professor of Mathematics and Frank J. Gould Professor of Science at the Courant Institute of Mathematical Sciences, New York University, USA

View More### Prof. Srinivasa S. R. Varadhan

Professor of Mathematics and Frank J. Gould Professor of Science at the Courant Institute of Mathematical Sciences, New York University, USA

View More### Prof. Srinivasa S. R. Varadhan

Professor of Mathematics and Frank J. Gould Professor of Science at the Courant Institute of Mathematical Sciences, New York University, USA

View More### Prof. Srinivasa S. R. Varadhan

### Srinivasa S. R. Varadhan

### Srinivasa S. R. Varadhan

### Srinivasa S. R. Varadhan

### Srinivasa S. R. Varadhan

### Prof. Srinivasa S. R. Varadhan

### Prof. Srinivasa S. R. Varadhan

### Prof. Srinivasa S. R. Varadhan

### Mathematical Sciences 2024

Prof. Chandrashekhar Khare was born in Mumbai, and studied at Cambridge, Oxford and Caltech, where he obtained his Ph.D. in 1995. He worked at the Tata Institute of Fundamental Research and the University of Utah and is now a professor at the University of California, Los Angeles. Prof. Khare’s research is in number theory, especially on the relation between modular forms and Galois representations that underpins Wiles’ proof of Fermat’s Last Theorem. In 2008, he and Jean-Pierre Winterberger made a remarkable breakthrough with their proof of a celebrated conjecture of J.P. Serre. Prof. Khare’s honors and awards include the Fermat Prize (2007), Infosys Prize (2010) and the Cole Prize (2011), and he was elected as a Fellow of the Royal Society in 2012.

Hélène Esnault is Einstein Professor (Emeritus) at Free University Berlin’s Institute of Mathematics. Prof. Hélène Esnault specializes in algebraic geometry.

Prof. Esnault is a member of the Academia Europaea, the German National Academy of Sciences Leopoldina, the Berlin-Brandenburg Academy of Sciences and Humanities, the Nordrhein-Westfalen Academy of Sciences and the Arts, and a corresponding member of the Danish Royal Academy.

Esnault was awarded the Leibniz Prize 2003 and the Cantor Medal in 2019. She is or has been an editor of many journals, including Duke, Mathematische Annalen, Mathematical Research Letters, Algebra and Number Theory, Astérisque, J. of the European Mathematical Society, Memoirs of the European Mathematical Society and Acta Mathematica and Acta Mathematica. Prof. Esnault was a member of the Fields Committee (2018) and is Chair of the Shaw Prize Committee (2021-2025).

Meena Mahajan is a professor at The Institute of Mathematical Sciences (IMSc) in Chennai. Prof. Meena Mahajan's research interests encompass many aspects of computational complexity theory, including Boolean function complexity, algebraic circuits, proof complexity, and space bounded computation. Prof. Mahajan completed her undergraduate and postgraduate degrees from the department of computer science and engineering at IIT-Bombay and went on to receive her Ph.D. from IIT-Madras.

Mahajan has held several professional roles including member (and past chair) of the Steering Committee of the Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), the executive council of the Indian Association for Research in Computer Science IARCS, the editorial board of the ACM Books series, the editorial board of the Leibniz International Proceedings in Informatics (LIPIcs), the advisory board of the journal TheoretiCS, and the board of trustees of the Computational Complexity Foundation. Since 2019, Prof. Mahajan has been an ACM India Eminent Speaker. She is an elected Fellow of the Indian Academy of Sciences (2022) and a recipient of the J C Bose Fellowship (2024). Meena Mahajan serves on the ICM Structure Committee for ICM 2026.

Siddhartha Mishra is a professor in the Department of Mathematics at ETH Zürich. Prof. Siddhartha Mishra received an honors degree in Mathematics and Physics from Utkal University in Bhubaneswar in 2000. After his graduation he joined the Applied Mathematics program run jointly by IISc and TIFR in Bengaluru. Prof. Mishra received his M.S. and Ph.D. degrees from both.

Mishra went to CMA at University of Oslo as a post-doc (2005-2009) and followed it up with an Assistant Professorship at ETH Zürich (2009-2011). He became a full professor in 2015. Siddhartha Mishra is the recipient of many awards such as the Richard von Mises Prize (2015), the Jacques Louis Lions Award (2018), ICIAM Collatz Prize (2019), the SIAM Germund Dahlquist Prize (2021) and the Rössler Prize of ETH Zurich (2023). In 2024, he became an elected fellow of the European Academy of Sciences. Prof. Mishra was an invited speaker at the International Congress of Mathematicians held in Rio de Janeiro in 2018. In 2019, Prof. Siddhartha Mishra received the Infosys Prize in Mathematical Sciences.

Prof. Dipendra Prasad is a number theorist who specializes in automorphic forms and representation theory. After completing his Ph.D. from Harvard University in 1989, Prof. Prasad was with the Tata Institute of Fundamental Research in Mumbai, and the Harish-Chandra Research Institute in Allahabad, and is presently at the Indian Institute of Technology, Bombay. Prasad is a Fellow of all three science academies in India and is also a Fellow of the World Academy of Sciences (TWAS). He is a recipient of the Swarna Jayanti fellowship, the Shanti Swarup Bhatnagar award, the JC Bose fellowship, and the TWAS prize. Dipendra Prasad was an ICM speaker in 2018 at Rio de Janeiro. He held the Jean Morlet Chaire at CIRM, Luminy in 2016, and was the principal investigator for a mega grant at St. Petersburg University from 2018-2022.

### Mathematical Sciences 2023

Prof. Chandrashekhar Khare was born in Mumbai, and studied at Cambridge, Oxford and Caltech, where he obtained his Ph.D. in 1995. He worked at the Tata Institute of Fundamental Research and the University of Utah and is now a professor at the University of California, Los Angeles. Prof. Khare’s research is in number theory, especially on the relation between modular forms and Galois representations that underpins Wiles’ proof of Fermat’s Last Theorem. In 2008, he and Jean-Pierre Winterberger made a remarkable breakthrough with their proof of a celebrated conjecture of J.P. Serre. Prof. Prof. Khare’s honors and awards include the Humboldt Research Award (2011), Cole Prize (2011), Infosys Prize (2010), the Guggenheim fellowship (2008), Fermat Prize (2007), and the INSA Young Scientist Award (1999). In 2012, he was elected as a Fellow of the Royal Society (UK).

Meena Mahajan is a professor at The Institute of Mathematical Sciences (IMSc) in Chennai. Prof. Mahajan's research interests encompass many aspects of computational complexity theory, including Boolean function complexity, algebraic circuits, proof complexity, and space bounded computation. Prof. Mahajan completed her undergraduate and postgraduate degrees from the department of computer science and engineering at IIT-Bombay and went on to receive her Ph.D. from IIT-Madras.

Prof. Mahajan has held several professional roles including member (and past chair) of the Steering Committee of the Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), the executive council of the Indian Association for Research in Computer Science IARCS, the editorial board of the ACM Books series, the editorial board of the *Leibniz International Proceedings in Informatics* (LIPIcs), the advisory board of the journal *TheoretiCS*, and the board of trustees of the Computational Complexity Foundation. Since 2019, Prof. Mahajan has been an ACM India Eminent Speaker. She is an elected Fellow of the Indian Academy of Sciences (2022) and serves on the ICM Structure Committee for ICM 2026.

