Thin Orbits and Applications

Explore the fascinating world of thin orbits and their applications in this 56-minute lecture by Alex Kontorovich, presented as part of the International Centre for Theoretical Sciences' program on Zariski Dense Subgroups, Number Theory, and Geometric Applications. Delve into cutting-edge research on arithmetic and Zariski-dense subgroups, examining their impact on algebraic and differential geometry, combinatorics, and other mathematical fields. Gain insights into the use of algebraic and analytic number theory techniques to address long-standing problems in mathematics, including fake projective planes, isospectral and length-commensurable locally symmetric spaces, and expanding graphs. Discover how these concepts contribute to advancements in geometry, topology, and mathematical physics, and learn about recent developments in bounded generation, stability, and asymptotic cohomology.