IMSA Courses

A Categorical Description of Discriminants

Explore a categorical approach to discriminants in toric homological mirror symmetry, including B-side categories, spherical functors, and K-theoretic evidence. Joint work with Ludmil Katzarkov presented.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

The Hodge Filtration by Age and the Spectrum of Du Val Singularities

Explore the connection between cyclic homology's Hodge structure and the Ito-Reid age filtration in Mckay correspondence, with applications to Du Val singularities' spectrum computation.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

On Mapping Class Groups of Non-Orientable Surfaces

Exploración de grupos de clases de mapeo en superficies no orientables, abordando el problema de realización de Nielsen y la periodicidad p, con aplicaciones en cohomología de Farrell.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Geometry, Topology, Group Actions, and Singularities in the Americas

Explore the intersection of geometry, topology, group actions, and singularity theory in this conference talk, fostering collaboration among experts across the Americas and beyond.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Decomposition of Definable Sets in Algebraically Closed Fields

Exploration of definable set decomposition in algebraically closed fields, focusing on advanced concepts and techniques in geometric model theory and algebraic geometry.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Mirror Structure Constants via Non-Archimedean Analytic Disks

Exploration of mirror structure constants for smooth affine log Calabi-Yau varieties using non-archimedean analytic disks, generalizing previous constructions and discussing potential further applications.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Ernesto Lupercio- Quantum Toric Geometry Pt. II

Explores quantum toric geometry, generalizing toric geometry with moduli spaces. Advanced mathematical concepts for researchers in algebraic topology, geometry, and mathematical physics.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Quivers, Curve Counting, and Fermionic Sums in Topology

Explore connections between quantum groups, vertex algebras, and quiver representations in topology. Discover how fermionic forms link these areas, shedding new light on enumerative geometry and curve counting.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Andras Nemethi- Multivariable Poincaré Series of Complex Singularities

Explore multivariable Poincaré series in complex singularities with Andras Nemethi. Delve into advanced mathematical concepts at the intersection of geometry, topology, and singularity theory.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Braid Monodromy and Divisibility of Alexander Polynomials of Real Singular Curves

Explores Alexander polynomials in algebraic geometry, focusing on braid monodromy symmetries of real plane curves and their impact on divisibility relations for Alexander invariants.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Decomposition of Definable Sets in Algebraically Closed Fields

Explore definable set decomposition in algebraically closed fields. Delve into geometric and topological aspects of group actions, connecting algebraic topology, geometry, and mathematical physics.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Deformation Theory for Finite Cluster Complexes

Explore geometric relationships between cluster varieties and complexes, focusing on finite cluster types with universal coefficients and their connection to Hilbert schemes via torus actions.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Donaldson-Thomas and Gromov-Witten Theories - Part XI

Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their connections to superstring theory.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Ernesto Lupercio: Quantum Toric Geometry

Explore quantum toric geometry, a generalization of toric geometry analogous to how quantum torus extends the usual torus. Delve into quantum toric varieties and their moduli spaces.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Pontrjagin Duality on Multiplicative Gerbes

Exploration of Pontrjagin Duality on Multiplicative Gerbes, proposing a generalization of the Twisted Drinfeld Double to continuous groups. Part of a conference on geometry, topology, group actions, and singularities.

• YouTube
• 46 minutes
• Self-Paced
• Free Video