Geometry and Integers - Connections Between Number Theory and Geometric Structures
Explore connections between non-negative integer sets and diverse geometries, examining functions associated with primitive integer vectors and their relation to convex, toric, and birational geometries.
Magnitude and Path Homology
Explore magnitude and path homology concepts with mathematician Sergei Ivanov, delving into homological algebra, algebraic topology, and simplicial homotopy theory.
Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications
Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.
Quantitative Cobordism - Exploring Topology and Geometry
Explore quantitative cobordism in topology, focusing on non-constructive existence proofs and connections to geometry. Delve into Manin's principle, Cheeger-Gromov heuristic, and manifold constructions.
Homotopy Groups of Spheres - Computation Methods and Recent Progress
Explore homotopy groups of spheres, their computational methods, and recent advancements in topology using motivic homotopy theory and related techniques.
Linear Stability of Ricci Solitons - ICBS2024
Explore linear stability of compact shrinking Ricci solitons, including positive Einstein manifolds. Examine critical aspects, open problems, and recent research findings in Ricci flow and geometric analysis.
Stability of Sobolev Inequalities - ICBS 2024
Explore quantitative stability of Sobolev inequalities, focusing on Struwe's decomposition and recent advancements in dimensional-dependent estimates for multiple bubbles in various dimensions.
Recent Progress on Minimal and Constant Mean Curvature Surfaces
Explore recent advancements in the existence theory of minimal and constant mean curvature surfaces, surveying cutting-edge developments in this mathematical field.
Sheaves on Calabi-Yau 4-folds and Virtual Invariants - An Overview
Explore developments in enumerative geometry on Calabi-Yau 4-folds, including point counting, curve counting, and surface counting, with connections to string theory and physics.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
The Local Langlands Program and Characteristic p
Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.
Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves
Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
Integrable Billiards and Rigidity - Lecture 1
Explore integrable billiards and the Birkhoff-Poritsky conjecture, focusing on Hopf-type rigidity and its extension to Twist symplectic maps and billiards.
Divisibility of Spheres with Measurable Pieces - Oleg Pikhurko
Explore divisibility of spheres with measurable pieces, focusing on Euclidean (d-1)-dimensional sphere S^(d-1) and special orthogonal matrices. Examine impossibility of measurable divisibility for generic rotations.
Coxeter Groups are Biautomatic - Workshop on Cube Complexes and Combinatorial Geometry
Explore the biautomaticity of Coxeter groups and its implications for uniform lattices in building isometry groups. Gain insights from recent mathematical research.
Finite Quotients of Generic Free-by-Cyclic Groups
Explorez les groupes libres-par-cycliques et leurs quotients finis. Découvrez les résultats récents sur la distinction de ces groupes par leurs quotients finis dans le cadre de la géométrie combinatoire.
Sharp Stability for the Brunn-Minkowski Inequality for Arbitrary Sets
Explore sharp stability in the Brunn-Minkowski inequality for arbitrary sets, delving into combinatorics and its connections with metric geometry and analysis.
Exponential Decay of Intersection Volume and Applications
Explore exponential decay of intersection volume and its applications in extremal and probabilistic combinatorics with distinguished researcher Hong Liu.
Two Geometric Applications of the Linear Algebra Method
Explore geometric applications of linear algebra with János Pach, covering discrete geometry, convexity, and combinatorics in this research seminar.
Spherical Functions and Mirror Symmetry
Explore spherical functions and mirror symmetry in mathematics, bridging quantum physics and the Langlands Program through innovative interdisciplinary approaches.
Schobers and Riemann-Hilbert Correspondence
Explore geometric representation theory, super groups, and non-commutative algebraic geometry with a focus on Schobers and Riemann-Hilbert correspondence.