IMSA Courses

On Rational Cubic Fourfolds Containing Veronese Surfaces

Explore birational automorphisms and rationality of cubic fourfolds containing Veronese surfaces, with insights on K3 categories and Cremona transformations in algebraic geometry.

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

Factorization Centers in Dimension Two and the Grothendieck Ring of Varieties

Explores factorization centers in birational isomorphisms for smooth projective surfaces, discussing their independence and relation to rationality problems and the Grothendieck ring of varieties.

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

Equivariant Birational Types

Explore obstructions in equivariant birational geometry, covering rationality, basic facts, refined invariants, and applications to abelian and non-abelian actions on surfaces.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Rationality for Threefolds Over Non-Closed Fields

Explore recent developments in rationality of geometrically rational threefolds over non-closed fields, including symbol invariants and new approaches to longstanding questions in algebraic geometry.

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

Wall Finiteness Obstruction for DG Categories II

Exploration of Wall finiteness obstruction theorem for DG categories, including applications to phantom DG categories and derived categories of algebraic varieties. Discusses extensions to algebras over DG operads.

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

Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity of Mixed Hodge Structure

Explore holomorphic bisectional curvature in Hodge theory, focusing on mixed Hodge metrics, rigidity results, and applications to geometric examples.

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

A Categorical Interpretation of the GKZ D-Module

Explore the categorical interpretation of GKZ D-modules in toric homological mirror symmetry, focusing on B-side categories and characteristic cycle strata.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1

Explore quantum toric geometry, a non-commutative generalization of toric geometry. Learn about stacks, quantum tori, and quantum toric varieties, building on foundations of traditional toric geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hans Boden, McMaster University - Virtual Knots and Algebraic Concordance

Explore virtual knots, concordance groups, and new invariants using mock Seifert matrices. Discover algebraic structures and open problems in knot theory.

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

Cohomology of Hurwitz Spaces

Explore the cohomology of Hurwitz spaces, focusing on branched covers of the affine line and their connections to braided Hopf algebras and a new family of braided operads.

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

Group Cohomology and Topological K-Theory of Semidirect Product Groups - Mario Velasquez

Explore group cohomology and topological K-theory for semidirect products of Z^n and Z/m, with m square-free. Learn about Z/m-lattice decomposition and the Baum-Connes conjecture.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Bernhard Hanke, Augsburg University - Large and Small Group Homology

Explore group homology's surprising role in encoding metric properties of smooth manifolds, including enlargeability and positive scalar curvature, with applications and key concepts explained.

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

Topological Components of Commuting Elements of Nilpotent Lie Groups

Explore topological components of commuting elements in nilpotent Lie groups, focusing on reduced upper unitriangular matrix groups and generalized Heisenberg groups. Discover connections to cohomology classes and symplectic Stiefel manifolds.

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

Yuri Tschinkel, Courant Institute - New Invariants in Equivariant Birational Geometry

Explore new obstructions to equivariant birationality in higher-dimensional algebraic varieties, introduced by Tschinkel and Kresch, advancing the field of equivariant birational geometry.

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

The Z-P-Equivariant Steenrod Algebra and Its Applications

Explore recent advancements in Z/p-equivariant Steenrod algebra, including calculations of its dual with constant coefficients and applications to constructing Z/p-equivariant spectrum BPR at odd primes.

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