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#Sheaf Theory

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M-Seminar, Kansas State University

Cohomological Hall Algebra of Cyclic Quivers and Integral Form of Affine Yangians

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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…
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

The Completion of the Space of Lagrangian Submanifolds for the Spectral Metric

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Explore the spectral metric on Lagrangian spaces, its completion, and connections to symplectic topology and sheaf theory through quantization.
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1 Lesons
48 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

The Humilière Completion and Its Applications in Symplectic Geometry

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Explore the Humilière completion of Lagrangian spaces, its spectral distance study, and applications in conformal dynamics, singular Hamiltonian systems, and sheaf theory.
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1 Lesons
1 hour 6 minutes
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Free-Video
Models of Consciousness Conferences

Making Up Our Minds

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Explore how minds and thoughts are constructed through cognitive processes, examining the nature of consciousness, memory, and perception using interdisciplinary models and mathematical frameworks.
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7 Lesons
13 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Perverse Sheaves and Resurgence in Borel Summation

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Explore the connection between resurgence theory and perverse sheaves, focusing on Borel summation, Stokes phenomena, and alien derivatives in algebraic structures.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Exemplars of Sheaf Theory in TDA

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Exploring sheaf theory applications in topological data analysis through four case studies, covering level set persistence, merge trees, and innovative approaches to persistent homology.
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1 Lesons
57 minutes
On-Demand
Free-Video
Institute for Advanced Study

Introduction to Perverse Sheaves

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Dive into the fundamental concepts and theoretical foundations of perverse sheaves with expert mathematician Mark Goresky, exploring advanced mathematical structures and their applications.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Institute for Advanced Study

Sheaves on Graphs, the Hanna Neumann Conjecture, and Algebraic Geometry Applications

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Explore advanced graph theory concepts through sheaf theory and the Hanna Neumann conjecture, featuring innovative problem-solving approaches and applications in discrete mathematics.
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1 Lesons
2 hours 6 minutes
On-Demand
Free-Video
BunG Seminar

The Geometric Satake Correspondence - Talk 20

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Delve into the Geometric Satake Correspondence, exploring spherical perverse sheaves, affine Grassmannian geometry, and their connection to Langlands Dual Group representations in advanced mathematics.
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1 Lesons
2 hours
On-Demand
Free-Video
BunG Seminar

Derived Categories of Sheaves on Schemes and Prestacks - Talk 14

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Delve into advanced sheaf theory concepts, exploring six-functor formalism, derived categories, and D-modules through an in-depth examination of prestacks and scheme applications.
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1 Lesons
1 hour 41 minutes
On-Demand
Free-Video
BunG Seminar

Compact Generation of D-modules on BunG - Talk 15

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Delve into advanced mathematical concepts of D-modules on Bun_G, exploring compact generation, DG categories, and applications in algebraic geometry through detailed theoretical analysis.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sheaves as Computable and Stable Topological Invariants for Datasets

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Explores sheaf theory in topological data analysis, connecting level-sets persistence with derived sheaves. Presents functorial equivalences, stability theorems, and barcode decompositions for continuous data analysis.
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14 Lesons
23 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sheaf Based Modeling of Wireless Communications

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Explore sheaf-based modeling for wireless communications, covering topology, simplicial complexes, interference, and network activation. Learn about persistence, homological invariants, and simulation examples.
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26 Lesons
57 minutes
On-Demand
Free-Video
IMSA

Stability Structures in Holomorphic Morse-Novikov Theory

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Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Constructible Sheaves and Filtered D-Modules

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Explore the Riemann-Hilbert correspondence and its p-adic analogue, connecting constructible sheaves to filtered D-modules with applications in algebraic geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
IMSA

Filtered Ends and Bochner Hartogs Dichotomy on Complete Kahler Manifolds

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Explore filtered ends and Bochner Hartogs dichotomy on complete Kahler manifolds, examining relationships between generalized ends and first compactly supported cohomology.
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1 Lesons
46 minutes
On-Demand
Free-Video
IMSA

