IMSA Courses

The $K(\pi, 1)$ Conjecture - Part 2

1 review

Explore the recent proof of the classical K(π,1) conjecture for affine Artin groups, delving into its mathematical intricacies and implications for algebraic topology.

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

Interpolation for Polynomials in Two Variables

1 review

Explore advanced polynomial interpolation techniques in two variables, covering dimension counts, Picard groups, and conjectures like Segre's and Nagata's. Delve into cones, extremal rays, and the A-Conjecture.

• YouTube
• 53 minutes
• On-Demand
• Conference Talk

Equivariant Birational Geometry of 3-Dimensional Projective Space

1 review

Explore G-equivariant birational geometry of 3D projective space, focusing on finite group actions and their impact on fibrations into rational curves or surfaces.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

NCHS and Rationality

Explore new approaches to nonrationality through Mirror Symmetry, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

A Look at Fourier-Mukai Transforms and GIT in the Smooth and Singular Settings

Explore recent advancements in derived equivalences and birational geometry, focusing on Fourier-Mukai functors and geometric invariant theory quotients in both smooth and singular settings.

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

A Biased Survey of Some Results Inspired by Stable Rationality Problem for Cubic Hypersurfaces

Explore recent developments in algebraic geometry, focusing on the (stable) rationality problem for cubic hypersurfaces and advancements in degeneration methods involving p-torsion and prelog Chow groups.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Rigid, Not Infinitesimally Rigid Surfaces of General Type with Ample Canonical Bundle

Explore construction of surfaces with unique properties using line configurations and abelian cover theory. Delve into advanced algebraic geometry concepts and their applications.

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

Loci of Rational Varieties

Explore structure theorems and examples like cubic fourfolds to understand rationality in smooth complex projective varieties with Brendan Hassett from Brown University.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Finite-Dimensional DG Algebras and Their Properties

Explore finite-dimensional DG algebras, perfect complexes, and their role in noncommutative schemes. Discover connections to DG categories with (semi)exceptional collections.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Rationality, Unirationality and Infinite Transitivity

Explore classical approaches to proving rationality and the relationship between unirationality and infinite transitivity in algebraic geometry with expert Fedor Bogomolov.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Old and New Birational Invariants

Explore new birational invariants combining Hodge theory and Symplectic Geometry in this advanced mathematics lecture by Ludmil Katzarkov.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

An Introductory Mini Course into Quantum Toric Geometry Lecture II

Explore quantum toric geometry, including LVM theory, quantum GIT, and moduli spaces of toric varieties. Delve into non-commutative spaces and their relation to traditional toric geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Integral PL Actions from Birational Geometry

Explore birational automorphisms, tropicalization, and their applications to Calabi-Yau varieties. Discover connections between algebraic geometry and piece-wise linear homeomorphisms.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Poisson and Quantum Algebras of SL(n) Monodromies and Groupoid Action

Explore Poisson and quantum algebras of SL(n) monodromies, delving into advanced mathematical concepts and their applications in theoretical physics and geometry.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Holomorphic Lagrangian Foliation and Gaiotto's Conformal Limit

Explore holomorphic Lagrangian foliation and Gaiotto's conformal limit in this advanced mathematics lecture by UC Davis professor Motohico Mulase.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video