University of Chicago Department of Mathematics Courses

Proof of the Geometric Langlands Conjecture

Delve into advanced mathematical concepts exploring the Geometric Langlands Conjecture, including de Rham, Betti, and l-adic contexts, presented by Dennis Gaitsgory with collaborative insights.

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

Generalizations of the Bernstein Problem

Dive into Otis Chodosh's exploration of the Bernstein Problem's generalizations, examining minimal surface equations and their connections to higher dimensions.

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

Stochastic Quantisation of Yang-Mills

Dive into stochastic processes and Yang-Mills theory with Martin Hairer's talk on building a process admitting the 3D Yang-Mills measure as its invariant measure, exploring gauge-covariance and UV regularization.

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

Nonlinear Harmonic Maps and the Energy Identity

Dive into nonlinear harmonic maps, exploring singularity formation and defect measures. Gain insights into the Energy Identity conjecture and its recent proof in this advanced mathematics lecture.

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

Poisson Algebra, Combinatorics and Representations of Surface Groups

Dive into Poisson algebras, combinatorics, and surface group representations. Explore Goldman's Lie algebra construction and its applications to character varieties and Anosov representations.

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

A Descriptive Approach to Pointwise Ergodic Theorems

Dive into a descriptive approach to pointwise ergodic theorems, exploring their applications in dynamical systems, probability, and number theory.

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

Representations of Reductive Groups Over Local and Global Fields

Dive into Langlands' theory of reductive groups and their representations in number theory, exploring local and global fields and their connections to arithmetic and geometry.

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

Mathematical Snippets From Developments in AI

Explore mathematical insights arising from AI developments in this colloquium by Lek-Heng Lim, examining key observations and their implications for the field.

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

Symmetries of Manifolds - Lecture 3

Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.

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

Symmetries of Manifolds - Lecture 2

Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.

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

Symmetries of Manifolds - Lecture 1

Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.

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

The Fundamental Group of Random 3-Manifolds and Other Random Objects

Dive into the fundamental group of random 3-manifolds, exploring probability distributions and their applications to various categories in mathematics.

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

Cohomology of Moduli Spaces of Curves

Dive into the cohomology of moduli spaces of curves with Hannah Larson. Explore tautological rings, compactifications, and the mysteries of non-tautological cohomology groups in algebraic geometry.

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

The Weil Conjectures and A1-homotopy Theory

Dive into the Weil Conjectures and A1-homotopy theory, exploring connections between algebraic topology and finite field equations in this mathematical colloquium.

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

Hidden Structures on de Rham Cohomology of P-adic Analytic Varieties

Dive into hidden structures on de Rham cohomology of p-adic analytic varieties. Explore Hodge filtration, Frobenius, and monodromy in this advanced mathematical colloquium.

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