Rigidity and Stiffness of Arithmetic Groups
Explore rigidity and stiffness properties of arithmetic groups, examining recent advancements in Zariski-dense subgroup theory and its applications to geometry 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.
On Kissing Number of Hyperbolic Manifolds
Explore hyperbolic manifolds' kissing numbers with Plinio G. P. Murillo. Delve into Zariski dense subgroups, number theory, and geometric applications in this theoretical sciences lecture.
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 mathematical concepts and their geometric applications.
Hecke Actions on Loops and Periods of Iterated Shimura Integrals
Explore Hecke actions on loops and periods of iterated Shimura integrals in this advanced number theory seminar by Richard Hain from Duke University.
Understanding Tumour Responses to Radiotherapy Using Mathematical Models - Lecture 2
Explores mathematical modeling of tumor responses to radiotherapy, focusing on theoretical approaches to understand and predict treatment outcomes in cancer progression.
Minimal Rank of Submatrices of Random Rectangular Matrices
Explore the minimal rank of square submatrices in random rectangular matrices, proving a conjecture on their behavior as matrix dimensions vary.
Recent Advances in Valuations on Function Spaces
Explore recent developments in valuations on function spaces, focusing on convex and continuous functions, with insights into measure-valued valuations and their classifications.
Around the Nash Problem for Smooth Valuations
Explore smooth valuations on manifolds, their relation to translation-invariant valuations, and Crofton formulas. Discover surprising flexibility properties in finite subspace families.
Lefschetz Operators on Minkowski Valuations
Explore Lefschetz operators' action on continuous Minkowski valuations compatible with rigid motions, including difference body, projection body, and mean section body maps.
Entropy, Isotropic Constant and Mahler's Conjecture
Explores connections between entropy, isotropic constant, and Mahler's conjecture in convex geometry. Discusses functional forms of Klartag's work and adaptations for log-concave functions.
Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces
Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.
Comparison Problems for the Radon Transform
Explores comparison problems for Radon transforms, examining conditions for L^p-norm inequalities and introducing function classes generalizing intersection bodies, with applications to slicing inequalities.
Mathematical and Computational Modelling to Explore Various Potential Cancer Treatments
Explore mathematical and computational modeling approaches for cancer research, covering topics from age-structured populations to machine learning techniques for understanding disease progression and treatment.
Arithmetic Groups of Higher Real Rank Are Not Left-orderable
Explore the non-left-orderability of arithmetic groups with higher real rank in this mathematical lecture, delving into advanced concepts in group theory and algebraic structures.
CSP and Unipotent Generators for Higher Rank Nonuniform Arithmetic Groups
Exploration of CSP and unipotent generators in higher rank nonuniform arithmetic groups, discussing recent advancements and applications in algebraic and differential geometry.
Hypergeometric Groups and their Arithmeticity
Explore hypergeometric groups and their arithmeticity in this advanced mathematics lecture, delving into Zariski-dense subgroups and their applications in geometry and number theory.
Non-virtually Abelian Discontinuous Group Actions vs Proper SL(2,R)-Actions - Aleksy Tralle
Explore non-virtually Abelian discontinuous group actions and proper SL(2,R)-actions in this advanced mathematics lecture, part of a program on Zariski dense subgroups and geometric applications.
The Systolic Geometry of Arithmetic Locally Symmetric Spaces
Explore systolic geometry of arithmetic locally symmetric spaces, focusing on recent advancements and applications in algebraic and differential geometry, number theory, and related fields.
Introduction to Bruhat-Tits Theory - Lecture 3
Explore Bruhat-Tits theory in algebraic groups with Brian Conrad, focusing on applications to arithmetic, geometry, and number theory in this advanced mathematics lecture.
Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 2
Explore advanced topics in linear groups and Diophantine approximation, focusing on bounded generation and its applications in number theory and geometric analysis.