IMSA Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Moduli Spaces on K3 Categories Are Irreducible Symplectic Varieties

Explore irreducible symplectic varieties as building blocks in singular projective varieties, focusing on moduli spaces of Bridgeland stable objects in Kuznetsov components of specific fourfolds.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Homology Planes and Fundamental Groups

Explore homology planes and fundamental groups in complex surfaces, focusing on an algorithm for line arrangements and its applications to log-general type surfaces with infinite fundamental groups.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Windows and the BGMN Conjecture

Explore the BGMN Conjecture in algebraic geometry using moduli spaces, derived categories, and GIT wall crossing. Uncover insights into vector bundles and symmetric powers of curves.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Birational Geometry of Moduli Spaces via the Essential Skeleton

Explore the essential skeleton in birational geometry, linking it to tropical geometry and moduli spaces, with a focus on $\mathcal{M}_{0,n}$ and potential applications to hyperplane arrangements.

• YouTube
• 53 minutes
• On-Demand
• Free Video

K-Stability of Fano Varieties

Explores K-stability of Fano varieties, connecting complex geometry and algebraic geometry. Discusses recent developments, including solved conjectures and the construction of a moduli space for Fano varieties.

• YouTube
• 58 minutes
• On-Demand
• Free Video