Topological Invariants of Gapped States and 't Hooft Anomalies
Explore topological invariants of gapped ground-states in lattice systems, their interpretation as obstructions to gauging, and the role of locality in infinite-volume systems with rapidly decaying interactions.
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.
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.
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.
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.
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.
Spectra of Laplace and Dirac Operators on Noncompact Manifolds
Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.
On the L^p Spectrum of the Laplacian on Riemannian Manifolds
Explore the $L^p$ spectrum of the Laplacian on manifolds, including resolvent sets, Weyl criterion, and hyperbolic space, with insights on conformally compact manifolds.
Three Problems in the Mathematics of Deep Learning
Explore mathematical concepts behind aligning neural networks with classical programs, including polynomial functors, cohomology, and higher categories.
Another Aspect of Gromov's Conjectures on Scalar Curvature
Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.
Geometric Variational Methods for Scalar Curvature and Other Curvature Problems
Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.
Integrality of the Betti Moduli Space
Explore the integrality of Betti moduli spaces for smooth projective varieties, examining representations of fundamental groups and their implications for algebraic geometry.