Hausdorff Center for Mathematics Courses

Scott Balchin- The Local-to-Global Principle

Explore the local-to-global principle in tensor-triangulated categories, examining its role in object reconstruction and its connection to the Balmer spectrum's pointless topology.

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

Jacob Lurie: A Riemann-Hilbert Correspondence in P-Adic Geometry

Explore p-adic geometry through Riemann-Hilbert correspondence, covering perfectoid rings, prismatic cohomology, and sheaf theory in characteristic p and beyond.

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

Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry

Explore p-adic geometry through Riemann-Hilbert correspondence, covering local systems, Galois representations, Hodge theory, and cohomology in this advanced mathematics lecture.

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

Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 2

Explore p-adic geometry through a Riemann-Hilbert correspondence, examining algebraic differential equations, perverse sheaves, and prismatic cohomology in nonarchimedean fields.

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

Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 1

Explores the Riemann-Hilbert correspondence in complex and p-adic geometry, discussing its historical context, mathematical foundations, and recent developments in prismatic cohomology.

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

Lambda-Coalescents Arising in a Population With Dormancy

Explore Lambda-coalescents in populations with dormancy, examining genealogy and multiple ancestral line mergers through a three-season model of spring awakening, summer reproduction, and winter dormancy.

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

The Convex Geometry of Blind Deconvolution and Matrix Completion Revisited

Explores convex geometry in blind deconvolution and matrix completion, analyzing dimensional factors in noise bounds and proposing alternative error scaling approaches for low-rank matrix recovery problems.

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

Optimal Learning from Data

Explore optimal learning from data, including error recovery, discrete optimization, and handling noisy measurements. Insights on deep learning and stochastic settings provided.

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

Generalization in Deep Learning Through the Lens of Implicit Rank Minimization

Explores implicit regularization in deep learning through matrix and tensor factorizations, revealing tendencies towards low ranks. Discusses implications for generalization and potential improvements in neural network design.

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

Machine Learned Regularisation for Solving Inverse Problems

Machine learned regularization techniques for solving inverse problems, focusing on image reconstruction from tomographic and blurred measurements. Explores data-driven approaches and discusses open mathematical challenges.

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

Alexander Volberg: The Probability of Buffon Needle to Land Near Cantor Set

Explore the probability of Buffon's needle landing near Cantor sets, delving into unexpected connections with various mathematical fields and theories.

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

Joshua Zahl- Lens Counting and Restricted Projections

Explore planar incidence geometry and lens counting theory to understand projection theorems, with applications in curve arrangements and intersection patterns.

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

Carlos Pérez- Fractional Poincaré Inequalities for Doubling and Non-Doubling Weights

Explore fractional Poincaré-Sobolev inequalities using Harmonic Analysis, unifying and improving known results for doubling and non-doubling weights in mathematical analysis.

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

Endpoint Fourier Restriction and Unrectifiability

Explore endpoint Fourier restriction and its connection to measure unrectifiability in R^d, featuring a dichotomy between absolute continuity and 1-pure unrectifiability.

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

Bounds on the Hausdorff Measure of Zero Sets of Steklov Eigenfunctions

Explore upper bounds on Hausdorff measure of Steklov eigenfunction zero sets, comparing with Laplace eigenfunctions and discussing recent breakthroughs in this mathematical domain.

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