Abstract: 

I will describe some beautiful limiting theorems on continued fractions. I will then introduce a method of interpreting these theorems using dynamical systems on homogeneous spaces. This interpretation allows us to provide a new perspective on this classical question and to prove new results.

About the Speaker: 

Dr. Anish Ghosh is a Professor at the Tata Institute of Fundamental Research (TIFR) and a Fellow of the Indian Academy of Sciences. His research spans the intersection of group actions on homogeneous spaces and number theory, with a particular emphasis on Diophantine approximation and lattice point counting. He is widely recognized for resolving the Kleinbock–Tomanov conjecture and advancing effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. By methods from ergodic theory, Dr. Ghosh has provided deep statistical information about the distribution of number-theoretic functions, particularly those emerging from Diophantine problems.
For his groundbreaking contributions, Dr. Ghosh was awarded the Shanti Swarup Bhatnagar Prize in Mathematical Sciences in 2021, one of India's highest honors in scientific research.