IMSA Courses

Higgs Bundles and the Topology of Higher Teichmüller Spaces

Explore advanced mathematical concepts in topology, focusing on Higgs bundles and their role in understanding higher Teichmüller spaces for non-compact real Lie groups.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Functorial Construction of Lagrangian Floer Theory and Its Possible Applications

Explore functorial construction of Lagrangian Floer theory and its potential applications in symplectic geometry with renowned mathematician Kenji Fukaya from Stony Brook University.

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

Higher Fano Manifolds in Algebraic Geometry

Explore higher Fano manifolds in algebraic geometry, their properties, and recent developments. Learn about positivity of higher Chern characters and research on homogeneous and toric higher Fano manifolds.

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

How to Enhance Categories and Why - Localization and Homotopical Enhancement

Exploring alternative techniques for enhancing localized categories using Grothendieck's derivator concept, offering a conceptually clearer approach than infinity-categories or quasicategories.

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

Proof of the Geometric Langlands Conjecture

Explore recent breakthroughs in the geometric Langlands conjecture, including its proof in characteristic zero settings, framework, obstacles, and solutions in this advanced mathematics lecture.

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

Cohomology Rings of Character Varieties

Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.

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

Results for Functional Differential Equations with State-Dependent Delays

Explores existence and uniqueness of solutions for functional differential equations with state-dependent delays, including applications and a linearized instability principle for neutral FDEs.

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

Equivariant Birational Geometry

Explore new results and constructions in equivariant birational geometry, delving into advanced mathematical concepts and their applications in this specialized field.

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

Fractal Dimensions of Critical Loci in Algebraic Geometry

Explore fractional dimensions in mathematics, focusing on critical loci of holomorphic functions. Discover theories from algebraic geometry, singularity theory, and more, with the smallest non-zero dimension at 1/3.

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

Chern Classes and Indices of Vector Fields on Singular Varieties

Explore Chern classes and vector field indices on singular varieties, examining fundamental invariants in geometry and topology and their evolving theory for non-smooth spaces.

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

Universally Counting Curves in Calabi-Yau Threefolds

Explore enumerative geometry through a new perspective on curve counting in complex threefolds, focusing on the Grothendieck group of 1-cycles and its implications for the MNOP conjecture.

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

The Shape of a Minimal Resolution

Explore the intricacies of minimal free resolutions, delving into open questions and recent findings on their shape. Survey both established and innovative methods in this mathematical exploration.

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

Fourier Uniformity of Multiplicative Functions

Explore Fourier uniformity of multiplicative functions, its connection to prime number distribution, and related conjectures like Chowla and Sarnak in this advanced mathematics lecture.

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

Convergence of Manifolds and Metric Spaces

Explore Riemannian manifolds, Gromov-Hausdorff and Intrinsic Flat distances, and their applications in solving stability problems in metric spaces.

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

Low-Dimensional Solenoidal Manifolds

Exploración de manifolds solenoidales de baja dimensión, sus propiedades topológicas y estructurales, y nuevos resultados en este campo de la geometría y topología.

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