IMSA Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Lattice Cohomology - Part 1

Explore topological lattice cohomology in plumbed 3-manifolds, its connection to Heegaard Floer theory, and its applications in analyzing surface singularities and geometric structures.

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

Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations

Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Birational Geometry of Sextic Double Solids with a Compound A_n Singularity

Explore birational geometry of sextic double solids with compound A_n singularities, examining rigidity properties and divisorial contractions in this advanced algebraic geometry topic.

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

Windows and Geometric Invariant Theory

Explore windows theory in algebraic geometry, its applications to GIT constructions, and its impact on derived categories and stability conditions in various mathematical contexts.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Subgroups of Right-Angled Coxeter Groups via Stallings-like Techniques

Exploration of Stallings-like techniques for subgroups of right-angled Coxeter groups, with applications to hyperbolic groups and algorithmic insights in geometric group theory.

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

Bounds on Morse-Novikov Numbers of 3-Manifolds

Explore bounds on Morse-Novikov numbers of 3-manifolds, examining circle-valued Morse functions and their critical points, with applications to knot theory and topology.

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

Crossing Numbers of Whitehead Doubles

Explore the connection between colored Jones polynomials and crossing numbers of Whitehead doubles, revealing insights into satellite knots' minimum crossing numbers.

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

Pencils on Algebraic Surfaces with Prescribed Classes of Irreducible Components

Exploring bounds on reducible fibers in curve pencils on projective surfaces, with focus on irreducible components' classes in Neron-Severi group. Generalizes results on fundamental groups of line arrangement complements.

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

Links in Math and in Life

Explore the fascinating connections between mathematical links and real-life applications through braids, knots, and topology in this engaging presentation.

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

Braids and Configuration Spaces

Explore topology, homotopy, and braid groups in this talk on configuration spaces. Discover connections between fundamental groups, loop spaces, and unordered configurations in mathematics.

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