IMSA Courses

Homological Mirror Symmetry - Lagrangian SYZ Fibrations

Explore Lagrangian SYZ fibrations in symplectic geometry, focusing on integral affine manifolds with singularities and the construction of local models and gluing techniques.

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

Homological Mirror Symmetry - Toward the Logarithmic Hilbert Scheme

Explore logarithmic geometry and its applications in mirror symmetry, focusing on the development of a logarithmic Hilbert scheme and its implications for degenerations and tropical mathematics.

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

Homological Mirror Symmetry - Atsushi Takahashi, Osaka University

Exploring generalized root systems of type D, constructing Frobenius manifolds, and examining their potential applications in algebraic geometry and mathematical physics.

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

Homological Mirror Symmetry - Nikita Nekrasov

Explore homological mirror symmetry and integrable systems through Lax operators, intersection theory, and gauge theory. Delve into Garnier models, Hitchin systems, and quiver gauge theories.

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

Homological Mirror Symmetry - Moduli Space of Non-Archimedean Holomorphic Disks Pt. II

Explore non-Archimedean holomorphic disks in affine log Calabi-Yau varieties, covering boundary conditions, smoothness, dimension, and properness. Gain insights into non-Archimedean mirror symmetry and related theories.

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

Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond

Explore advanced concepts in Donaldson-Thomas theory, including categorifications, refinements, and applications to C^3 and beyond, with a focus on categorical invariants and correspondences.

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

Frontiers in Mathematics Lecture Series - Research Talk

Explore Lie theory, groupoids, and algebroids in this advanced mathematics seminar. Discover local integration techniques and their implications for non-integrable Lie algebroids.

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

Homological Mirror Symmetry - Maxim Kontsevich Pt. III

Explore advanced algebraic concepts with Maxim Kontsevich, focusing on Getzler-Gauss-Manin connections for non-commutative algebras and their applications in quantum mathematics.

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

Special Lecture Series on Numerical Geometry - Tristan Collins

Explore complete Calabi-Yau metrics on Fano manifolds with singular divisors, focusing on two-component cases and discussing potential generalizations to more complex scenarios.

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

Research Seminar - Arc-Connectedness of the Space of 1-Dimensional Commuting Diffeomorphisms

Explore arc-connectedness in 1D commuting diffeomorphisms with Andrés Navas. Gain insights into group actions, community spaces, and rotational concepts in this advanced mathematics seminar.

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

Functional Inequalities and Improvements: Stability - Part 2

Explore functional inequalities, their optimal constants, and stability properties. Learn strategies for addressing these issues and recent developments in improved inequalities for non-optimizers.

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

An Application of Symplectic Topology to Algebraic Geometry

Explore symplectic topology's application to algebraic geometry, connecting Rouquier's triangulated category dimension to Krull dimension via homological mirror symmetry.

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

Canonical Wall Structures via Punctured Gromov-Witten Theory

Exploration of canonical wall structures in logarithmic Calabi-Yau pairs using punctured Gromov-Witten theory, connecting intrinsic mirror construction with earlier approaches.

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

Ẑ-Invariants and Universal Abelian Cover

Explore Ẑ-invariants of plumbed 3-manifolds through universal abelian covers, linking analytic invariants to topological properties. Gain insights into cutting-edge research in algebraic topology and singularity theory.

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

On the Nielsen Realization Problem and Cohomology of Mapping Class Groups of Non-orientable Surfaces

Exploración del problema de realización de Nielsen y cohomología de grupos de clases de mapeo en superficies no orientables, con aplicaciones en topología y teoría de grupos.

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