Prof. Siddhartha Mishra received an honors degree in Mathematics and Physics from Utkal University in Bhubaneswar in 2000. After his graduation he joined the Applied Mathematics program run jointly by IISc and TIFR in Bengaluru. Prof. Mishra received his M.S. and Ph.D. degrees from both.

Prof. Mishra went to CMA at University of Oslo as a post-doc (2005-2009) and followed it up with an Assistant Professorship at ETH Zürich (2009-2011). He became a full Professor in 2015. Mishra is the recipient of many awards such as the Richard von Mises Prize (2015), the Jacques Louis Lions Award (2018), and the ICIAM Collatz Prize (2019). He was an invited speaker at the International Congress of Mathematicians held in Rio de Janeiro in 2018. In 2019, Prof. Mishra received the Infosys Prize in Mathematical Sciences.

Prof. Dipendra Prasad is a number theorist who specializes in automorphic forms and representation theory. After completing his Ph.D. from Harvard University in 1989, Prof. Prasad was with the Tata Institute of Fundamental Research in Mumbai, and the Harish-Chandra Research Institute in Allahabad, and is presently at the Indian Institute of Technology, Bombay. Prasad is a Fellow of all three science academies in India and is also a Fellow of the World Academy of Sciences (TWAS). He is a recipient of the Swarna Jayanti fellowship, the Shanti Swarup Bhatnagar award, the JC Bose fellowship, and the TWAS prize. Dipendra Prasad was an ICM speaker in 2018 at Rio de Janeiro. He held the Jean Morlet Chaire at CIRM, Luminy in 2016, and was the principal investigator for a mega grant at St. Petersburg University from 2018-2022.

Prof. Hélène Esnault is a French-German mathematician specializing in algebraic geometry. Prof. Esnault is Einstein Professor (Emeritus) at Free University Berlin’s Institute of Mathematics. She was awarded the Leibniz Prize in 2003. In 2014 Prof. Esnault was elected to the Academia Europaea. She is also a member of the (German) National Academy of Sciences Leopoldina, the Berlin-Brandenburg Academy of Sciences and Humanities, and the Nordrhein-Westfalen Academy of Sciences and the Arts. In 2019 Hélène Esnault was awarded the Cantor Medal. She is or has been an editor of many journals, including *Duke, Mathematische Annalen, Mathematical Research Letters, Algebra and Number Theory, Astérisque, J. of the European Mathematical Society, and Acta Mathematica*. Prof. Esnault is a member of the Fields Committee (2018) and Chair of the Shaw Prize Committee (2021-2025).

### Mathematical Sciences 2022

Prof. Chandrashekhar Khare was born in Mumbai, and after finishing his higher secondary education there, studied for the Mathematical Tripos at Trinity College, Cambridge. After a year of study at Oxford, he moved to Caltech and obtained his Ph.D. in 1995. He returned to India to work for almost a decade at the Tata Institute of Fundamental Research in Mumbai. He moved thereafter to the University of Utah and has been at the University of California at Los Angeles since 2007.

He is a number theorist and works on the connection between modular forms and Galois representations (such a connection plays a key role in Wiles's solution of Fermat's Last Theorem). Prof. Khare's work with Jean-Pierre Wintenberger gave proof of a celebrated conjecture of J.-P. Serre in the subject. The conjecture had motivated much work in this central area of number theory and had remained unresolved for more than three decades after it was first formulated.

Prof. Khare has received several honors and awards in recognition of his work. He received the Humboldt Research Award in 2011, Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held in Hyderabad in August 2010. In 2012, he was elected as a Fellow of the Royal Society.

Andrew Wiles is an English mathematician and Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat’s Last Theorem for which he was awarded the Abel Prize in 2016 and the Copley Medal in 2017 by the Royal Society.

He is a number theorist and works on the connection between modular forms and Galois representations. Prof. Wiles was made Knight Commander of the Order of the British Empire in 2000 for his exceptional services to mathematics. Amongst his numerous awards, he has received the prestigious Wolf Prize and Shaw Prize in Mathematics.

Prof. Wiles completed his undergraduate degree at Merton College at the University of Oxford and undertook his Ph.D at the University of Cambridge under the supervision of Prof. John Coates. As a graduate student, he made a major breakthrough in the diophantine theory of cubic equations, proving a result that became known as the Coates-Wiles Theorem. As a Benjamin Pierce Instructor at Harvard University he collaborated with Barry Mazur to resolve a long-standing conjecture in Iwasawa Theory.

Prof. Mahan Mj is Senior Professor of Mathematics at Tata Institute of Fundamental Research (TIFR), Mumbai. He is best known for his work in hyperbolic geometry, geometric group theory, low-dimensional topology, and complex geometry.

He was born Mahan Mitra in 1968 and went to St. Xavier’s Collegiate School in Kolkata. He went to IIT-Kanpur, initially to major in Electrical Engineering, but switched later to mathematics. He graduated with a Master’s degree in 1992. He received his Ph.D. from the University of California, Berkeley in 1997. He is a monk of the Ramakrishna Order since 1998. He received the Shanti Swarup Bhatnagar award in 2011, and the Infosys Prize (Mathematical Sciences) in 2015. He was an invited speaker at the International Congress of Mathematicians in 2018 in Rio de Janeiro.

He is also a founding member of the Infosys-Chandrasekharan Virtual Centre for Random Geometry at the Tata Institute for Fundamental Research.

Prof. Avi Wigderson has been the Herbert H. Maass Professor at the School of Mathematics, Institute for Advanced Study in Princeton since 1999, where he leads the institute’s Computer Science and Discrete Math program. His research interests include computational complexity theory, algorithms, graph theory, cryptography, and pseudo-randomness, as well as connections of the theory of computation to mathematics and the sciences. Prof. Wigderson received his Ph.D. in Computer Science in 1983 from Princeton University. During 1986-2001 he held a permanent position at the Hebrew University Computer Science Institute, where he was the chair from 1992-95. Wigderson has held visiting positions at the University of California, Berkeley, IBM Research, the Mathematical Sciences Research Institute, Princeton University, and the Institute for Advanced Study.

His honors include being a two-time invited speaker at the International Congress of Mathematicians, where he was also presented in 1994 with the Nevanlinna Prize for outstanding contributions in mathematical aspects of information sciences. He gave the AMS Gibbs Lectures and received the AMS Conant Prize for mathematical exposition in 2008. He was the recipient of the 2009 Gödel Prize, which recognizes outstanding papers in theoretical computer science. In 2011 he was elected to the American Academy of Arts and Sciences, and in 2013 he was elected to the National Academy of Sciences. Wigderson received the Abel Prize in 2021 with Hungarian mathematician László Lovász for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.

Sylvia Serfaty is a French mathematician working in the field of partial differential equations and mathematical physics. Her work has particularly focused on the Ginzburg-Landau model of superconductivity and quantum vortexes in the Ginzburg–Landau theory and on the statistical mechanics of Coulomb-type systems.

Prof. Serfaty authored a book on the Ginzburg-Landau theory with Étienne Sandier, Vortices in the Magnetic Ginzburg-Landau Model in 2007, and is one of the Editors-in-Chief of the scientific journal Probability and Mathematical Physics.

In 2004, she was awarded the EMS Prize for her contributions to the Ginzburg–Landau theory. Her other achievements include the Henri Poincaré Prize in 2012, and the Mergier–Bourdeix Prize of the French Academy of Sciences in 2013. She was elected to the American Academy of Arts and Sciences in 2019.

