Hausdorff Center for Mathematics Courses

Harry Altman- Lower Sets in Products of Well Ordered Sets

Explore well partial orders, lower sets in products of ordinals, and weakly decreasing sequences. Gain insights into maximum linearizations and the surreal exponential.

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

Graham Leigh: On the Computational Content of Classical Sequent Calculus

Explore computational interpretations of classical logic through Herbrand's Theorem, focusing on a language-theoretic representation using higher-order recursion schemes in classical sequent calculus.

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

Topological Generalizations of Possible Worlds Semantics and Their Proof Systems

Topological generalizations of possible worlds semantics and their proof systems for modal and conditional logics, focusing on structural and computational aspects.

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

Sam Sanders - Uniformity in Mathematics

Explore uniformity in mathematics, from historical examples to modern applications. Examine how uniform theorems challenge traditional logical systems and impact proof methods across various mathematical domains.

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

A Fibrational Framework for Modal Dependent Type Theories

Explore modal extensions of homotopy type theory, their frameworks, and applications in real-cohesive and differential-cohesive HoTT. Gain insights into fibrational frameworks for modal type theories.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Peter Dybjer - Intuitionistic Type Theory

Explore intuitionistic type theory, inductive definitions, and finite axiomatizations in this advanced lecture on mathematical foundations and type systems.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Peter Dybjer - Intuitionistic Type Theory - Lecture I

Explore intuitionistic type theory's foundations, historical context, and applications in mathematics and computer science with Prof. Peter Dybjer's comprehensive lecture.

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

Cyclotomic KLR Algebras - Part 1 of 4

Exploring cyclotomic KLR algebras, their connection to quantum groups, and their role in categorifying highest weight representations, with a focus on type A and the Ariki–Brundan–Kleshchev theorem.

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

Ran Levi- Topological Analysis of Neural Networks

Explore topological analysis of neural networks, from C. elegans to complex brain structures. Discover surprising findings and innovative approaches in computational neuroscience.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

The Transfer in Algebraic K-Theory and THH

Explore algebraic K-theory transfers, their applications in A-theory, and connections to THH. Gain insights into fundamental questions and trace methods in this advanced mathematics lecture.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Refined Enumerative Geometry

Explore Milnor-Witt sheaves, motivic homotopy theory, and Chow-Witt groups. Gain insights into refined enumerative geometry and its applications in algebraic geometry and topology.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Stabilizing the Unstable Output of Persistent Homology Computations

Explore stabilizing techniques for persistent homology computations, focusing on generating cycles and their applications in topological data analysis.

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

Statistical Shape Analysis Using the Persistent Homology Transform

Explore statistical shape analysis using persistent homology transform, covering classical methods, TDA approaches, and recent advancements in multidimensional scaling and alignment.

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

Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes

Explore efficient computation of Vietoris-Rips persistence barcodes using Ripser software. Learn about matrix reduction algorithms, persistent cohomology, and discrete Morse theory applications in topological data analysis.

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

Paul Arne Østvær- A1 Contractible Varieties

Explore A1 contractible varieties in algebraic geometry, covering cancellation theorems, local model structures, and related proofs in this advanced mathematics lecture.

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