University of Chicago Department of Mathematics Courses

Categorical Noncommutative Geometry

Dive into categorical noncommutative geometry, exploring algebraic varieties through derived categories of coherent sheaves and extending classical concepts to differential graded categories.

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

Symmetries, Anomalies and Anomaly Inflow in Physics and Mathematics

Explore symmetries in physics, quantum effects, and their mathematical connections in this insightful colloquium by Jeff Harvey on "Symmetries, Anomalies and Anomaly Inflow".

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

Anosov Flows on 3-Manifolds

Dive into Anosov flows on 3-manifolds, exploring their chaotic yet stable nature, classification challenges, and recent advancements in low-dimensional geometric topology.

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

Random Planar Geometry and the Directed Landscape

Dive into random planar geometry and the directed landscape, exploring universal scaling limits in random metrics and interface growth models with Duncan Dauvergne.

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

Spectra and Definability in Combinatorial Sets of Reals

Dive into the intricacies of spectra and definability in set theory with Vera Fischer's exploration of combinatorial sets of reals and cardinal characteristics of the continuum.

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

The Ramanujan Conjecture for Modular Forms

Dive into the Ramanujan conjecture for modular forms, exploring its history and recent developments in a gentle overview suitable for all levels of mathematical background.

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

Growth of Laplacian Eigenfunctions

Delve into the growth patterns of Laplacian eigenfunctions on compact manifolds, exploring concentration phenomena and the intriguing 'spooky action at a distance' in mathematical contexts.

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

The Landscape Law and Wave Localization

Explore the landscape function's role in predicting wave localization patterns and eigenfunction behavior in complex systems with Svitlana Mayboroda's mathematical insights.

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

Counting Closed Geodesics and Improving Weyl's Law for Predominant Sets of Metrics

Dive into the behavior of closed geodesics and Weyl's law on compact manifolds. Explore predominance in Riemannian metrics and its implications for quantitative bounds in geometry.

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

Semiclassical Measures for Laplacian Eigenfunctions and Quantum Cat Maps

Dive into semiclassical measures for Laplacian eigenfunctions and quantum cat maps, exploring quantum chaos and high-energy limit behavior in mathematics.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Courant, Bezout, and Persistence - Lecture 2

Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1

Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.

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

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
• Self-Paced
• Free Video

Minimal Submanifolds in Riemannian Geometry

Explore the connection between stable minimal hypersurfaces and Riemannian manifolds with scalar curvature lower bounds, including recent progress in higher codimension theory for surfaces.

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

Interpolation for Brill-Noether Curves

Explore the complete solution to the interpolation problem for Brill--Noether curves, examining when curves of specific types can pass through general points.

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