### Mathematical Sciences 2021

Prof. Chandrashekhar Khare was born in Mumbai, and after finishing his higher secondary education there, studied for the Mathematical Tripos at Trinity College, Cambridge. After a year of study at Oxford, he moved to Caltech and obtained his Ph.D. in 1995. He returned to India to work for almost a decade at the Tata Institute of Fundamental Research in Mumbai. He moved thereafter to the University of Utah, and has been at the University of California at Los Angeles since 2007.

He is a number theorist and works on the connection between modular forms and Galois representations (such a connection plays a key role in Wiles's solution of Fermat's Last Theorem). Prof. Khare's work with Jean-Pierre Wintenberger gave a proof of a celebrated conjecture of J.-P. Serre in the subject. The conjecture had motivated much work in this central area of number theory and had remained unresolved for more than three decades after it was first formulated.

Prof. Khare has received a number of honors and awards in recognition of his work. He received the Humboldt Research Award in 2011, Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held at Hyderabad in August 2010. In 2012, he was elected as a Fellow of the Royal Society.

Prof. Akshay Venkatesh is a broad mathematician who has worked on many topics at the interface between number theory and other fields, including representation theory, dynamics, and algebraic topology. He received his Ph.D. in 2002 from Princeton University and did his postdoctoral work at MIT, before moving to faculty positions at NYU and Stanford.

He is currently a professor at the Institute for Advanced Study. Prof. Venkatesh has been honored with numerous accolades for his contributions in the subject. An Infosys Prize Laureate, 2016 and more recently, a recipient of the prestigious Fields Medal, 2018, his list of honors also include: the Ostrowski Prize (2017); Aisenstadt Chair, Université de Montreal (2010); SASTRA Ramanujan Prize (2008) and the Salem Prize (2007).

Prof. Parimala Raman is a well-known name in the field of algebra. She has been credited for achieving many firsts in the field of Algebra, including publishing the first example of a nontrivial quadratic space over an affine plane at a young age - an achievement that is said to have surprised even the experts in the field. Apart from looking forward to new research challenges in mathematics, Prof. Raman also enjoys teaching. For many years, she was a professor at Tata Institute of Fundamental Research (TIFR), Mumbai. Prof. Raman has received many accolades for her contributions to mathematics. In 2010, she received one of the highest global honors in her field when she was selected as the plenary speaker at the International Congress of Mathematicians. She spoke about the arithmetic of two-dimensional fields. She is also a recipient of the Shanti Swarup Bhatnagar Prize in 1987; an honorary doctorate from the University of Lausanne in 1999, and the Srinivasa Ramanujan Birth Centenary Award in 2003.

Prof. Avi Wigderson is the Herbert H. Maass Professor in the school of mathematics at the Institute for Advanced Study in Princeton since 1999, where he leads the Insitute’s Computer Science and Discrete Math program. His research interests include complexity theory, parallel algorithms, graph theory, cryptography, distributed computing, and neural networks. Prof. Wigderson received his Ph.D. in computer science in 1983 from Princeton University. During 1986-2001 he has held a permanent position at the Hebrew University Computer Science Institute, where he was the chair from 1992-95. Wigderson has held visiting positions at the University of California, Berkeley, IBM Research, the Mathematical Sciences Research Institute, Princeton University and the Institute for Advanced Study. His honors include being a two-time invited speaker at the International Congress of Mathematicians, where he was also presented in 1994 with the Nevanlinna Prize for outstanding contributions in mathematical aspects of information sciences. He gave the AMS Gibbs Lectures and received the AMS Conant Prize for mathematical exposition in 2008. He was the recipient of the 2009 Gödel Prize, which recognizes outstanding papers in theoretical computer science. In 2011 he was elected to the American Academy of Arts and Sciences, and in 2013 he was elected to the National Academy of Sciences. Wigderson received the Abel Prize in 2021 with Hungarian mathematician László Lovász for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.

Prof. Rajeeva Laxman Karandikar is an Indian mathematician, statistician and psephologist. He served as the director of Chennai Mathematical Institute from 2010 to 2021.

He received his B.Sc. degree in Mathematics from Holkar Science College, University of Indore, Indore in June 1976 and his M.Stat. from Indian Statistical Institute in July 1978. He later obtained his PhD degree from ISI, Calcutta in December 1981. He went for his postdoctoral research to University of North Carolina, Chapel Hill to work under Gopinath Kallianpur. He spent three years as a visiting professor at University of North Carolina at Chapel Hill and returned to Indian Statistical Institute, Delhi in 1984 as an associate professor, becoming a full professor in 1989. In 2006, he moved to Cranes Software International Limited as executive vice president for analytics. He moved to Chennai Mathematical Institute in 2010 and is currently the Director. He is a Fellow of the Indian Academy of Sciences and Indian National Science Academy.

His research interests include several areas of probability theory, finitely additive probability measures, stochastic calculus, martingale problems and Markov processes, Filtering theory, option pricing theory, psephology in the context of Indian elections and cryptography, among others.

Prof. Terence Tao is an Australian-American mathematician. He received his Bachelor's and Master's degrees at the age of 16 from Flinders University and in 1992, he won a Postgraduate Fulbright Scholarship to undertake research in mathematics at Princeton University, USA. From 1992 to 1996, Prof. Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his Ph.D. at the age of 21. He became a professor of mathematics at UCLA since 1999.

Tao has published nearly 350 research papers and 18 books. Tao's areas of research include harmonic analysis, PDE, combinatorics, probability theory, compressed sensing, and analytic number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal in 2006, the MacArthur Fellowship in 2007, the Waterman Award in 2008, the Nemmers Prize in 2010, the Crafoord prize in 2012, and the Breakthrough Prize in Mathematics in 2015. Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society, the Australian Academy of Sciences (Corresponding Member), the National Academy of Sciences (Foreign member), and the American Academy of Arts and Sciences.

### Mathematical Sciences 2020

Prof. Chandrashekhar Khare was born in Mumbai, and after finishing his higher secondary education there, studied for the Mathematical Tripos at Trinity College, Cambridge. After a year of study at Oxford, he moved to Caltech and obtained his Ph.D. in 1995. He returned to India to work for almost a decade at the Tata Institute of Fundamental Research in Mumbai. He moved thereafter to the University of Utah, and has been at the University of California at Los Angeles since 2007.

He is a number theorist and works on the connection between modular forms and Galois representations (such a connection plays a key role in Wiles's solution of Fermat's Last Theorem). Prof. Khare's work with Jean-Pierre Wintenberger gave a proof of a celebrated conjecture of J.-P. Serre in the subject. The conjecture had motivated much work in this central area of number theory and had remained unresolved for more than three decades after it was first formulated.

Prof. Khare has received a number of honors and awards in recognition of his work. He received the Humboldt Research Award in 2011, Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held at Hyderabad in August 2010. In 2012, he was elected as a Fellow of the Royal Society.

Prof. Akshay Venkatesh is a broad mathematician who has worked on many topics at the interface between number theory and other fields, including representation theory, dynamics, and algebraic topology. His recent work examines new algebraic structures related to the topology of locally symmetric spaces. He received his Ph.D. in 2002 from Princeton University and did his postdoctoral work at MIT, before moving to faculty positions at NYU and Stanford.

He is currently a professor at the Institute for Advanced Study. Prof. Venkatesh has been honored with numerous accolades for his contributions in the subject. An Infosys Prize Laureate, 2016 and more recently, a recipient of the prestigious Fields Medal, 2018, his list of honors also include: the Ostrowski Prize (2017); Aisenstadt Chair, Université de Montreal (2010); SASTRA Ramanujan Prize (2008) and the Salem Prize (2007).

