Institute for Pure & Applied Mathematics (IPAM) Courses

Branching Random Walks on Zd for d ≥ 4 - Excess Folding and Branching Capacity

Explore estimates for excess folding in Branching Random Walks and the role of branching capacity in higher dimensions, presented by Amine Asselah at IPAM's Statistical Mechanics Workshop.

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

Sharp Threshold for Rigidity of Random Graphs

Explore the evolution of random graphs and discover key moments when they become rigid and globally rigid, with implications for vertex embedding and distance preservation.

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

Cutoff for Biased Transpositions in Card Shuffling

Explore card shuffling algorithms and mixing times with biased transpositions, extending Diaconis and Shahshahani's work on random transpositions in deck shuffling.

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

Minkowski Content of the Scaling Limit of 3D Loop-Erased Random Walk

Explores Minkowski content of 3D loop-erased random walk's scaling limit, focusing on discrete space analysis, one-point function estimates, and ball-hitting probabilities in Z^3.

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

The Density Conjecture for Activated Random Walk

Explore self-organized criticality in activated random walk models, examining critical densities across various configurations and their implications for understanding energy release patterns in physical systems.

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

Radon-Nikodym Topography of Amenable Equivalence Relations in Acyclic Graphs

Explore the extension of Adams's dichotomy to measure-class-preserving settings, examining Radon-Nikodym cocycle behavior in acyclic graphs and its connection to global properties like amenability.

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

Interacting Polya Urns - Statistical Mechanics Beyond 2D

Explore interacting Polya urns on graphs, their asymptotic behavior, and convergence to equilibrium in this statistical mechanics presentation by Omer Angel at UCLA's IPAM workshop.

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

S-embeddings and Discrete Maximal Lorentz Surfaces

Explore s-embeddings and discrete maximal Lorentz surfaces in this advanced mathematics talk, focusing on isothermic surfaces, mean curvature, and associated families in discrete geometry.

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

Perfect t-embeddings of Uniform Aztec Diamond Graphs

Explores t-embeddings of uniform Aztec diamond graphs, providing new formulas and asymptotic analysis to prove convergence of dimer model height fluctuations to a Gaussian Free Field.

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

Dimers on a Riemann Surface and Compactified Free Field

Explore dimer models on Riemann surfaces, height function convergence, and connections to compactified free fields. Gain insights into probabilistic methods and discrete complex analysis in statistical mechanics.

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

Tannakian Formalism for Stacks

Explores Tannakian formalism for stacks, discussing representation categories of affine group schemes and characterizing symmetric monoidal Grothendieck categories equivalent to quasi-coherent sheaves on stacks.

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

Representations of General Linear Groups in the Verlinde Category

Exploration of representations of general linear groups in the Verlinde category, discussing known aspects, highest weight structure, and open questions in this area of symmetric tensor categories.

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

Growth in Tensor Powers - Representation Theory

Explores growth patterns in tensor powers of group representations, introducing a new invariant and its properties using tensor category theory.

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

Growth and Tensor Products in Representation Theory - Lecture 1

Explore asymptotic counting of summands in tensor products of representations, with numerous examples to illustrate concepts in symmetric tensor categories and representation theory.

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

Symmetric Tensor Categories of Moderate Growth

Explore symmetric tensor categories in positive characteristic fields, recent breakthroughs, and collaborative research findings in this advanced mathematics lecture.

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