Stable Pair Invariants and Derived Categories - Lecture 1
Explore stable pair invariants and derived categories in mathematics with expert Y. Toda in this comprehensive lecture from ICTP Mathematics.
Perverse Sheaves and Schobers on Riemann Surfaces - Tobias Dyckerhoff
Explore derived constructible categories on stratified Riemann surfaces, t-structures, Verdier duality, and categorified perverse sheaves with applications in algebraic geometry and topology.
Generic Character Sheaves for Parahoric Subgroups
Exploration of Lusztig's character sheaves theory, extending to positive-depth cases and addressing Lusztig's conjecture. Focuses on perverse sheaves and parahoric Deligne-Lusztig induction in representation theory.
Residues and Trace Maps in Grothendieck Duality - Lecture 3
Explores residues and trace maps in Grothendieck duality theory, advancing understanding of algebraic geometry and commutative algebra concepts for researchers and advanced students.
Residues and Trace Maps in Grothendieck Duality - Lecture 4
Explore residues and trace maps in Grothendieck Duality, advancing understanding of algebraic geometry and commutative algebra concepts within the broader context of dualities in topology and algebra.
A Sheaf-Theoretic Construction of Shape Space
Sheaf-theoretic approach to construct shape space using Persistent Homology Transform. Explores homotopy sheaves, metrics, stability theorems, and approximation of manifolds.
A Sheaf-based Approach to Graph Neural Networks
Explore sheaf theory's application to Graph Neural Networks, offering a novel perspective on Geometric Deep Learning beyond traditional geometric structures.
Resurgent Perverse Sheaves and Topological Resurgence Theory
Explore topological counterparts of resurgence theory using perverse sheaves on C as convolution algebras, extending beyond regular holonomic D-modules to infinitely singular cases.
Cohomological Hall Algebras of 0-Dimensional Sheaves on Surfaces
Explore cohomological Hall algebras of 0-dimensional sheaves on surfaces, their explicit description, and applications to moduli spaces of sheaves with positive-dimensional support.
Perverse Sheaves in Deformation Quantization
Explore holomorphic symplectic manifolds, deformation quantization modules, and perverse sheaves in Lagrangian intersections and BV quantization.
Virasoro Constraints in Sheaf Theory
Explore Virasoro constraints in sheaf theory, focusing on recent developments and their application to moduli spaces of sheaves using vertex algebra and wall-crossing techniques.
Categorification of Donaldson-Thomas Invariants
Explore categorification of Donaldson-Thomas invariants through derived foliations, extending BBDJS construction with a sheaf of 2-periodic dg-categories modeled on matrix factorizations.
Singularities of Constructible Sheaves
Explore advanced mathematical concepts in constructible sheaves and their singularities, delving into complex algebraic geometry and topology.
Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds
Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.
Quantitative Ell-Adic Sheaf Theory
Explore quantitative bounds for étale cohomology groups and their applications in algebraic geometry. Learn about complexity measures for sheaves and how they interact with various functors.
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.
Analytic Stacks - Lecture 6
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Analytic Stacks - Lecture 5
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
Functoriality and Sheaf Property for Wrapped Fukaya Categories
Explore functorial and sheaf-theoretic properties of wrapped Fukaya categories, surveying key results and insights in this advanced mathematical topic.
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.
Derived Approach to Highest Weight Categories
Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.