Prof. Parimala Raman is a well-known name in the field of algebra. She has been credited for achieving many firsts in the field of Algebra, including publishing the first example of a nontrivial quadratic space over an affine plane at a young age - an achievement that is said to have surprised even the experts in the field.

Apart from looking forward to new research challenges in mathematics, Prof. Raman also enjoys teaching. For many years, she was a professor at Tata Institute of Fundamental Research (TIFR), Mumbai.

Prof. Raman has received many accolades for her contributions to mathematics. In 2010, she received one of the highest global honors in her field when she was selected as the plenary speaker at the International Congress of Mathematicians. She spoke about the arithmetic of two-dimensional fields. She is also a recipient of the Shanti Swarup Bhatnagar Prize in 1987; an honorary doctorate from the University of Lausanne in 1999, and the Srinivasa Ramanujan Birth Centenary Award in 2003.

Prof. Srinivasa Varadhan is an Indian-American mathematician known for his extensive contributions to probability theory and the field of mathematics as a whole. Prof. Varadhan's awards and honours include the National Medal of Science (2010) from US President Barack Obama, "the highest honor bestowed by the United States government on scientists, engineers and inventors". He is also the winner of the Abel Prize (2007), the Leroy Steele Prize (1996), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995) and the Birkhoff Prize (1994). He was awarded the Padma Bhushan in 2008. He also has honorary degrees from the Chennai Mathematics Institute (2008), the Indian Statistical Institute in Kolkata, India (2004), Université Pierre et Marie Curie in Paris (2003), and from Duke University in USA (2016).

A professor of Electrical Engineering and Computer Science at MIT, and a professor of Mathematical Sciences at the Weizmann Institute of Science, Israel, Prof. Shafi Goldwasser continues to make some fundamental contributions in the fields of cryptography, computational complexity, computational number theory and probabilistic algorithms. Her illustrious career includes many landmark papers, which span topics like creating the theoretical foundations of modern cryptography, the introduction of zero-knowledge interactive proofs, the introduction of multi-prover proofs , discovering the connection between probabilistically checkable proofs and the intractability of approximation problems, showing how to use the theory of elliptic curves to distinguish primes from composites, and launching combinatorial property testing.

Born in 1959 in New York City, she went on to earn her B.S. (1979) in Mathematics and Science from Carnegie Mellon University, and M.S. (1981) and Ph.D. (1984) in Computer Science from the University of California, Berkeley.

A two time recipient of the Gödel Prize in theoretical computer science (1993 and 2001), she has gone on to receive several accolades for her outstanding contributions in Computing and Mathematics. Some of them include: ACM Grace Murray Hopper Award (1996), RSA Award in Mathematics (1998), the ACM Athena award for women in computer science (2008), the Benjamin Franklin Medal in Computer and Cognitive Science (2010), the IEEE Emanuel R. Piore Award (2011), ACM Turing Award (2012), the Barnard College Medal of Distinction (2016), and the Suffrage Science Award (2016). She is a member of the AAAS, ACM, NAE, NAS, Israeli Academy of Science, London Mathematical Society, and Russian Academy of Science.

A leading expert in the Theory of Lie groups, Prof. M.S. Raghunathan has won international recognition for his pioneering research in this area.

Formerly the Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai and a professor of eminence at TIFR in Homi Bhabha Chair, he is one of the few Indian mathematicians to be elected a Fellow of the Royal Society of London. He was awarded the Shanti Swarup Bhatnagar prize (1977) and The World Academy of Sciences prize (1990) for his contributions to mathematics. He is also a recipient of the prestigious Padma Shri and Padma Bhushan awards. Prof. Raghunathan has also played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He has organized several international mathematical meetings in India, among them, Ramanujan centenary celebrations in Chennai in 1987, International Mathematical Olympiad in Mumbai in 1996 and International Congress of Mathematicians in Hyderabad in 2010. Prof. Raghunathan served on the Abel Prize Committee during 2012-2014 and on the Fields Medal Committee in 2017-2018. He served on the Executive Committee of the International Mathematical Union during 1998-2006. His most important and comprehensive contribution in this sphere has been his role in the National Board for Higher Mathematics (NBHM). Prof. Raghunathan has been a member of the Board since its formation in 1983 and became its chairman in 1987. He went on to serve till 2010.

### Mathematical Sciences 2019

Varadhan's awards and honours include the National Medal of Science (2010) from US President Barack Obama, "the highest honor bestowed by the United States government on scientists, engineers and inventors". He is also the winner of the Abel Prize (2007), the Leroy Steele Prize (1996), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995) and the Birkhoff Prize (1994). He was awarded the Padma Bhushan in 2008. He also has honorary degrees from the Chennai Mathematics Institute (2008), the Indian Statistical Institute in Kolkata, India (2004), Université Pierre et Marie Curie in Paris (2003), and from Duke University in USA (2016).

Sanjeev Arora is a theoretical computer scientist who is best known for his work on probabilistically checkable proofs and, in particular, the PCP theorem. More recently he works on theory of machine learning, especially deep learning. Currently the Charles C. Fitzmorris Professor in Computer Science and a visiting Professor of Mathematics at the Institute for Advanced Study, he joined Princeton in 1994 after earning his doctorate from the University of California, Berkeley.

Professor Arora’s honors include the D.R. Fulkerson Prize in Discrete Mathematics (awarded by the American Mathematical Society and Math Optimization Society) in 2012, the ACM-Infosys Foundation Award in the Computing Sciences in the same year, the Best paper award from IEEE Foundations of Computer Science in 2010, and the EATCS-SIGACT Gödel Prize (co-winner), in 2001 and 2010. He was appointed a Simons Foundation investigator in 2012, and was elected an ACM fellow in 2009. In 2012 he became a Simons Investigator and he was elected to the National Academy of Sciences on May 2, 2018.

Professor Khare after obtaining his Ph.D. from Caltech in 1995, he returned to India to work at the Tata Institute of Fundamental Research. In 2005, he moved to the United States, first to the University of Utah and then to the University of California at Los Angeles, where he is now Professor of Mathematics. He received the Humboldt Research Award in 2011, Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held at Hyderabad in August 2010. In 2012, he became Fellow of the American Mathematical Society and was elected as a Fellow of the Royal Society.

Professor Claire Voisin is Professor at Collège de France (Algebraic geometry chair), and member of the Académie des sciences, Paris. She was awarded the Shaw prize in Mathematics, that she shared with J. Kollàr, in 2017 and the CNRS Gold medal, the highest scientific award in France, in 2016. She has been plenary speaker at the International Congress of Mathematicians. Voisin has been distinguished visiting professor at IAS (Princeton, 2014-2015) and invited Senior fellow of ETH (Zurich 2017). Prof. Voisin is foreign associate of the Accademia Nazionale dei Lincei and the National Academy of Sciences. She is recognized for her work on Hodge theory and algebraic cycles. Prof. Voisin is known particularly for her construction of compact Kähler manifolds not homeomorphic to complex projective manifolds, for her proof of the generic Green conjecture on syzygies of canonical curves, and for her contribution to the stable Lüroth problem.

Prof. Raman is a well-known name in the field of algebra. She has been credited for achieving many firsts in the field of Algebra, including publishing the first example of a nontrivial quadratic space over an affine plane at a young age - an achievement that is said to have surprised even the experts in the field.

Apart from looking forward to new research challenges in mathematics, Prof. Raman also enjoys teaching. For many years, she was a professor at Tata Institute of Fundamental Research (TIFR), Mumbai.

