IMSA Courses

From Turaev to Rokhlin via VOA Characters and Curve Counting

Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into recent developments in this mathematical field.

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

From Turaev to Rokhlin via VOA Characters and Curve Counting

Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into Spin-C structures and related mathematical concepts.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Restricted Geometric Langlands as a Common Denominator

Explore the unifying framework of restricted geometric Langlands correspondence, connecting various contexts and its relation to classical Langlands conjecture via categorical trace.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Geometric Langlands in Its Various Contexts

Explore geometric Langlands correspondence, its contexts, and related conjectures. Unify different perspectives through restricted Langlands correspondence and its relation to classical theory.

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

Spectrum of Singularities

Explore hypersurface singularity spectra: definition, properties, and computational techniques. Learn about Thom-Sebastiani theorem, semicontinuity, and applications in algebraic geometry.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Deformations of Semi-Smooth Varieties

Explore deformation theory of semi-smooth varieties, focusing on tangent sheaf and T^1 sheaf. Discusses smoothability of semi-smooth Godeaux surfaces as an application.

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

CoFTs for GLSMs

Explore enumerative invariants for GLSMs, generalizing Gromov-Witten and FJRW theories. Learn about virtual fundamental classes, Atiyah classes, and matrix factorizations in this context.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Homological Mirror Symmetry for Log Calabi-Yau Surfaces

Explore homological mirror symmetry for log Calabi-Yau surfaces, including construction of mirror Landau-Ginzburg models and connections to SYZ fibrations and previous research.

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

Unitary Representations of Reductive Lie Groups

Explore unitary representations of reductive Lie groups using Hodge theory, including progress on a conjecture. Joint work with Kari Vilonen presented by Harvard's Wilfried Schmid.

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

Minimal Exponents of Singularities

Explore advanced mathematical concepts like minimal exponents, Bernstein-Sato polynomials, and their connections to D-modules, Hodge theory, and birational geometry in this in-depth lecture.

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

Fixed Points in Toroidal Compactifications and Essential Dimension of Covers

Explores essential dimension in algebraic objects, focusing on congruence covers of Shimura varieties. Presents new geometric approaches and fixed point theorems, extending incompressibility results to exceptional types.

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

A Non-Archimedean Definable Chow Theorem

Explore non-archimedean algebraization theorems and their applications in Diophantine geometry, focusing on a p-adic analogue of the definable Chow theorem.

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

Log Symplectic Pairs and Mixed Hodge Structures

Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.

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

Model Theory - From Logic to Geometric Stability Theory and O-Minimality I

Explore model theory principles, focusing on o-minimality and stability theory, with applications to complex geometry and arithmetic aspects.

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

O-Minimality and Hodge Theory - Definable GAGA + Griffiths Conjecture

Explore o-minimal geometry, definable GAGA, and Griffiths Conjecture in algebraic geometry. Learn about definable analytic spaces, Oka coherence, and their applications to period maps and variations of mixed Hodge structures.

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