IMSA Courses

Filtered Ends and Bochner Hartogs Dichotomy on Complete Kahler Manifolds

Explore filtered ends and Bochner Hartogs dichotomy on complete Kahler manifolds, examining relationships between generalized ends and first compactly supported cohomology.

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

Fake Projective Planes: Properties and Recent Progress

Explore fake projective planes: complex surfaces with unique properties, their construction via uniformization, and recent advancements in understanding their algebraic and geometric characteristics.

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

Exploring the Boundary of the Moduli Space of Stable Surfaces - I-Surfaces as a Test Case

Exploring I-surfaces: minimal complex surfaces with K^2=1 and p_g=2. Recent research on boundary points of KSBA compactification for I-surfaces' moduli space.

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

The Geometric Andre-Grothendieck Period Conjecture

Explore complex algebraic varieties, period integrals, and the Ax-Schanuel conjecture. Delve into transcendence theory of period maps and the Andre-Grothendieck period conjecture's functional version.

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

Perverse Sheaves on Varieties with Large Fundamental Group

Explore perverse sheaves on Kähler manifolds, focusing on a generalization of the Singer-Hopf conjecture and its proof using Shafarevich conjecture ideas. Joint work with Donu Arapura presented.

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

Hecke Actions on Loops and Periods of Iterated Shimura Integrals

Exploration of Hecke actions on loops and periods of iterated Shimura integrals, focusing on SL_2(Z) and modular curves, with insights into mixed modular motives and Galois action.

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

Mixed Hodge Structures on Cohomology Jump Ideals

Explore mixed Hodge structures on cohomology jump ideals in representation varieties, extending Goldman and Millson's work to non-compact Kähler manifolds and variations of mixed Hodge structures.

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

Complex Hyperbolicity and Representations of the Fundamental Group in Non-Compact Varieties

Explore complex hyperbolicity and fundamental group representations in quasi-projective varieties, blending archimedean and non-archimedean approaches to extend previous research in algebraic geometry.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Hyperbolicity in Presence of a Large Local System

Explore hyperbolicity in complex algebraic varieties with Yohan Brunebarbe. Learn about Green-Griffiths and Lang conjectures, and their validity for varieties with large complex local systems.

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

On Nilpotent Quotients of Quasi-Kähler Groups

Exploration of nilpotent quotients of quasi-Kähler groups, focusing on smooth complex quasi-projective manifolds and their quasi-Albanese maps, with implications for holomorphic convexity and special manifolds.

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

Periods, Shafarevich Maps and Applications - Nodal Surfaces and Coding Theory

Explore nodal surfaces and coding theory in K3 geometry. Learn about period maps, Torelli theorem, and binary codes in relation to polarized nodal K3 surfaces and their components.

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

Torelli Action on SU(n) Representation Varieties of Projective Curves

Explore Torelli group action on SU(n) representation varieties, its nontriviality in degree 6 cohomology, and implications for moduli of semistable bundles with trivial determinant.

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

Hyperbolicity of Algebraic Varieties via Fundamental Groups

Explore hyperbolicity of algebraic varieties through fundamental groups, examining linear representations and their implications for complex quasi-projective varieties and the Green-Griffiths-Lang conjecture.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

L2 Invariants of Hodge Modules and Shafarevich Morphisms

Explore L2 invariants of Hodge Modules and Shafarevich morphisms, including L2 constructible cohomology and Mixed Hodge structures, with potential topological implications of linear Shafarevich conjecture.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Extension Data of Global Families of Mixed Hodge Structures - Applications to Shafarevich Conjecture

Extension data analysis in mixed Hodge structures: capturing global family invariants and proving Shafarevich's Conjecture in the nilpotent case through monodromy and level 1-2 extensions.

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