Prof. Raman has received many accolades for her contributions to mathematics. In 2010, she received one of the highest global honors in her field when she was selected as the plenary speaker at the International Congress of Mathematicians. She spoke about the arithmetic of two-dimensional fields. She is also a recipient of the Shanti Swarup Bhatnagar Prize in 1987; an honorary doctorate from the University of Lausanne in 1999, and the Srinivasa Ramanujan Birth Centenary Award in 2003.

A leading expert in the Theory of Lie groups, Prof. Raghunathan has won international recognition for his pioneering research in this area.

Formerly the Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai and a professor of eminence at TIFR in Homi Bhabha Chair, he is one of the few Indian mathematicians to be elected a Fellow of the Royal Society of London. He was awarded the Shanti Swarup Bhatnagar prize for his contributions to mathematics. He is also a recipient of the prestigious Padma Shri and Padma Bhushan awards. Prof. Raghunathan has also played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He organized the Ramanujan centenary celebrations in Chennai in 1987, with an international conference attended by the foremost number theorists. His most important and comprehensive contribution in this sphere has been his role in the National Board for Higher Mathematics (NBHM). Raghunathan was a member of the Board since it was formed in 1983 and became its chairman in 1987. He went on to serve till 2010.

### Mathematical Sciences 2018

Varadhan's awards and honours include the National Medal of Science (2010) from US President Barack Obama, "the highest honor bestowed by the United States government on scientists, engineers and inventors". He is also the winner of the Abel Prize (2007), the Leroy Steele Prize (1996), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995) and the Birkhoff Prize (1994). He was awarded the Padma Bhushan in 2008. He also has honorary degrees from the Chennai Mathematics Institute (2008), the Indian Statistical Institute in Kolkata, India (2004), Université Pierre et Marie Curie in Paris (2003), and from Duke University in USA (2016).

Professor Khare after obtaining his Ph.D. from Caltech in 1995, he returned to India to work at the Tata Institute of Fundamental Research. In 2005, he moved to the United States, first to the University of Utah and then to the University of California at Los Angeles, where he is now Professor of Mathematics. He received the Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held at Hyderabad in August 2010. In 2012, he became Fellow of the American Mathematical Society and was elected as a Fellow of the Royal Society.

Jennifer Chayes is Technical Fellow and Managing Director of Microsoft Research New England, New York City, and Montreal. She was for many years Professor of Mathematics at UCLA. She is author of over 140 academic papers and inventor of over 30 patents. Her research areas include phase transitions in computer science, structural and dynamical properties of networks, graph theory, graph algorithms, and computational biology. She is one of the inventors of the field of graphons, which are now widely used in the machine learning of massive networks. Chayes’ recent work focuses on machine learning, broadly defined.

Chayes holds a BA in physics and biology from Wesleyan, where she graduated first in her class, and a PhD in physics from Princeton. She was a postdoctoral fellow at Harvard and Cornell. She is the recipient of the NSF Postdoc Fellowship, the Sloan Fellowship, the UCLA Distinguished Teaching Award, and the Anita Borg Institute Women of Leadership Vision Award. She has twice been a member of the Institute for Advanced Study in Princeton. Chayes is Fellow of the American Association for the Advancement of Science, the Fields Institute, the Association for Computing Machinery, and the American Mathematical Society, and the American Academy of Arts and Sciences. She is the winner of the 2015 John von Neumann Lecture Award, the highest honor of the Society of Industrial and Applied Mathematics. In 2016, she received an Honorary Doctorate from Leiden University.

Chayes serves on numerous scientific boards and committees. She is a past VP of the American Mathematical Society, past Chair of Mathematics for the Association for the Advancement of Science, and past Chair of the Turing Award Selection Committee. She is also committed to diversity in the science and technology, and serves on many boards to increase representation of women and minorities in STEM.

Professor Gopal Prasad's mathematical interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, Bruhat-Tits theory, and representation theory of reductive p-adic groups. He was with the School of Mathematics, TIFR, for 26 years and thereafter with the University of Michigan for over 25 years. He was awarded the Shanti Swarup Bhatnagar prize and made Fellow of the Indian National Science Academy, the Indian Academy of Sciences, and the American Mathematical Society. He was awarded a fellowship by the Guggenheim Foundation. He also won the Humboldt Senior Research Award.

Professor Claire Voisin is Professor at Collège de France (Algebraic geometry chair), and member of the Académie des sciences, Paris. She was awarded the Shaw prize in Mathematics, that she shared with J. Kollàr, in 2017 and the CNRS Gold medal, the highest scientific award in France, in 2016. She has been plenary speaker at the International Congress of Mathematicians. Voisin has been distinguished visiting professor at IAS (Princeton, 2014-2015) and invited Senior fellow of ETH (Zurich 2017). Prof. Voisin is foreign associate of the Accademia Nazionale dei Lincei and the National Academy of Sciences. She is recognized for her work on Hodge theory and algebraic cycles. Prof. Voisin is known particularly for her construction of compact Kähler manifolds not homeomorphic to complex projective manifolds, for her proof of the generic Green conjecture on syzygies of canonical curves, and for her contribution to the stable Lüroth problem.

A leading expert in the Theory of Lie groups, Prof. Raghunathan has won international recognition for his pioneering research in this area.

Formerly the Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai and a professor of eminence at TIFR in Homi Bhabha Chair, he is one of the few Indian mathematicians to be elected a Fellow of the Royal Society of London. He was awarded the Shanti Swarup Bhatnagar prize for his contributions to mathematics. He is also a recipient of the prestigious Padma Shri and Padma Bhushan awards. Prof. Raghunathan has also played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He organized the Ramanujan centenary celebrations in Chennai in 1987, with an international conference attended by the foremost number theorists. His most important and comprehensive contribution in this sphere has been his role in the National Board for Higher Mathematics (NBHM). Raghunathan was a member of the Board since it was formed in 1983 and became its chairman in 1987. He went on to serve till 2010.

### Mathematical Sciences 2017

Varadhan's awards and honours include the National Medal of Science (2010) from US President Barack Obama, "the highest honor bestowed by the United States government on scientists, engineers and inventors". He is also the winner of the Abel Prize (2007), the Leroy Steele Prize (1996), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995) and the Birkhoff Prize (1994). He was awarded the Padma Bhushan in 2008. He also has honorary degrees from the Chennai Mathematics Institute (2008), the Indian Statistical Institute in Kolkata, India (2004), Université Pierre et Marie Curie in Paris (2003), and from Duke University in USA (2016).

Professor Khare after obtaining his Ph.D. from Caltech in 1995, he returned to India to work at the Tata Institute of Fundamental Research. In 2005, he moved to the United States, first to the University of Utah and then to the University of California at Los Angeles, where he is now Professor of Mathematics. He received the Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held at Hyderabad in August 2010. In 2012, he became Fellow of the American Mathematical Society and was elected as a Fellow of the Royal Society.

Jennifer Tour Chayes is Distinguished Scientist, Managing Director and Cofounder of Microsoft Research New England and Microsoft Research New York City. Before joining Microsoft in 1997, Chayes was for many years Professor of Mathematics at UCLA. Chayes is the author of over 130 academic papers and the inventor of over 30 patents. Her research areas include phase transitions in discrete mathematics and computer science, structural and dynamical properties of self-engineered networks, graph theory, graph algorithms, algorithmic game theory, and computational biology. Chayes is one of the inventors of the theory of graph limits, which is widely used for machine learning of massive networks.

