Derived Categories Courses and Certifications

Institute for Advanced Study

Derived Categories of the Permutahedral Varieties

Delve into the geometric and combinatorial analysis of derived categories in toric varieties, exploring permutahedron's role in matroid theory through convex-geometric approaches.

• YouTube
• 55 minutes
• On-Demand
• Free Video

BIMSA

Tilting Theory Revisited - Developments in Real Grothendieck Groups

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.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Institute for Advanced Study

Seminar on Geometric and Modular Representation Theory

Explore advanced topics in geometric and modular representation theory through expert lectures on Broué's conjecture, affine Grassmannians, Satake equivalence, and Hecke categories.

• YouTube
• 1 day 8 hours 29 minutes
• On-Demand
• Free Video

ICTP Mathematics

Moduli Spaces, Mirror Symmetry, and Enumerative Geometry

Explore advanced algebraic geometry through moduli spaces, mirror symmetry, and enumerative geometry with leading experts from top institutions worldwide.

• YouTube
• 1 day 9 hours 46 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Introduction to A-Infinity Structures - Bernhard Keller

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

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Geometry of Matroids Workshop

Explore advanced geometric structures and tropical methods in matroid theory through expert lectures on delta-matroids, quiver representations, and moduli spaces.

• YouTube
• 15 hours 29 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Connections Between Representation Theory and Geometry - Winter School

Explore advanced connections between representation theory and geometry through A-infinity structures, Fukaya categories, and homological mirror symmetry techniques.

• YouTube
• 15 hours 27 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Introduction to A-Infinity Structures - Bernhard Keller

Explore A-infinity algebras, modules, and derived categories. Learn about topological origins, minimal models, and twisted objects in this advanced mathematics lecture.

• YouTube
• 1 hour
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Arend Bayer- Non-Commutative Abelian Surfaces and Generalised Kummer Varieties

Explore non-commutative abelian surfaces and generalized Kummer varieties, examining deformations of derived categories and their impact on moduli spaces of stable objects in algebraic geometry.

• YouTube
• 1 hour
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Ambidexterity I by Neil Strickland

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.

• YouTube
• 1 hour 41 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

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.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Gorenstein Duality in Topology - Lecture 3

Explore Gorenstein duality in topology, examining its connections to algebraic geometry and representation theory. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Gorenstein Duality in Topology - Lecture 2

Explore Gorenstein duality in topology, connecting algebraic concepts to topological structures and generalizing Poincaré duality for manifolds in this advanced mathematical lecture.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra - Lecture 2

Explore duality and stratification in commutative algebra, focusing on derived categories, triangulated structures, and connections to algebraic topology and representation theory.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video