Perverse Sheaves on Varieties with Large Fundamental Group

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Explore perverse sheaves on Kähler manifolds, focusing on a generalization of the Singer-Hopf conjecture and its proof using Shafarevich conjecture ideas. Joint work with Donu Arapura presented.
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1 Lesons
52 minutes
On-Demand
Free-Video
IMSA

D-Modules and Toric Schobers

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Exploring mirror symmetry using perverse sheaves of categories and schobers, with focus on B-side category in toric homological mirror symmetry and associated D-module characteristic cycles.
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1 Lesons
59 minutes
On-Demand
Free-Video
IMSA

Homotopy Path Algebras

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Explore Homotopy Path Algebras and their applications in algebraic topology, sheaf theory, and toric geometry. Discover connections to homological mirror symmetry and recent developments in the field.
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1 Lesons
54 minutes
On-Demand
Free-Video
ICTP Mathematics

Algebraic Geometry - Lecture 10

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Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Algebraic Geometry - Lecture 8

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Explore advanced concepts in algebraic geometry, focusing on complex mathematical structures and their applications in modern mathematics and theoretical physics.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Stable Pair Invariants and Derived Categories - Lecture 1

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Explore stable pair invariants and derived categories in mathematics with expert Y. Toda in this comprehensive lecture from ICTP Mathematics.
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1 Lesons
1 hour
On-Demand
Free-Video
Hausdorff Center for Mathematics

Perverse Sheaves and Schobers on Riemann Surfaces - Tobias Dyckerhoff

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Explore derived constructible categories on stratified Riemann surfaces, t-structures, Verdier duality, and categorified perverse sheaves with applications in algebraic geometry and topology.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Generic Character Sheaves for Parahoric Subgroups

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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.
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1 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Residues and Trace Maps in Grothendieck Duality - Lecture 3

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Explores residues and trace maps in Grothendieck duality theory, advancing understanding of algebraic geometry and commutative algebra concepts for researchers and advanced students.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Residues and Trace Maps in Grothendieck Duality - Lecture 4

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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.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

A Sheaf-Theoretic Construction of Shape Space

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Sheaf-theoretic approach to construct shape space using Persistent Homology Transform. Explores homotopy sheaves, metrics, stability theorems, and approximation of manifolds.
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1 Lesons
53 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

A Sheaf-based Approach to Graph Neural Networks

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Explore sheaf theory's application to Graph Neural Networks, offering a novel perspective on Geometric Deep Learning beyond traditional geometric structures.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
M-Seminar, Kansas State University

Resurgent Perverse Sheaves and Topological Resurgence Theory

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Explore topological counterparts of resurgence theory using perverse sheaves on C as convolution algebras, extending beyond regular holonomic D-modules to infinitely singular cases.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Cohomological Hall Algebras of 0-Dimensional Sheaves on Surfaces

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Explore cohomological Hall algebras of 0-dimensional sheaves on surfaces, their explicit description, and applications to moduli spaces of sheaves with positive-dimensional support.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Perverse Sheaves in Deformation Quantization

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Explore holomorphic symplectic manifolds, deformation quantization modules, and perverse sheaves in Lagrangian intersections and BV quantization.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Virasoro Constraints in Sheaf Theory

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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.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Categorification of Donaldson-Thomas Invariants

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Explore categorification of Donaldson-Thomas invariants through derived foliations, extending BBDJS construction with a sheaf of 2-periodic dg-categories modeled on matrix factorizations.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Institute for Advanced Study

Singularities of Constructible Sheaves

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Explore advanced mathematical concepts in constructible sheaves and their singularities, delving into complex algebraic geometry and topology.
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1 Lesons
18 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds

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Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.
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16 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Quantitative Ell-Adic Sheaf Theory

