Isoperimetric and Poincaré Inequalities on the Hamming Cube
Explore isoperimetric inequalities on the Hamming cube near and at the critical exponent 1/2, as well as closely related L1 Poincaré inequalities in this one-hour lecture. Delve into joint research conducted with P. Durcik and P. Ivanisvili, focusing on…
Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds
Explore the intricacies of the Arithmetic Quantum Unique Ergodicity (AQUE) conjecture in this advanced mathematics seminar. Delve into the groundbreaking research on non-escape of mass for Hecke-Maass cusp forms on congruence quotients of hyperbolic 4-sp…
Superabundance and Unobstructedness in Lagrangian Torus Fibrations - Lecture
Explore the concept of Lagrangian realization in tropical geometry through this M-Seminar talk by Jeff Hicks from the University of Edinburgh. Delve into the relationship between tropical curves in the base of a Lagrangian torus fibration and their corre…
Certain Polytopes Associated to Algebraic Integer Conjugates
Explore the fascinating world of algebraic number theory in this 40-minute Fields Number Theory Seminar presented by Samprit Ghosh from the University of Calgary. Delve into the intriguing relationship between certain polytopes and algebraic integer conj…
The Shape of Relations: Knots and Other Stories in Topological Data Analysis
Explore the fascinating world of Topological Data Analysis in this 59-minute conference talk by Radmila Sazdanovic, presented by the Applied Algebraic Topology Network. Discover how TDA tools can uncover relevant features in data by analyzing the shape o…
Cohomological Hall Algebra of Cyclic Quivers and Integral Form of Affine Yangians
Explore the intricate world of Hall algebra-type constructions and their applications in a lecture by Shivang Jindal from the University of Edinburgh. Delve into the complexities of studying algebras related to the moduli space of representations of the…
Entropy and Curvature of Markov Chains on Metric Spaces
Explore the Peres-Tetali conjecture and its implications for Markov chains in this 57-minute lecture by Justin Salez from the Hausdorff Center for Mathematics. Delve into the relationship between contraction in Wasserstein distance and relative entropy f…
Differential Equations, Geometry and Arithmetic - Lecture 2
Explore advanced concepts in differential equations, geometry, and arithmetic with a focus on algebraicity and transcendence in singular differential equations.
Differential Equations, Geometry and Arithmetic - Lecture 1
Explore connections between differential equations, geometry, and arithmetic in this advanced mathematics lecture by Duco van Straten.
A Higher Spin Statistics Theorem for Invertible Quantum Field Theories
Explore advanced concepts in quantum field theory, focusing on higher spin statistics and invertible theories. Gain insights from expert Lukas Mueller's seminar on geometry and physics.
Floer Homology with DG Coefficients - Applications to Cotangent Bundles
Explore Floer homology with DG coefficients and its applications to cotangent bundles. Gain insights into symplectic geometry and dynamical systems through advanced mathematical concepts.
Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds
Explore non-escape of mass for Hecke-Maass cusp forms on hyperbolic 4-manifolds, addressing challenges in unbounded Hecke relations and utilizing quaternionic matrices for unique factorization.
Spectral Analysis of Dirac Operators with a Purely Imaginary Dislocation
Explore spectral analysis of Dirac operators with imaginary dislocation, covering Green functions, pseudospectra, and effects of matrix potentials on essential and discrete spectra.
A Panorama of Singular Sub-Laplacians and Their Spectra
Explore exotic properties of Laplace-Beltrami operators on rank-varying sub-Riemannian structures. Delve into self-adjointness, spectral properties, and sub-Riemannian Weyl laws. Discover open questions in this fascinating field.
The Moduli Space of Twisted Laplacians and Random Matrix Theory
Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.
MetaHKG: Meta Hyperbolic Learning for Few-shot Temporal Reasoning - M1.2
Explore meta hyperbolic learning for few-shot temporal reasoning in knowledge graphs, enhancing reasoning capabilities with limited data.
Decoupling Identities and Oriented Matroids and Beyond
Explore advanced mathematical concepts in decoupling identities and oriented matroids, delving into their applications and extensions in physics and beyond.
Closure of Orbits of the Pure Mapping Class Group on the Character Variety
Explore the pure mapping class group's action on character varieties, examining orbit closures and their implications for various mathematical contexts and applications.
The Ramsey Numbers - New Results and New Perspectives
Explore fundamental Ramsey numbers in combinatorics, recent advancements, and connections to high-dimensional random variable geometry with Julian Sahasrabudhe.
Serrin's Overdetermined Problem in Rough Domains
Explore Serrin's overdetermined theorem extension to rough domains, including Lipschitz and finite perimeter sets, with insights on slit discontinuities and density bounds.
Geometric Representations of Far Future Predictions in Deep Neural Networks - Next-Token Training
Explore universal geometric representations of far-future beliefs in deep neural networks trained on next-token prediction, uncovering fractal and quantum-like structures embedded in network activations.