Algebraic Geometry Courses and Certifications

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

Twistor Space for Moduli of Local Systems on Open Curves

Explore Deligne-Hitchin twistor spaces for moduli of framed local systems on open curves, examining harmonic bundles, preferred sections, and mixed twistor structures in moduli space geometry.

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

IMSA

Homological Mirror Symmetry - Counting Curves on Calabi-Yau Threefolds

Explore advanced mathematical concepts in counting curves on Calabi-Yau threefolds, including Grothendieck groups, Gopakumar-Vafa conjecture, and MNOP conjecture implications.

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

IMSA

Surface Quotient Singularities and Big Cotangent Bundle

Explore hyperbolic properties of surfaces with big cotangent bundle, including the Green-Griffiths-Lang conjecture and a new bigness criterion for orbifold surface resolutions.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

IMSA

Motivic Integration & Stringy Chern Classes

Explore motivic integration basics and learn how stringy Chern classes apply to singular varieties in this advanced mathematics lecture by Ernesto Lupercio.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

Discriminants and Toric Birational Geometry

Explore Gorenstein toric singularities, B-side categories in toric homological mirror symmetry, and GKZ hypergeometric D-modules. Discover the conjectural construction of associated spherical functors.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

Non-Archimedean Quantum K-Theory and Gromov-Witten Invariants

Explore non-archimedean geometry's role in Gromov-Witten invariants, focusing on derived approaches, K-theory, and motivic cohomology. Learn about geometric relations and their implications for numerical invariants.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

Global Shifted Potentials for Moduli Stack of Sheaves over Calabi-Yau 4 Folds

Explores construction of globally defined shifted potential functionals on moduli stacks of stable sheaves on Calabi-Yau 4-folds, discussing DG Quot schemes, Lagrangian distributions, and applications to derived algebraic geometry.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video