Explore advanced mathematical concepts through this comprehensive lecture series from the International Centre for Theoretical Sciences covering probabilistic methods in negative curvature geometry. Delve into four major topic areas through sequential lectures by leading experts: diffeomorphism groups of critical regularity presented by Sang-hyun Kim, finite index rigidity of hyperbolic groups taught by Nir Lazarovitch, probability theory on Kazhdan groups delivered by Gábor Pete, and measure equivalence and negative curvature rigidity explored by Camille Horbez. Study harmonic measures and Poisson boundaries for random walks on groups through Giulio Tiozzo's detailed presentations, and examine random covers of hyperbolic surfaces in Doron Puder's four-part lecture sequence. Gain deep insights into the intersection of probability theory, geometric group theory, and hyperbolic geometry through these research-level presentations that cover cutting-edge developments in mathematical analysis of negatively curved spaces and their probabilistic properties.

Syllabus

Diffeomorphism groups of critical regularity by Sang-hyun Kim
Finite Index Rigidity of Hyperbolic Groups by Nir Lazarovich
Diffeomorphism groups of Critical Regularity (Lecture 2) by Sang-hyun Kim
Finite Index Rigidity of Hyperbolic Groups (Lecture 2) by Nir Lazarovich
Finite Index Rigidity of Hyperbolic Groups (Lecture 3) by Nir Lazarovich
Diffeomorphism Groups of Critical Regularity (Lecture 3) by Sang-hyun Kim
Diffeomorphism Groups of Critical Regularity (Lecture 4) by Sang-hyun Kim
Finite Index Rigidity of Hyperbolic Groups (Lecture 4) by Nir Lazarovich
Probability on Kazhdan Groups (Lecture 1) by Gábor Pete
Measure Equivalence, Negative Curvature, Rigidity (Lecture 1) by Camille Horbez
Harmonic Measures and Poisson Boundaries for Random Walks on Groups (Lecture 1) by Giulio Tiozzo
Probability on Kazhdan Groups (Lecture 2) by Gábor Pete
Measure Equivalence, Negative Curvature, Rigidity (Lecture 2) by Camille Horbez
Harmonic Measures and Poisson Boundaries for Random Walks on Groups (Lecture 2) by Giulio Tiozzo
Probability on Kazhdan Groups (Lecture 3) by Gábor Pete
Harmonic Measures and Poisson Boundaries for Random Walks on Groups (Lecture 3) by Giulio Tiozzo
Probability on Kazhdan Groups (Lecture 4) by Gábor Pete
Measure Equivalence, Negative Curvature, Rigidity (Lecture 3) by Camille Horbez
Harmonic measures and Poisson boundaries for random walks on groups (Lecture 4) by Giulio Tiozzo
Measure Equivalence, Negative Curvature, Rigidity by Camille Horbez
Random Covers of Hyperbolic Surfaces (Lecture 1) by Doron Puder
Random Covers of Hyperbolic Surfaces (Lecture 2) by Doron Puder
Random Covers of Hyperbolic Surfaces (Lecture 3) by Doron Puder
Random Covers of Hyperbolic Surfaces (Lecture 4) by Doron Puder