IMSA Courses

Interpolation for Polynomials in Two Variables

1 review

Explore advanced polynomial interpolation techniques in two variables, covering dimension counts, Picard groups, and conjectures like Segre's and Nagata's. Delve into cones, extremal rays, and the A-Conjecture.

• YouTube
• 53 minutes
• On-Demand
• Conference Talk

The $K(\pi, 1)$ Conjecture - Part 2

1 review

Explore the recent proof of the classical K(π,1) conjecture for affine Artin groups, delving into its mathematical intricacies and implications for algebraic topology.

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

Equivariant Birational Geometry of 3-Dimensional Projective Space

1 review

Explore G-equivariant birational geometry of 3D projective space, focusing on finite group actions and their impact on fibrations into rational curves or surfaces.

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

A Parallel Reality Look at Generalized Geometry

Explore generalized geometries and related "Hodge theory" through a fresh perspective, building on classical works by Donaldson and Simpson in this advanced mathematics seminar.

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

Remarks on Lagrangian Submanifolds of Hyper-Kaehler Manifolds

Explore properties of Lagrangian subvarieties in hyper-Kaehler manifolds, focusing on interactions with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.

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

On the Second Homotopy Group of Spaces of Commuting Elements in Lie Groups

Explore the computation of the second homotopy group of Hom(Z^n, G) spaces, focusing on compact Lie groups. Learn about geometric generators and specific results for simply connected, simple groups.

• YouTube
• 1 hour
• 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

Homotopy Theories of Coalgebras

Explore homotopy theories of simplicial coalgebras, extending algebraic models for p-adic homotopy theory to include fundamental groups. Discover key ideas and potential G-equivariant analogs.

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

Equivariant A-Theory & Spaces of Equivariant H-Cobordisms

Explore equivariant A-theory and h-cobordisms, focusing on Waldhausen's algebraic K-theory of manifolds and its role in classifying manifolds and diffeomorphisms.

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

Invariants of Manifolds and Relations to Cobordism

Explore manifold invariants, cut-and-paste equivalence, and cobordism relations. Discover recent advancements in categorifying these concepts and their connections to algebraic K-theory.

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

The Stringy Spectrum of Orbifolds

Explore the stringy spectrum as an additive invariant of orbifolds, its properties, and its connection to isolated hypersurface singularities through examples and explanations.

• YouTube
• 52 minutes
• 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