IMSA Courses

More Instances of Steenbrink Spectra in Singularity Categories

Explore Steenbrink spectra in singularity categories, focusing on non-commutative mixed Hodge structures and dimensional properties. Gain insights into natural and mysterious appearances of this concept.

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

Steenbrink Spectra in Singularity Categories

Explore Steenbrink spectra's role in singularity categories, examining how spectral numbers manifest in triangulated singularity categories associated with singularities.

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

Alexander Polynomials of Algebraic Links

Explore Alexander polynomials of algebraic links, their definitions, examples, and connections to algebraic geometry. Discover the relationship between plane curve singularity spectra and link polynomials.

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

Surface Singularities and Invariants of Their Links

Explore the connection between surface singularities and their link's topology, focusing on quantum invariants and their relation to the spectrum of Brieskorn spheres.

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

Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity II

Explores Hodge theory, Higgs bundles, and their applications to moduli spaces and hyperbolicity, focusing on complex geometry and variation of Hodge structures.

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

Comparing Geometric and Hodge-Theoretic Compactifications I

Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, comparing geometric and Hodge-theoretic approaches. Discusses recent work on stable K3 surfaces and recognizable divisors.

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

Kazhdan-Lusztig Theory and Singular Hodge Theory for Matroids I

Explore the fascinating parallel between Coxeter groups and matroids in combinatorial cohomology, featuring recent research on singular Hodge theory for combinatorial geometries.

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

Volumes of Definable Sets in O Minimal Expansions and Affine GAGA Theorems

Explore o-minimal methods in algebraic geometry, focusing on volume estimates for definable sets and their application to affine GAGA theorems, with implications for Hodge theory.

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

Products of Matrices, Non-Abelian Hodge Theory, Integrable Systems, and Theories of Class S

Explore connections between Deligne-Simpson problem and Hitchin systems, delving into SCF Theories of Class S and 3D mirror symmetry in this advanced mathematics lecture.

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

Periods and Moduli of Elliptic Surfaces I

Explore the derivative of period maps for Kaehler elliptic surfaces, examining the relationship with j-invariants and proving a generic Torelli theorem for simple elliptic surfaces.

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

A Guide to Variations of Mixed Hodge Structure - Generalities and Examples

Explore mixed Hodge structures, their variations, and computational methods using global monodromy and iterated integrals. Illustrates concepts with the elliptic KZB variation over the universal elliptic curve.

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

Kazhdan-Lusztig Theory and Singular Hodge Theory for Matroids II

Explore the parallel between Coxeter groups and matroids in combinatorial cohomology, with insights on singular Hodge theory for combinatorial geometries from recent collaborative research.

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

Extensions of Hodge Structure and Completions of Fundamental Groups

Explore extensions of mixed Hodge structures, unipotent and relative completions of fundamental groups, and their geometric interpretations in L-functions and motives theory.

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

Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity I

Explores connections between Hodge theory, Higgs bundles, and moduli spaces, focusing on geometric properties of log spaces and variations of Hodge structures in complex manifolds.

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

Comparing Geometric and Hodge-Theoretic Compactifications II

Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, focusing on geometric interpretations and connections to Hodge theory and polyhedral decompositions.

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