Algebraic Correspondences: Where Mandelbrot Sets Meet Teichmuller Spaces

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Infosys Prize Lecture

Algebraic Correspondences: Where Mandelbrot Sets Meet Teichmuller Spaces

05:00 PM

September 17, 2026

Platinum Jubilee Auditorium (PJA), Indian Statistical Institute, Bangalore Centre

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Algebraic Correspondences: Where Mandelbrot Sets Meet Teichmuller Spaces

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Connections between two branches of conformal dynamics–rational dynamics on the Riemann sphere and actions of Kleinian groups–have long been observed. Fatou envisioned in the 1920s that these actions could be studied within a unified framework of iterated algebraic correspondences. We provide concrete evidence to this vision by constructing algebraic corre spondences as combinations/matings of complex polynomials and Fuchsian groups, allowing features of both theories to coexist in a single dynamical setting. At the level of parameter spaces, this leads naturally to products of Teichm¨uller spaces and Mandelbrot sets inside appropriate moduli spaces of ramified covers of the Riemann sphere. We will outline the main analytic and algebraic ideas of this program, discuss connections with other areas of mathematics, and highlight several open questions.

Speaker

Sabyasachi Mukherjee

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