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#Derived Categories

Showing: 49 courses
University of Chicago Department of Mathematics

Categorical Noncommutative Geometry

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Dive into categorical noncommutative geometry, exploring algebraic varieties through derived categories of coherent sheaves and extending classical concepts to differential graded categories.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

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Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.
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18 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

On the Left Adjoint of mod p Smooth Parabolic Induction

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Delve into advanced mathematical concepts exploring parabolic induction functors, focusing on left adjoint properties and their behavior with algebraic weights in p-adic field extensions.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
BIMSA

Tilting Theory Revisited - Developments in Real Grothendieck Groups

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Explore recent developments in tilting theory, focusing on real Grothendieck groups and 2-term silting complexes. Gain insights into g-fans, representation theory, and connections with canonical decompositions.
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1 Lesons
52 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
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
IMSA

Windows and the BGMN Conjecture

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Explore the BGMN Conjecture in algebraic geometry using moduli spaces, derived categories, and GIT wall crossing. Uncover insights into vector bundles and symmetric powers of curves.
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15 Lesons
1 hour 7 minutes
On-Demand
Free-Video
IMSA

Windows and Geometric Invariant Theory

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Explore windows theory in algebraic geometry, its applications to GIT constructions, and its impact on derived categories and stability conditions in various mathematical contexts.
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8 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Comparative Stability of Two Zigzag Bottleneck Distances

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Explores zigzag persistence in algebraic topology, comparing bottleneck distances for zigzag modules. Analyzes similarities and differences between approaches, focusing on Auslander-Reiten quiver perspective.
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1 Lesons
29 minutes
On-Demand
Free-Video
IMSA

Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves

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Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.
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1 Lesons
47 minutes
On-Demand
Free-Video
IMSA

Complex Surfaces with P_g=Q=0 via Birational Geometry, Derived Category and Gauge Theory

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Exploration of complex surfaces with p_g=q=0, examining their significance and recent developments through birational geometry, derived category, and gauge theory perspectives.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Intermediate Jacobians of Gushel-Mukai Varieties

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Explore intermediate Jacobians of Gushel--Mukai varieties, focusing on threefolds and fivefolds. Discover their connection to Albanese varieties of double EPW surfaces and related birational and categorical aspects.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

Generation in Characteristic P

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Explore techniques for constructing generators in derived categories in nonzero characteristic, including joint research findings on this advanced mathematical topic.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Mathematical Union

A Classical View on Derived Algebraic Geometry

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Explore derived algebraic geometry from a classical perspective, gaining insights into this advanced mathematical field and its applications.
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1 Lesons
43 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
International Centre for Theoretical Sciences

Ambidexterity I by Neil Strickland

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Explore duality phenomena in algebraic topology, commutative algebra, and modular representation theory. Learn about derived categories, triangulated structures, and Grothendieck duality theory in this advanced mathematics lecture.
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1 Lesons
1 hour 41 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Introduction to A-Infinity Structures - Bernhard Keller

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Explore A-infinity algebras, modules, and derived categories. Learn about topological origins, minimal models, and twisted objects in this advanced mathematics lecture.
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1 Lesons
1 hour
On-Demand
Free-Video
Hausdorff Center for Mathematics

Introduction to A-Infinity Structures - Bernhard Keller

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Explore A-infinity algebras, their modules, and derived categories. Learn about topological origins, definitions, morphisms, bar construction, and Kadeishvili's theorem on minimal models.
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1 Lesons
1 hour 9 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

Gorenstein Duality in Topology - Lecture 3

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Explore Gorenstein duality in topology, examining its connections to algebraic geometry and representation theory. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Gorenstein Duality in Topology - Lecture 2

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Explore Gorenstein duality in topology, connecting algebraic concepts to topological structures and generalizing Poincaré duality for manifolds in this advanced mathematical lecture.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra - Lecture 2

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Explore duality and stratification in commutative algebra, focusing on derived categories, triangulated structures, and connections to algebraic topology and representation theory.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Localisation in Homotopy Theory by Abhinandan Das

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Explore localization techniques in homotopy theory, focusing on applications and implications for understanding topological spaces and their properties.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra by Srikanth B. Iyengar

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Explore duality and stratification in commutative algebra, focusing on derived categories, triangulated structures, and connections to algebraic topology and representation theory.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra - Lecture 4

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Explore duality and stratification in commutative algebra, focusing on derived categories, Grothendieck duality, and connections to algebraic topology and representation theory.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra - Lecture 3

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Explore duality and stratification in commutative algebra, focusing on derived categories, Grothendieck duality, and connections to algebraic topology and representation theory.
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1 Lesons
1 hour 31 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
International Centre for Theoretical Sciences