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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.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks - New Foundations for Analytic Geometry

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Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks - Lecture 6

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Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
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1 Lesons
1 hour 49 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks - Lecture 5

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Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.
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1 Lesons
1 hour 46 minutes
On-Demand
Free-Video
BIMSA

Functoriality and Sheaf Property for Wrapped Fukaya Categories

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Explore functorial and sheaf-theoretic properties of wrapped Fukaya categories, surveying key results and insights in this advanced mathematical topic.
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1 Lesons
44 minutes
On-Demand
Free-Video
BIMSA

Sheaves on Calabi-Yau 4-folds and Virtual Invariants - An Overview

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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.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
BIMSA

Derived Approach to Highest Weight Categories

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Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
BIMSA

Langlands Duality for the Affine Hecke Category

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Explore Langlands duality for affine Hecke category, its applications in representation theory, and potential generalizations to symplectic singularities. Gain insights into geometric local Langlands duality.
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1 Lesons
51 minutes
On-Demand
Free-Video
BIMSA

The Global Unramified Geometric Langlands Equivalence

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Explore the global unramified geometric Langlands conjecture, its history, motivation, and recent proof, along with remaining open questions in the field.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Circle Action of Microlocal Kernels

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Explore the construction of an S^1 action using microlocal kernels and its application in the sheaf theoretical proof of the contact non-squeezing theorem.
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1 Lesons
56 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Instanton Sheaves - The Next Frontier in Algebraic Geometry

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Explore instanton sheaves, a frontier in algebraic geometry. Gain insights from expert Marcos Jardim on this advanced mathematical topic within the V Latin American School of Algebraic Geometry.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Applied Algebraic Topology Network

Modeling Shapes and Fields - A Sheaf Theoretic Perspective

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Explore topological transforms for shape and field modeling, including Euler Characteristic and Lifted Euler Characteristic. Learn about sheaf theory in shape space construction and its applications in statistical analysis.
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1 Lesons
50 minutes
On-Demand
Free-Video
BunG Seminar

Localizing Invariants of Large Categories: General Theory

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Delve into advanced algebraic K-theory concepts, exploring dualizable stable categories, continuous K-theory applications, and their relationship with sheaf categories on Hausdorff spaces.
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1 Lesons
2 hours 16 minutes
On-Demand
Free-Video
BunG Seminar

Localizing Motives, Algebraic KK-Theory and Refined Negative Cyclic Homology

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Delve into advanced algebraic geometry concepts exploring localizing motives, their rigidity properties, and applications in refined negative cyclic homology and topological cyclic homology.
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1 Lesons
2 hours 29 minutes
On-Demand
Free-Video
BunG Seminar

Overview of Restricted Geometric Langlands Theory

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Delve into categorical formulations of geometric Langlands theory, exploring restricted local systems, their applications in arithmetic, and connections to automorphic forms through Frobenius traces.
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1 Lesons
2 hours 5 minutes
On-Demand
Free-Video
BunG Seminar

The Global Hecke Action - Talk 41

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Delve into geometric Satake theory and explore how Rep(G^vee) actions on BunG sheaves integrate into global Hecke modifications, with applications in Betti, de Rham, and étale settings.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

How Can Large Language Models Learn From Humans? - Understanding Psycholinguistic Predictions and Sheaf Theory

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Explore how combining lexical predictions from LLMs with syntactic structures can improve language understanding, using sheaf theory to better match human reading patterns and comprehension.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Advanced Study

Introduction to Perverse Sheaves - Part 2

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Delve into advanced mathematical concepts of perverse sheaves, exploring theoretical foundations and applications in topology and algebraic geometry through expert insights.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Cohomological Hall Algebras, Their Representations, and Nakajima Operators

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Delve into advanced algebraic geometry concepts, exploring cohomological Hall algebras, geometric representations, and Nakajima operators through the lens of zero-dimensional sheaves on smooth surfaces.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video