Chayes holds a BA in biology and physics from Wesleyan, where she graduated first in her class, and a PhD in mathematical physics from Princeton. She did postdoctoral work in the Mathematics and Physics Departments at Harvard and Cornell. She is the recipient of an NSF Postdoctoral Fellowship, a Sloan Fellowship, the UCLA Distinguished Teaching Award, and the ABI Women of Vision Leadership Award. She has twice been a member of the IAS in Princeton. Chayes is a Fellow of the American Association for the Advancement of Science, the Fields Institute, the Association for Computing Machinery, and the American Mathematical Society, and an Elected Member of the American Academy of Arts and Sciences. She is the winner of the 2015 John von Neumann Lecture Award, the highest honor of the Society of Industrial and Applied Mathematics. Chayes received an Honorary Doctorate from Leiden University in 2016.

Professor Gopal Prasad's mathematical interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, Bruhat-Tits theory, and representation theory of reductive p-adic groups. He was with the School of Mathematics, TIFR, for 26 years and thereafter with the University of Michigan for over 25 years. He was awarded the Shanti Swarup Bhatnagar prize and made Fellow of the Indian National Science Academy, the Indian Academy of Sciences, and the American Mathematical Society. He was awarded a fellowship by the Guggenheim Foundation. He also won the Humboldt Senior Research Award.

Professor Claire Voisin is Professor at Collège de France (Algebraic geometry chair), and member of the Académie des sciences, Paris. In September 2016 she was awarded the CNRS Gold medal, the highest scientific award in France. She has been plenary speaker at the International Congress of Mathematicians. Voisin has been distinguished visiting professor at IAS (Princeton, 2014-2015) and invited Senior fellow of ETH (Zurich 2017). Prof. Voisin is foreign associate of the Accademia Nazionale dei Lincei and the National Academy of Sciences. She is recognized for her work on Hodge theory and algebraic cycles. Prof. Voisin is known particularly for her construction of compact Kähler manifolds not homeomorphic to complex projective manifolds, for her proof of the generic Green conjecture on syzygies of canonical curves, and for her contribution to the stable Lüroth problem.

Professor Raghunathan is currently the Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly, he was a professor of eminence at TIFR in Homi Bhabha Chair. He is a leading expert in the Theory of Lie groups and has won international recognition for his pioneering research in this area.

Prof. Raghunathan is one of the few Indian mathematicians to be elected a Fellow of the Royal Society of London. He was awarded the Shanti Swarup Bhatnagar prize for his contributions to mathematics. He is also a recipient of the prestigious Padma Shri and Padma Bhushan awards. Prof. Raghunathan has also played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He organized the Ramanujan centenary celebrations in Chennai in 1987, with an international conference attended by the foremost number theorists. His most important and comprehensive contribution in this sphere has been his role in the National Board for Higher Mathematics (NBHM). Raghunathan was a member of the Board since it was formed in 1983 and became its chairman in 1987. He continues to serve in that capacity.

### Mathematical Sciences 2016

Varadhan's awards and honours include the National Medal of Science (2010) from US President Barack Obama, "the highest honor bestowed by the United States government on scientists, engineers and inventors". He is also the winner of the Abel Prize (2007), the Leroy Steele Prize (1996), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995) and the Birkhoff Prize (1994). He also has honorary degrees from the Chennai Mathematics Institute (2008), the Indian Statistical Institute in Kolkata, India (2004), Université Pierre et Marie Curie in Paris (2003), and from Duke University in USA (2016).

Professor Villani, member of the French Academy of Sciences, has been honored with several national and international prizes for his research, in particular the Fields Medal, awarded at the 2010 International Congress of Mathematicians in Hyderabad (India), by the President of India. Since then he has served as a spokesperson for the French mathematical community in media and political circles. His main research interests are in kinetic theory (Boltzmann and Vlasov equations and their variants), and optimal transport and its applications, a field in which he wrote the two main reference books: Topics in Optimal Transportation (2003); Optimal Transport, old and new (2008). He is a part of the editorial boards of Inventiones Mathematicae, the Journal of Functional Analysis (JFA), among others. He serves on many national and international scientific boards, including the Scientific Advisory Board of the European Commission and the one of the panafrican institute AIMS. He also serves as an administrator for several associations, in particular the pro-European Think-Tank EuropaNova.

Professor Khare after obtaining his Ph.D. from Caltech in 1995, he returned to India to work at the Tata Institute of Fundamental Research. In 2005, he moved to the United States, first to the University of Utah and then to the University of California at Los Angeles, where he is now Professor of Mathematics. He received the Cole Prize in 2011, Infosys Prize in 2010, Guggenheim fellowship in 2008, Fermat prize in 2007, and the INSA Young Scientist Award in 1999. He was an invited speaker at the International Congress of Mathematicians, held at Hyderabad in August 2010. In 2012, he became Fellow of the American Mathematical Society and was elected as a Fellow of the Royal Society.

Jennifer Tour Chayes is Distinguished Scientist, Managing Director and Cofounder of Microsoft Research New England and Microsoft Research New York City. Before joining Microsoft in 1997, Chayes was for many years Professor of Mathematics at UCLA. Chayes is the author of over 130 academic papers and the inventor of over 30 patents. Her research areas include phase transitions in discrete mathematics and computer science, structural and dynamical properties of self-engineered networks, graph theory, graph algorithms, algorithmic game theory, and computational biology. Chayes is one of the inventors of the theory of graph limits, which is widely used for machine learning of massive networks.

Chayes holds a BA in biology and physics from Wesleyan, where she graduated first in her class, and a PhD in mathematical physics from Princeton. She did postdoctoral work in the Mathematics and Physics Departments at Harvard and Cornell. She is the recipient of an NSF Postdoctoral Fellowship, a Sloan Fellowship, the UCLA Distinguished Teaching Award, and the ABI Women of Vision Leadership Award. She has twice been a member of the IAS in Princeton. Chayes is a Fellow of the American Association for the Advancement of Science, the Fields Institute, the Association for Computing Machinery, and the American Mathematical Society, and an Elected Member of the American Academy of Arts and Sciences. She is the winner of the 2015 John von Neumann Lecture Award, the highest honor of the Society of Industrial and Applied Mathematics. Chayes received an Honorary Doctorate from Leiden University in 2016.

Gopal Prasad's mathematical interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups. He was with the School of Mathematics, TIFR, for 26 years and thereafter with the University of Michigan for 20 years and counting. He was awarded the Shanti Swarup Bhatnagar prize and made Fellow of the Indian National Science Academy, the Indian Academy of Sciences, and the American Mathematical Society. He was awarded a fellowship by the Guggenheim Foundation. He also won the Humboldt Senior Research Award.

Professor Raghunathan is currently the Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly, he was a professor of eminence at TIFR in Homi Bhabha Chair. He is a leading expert in the Theory of Lie groups and has won international recognition for his pioneering research in this area.

Prof. Raghunathan is one of the few Indian mathematicians to be elected a Fellow of the Royal Society of London. He was awarded the Shanti Swarup Bhatnagar prize for his contributions to mathematics. He is also a recipient of the prestigious Padma Shri and Padma Bhushan awards.

Prof. Raghunathan has also played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He organized the Ramanujan centenary celebrations in Chennai in 1987, with an international conference attended by the foremost number theorists. His most important and comprehensive contribution in this sphere has been his role in the National Board for Higher Mathematics (NBHM). Raghunathan was a member of the Board since it was formed in 1983 and became its chairman in 1987. He continues to serve in that capacity.

