IMSA Courses

Extensions in MHM and Hain's Biextension Line Bundle - Part 1

Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.

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

Equivariant Birational Geometry of Three-Dimensional Projective Space

Explore finite group actions on 3D projective space, focusing on G-solid cases and their G-Mori fiber spaces. Gain insights into advanced algebraic geometry concepts.

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

Finite Generation and K-Stability

Explore recent advances in birational geometry and their impact on K-stability, including finite generation of valuations and connections to major conjectures in algebraic geometry.

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

Lattice Cohomology - Part 2

Explores advanced concepts in lattice cohomology, focusing on topological and analytic aspects, their connections to singularity theory, and implications for geometric structures.

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

Hyper-Kähler Manifolds - Part 2

Explore advanced properties of hyper-Kähler manifolds, focusing on 4-dimensional cases and their topological characterization in relation to K3 surfaces and abelian surfaces.

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

Constructible Sheaves and Filtered D-Modules

Explore the Riemann-Hilbert correspondence and its p-adic analogue, connecting constructible sheaves to filtered D-modules with applications in algebraic geometry.

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

Hyper-Kähler Manifolds - Part 1

Explore the foundations of hyper-Kähler manifolds, their connection to K3 surfaces, and key properties in this advanced mathematics lecture by renowned expert Claire Voisin.

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

On the Geometry of Cubics

Explore classical and new results on the geometry of cubics in three, four, and five dimensions, delving into their fascinating mathematical properties and structures.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Quantum Representations and Bogomolov-Katzarkov Surfaces

Exploring quantum representations and their application to Bogomolov-Katzarkov surfaces, addressing the Shafarevich conjecture on holomorphic convexity in algebraic geometry.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Hilbert Schemes of Plane Curve Singularities and Matrix Factorizations

Explore connections between algebraic geometry and topology through plane curve singularities, Hilbert schemes, and matrix factorizations in this advanced mathematics lecture.

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

GPPV Invariants and the Spectrum of Singularities

Explore complex surface singularities, their 3-manifold links, and GPPV invariants. Discover new connections between modular forms and singularity spectra for Brieskorn homology spheres and ADE singularity links.

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

Representations of the Classical, Virtual, and Welded Braid Groups

Explore generalizations of classical braid groups with new crossings and relations, focusing on extended representations in virtual and welded braid groups.

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

Welded Tangles and a Topological Interpretation of the Kashiwara-Vergne Group

Explores welded tangles and foams as higher-dimensional knot theory, connecting their automorphisms to the Kashiwara-Vergne group in Lie theory and relating to knot invariants and Baker-Campbell-Hausdorff series.

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

On the Deleted Squares of Lens Spaces

Explores homotopy equivalence of configuration spaces in lens spaces, using differential characters and Massey products to investigate topological properties of deleted squares.

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

Divergence in Coxeter Groups

Explores divergence in Coxeter groups, introducing the 'hypergraph index' to characterize linear, quadratic, and exponential divergence in these mathematical structures.

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