Graph Theory Courses

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
• Self-Paced
• Free Video

IMSA

Holomorphic Floer Theory, Quantum Wave Functions and Resurgence

Explore holomorphic Floer theory, exponential integrals, and resurgence in algebraic geometry. Discover connections to quantum wave functions and infinite-dimensional applications.

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

IMSA

Stability Structures in Holomorphic Morse-Novikov Theory

Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.

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

IMSA

Virtual Reductions and Intersection Theory on Moduli Space of Sheaves on Calabi-Yau 4 Folds

Explore virtual reductions of fundamental classes on moduli spaces of sheaves in Calabi-Yau 4-folds, examining applications to Donaldson-Thomas invariants and connections to threefold theories.

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

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

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

IMSA

Compactifications of Moduli — Geometry vs. Hodge Theory

Exploration of geometric and Hodge theoretic approaches to compactifying moduli spaces in algebraic geometry, with focus on classical cases and H and I-surfaces.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

IMSA

Blow Up Formulae and Invariants II - Dimension Theory

Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.

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

IMSA

Model Theory: From Logic to Geometric Stability Theory and O-Minimality II

Explore model theory principles, focusing on o-minimality and stability theory, with applications to complex geometry and arithmetic aspects.

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

IMSA

Tame Geometry and Hodge Theory II

Explores applications of tame geometry in Hodge theory, covering algebraization results, tameness of period maps, functional transcendence, and atypical intersection conjectures in complex algebraic geometry.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

IMSA

Complex Surfaces with P_g=Q=0 via Birational Geometry, Derived Category and Gauge Theory

Exploration of complex surfaces with p_g=q=0, examining their significance and recent developments through birational geometry, derived category, and gauge theory perspectives.

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

IMSA

Quantum Toric Geometry II - Non-Commutative Geometric Invariant Theory

Explore quantum geometric invariant theory, extending classical GIT to non-commutative cases. Gain insights into cutting-edge research in quantum toric geometry.

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