IMSA Courses

Quantum Toric Geometry and Tame Geometry via Motivic Rings II

Explore the connection between quantum toric manifolds and tame geometry through Hodge number computations of LVM manifolds, providing insights for future research in non-commutative geometry.

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

Quantum Toric Geometry and Tame Geometry via Motivic Rings I

Explore the connection between quantum toric manifolds and tame geometry through Hodge number computations of LVM manifolds, providing insights for future research in non-commutative geometry.

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

Generalized Complex Branes, Doubling, and Shifted Symplectic Geometry, Part I

Explore symplectic approaches to generalized complex geometry, focusing on brane construction and implications for Kaehler geometry. Delve into shifted symplectic geometry and homotopy complex structures.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Generalized Complex Branes, Doubling, and Shifted Symplectic Geometry, Pt II

Explore symplectic approaches to generalized complex geometry, focusing on brane construction and implications for generalized Kaehler geometry. Delve into shifted symplectic geometry and homotopy complex structures.

• YouTube
• 1 hour
• 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

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

Enrique Becerra, University of Miami - Some Remarks on the Spectrum of Finite Groups and the Ekedahl Invariant

Explore the stringy spectrum of orbifolds from finite group quotients and its connection to the Ekedahl invariant in this mathematical discourse on group theory and algebraic geometry.

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

Bernardo Uribe, UniNorte - Bordism and Birational Invariants of Finite Groups

Explore birational invariants of finite groups and their connection to bordism invariants of equivariant manifolds, focusing on Bogomolov's results in this advanced mathematical topic.

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

Cohomological Donaldson-Thomas Invariants of 3-Manifolds

Explore Morse homology of complex Chern-Simons functional, its connections to 4D supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.

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

Ernesto Lupercio, CINVESTAV - Stringy Motives

Explore the localization principle for orbifolds in this advanced mathematical survey, featuring joint research on stringy motives and their applications.

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

On Mapping Class Groups of Non-Orientable Surfaces

Exploración de la estructura y cohomología de grupos de clases de mapeo en superficies no orientables, incluyendo resultados recientes sobre el plano proyectivo y la botella de Klein.

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