IMSA Courses

An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1

Explore quantum toric geometry, a non-commutative generalization of toric geometry. Learn about stacks, quantum tori, and quantum toric varieties, building on foundations of traditional toric geometry.

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

A Tropical Approach to Homological Mirror Symmetry of Quadrics

Tropical geometry approach to homological mirror symmetry of quadrics, exploring new anti-canonical divisor and potential construction. Compares with previous work and discusses exceptional collections.

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

Period Mapping at Infinity

Explore Hodge theory's global study of period mapping at infinity, including new invariants, moduli space implications, and geometric insights for singular varieties.

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

On the Spectral Problem of a Three Term Difference Operator

Explore the spectral problem of quantum mechanical operators in complex Planck's constant scenarios, focusing on toric Calabi-Yau threefolds and their implications.

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

Is There Geometric Recursion for the Moduli Space of Toric Varieties?

Explore moduli space of quantum toric varieties, drawing parallels with geometric recursion. Delve into quantum lattices, tori, and CP1, examining group actions, calibration, and quantum geometric invariant theory.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

The Pushforward Theorem and Applications

Explore relative shifted symplectic structures, their pushforward theorem, and applications to Poisson structures on derived moduli of Stokes data, with insights on symplectic leaves and irregular types.

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

Geometric Recursion - Lecture I

Explore geometric recursion, its relation to topological recursion, and applications in Teichmüller spaces, moduli spaces, and mapping class group invariant functions.

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

A Proposal for Open DT Invariants

Explore open DT invariants, refined invariance, and boundary conditions in moduli spaces with Sergei Gukov. Delve into generating series, topological vertex, and infinite projects in this advanced mathematics lecture.

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

Microbial Communities - From Modelling to Understanding Ecological Organization

Explore microbial communities' complexity, diversity, and ecological significance. Discover insights into early life, species coexistence, and community assembly through interdisciplinary research and advanced modeling techniques.

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

Floer Homotopy Without Spectra

Explore advanced mathematical concepts in Floer homotopy, including manifold categories, moduli spaces, and K-homology, without relying on spectral theory.

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

Subtly Knotted Surfaces Separated by Many Internal Stabilizations

Exploration of smoothly knotted surfaces in 4-manifolds, focusing on isotopy, internal stabilizations, and diffeomorphisms. Discusses infinite collections of surfaces with unique properties and infinite stabilization diameter.

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

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

Explore the interaction between hyperbolic geometry and homology cobordism using monopole Floer homology, focusing on subgroups generated by hyperbolic homology spheres.

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

Ribbon Concordances and Slice Obstructions: Experiments and Examples

Explore ribbon concordances between knots, computational methods, and results in low-dimensional topology. Joint work with Nathan Dunfield on slice obstructions and experimental approaches.

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

Instantons, Suspension, and Surgery

Explore advanced concepts in gauge theory, including instantons, suspension, and surgery techniques for manifolds with boundary components and their applications in cobordism maps.

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

Instantons, Suspension, and Surgery - Part 1

Explore Dehn surgery number in 3-manifolds, using mod 2 instanton homology and Froyshov's q_3 invariant to prove existence of integer homology 3-spheres with arbitrarily large surgery numbers.

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