### Mathematical Sciences 2015

### Mathematical Sciences 2014

Irene Fonseca is an applied mathematician who is on committees and boards of several major international universities and research centers.

In 1997, she was bestowed knighthood in the Military Order of St. James (Grande Oficial da Ordem Militar de Sant'Iago da Espada) by the president of Portugal. In 2004, she received a Women of Distinction Award in Math and Technology from the Western Pennsylvania Girl Scouts Trillium Council, and she was chosen to deliver the prestigious Sonia Kovalevsky Lecture at SIAM's Annual Meeting in 2006. She is a Fellow of the American Mathematical Society and of the Society for Industrial and Applied Mathematics (SIAM). She received a Doctor Honoris Causa from the Universidade Nova de Lisboa (Portugal) in 2012. She has written over 100 papers. Degree Theory in Analysis and Applications, a book co-authored with Wilfrid Gangbo, was published by Oxford University Press in 1995, and Modern Methods in the Calculus of Variations: L^p Spaces, is a book co-authored with Giovanni Leoni and published by Springer-Verlag in 2007. In 2012, she began a term as president-elect of the Society for Industrial and Applied Mathematics, an international professional society for applied mathematicians, with a two-year term as president starting in 2013.

### Mathematical Sciences 2013

Daubechies is best known for her work with wavelets in image compression while her research interests focus on the mathematical aspects of time-frequency analysis, in particular wavelets, as well as applications. She is the first woman president of the International Mathematical Union (2011–2014). In 1998 she was elected to be a member of the National Academy of Sciences and a Fellow of the Institute of Electrical and Electronics Engineers. She has been awarded the Louis Empain Prize for Physics (Belgium, 1984), the American Mathematical Society Steele Prize: for Exposition (1994), for Seminal Research (2011), the American Mathematical Society Ruth Lyttle Satter Prize (1997), The International Society for Optical Engineering Recognition of Outstanding Achievement (1998), IEEE Information Theory Society Golden Jubilee Award for Technological Innovation (1998),National Academy of Sciences Medal in Mathematics (2000),Eduard Rhein Foundation 2000 Basic Research Award (2000), Gold Medal (Gouden Penning) of the Flemish Royal Academy of Arts and Sciences, Belgium (2005), ICIAM Pioneer Prize (2008), Lars Onsager Medal (2010),Guggenheim Fellow (2010), Benjamin Franklin Medal for Electrical Engineering (2011), Booker Gold Medal of the URSI (2011), James Kilby Medal of the IEEE Signal Processing Society (2011), Okawa Prize (2011) and most recently the Nemmers prize (2012). She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronics Engineers.

Photograph By: David von Becker

### Mathematical Sciences 2012

Varadhan's awards and honours include the National Medal of Science (2010) from US President Barack Obama,

Kannan, before joining Microsoft, was the William K. Lanman Jr. Professor of Computer Science and Professor of Applied Mathematics at Yale University. He has also taught at CMU and MIT. The ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) presented its 2011 Knuth Prize to Ravi Kannan for ``developing influential algorithmic techniques aimed at solving long-standing computational problems.’’ He is the recipient of the 1992 Fulkerson Prize in Discrete Mathematics. His research interests include Algorithms, Theoretical Computer Science and Discrete Mathematics as well as Optimization. His work has mainly focused on efficient algorithms for problems of a mathematical (often geometric) flavor that arise in Computer Science. He has worked on algorithms for integer programming and the geometry of numbers, random walks in n-space, randomized algorithms for linear algebra and learning algorithms for convex sets.

Daubechies is best known for her work with wavelets in image compression while her research interests focus on the mathematical aspects of time-frequency analysis, in particular wavelets, as well as applications. She is the first woman president of the International Mathematical Union (2011–2014). In 1998 she was elected to be a member of the National Academy of Sciences and a Fellow of the Institute of Electrical and Electronics Engineers. She has been awarded the Louis Empain Prize for Physics (Belgium, 1984), the American Mathematical Society Steele Prize: for Exposition (1994), for Seminal Research (2011), the American Mathematical Society Ruth Lyttle Satter Prize (1997), The International Society for Optical Engineering Recognition of Outstanding Achievement (1998), IEEE Information Theory Society Golden Jubilee Award for Technological Innovation (1998),National Academy of Sciences Medal in Mathematics (2000),Eduard Rhein Foundation 2000 Basic Research Award (2000), Gold Medal (Gouden Penning) of the Flemish Royal Academy of Arts and Sciences, Belgium (2005), ICIAM Pioneer Prize (2008), Lars Onsager Medal (2010),Guggenheim Fellow (2010), Benjamin Franklin Medal for Electrical Engineering (2011), Booker Gold Medal of the URSI (2011), James Kilby Medal of the IEEE Signal Processing Society (2011), Okawa Prize (2011) and most recently the Nemmers prize (2012). She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronics Engineers.

Prasad's mathematical interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups. He was with the School of Mathematics, TIFR for 26 years and thereafter with the University of Michigan for 20 years and counting. He was awarded the Shanti Swarup Bhatnagar prize and made Fellow of the Indian National Science Academy and the Indian Academy of Sciences. He was awarded a fellowship by the Guggenheim Foundation. He also won the Humboldt Senior Research Award

A leader in the field of number theory and in particular Galois representations, automorphic forms, and Shimura variations, Richard Taylor, with his collaborators, has developed powerful new techniques for use in solving longstanding problems, including the Shimura-Taniyama conjecture, the local Langlands conjecture, and the Sato-Tate conjecture. Currently, Taylor is interested in the relationship between l-adic representations for automorphic forms—how to construct l-adic representations for automorphic forms and how to prove given l-adic representations that arises in this way. He received the LMS Whitehead Prize in 1990, the Prix Franco-Brittanique from the French Academie des Sciences in 1992, the Fermat Prize and the Ostrowski Prize in 2001, a Guggenheim Fellowship and the Cole Prize of the American Mathematical Society in 2002, the Dannie Heinemann Prize of the Gottingen Academy of Sciences in 2005, and the Clay Research Award and the Shaw Prize for Mathematics in 2007. He was also elected a Fellow of the Royal Society in 1995.

Diaconis is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards. His main work is in mathematical statistics, algebraic combinatorics, and rates of convergence for Markov chains. He was elected as Fellow of the Institute of Mathematical Statistics, American Academy of Arts and Sciences, American Statistical Association and is a Member of National Academy of Sciences. An early recipient of a Macarthur prize , he is also the winner of the Rollo Davidson Prize and has received Honorary Degrees from University of Chicago, Universite Paul Sabatier (Toulouse) , Uppsala University, Queen Mary University of London and Athens (Greece) University of Economics and Business.

### Mathematical Sciences 2011

Prof. Srinivasa S.R. Varadhan is a winner of the Birkhoff Prize (1994), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995), the Leroy Steele Prize (1996) and the Abel Prize (2007). He also has honorary degrees from Université Pierre et Marie Curie in Paris (2003)), from the Indian Statistical Institute in Kolkata, India (2004) and from the Chennai Mathematics Institute (2008).

Ingrid Daubechies is best known for her work with wavelets in image compression while her research interests focus on the mathematical aspects of time-frequency analysis, in particular wavelets, as well as applications. She is the first woman president of the International Mathematical Union (2011–2014). In 1998 she was elected to be a member of the National Academy of Sciences and a Fellow of the Institute of Electrical and Electronics Engineers. The American Mathematical Society awarded her a Leroy P. Steele prize for exposition in 1994 for her book "Ten Lectures on Wavelets," as well as the 1997 Ruth Lyttle Satter Prize. She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronics Engineers.

