IMSA Courses

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

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

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

A Parallel Reality Look at Generalized Geometry

Explore generalized geometries and related "Hodge theory" through a fresh perspective, building on classical works by Donaldson and Simpson in this advanced mathematics seminar.

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

Remarks on Lagrangian Submanifolds of Hyper-Kaehler Manifolds

Explore properties of Lagrangian subvarieties in hyper-Kaehler manifolds, focusing on interactions with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.

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

The Calabi Problem from a Birational Geometer's Viewpoint - Part 2

Explore the Calabi problem in Fano manifolds, focusing on recent developments in birational geometry and K-polystability. Gain insights from a renowned algebraic geometer.

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

The Calabi Problem from a Birational Geometer's Viewpoint - Part 1

Explore the Calabi problem in complex geometry, focusing on Kähler-Einstein metrics and recent developments in birational geometry. Learn from renowned algebraic geometer Carolina Araujo.

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

Deformed Hermitian Yang-Mills Equation on Rational Homogeneous Varieties

Explore the deformed Hermitian Yang-Mills equation on rational homogeneous varieties, its solutions, and algebraic obstructions to supercritical solutions using central charges defined by analytic subvarieties.

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

Almost Schur Lemma and Positivity Conditions in Quaternionic Contact Geometry

Explore quaternionic contact geometry, focusing on the Almost Schur Lemma and its implications for estimating qc scalar curvature under specific conditions.

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

On Some Fans and Toric Varieties Related to Branching Laws for Reductive Groups

Explore algebraic group embeddings and their representation theory through Geometric Invariant Theory, focusing on H-invariant vectors and the GIT-fan's role in encoding information.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Quantum Toric Geometry, Generalized Geometries and O-Minimality - Enrique Becerra

Explore quantum toric geometry, generalized geometries, and o-minimality with expert Enrique Becerra in this advanced mathematics lecture from the University of Miami.

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

Symmetric Approach to General Relativity - Applications to Exotic Spheres

Exploring Cheeger deformation to derive Lorentzian metrics on spheres and exotic spheres, with implications for physics and geometry in compact models of spacetime.

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

Canonical Metrics in Complex Geometry

Explore canonical metrics in complex geometry, focusing on pluriclosed and balanced metrics. Learn about new constructions of compact non-Kähler manifolds and their properties.

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

Canonical Weierstrass Representation of Minimal Lorentz Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric

Explore canonical Weierstrass representation of minimal Lorentz surfaces in pseudo-Euclidean 4-space, including isothermal parameters, PDEs, and explicit solutions.

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

On the Second Homotopy Group of Spaces of Commuting Elements in Lie Groups

Explore the computation of the second homotopy group of Hom(Z^n, G) spaces, focusing on compact Lie groups. Learn about geometric generators and specific results for simply connected, simple groups.

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