Introduction to Bruhat-Tits Theory - Lecture 2
Explore Bruhat-Tits theory in this advanced mathematics lecture, focusing on Zariski dense subgroups and their applications in algebraic geometry and number theory.
Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 3
Explore advanced concepts in linear groups and Diophantine approximation, focusing on bounded generation techniques and their applications in number theory and geometric analysis.
Things We Can Learn by Looking at Random Manifolds
Explore insights gained from studying random manifolds, covering applications in geometry, topology, and mathematical physics. Uncover connections between diverse mathematical fields.
Standard Compact Clifford-Klein Forms and Lie Algebra Decompositions
Explore Lie algebra decompositions and standard compact Clifford-Klein forms in this advanced mathematics lecture, delving into geometric applications of Zariski dense subgroups and number theory.
Uniform Stability of Higher-rank Arithmetic Groups - Lecture 1
Explore uniform stability in higher-rank arithmetic groups with Alex Lubotzky & Bharatram. Delve into advanced mathematical concepts and their applications in this in-depth lecture.
Random Walks on Group Extensions
Explore random walks on group extensions in this advanced mathematics lecture, covering Zariski dense subgroups and their applications in algebraic geometry and number theory.
Property (T) for Automorphism Groups of Free Groups - Lecture 2
Explore Property (T) for automorphism groups of free groups in this advanced mathematics lecture, part of a program on Zariski dense subgroups and their applications in geometry and number theory.
Hasse Principle for Reductive Groups over P-Adic Function Fields
Explore the Hasse Principle for reductive groups over p-adic function fields in this advanced mathematics lecture by Raman Parimala, part of a program on Zariski dense subgroups and number theory.
Sum of Squares, Positivity and Property (T) - Lecture 1
Explore sum of squares, positivity, and Property (T) in this lecture by Marek Kaluba. Gain insights into advanced mathematical concepts and their applications in group theory and geometry.
The Existence Problem of Compact Quotients of Pseudo-Riemannian Homogeneous Spaces
Explore the existence of compact quotients in pseudo-Riemannian homogeneous spaces, delving into advanced geometric concepts and their applications in mathematical physics and topology.
Thin Orbits and Applications
Explore thin orbits in number theory and their geometric applications with Alex Kontorovich. Gain insights into Zariski-dense subgroups and their impact on various mathematical fields.
Minicourse: Uniform Stability of Higher-rank Arithmetic Groups - Lecture 3
Explore uniform stability in higher-rank arithmetic groups. Delve into advanced mathematical concepts, focusing on Zariski dense subgroups and their applications in geometry and number theory.
Geometric Functionals of Polyconvex Excursion Sets of Poisson Shot Noise Processes
Explore geometric functionals of polyconvex excursion sets in Poisson shot noise processes, including asymptotics, variance bounds, and central limit theorems for intrinsic volumes.
MM-Estimates, Regular M-Ellipsoids and Distances Between Convex Bodies
Explores convex bodies in n-dimensional space, focusing on mean width, MM* estimates, and their relation to covering efficiency and distances between convex bodies. Discusses symmetric vs non-symmetric cases.
Homological Mirror Symmetry: Recent Developments and Future Directions
Explore recent advancements in Homological Mirror Symmetry and honor Jeffrey Fuqua's contributions to Mathematics in this insightful conference talk.
Homological Mirror Symmetry - Recent Developments and Future Directions
Explore recent advancements in Homological Mirror Symmetry, surveying new results and opening avenues for future research and collaboration in this mathematical field.
Dimer Models and Random Tilings - Part 2
Explore dimer models, perfect matchings, and tilings with advanced mathematical tools. Delve into Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for large-scale limits.
Dylan Langharst: Higher-Order Affine Isoperimetric Inequalities
Explores extensions of geometric inequalities to higher-order bodies, including projection, centroid, LYZ, and radial mean bodies, with proofs of associated inequalities in convex geometry.
Dimers and M-curves: Limit Shapes from Riemann Surfaces
Explore dimer models, M-curves, and limit shapes through algebraic geometry, integrating Riemann surfaces and Schottky uniformization. Gain insights into statistical mechanics and discrete geometry.
Eulerian Magnitude Homology - Subgraph Structure and Random Graphs
Explore connections between magnitude homology group ranks and graph substructures. Introduces eulerian and discriminant magnitude homology, relating them to subgraph counts and random graph models.
Geometric Bounds for Spanning Tree Entropy of Planar Lattices
Explores geometric bounds for spanning tree entropy in planar lattices, connecting hyperbolic geometry, number theory, probability, and graph theory. Discusses conjectures and recent progress.