IMSA Courses

Invariants of Normal Functions in Algebraic Geometry

Delve into the theory of normal functions in algebraic geometry, exploring their invariants, applications in physics, and relationships to Calabi-Yau 3-folds and Hodge theory.

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

Which Cubic 3-Folds Are Rational? - A Survey of Complex and Real Cases

Explore the fascinating world of cubic 3-folds, examining rationality in smooth and singular cases while delving into complex mathematical theorems and recent research findings.

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

Birational Geometry of Algebraically Integrable Foliations

Explore advanced concepts in birational geometry through an examination of algebraically integrable foliations, focusing on recent developments in the Minimal Model Program.

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

Non-commutative Deformation of Moduli Space of Flat Connections on Riemann Surfaces

Explore the mathematical foundations of quantum mechanics through formal deformations of functions on manifolds, focusing on flat connections on Riemann surfaces and Kontsevich's revolutionary framework.

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

Atoms Meet Symbols - Theory of G-Equivariant Birational Geometry

Explore the intersection of atomic theory and symbolic mathematics in G-equivariant birational geometry, examining new Z-module applications and invariants in geometric information.

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

Smoothing Toric Fano 3-folds

Explore advanced mathematical concepts in toric Fano 3-folds and their deformation properties, focusing on terminal quotient singularities and optimal deformation criteria.

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

Schwartz Spaces Associated with the Stack of Rank 2 Bundles on a Curve over a Local Field

Delve into advanced mathematical concepts of Schwartz spaces, exploring their connection to rank 2 bundles on curves over local fields and the Analytic Langlands program's implications.

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

The Quantum Connection and Its Mod p Reductions

Delve into advanced mathematical concepts exploring quantum connections on Fano manifolds, focusing on Steenrod-type quantum operations and recent structural developments.

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

Non-perturbative Deformation Quantization in Kähler Manifolds

Delve into advanced mathematical concepts of non-perturbative deformation quantization, exploring formality theorems, Poisson varieties, and Kähler manifolds with expert Maxim Kontsevich.

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

The Ising Model in Statistical Mechanics - Features and Solutions in Two Dimensions

Delve into the two-dimensional Ising model in statistical mechanics, exploring exact solutions, scaling properties, correlation functions, and conformal invariance in magnetization phenomena.

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

Invariants of Tangles with Flat Connections in the Complement

Delve into quantum group theory and its applications to tangle invariants, exploring flat connections, Poisson structures, and their geometric interpretations in topology.

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

Extending Hodge Polynomials to Non-Kähler Geometry

Delve into advanced mathematical concepts exploring Hodge polynomials beyond Kähler geometry, examining LVMB manifolds and motivic properties through pluri-logarithmic transforms.

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

Bordism and Resolution of Singularities in Gromov-Witten Theory

Delve into complex geometric theory exploring moduli spaces, derived orbifolds, and resolution algorithms in symplectic topology through Gromov-Witten invariants and unitary bordism.

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

Hyperbolicity and Holomorphic Jet Differentials in Complex Manifolds

Delve into complex manifold hyperbolicity theory, exploring function theory, holomorphic jet differentials, and connections between geometric and number-theoretic approaches to rational points.

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

Vanishing Arcs for Isolated Plane Curve Singularities

Delve into advanced singularity theory concepts, exploring variation operators, Milnor fiber homology, and framed mapping class groups in plane curve singularities.

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