IMSA Courses

Classifying Crystalline Interacting Topological Phases Through Equivariant Cohomology

Explore the classification of crystalline interacting topological phases using equivariant cohomology, examining assumptions and comparing with existing literature proposals.

• YouTube
• 55 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

Subtly Knotted Surfaces Separated by Many Internal Stabilizations

Exploration of smoothly knotted surfaces in 4-manifolds, focusing on isotopy, internal stabilizations, and diffeomorphisms. Discusses infinite collections of surfaces with unique properties and infinite stabilization diameter.

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

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

Explore the interaction between hyperbolic geometry and homology cobordism using monopole Floer homology, focusing on subgroups generated by hyperbolic homology spheres.

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

Ribbon Concordances and Slice Obstructions: Experiments and Examples

Explore ribbon concordances between knots, computational methods, and results in low-dimensional topology. Joint work with Nathan Dunfield on slice obstructions and experimental approaches.

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

Instantons, Suspension, and Surgery

Explore advanced concepts in gauge theory, including instantons, suspension, and surgery techniques for manifolds with boundary components and their applications in cobordism maps.

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

Instantons, Suspension, and Surgery - Part 1

Explore Dehn surgery number in 3-manifolds, using mod 2 instanton homology and Froyshov's q_3 invariant to prove existence of integer homology 3-spheres with arbitrarily large surgery numbers.

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

Fan Ye, Harvard University - 2-Torsions in Singular Instanton Homology

Exploration of 2-torsions in singular instanton homology for knots, comparing complex and Z/2 coefficients, with focus on fibered knots and genus 1 knot surgeries.

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

Instanton Floer Homology and Heegaard Diagrams

Exploring the connection between instanton Floer homology and Heegaard diagrams in 3-manifolds, with insights on extracting information and potential applications in topology.

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

Toda Lattice, Billiards & the Viterbo Conjecture

Exploração da relação entre o reticulado de Toda, bilhares e a conjectura de Viterbo, com foco em sistemas integráveis e transformações simpléticas de produtos lagrangianos.

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

Gauge Theory and Low Dimensional Topology - Conference Lecture

Explore gauge theory and low-dimensional topology with expert insights from Paul Feehan in this engaging 48-minute conference talk at the University of Miami.

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

Smooth Closing Lemma for Area-Preserving Diffeomorphisms of Surfaces

Explore the smooth closing lemma for area-preserving diffeomorphisms on surfaces, featuring a proof based on Weyl formula and Seiberg-Witten Floer homology. Joint work with Cristofaro-Gardiner and Prasad.

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