Topological Recursion: A Recursive Way of Counting Surfaces
Explore topological recursion for enumerating surfaces in combinatorics, geometry, and physics. Learn how this universal method links to integrable systems and random matrices.
Waists Measured via Urysohn Width in Riemannian Manifolds
Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
Width, Scalar Curvature and Macroscopic Scalar Curvature
Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.
Analytic Stacks - Lecture 12
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Analytic Stacks - New Foundations for Analytic Geometry - Lecture 11/24
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Birational Invariants from Gromov-Witten Theory - Lecture 4
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
Solving Equations from Combinatorics via Computer Algebra
Explore advanced techniques for solving discrete differential equations in combinatorics using computer algebra, focusing on efficient methods for n=2 cases and recent developments in systems of equations.
Analytic Stacks - New Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Inequalities Defining Polyhedral Realizations of Affine Types and Extended Young Diagrams
Explore crystal bases in Lie algebra representation theory, focusing on polyhedral realizations and explicit inequalities for classical affine types using extended Young diagrams.
Combinatorics and Quantum Invariant Differential Operators on Reflection Equation Algebras
Explore quantum analogs of symmetric functions and differential operators in Reflection Equation Algebras, examining their properties and combinatorial applications.
The Redei-Berge Symmetric Function of a Directed Graph
Explore symmetric functions in directed graphs, examining Redei's theorem on tournaments and Chow's path-cycle function. Discover new expansions and refinements in graph theory.
Graph Complex Action on Poisson Structures: From Theory to Computation
Explore graph complex action on Poisson structures, from theoretical foundations to computational applications using SageMath's gcaops package for advanced mathematical research.
Analytic Stacks - New Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.
Birational Invariants from Gromov-Witten Theory - Lecture 3
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
Demi-Shuffle Duals of Magnus Polynomials in a Free Associative Algebra
Explore linear bases in free associative algebra: Magnus polynomials and their demi-shuffle duals. Discover applications to group-like series coefficients using Le-Murakami, Furusho type formulas.
Analytic Stacks - Foundations for Analytic Geometry
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.
The Miracle of Integer Eigenvalues in Finite Poset Matrices
Explore the fascinating connection between finite posets and integer eigenvalues in matrix theory, with implications for symmetric group representations.
Periods of Hypersurfaces via Effective Homology
Explore numerical approximations of periods for hypersurfaces using effective homology, enabling computation of algebraic invariants for complex projective varieties.
Counting Partitions by Genus
Explore set partition counting by genus, focusing on primitive partitions and functional equations to reconstruct all partitions, with emphasis on genus 0-2 cases.
The Nullstellensatz and Positivstellensatz for Sparse Tropical Polynomial Systems
Explorez les avancées en algèbre tropicale, notamment le Nullstellensatz et le Positivstellensatz pour les systèmes polynomiaux tropicaux clairsemés, avec des applications aux jeux à paiement moyen paramétrique.
Counting Restricted Set Partitions with Hypergeometrics
Explore advanced set partition counting using hypergeometric functions and generalized Hermite polynomials. Gain insights into restricted Bell numbers and their closed-form expressions.