Gopal Prasad's mathematical interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups. He was with the School of Mathematics, TIFR for 12 years and thereafter with the University of Michigan for 9 years and counting. He was awarded the Shanti Swarup Bhatnagar prize and made Fellow of the Indian National Science Academy, Indian Academy of Sciences and the Guggenheim Foundation. He also won the Humboldt Senior Research Award and was given the NSF-research grant.

Prof. Kontsevich has made numerous contributions to the fields of pure mathematics and theoretical physics. His work concentrates on geometric aspects of mathematical physics, most notably on knot theory, quantization, and mirror symmetry. He received the Fields Medal in 1998. He has also been awarded the Crafoord Prize in 2008, the Otto Hahn Medal, Max Planck Gesellschaft in 1992, Prix de la Mairie de Paris in 1992, the Henri Poincare Prize in 1997, and the Prize of the International Congress of Mathematical Physics, Brisbane in 1997. Kontsevich is a member of the Academia Europaea, and a member of the Institut de France.

Prof. Seshadri is known for his work in algebraic geometry; the Sheshadri constant is named after him. He received the Padma Bhushan in 2009, the Shanti Swarup Bhatnagar Award, and the Srinivasa Ramanujan Medal from the Indian Academy of Sciences. He is Fellow of the Indian Academy of Sciences, fellow of the Indian National Science Academy and fellow of the Royal Society. He has also received an honorary degree from the Banaras Hindu University.

Persi Warren Diaconis is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards. He was elected as Fellow of the Institute of Mathematical Statistics, American Academy of Arts and Sciences, American Statistical Association and is a Member of National Academy of Sciences. He is a Winner of the Rollo Davidson Prize and has received Honorary Degrees from University of Chicago, Universite Paul Sabatier (Toulouse) , Uppsala University, Queen Mary University of London and Athens (Greece) University of Economics and Business.

### Mathematical Sciences 2010

Prof. Srinivasa S.R. Varadhan is a winner of the Birkhoff Prize (1994), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995), the Leroy Steele Prize (1996) and the Abel Prize (2007). He also has honorary degrees from Université Pierre et Marie Curie in Paris (2003)), from the Indian Statistical Institute in Kolkata, India (2004) and from the Chennai Mathematics Institute (2008).

Prof. Terry Speed's research concerns the application of statistics to problems in genetics and molecular biology. His major focus at the moment is in cancer genomics and cancer systems biology. He remains interested in the mapping of genes in humans and other organisms, the analysis of DNA and protein sequences, and the analysis of all types of next-generation sequence data. He is currently on the editorial board of the Journal of Computational Biology, JASA, Bernoulli and the Australian and New Zealand Journal of Statistics.

Before moving to Brown University, Prof. David Mumford served as Higgin's Professor of Mathematics at Harvard from 1977-1997. He was a MacArthur Fellow from 1987 to 1992. He won the Shaw Prize in 2006. In 2007 he was awarded the Steele Prize for Mathematical Exposition by the American Mathematical Society. In 2008 he was awarded the Wolf Prize. A member of the National Academy of Sciences, Prof. Mumford was also elected President of the International Mathematical Union from 1995-1999.

Prof. Sheshadri is known for his work in algebraic geometry; the Sheshadri constant is named after him. He received the Padma Bhushan in 2009, the Shanti Swarup Bhatnagar Award, and the Srinivasa Ramanujan Medal from the Indian Academy of Sciences. He is fellow of the Indian Academy of Sciences, fellow of the Indian National Science Academy and fellow of the Royal Society. He has also received an honorary degree from the Banaras Hindu University.

Prof. Weinan E moved to Princeton University in 1999 where he holds a professorship in the Department of Mathematics and in the Program in Applied and Computational Mathematics. He received his PhD from the University of California at Los Angeles in 1989 (under Björn Engquist). Prof. E was a long-term member of the Institute of Advanced Studies in Princeton from 1992 to 1994 and became a professor at the Courant Institute at New York University in 1994. In 1999, he received the US Presidential Early Career Award for Scientists and Engineers, in 1999 he was awarded the Feng Kang Prize for Scientific Computing, and in 2003 he received the ICIAM (International Congress of Industrial and Applied Mathematics) Collatz Prize. Prof. E's work is a sophisticated combination of modeling, mathematical analysis, and numerics, and it is always devoted to providing new insights into real-world processes.

Since 1986, Prof. Coates has worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory, including the study of the arithmetic of elliptic curves in nonabelian infinite extensions. He was elected a fellow of the Royal Society of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The LMS awarded him the Senior Whitehead Prize in 1997.

### Mathematical Sciences 2009

Prof. Srinivasa S.R. Varadhan is a winner of the Birkhoff Prize (1994), the Margaret and Herman Sokol Award of the Faculty of Arts and Sciences, New York University (1995), the Leroy Steele Prize (1996) and the Abel Prize (2007). He also has honorary degrees from Université Pierre et Marie Curie in Paris (2003)), from the Indian Statistical Institute in Kolkata, India (2004) and from the Chennai Mathematics Institute (2008).

Prof. Terry Speed's research concerns the application of statistics to problems in genetics and molecular biology. His major focus at the moment is in cancer genomics and cancer systems biology. He remains interested in the mapping of genes in humans and other organisms, the analysis of DNA and protein sequences, and the analysis of all types of next-generation sequence data. He is currently on the editorial board of the Journal of Computational Biology, JASA, Bernoulli and the Australian and New Zealand Journal of Statistics.

Before moving to Brown University, Prof. David Mumford served as Higgin's Professor of Mathematics at Harvard from 1977-1997. He was a MacArthur Fellow from 1987 to 1992. He won the Shaw Prize in 2006. In 2007 he was awarded the Steele Prize for Mathematical Exposition by the American Mathematical Society. In 2008 he was awarded the Wolf Prize. A member of the National Academy of Sciences, Prof. Mumford was also elected President of the International Mathematical Union from 1995-1999.

Prof. Weinan E moved to Princeton University in 1999 where he holds a professorship in the Department of Mathematics and in the Program in Applied and Computational Mathematics. He received his PhD from the University of California at Los Angeles in 1989 (under Björn Engquist). Prof. E was a long-term member of the Institute of Advanced Studies in Princeton from 1992 to 1994 and became a professor at the Courant Institute at New York University in 1994. In 1999, he received the US Presidential Early Career Award for Scientists and Engineers, in 1999 he was awarded the Feng Kang Prize for Scientific Computing, and in 2003 he received the ICIAM (International Congress of Industrial and Applied Mathematics) Collatz Prize. Prof. E's work is a sophisticated combination of modeling, mathematical analysis, and numerics, and it is always devoted to providing new insights into real-world processes.

Dr. M. S. Narasimhan was Professor of Mathematics at the Tata Institute of Fundamental Research, Mumbai, and Head of the Mathematics section at ICTP, Trieste. Dr. Narasimhan is a pioneer of the study of moduli spaces of holomorphic vector bundles on projective varieties. He was co-winner of the King Faisal Prize in 2006. In 1975, he received the Bhatnagar Prize for Mathematics (1975), which is the most prestigious award in Mathematics in India. He also received the Third World Academy Award for Mathematics in 1987 and is a Fellow of the Royal Society, London.

Since 1986, Prof. Coates has worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory, including the study of the arithmetic of elliptic curves in nonabelian infinite extensions. He was elected a fellow of the Royal Society of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The LMS awarded him the Senior Whitehead Prize in 1997.