IMSA Courses

Mixed Period Maps: Definability and Algebraicity

Explore definable analytic spaces and their applications in algebraic geometry, focusing on period maps and mixed Hodge structures. Learn about o-minimal geometry and its role in proving key conjectures.

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

Maximal Torus Actions, Equivariant Principal Bundles and Transverse Equivalence

Explore maximal torus actions, complex manifolds, and irrational fans, delving into their correspondence and connections to canonical foliations in this advanced mathematical lecture.

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

Enumerative Geometry and the Quantum Torus

Explore enumerative geometry through tropical curves, pseudotropical curves, and their connection to Lie algebras and quantum torus. Discover innovative approaches to classical counting problems in algebraic geometry.

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

Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families

Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.

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

Nonrational Toric Geometry I - Symplectic Toric Quasifolds Minicourse

Explore symplectic toric quasifolds, generalizing toric varieties to non-rational polytopes. Learn about quasilattices, quasirationality, and quasitori through examples like quasispheres and Penrose tilings.

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

Nonrational Toric Geometry II - Quasifolds, Foliations, Combinatorics and One-parameter Families

Explore complex toric quasifolds, their structure, and relation to rational toric varieties. Learn about extending constructions to nonsimple convex polytopes in symplectic and complex settings.

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

Quantum Toric Geometry I

Explore quantum toric geometry, a generalization of classical toric geometry using quantum tori, allowing for irrational fans. Learn foundations and motivations behind this advanced mathematical concept.

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

Wall Finiteness Obstruction for DG Categories I

Explore Wall finiteness obstruction theorem for DG categories, its applications to phantom DG categories, and implications for algebraic geometry, including results on Barlow surface and stratified varieties.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video