IMSA Courses

A Homological Interpretation of Higher Du Bois and Higher Rational Singularities

Explore homological interpretations of higher Du Bois and rational singularities, focusing on hypersurfaces and characteristic classes. Gain insights into advanced algebraic geometry concepts.

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

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