Explore advanced topics in ergodic theory and dynamical systems through this comprehensive conference featuring leading mathematicians from around the world. Delve into cutting-edge research on Diophantine approximation, homogeneous dynamics, and measure theory through expert presentations covering geometry of best approximations, multiplicative rational p-adic approximation, and Borel-Cantelli lemmas for inhomogeneous Diophantine approximations. Examine actions on delta-median spaces, invariant measures for horospherical flows, and the exact dimension of Oseledets measures while investigating multiplicatively badly approximable vectors and equidistribution phenomena. Study measure rigidity for forms of SL(2), effective versions of Ratner's equidistribution theorem, and dimension drop conjectures in homogeneous dynamics. Analyze bounded orbits for diagonal flows on lattice spaces, Martin boundaries of random walks on relatively hyperbolic groups, and entropy equipartition along geodesics in negatively curved groups. Discover connections between dynamical systems and number theory through discussions on geodesic random line processes, quadratic congruences, and p-adic Diophantine approximation with respect to fractal measures. Learn about variance estimates for geometric counting problems, joint distributions of integral points under quadratic forms, and rigidity properties on homogeneous bundles while gaining insights into India's mathematical heritage and Professor S.G. Dani's contributions to the field.

Syllabus

Geometry of best Approximations by Uri Shapira
Multiplicative Rational P-adic Approximation by Yann Bugeaud
Borel-Cantelli Lemmas for Inhomogeneous Diophantine Approximations and beyond by Victor Beresnevich
Actions on Delta-Median Spaces by Indira Chatterji
Invariant Measures for Horospherical Flows by Hee Oh
Exact dimension of Oseledets measures by Francois Ledrappier
Multiplicatively Badly Approximable Vectors by Reynold Fregoli
Equidistribution of Measures with High Entropy for General Surface Diffeomorphisms by Omri Sarig
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
Limiting Distributions of Stretching Translates of Shrinking Curves...by Nimish Shah
Measure Rigidity for forms of SL(2) by Manfred Einsiedler
Maps between Surfaces by Athanase Papadopoulos
Inner Functions Revisited by Jon Aaronson
An effective version of Ratner’s equidistribution theorem for SL(3, R) by Lei Yang
Effective Rational Approximation on Spheres by Zouhair Ouaggag
Dimension Drop Conjecture in Homogeneous Dynamics by Dmitry Kleinbock
Nearly Uniform Lattice Covers by Barak Weiss
Bounded Orbits for Diagonal Flows on the Space of Lattices (Lecture 1) by Erez Nesharim
Dirichlet improvable vectors on manifolds by Yang Pengyu
Martin Boundaries of Random Walks on Relatively Hyperbolic Groups by Debanjan Nandi
Towards a Zero-one Law for Improvements to Dirichlet’s Approximation Theorem by Shucheng Yu
Entropy Equipartition along almost Geodesics in Negatively Curved Groups by Amos Nevo
Bounded orbits for Diagonal Flows on the Space of Lattices by Erez Nesharim
Geodesic Random Line Processes and the Roots of Quadratic Congruences by Jens Marklof
Dynamical Questions Arising from Dirichlet’s Theorem on Diophantine by Anurag Rao
Some Lattice Subgroups that cannot Act on the line(after Deroin and Hurtado) by Dave Morris
On Ratner's Theorem by M. S. Raghunathan
Group Actions and Power Maps by C. R. E. Raja
The Embedding Problem of Infinitely Divisible Probability Measures on Groups by Riddhi Shah
Professor S.G. Dani's Contributions to Homogeneous Dynamics by Nimish Shah
p-adic Diophantine Approximation with Respect to Fractal Measures by Shreyasi Datta
Variance Estimates for Geometric Counting Problems by Jayadev Athreya
Joint Distribution of Values of Integral Points under Pairs of Quadratic Forms....by Jiyoung Han
Higher Dimensional Fine-Scale Statistics Arising from Homogeneous Dynamics by Samuel Pattison
Some Snapshots of India's Mathematical Past by S. G. Dani
Bounded Orbits for Diagonal Flows on the Space of Lattices by Erez Nesharim
Rigidity on Homogeneous Bundles by Alexander Gorodnik
Exact Approximation in Metric Measure Spaces by Prasuna Bandi