Ambidexterity III by Neil Strickland

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Explore advanced concepts in algebraic topology, focusing on ambidexterity and its applications in duality phenomena within tensor-triangulated categories.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

João Lourenço- Towards Bezrukavnikov via P-adic Central Sheaves

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Explore advancements in algebraic geometry, focusing on Bezrukavnikov's equivalence and p-adic central sheaves in the Witt vector affine flag variety, building on Kazhdan-Lusztig's work.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Brauer Groups, Twisted Derived Categories, and Hodge Theory

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Explore recent developments in Brauer group theory, examining the period-index problem through derived categories, Hodge theory, and enumerative geometry methods.
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1 Lesons
31 minutes
On-Demand
Free-Video
IMSA

Dispatches from the Ends of the Stability Manifold - Part I

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Explore noncommutative minimal model program, stability manifolds, and multi-scale decompositions in triangulated categories. Discover connections to moduli spaces and implications for semistable object classification.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Equivariant Lagrangian Correspondences and Applications

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Explore equivariant Lagrangian correspondences and their applications in mathematics, focusing on advanced concepts and theoretical frameworks.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Mathematical Sciences

On Deformations Over Non-Commutative Base

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Explore deformations over non-commutative base with Professor Yujiro Kawamata, delving into advanced mathematical concepts and their applications in algebraic geometry.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Dispatches from the Ends of the Stability Manifold - Lecture 1

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Explore Bridgeland stability conditions and their role in homological structures. Delve into noncommutative minimal model programs and their applications in algebraic geometry.
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1 Lesons
1 hour
On-Demand
Free-Video
M-Seminar, Kansas State University

Dispatches from the Ends of the Stability Manifold - Lecture 4

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Explore advanced concepts in algebraic geometry, including stability conditions, noncommutative minimal model programs, and multi-scale decompositions. Delve into cutting-edge research on augmented stability conditions.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Dispatches from the Ends of the Stability Manifold - Lecture 3

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Explore advanced concepts in algebraic geometry, including stability conditions, multi-scale decompositions, and the noncommutative minimal model program. Gain insights into cutting-edge research.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Dispatches from the Ends of the Stability Manifold - Lecture 2

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Explore noncommutative minimal model program, multi-scale decompositions, and augmented stability conditions in triangulated categories. Delve into cutting-edge research in algebraic geometry and homological algebra.
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1 Lesons
57 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Stable Envelopes from 2D Mirror Symmetry

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Explore stable envelopes through 2D mirror symmetry, connecting equivariant K-theory and Fukaya categories in Coulomb branches. Gain insights into homological mirror symmetry predictions.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Derived Deformation Theory - Lecture 2

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Explore advanced concepts in derived deformation theory, building on previous knowledge and delving into complex mathematical principles.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Advanced Study

Derived Categories of Permutahedral Varieties Through Matroids

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Explore derived categories of permutahedral varieties using matroid theory, uncovering connections between algebraic geometry and combinatorics.
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1 Lesons
21 minutes
On-Demand
Free-Video
Banach Center

Introduction to Koszul Duality - Part 2

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Explore advanced concepts of Koszul duality, building on previous knowledge and delving into complex mathematical theories and applications.
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1 Lesons
46 minutes
On-Demand
Free-Video
BIMSA

Structure of Equivariant Derived Categories - ICBS 2024

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Explore equivariant derived categories, their structure theorems, and applications to GIT quotients and hidden symmetries in algebraic geometry.
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1 Lesons
53 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

Categorification of Lagrangian Floer Theory and Its Relation to Various Mathematics

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Explore categorification of Lagrangian Floer theory and its connections to diverse mathematical fields with renowned mathematician Kenji Fukaya.
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1 Lesons
57 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
BunG Seminar

Commutation of K-theory with Inverse Limits in Adic Spaces

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Delve into advanced K-theory concepts, exploring nuclear modules, inverse limits, and Mittag-Leffler sequences in the context of adic spaces and condensed mathematics.
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1 Lesons
2 hours 1 minute
On-Demand
Free-Video
Institute for Advanced Study

Derived Categories of the Permutahedral Varieties

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Delve into the geometric and combinatorial analysis of derived categories in toric varieties, exploring permutahedron's role in matroid theory through convex-geometric approaches.
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1 Lesons
55 minutes
On-Demand
Free-Video
Institute for Advanced Study

Motives of the Hitchin System

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Delve into advanced algebraic geometry exploring the Hitchin system's topology, examining symmetries through algebraic cycles, Fourier-Mukai duality, and Springer theory applications.
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1 Lesons
1 hour 5 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