IMSA Courses

Eduardo Gonzalez- Quantum Cohomology, Seidel Elements, Shift Operators & Coulomb Branches

Explore advanced mathematical concepts in quantum cohomology, Seidel elements, and Coulomb branches. Discover the interplay between equivariant cohomology and symplectic homology in Lie group manifolds.

• YouTube
• 44 minutes
• 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

Equivariant Birational Geometry of Linear Actions

Explore equivariant birational geometry of linear actions, focusing on Burnside group formalism and its applications in 2D and 3D projective spaces and smooth quadrics.

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

Computation in Unitary Equivariant Bordism

Explore explicit computations of the unitary equivariant bordism ring, presented by Bernardo Uribe on behalf of Dev Sinha. Gain insights into advanced mathematical concepts and recent research findings.

• YouTube
• 47 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

Bifurcation Phenomena in Geometric Variational Problems

Explore classical Bifurcation Theory and its modern applications in Riemannian Geometry, covering minimal and constant mean curvature surfaces and the Yamabe problem.

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

Examples and Counterexamples in 2-D Equivariant Bordism

Explore finite group actions on surfaces and their extensions to 3-manifolds. Discover concrete answers and examine examples in equivariant bordism theory.

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