IMSA Courses

Generalized Logarithmic Transformation in Exotic Spheres and Homotopy Hopf Manifolds

Explore generalized logarithmic transformations in topology, including $\star$-diagrams, spherical T-duality, and applications to exotic spheres and homotopy Hopf manifolds.

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

Spherical T-Duality Meets Exotic Spheres and Homotopy Hopf Manifolds

Explore spherical T-duality, its relation to 7-dimensional homotopy spheres, and implications for complex structures on exotic manifolds in this advanced mathematical discussion.

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

Hodge Theory for Poisson Varieties and Nonperturbative Quantization

Explore Hodge theory for Poisson varieties and nonperturbative quantization, focusing on K-theory and mixed Hodge structures to simplify complex calculations in deformation quantization.

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

An Overview on Closed G2-Structures

Overview of closed G_2-structures on 7-manifolds, exploring their definition, examples, and applications in holonomy G_2-metrics. Discusses Hitchin flow equations and the Laplacian G_2-flow in compact settings.

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

Equivariant Geometry of Cubics - Applications to Cubic Threefolds and Fourfolds

Explore applications of new invariants in equivariant birational geometry to cubic threefolds and fourfolds, advancing understanding in algebraic geometry and related fields.

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

Calabi Problem in Generalized Kahler Geometry

Explores generalized Kahler structures, their connection to Kahler manifolds with holomorphic Poisson structures, and presents an approach to the Calabi problem in this context, with focus on toric complex Poisson varieties.

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

Best Lipschitz Maps and Transverse Measures - Part 2

Explores best Lipschitz maps between hyperbolic surfaces, focusing on approximation methods, transverse measures, and their connection to infinitesimal earthquakes in Teichmüller theory.

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

Wobbly Fixed Points, Equivariant Multiplicities and U(p,q)-Higgs Bundles

Explores geometry of Higgs bundle moduli spaces, focusing on nilpotent cone fixed points and their classification. Analyzes U(p,q)-Higgs bundles and compares results with equivariant multiplicities.

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

Calabi-Yau Theory in Generalized Kahler Geometry

Explore Calabi-Yau theory's extension to generalized Kahler geometry, examining connections to supergravity and geometric flow approaches for constructing solutions.

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

Commuting Pairs of Generalized Structures, Para-Hyper-Hermitian and Born Geometry

Explore generalized structures on manifolds, focusing on commuting pairs and their integrability. Delve into para-hyper-Hermitian and Born geometry within this context.

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

Milnor Spheres - 60 Years Later

Explore Milnor Spheres through a category theory lens, examining recent findings and insights in this seminar on classical differential topology by Ludmil Katzarkov.

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

Volumes of Lattice Path Matroids

Explore polytopes of lattice path matroids, their connection to order polytopes, and compute refined volumes using h^*-vectors. Gain insights into advanced mathematical concepts and techniques.

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

Hopf-Brauer-Severi Varieties

Explore Hopf Brauer Severi varieties with Professor Ludmil Katzarkov, delving into advanced algebraic geometry concepts and their applications in mathematics.

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

Rouquier Dimension Equals Krull Dimension for Toric Varieties

Explore the equality of Rouquier and Krull dimensions for toric varieties, delving into homological mirror symmetry and a multi-graded version of Hilbert's syzygy theorem.

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

On Some Aspects of Cosmological Fine-Tuning

Explore fine-tuning in cosmology through Bayesian and maximum entropy frameworks. Examine probabilistic measurements, distribution families, and the learnability of fine-tuning concepts.

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