IMSA Courses

Homological Mirror Symmetry for Theta Divisors

Exploring homological mirror symmetry for theta divisors in principally polarized abelian varieties, with insights from ongoing research in complex moduli and SYZ fibrations.

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

Progress on Quantum Toric Geometry

Explore quantum toric geometry, its key concepts, and recent advancements in moduli properties and mirror dualities with expert Ernesto Lupercio in this comprehensive lecture.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

On the Presentability of Artin Differentiable Stacks

Explore the global quotient presentability of Artin stacks in smooth settings, delving into advanced mathematical concepts in differential geometry and algebraic topology.

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

Lagrangian Intersections in Phase Tropical Hypersurfaces

Explore phase tropical hypersurfaces, their relation to complex hypersurfaces, and combinatorial analogs of Lagrangian spheres and thimbles. Discuss connections to mirror matrix factorization categories.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Gromov-Hausdorff Convergence of Filtered A Infinity Categories

Explore Floer homology's dependence on Hamiltonian isotopy, its multiplicative structure, and connections to homological Mirror symmetry in formal deformation theory.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Holomorphic Floer Theory, Quantum Wave Functions and Resurgence

Explore holomorphic Floer theory, exponential integrals, and resurgence in algebraic geometry. Discover connections to quantum wave functions and infinite-dimensional applications.

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

Spectra, Dynamical Systems, and RG Flows

Exploring connections between Frobenius manifolds and dynamical systems, recasting RG flows, and relating conformal dimensions to Steenbrink spectra in theoretical physics.

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

Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves

Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.

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

Stability Structures in Holomorphic Morse-Novikov Theory

Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.

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

Basic Remarks on Lagrangian Submanifolds of Hyper-Kähler Manifolds

Explore properties of Lagrangian subvarieties in hyper-Kähler manifolds, focusing on their interaction with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.

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

Topological Invariants of Compact Singular Varieties

Explore topological invariants of compact singular varieties with José Seade from UNAM. Gain insights into advanced mathematical concepts and their applications in algebraic geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Adelic Toric Varieties and Loop Groups

Explore proalgebraic spaces, adelic abelian algebraic groups, and vector bundle categories. Discover adelic loop groups, Grassmannians, and the Birkhoff-Grothendieck theorem for holomorphic bundles.

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

Oriented and Unitary Equivariant Bordism of Surfaces

Exploration of equivariant oriented and unitary bordism groups, focusing on torsion parts and obstruction classes for surfaces with free action. Presents key findings and non-trivial invariants.

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

Extensions in MHM and Hain's Biextension Line Bundle - Part 2

Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.

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

Counting Divisorial Contractions with Centre a $cA_n$-Singularity

Explore 3D divisorial contractions with $cA_n$-singularity centers, simplifying existing classifications and examining high-discrepancy contractions to fixed varieties.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video