Hausdorff Center for Mathematics Courses

Dormancy Phenomena in Cancer Progression

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Explore dormancy mechanisms in cancer progression, their role in therapy resistance and metastasis, and mathematical models used to study these phenomena. Gain insights into open questions and potential research directions.

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

A Rényi Entropy Interpretation of Anti-Concentration

Explore advanced mathematical concepts in concentration functions, examining multivariate entropic settings and volume bounds in isotropic convex bodies through Rényi entropy interpretation.

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

Combinatorial Applications of the Shearer and Han Inequalities in Graph Theory and Boolean Functions

Explore the powerful applications of Shearer's and Han's inequalities in information theory, focusing on their role in solving complex problems in graph theory and Boolean functions.

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

Fourier Multipliers for Functions on the Discrete n-Torus

Explore advanced Fourier multiplier theory and its applications in discrete n-torus, connecting transcendental number theory with dimension-free inequalities and Rademacher projections.

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

Counting Lattice Points in Ellipsoids and the Central Limit Theorem for Quadratic Forms

Delve into advanced mathematical concepts exploring lattice point counting in ellipsoids, error bounds, and their connection to probability theory's central limit theorem.

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

A Reverse Minkowski Theorem in Lattice Theory and Geometry

Explore the groundbreaking reverse Minkowski theorem and its applications in complexity theory, cryptography, and algorithms, building on fundamental concepts in geometry of numbers.

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

Some Conjectures Relating the Optimality of Dictator Functions and Connections to Discrete Isoperimetric Inequalities

Delve into advanced mathematical concepts exploring dictator functions, entropy, and discrete isoperimetric inequalities in relation to the Hamming cube and Talagrand-Bobkov studies.

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

Sharp Strichartz Estimates via Hermite Polynomials and Hypercontractivity

Delve into advanced mathematical concepts exploring Schrödinger propagator inequalities through pseudo-conformal transformation and hypercontractivity in Gauss space, featuring Hermite polynomials applications.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Reading Topological Ellipticity of G-manifolds from Their Quotients

Delve into rational ellipticity in topological spaces, exploring criteria for G-manifolds, applications to cohomogeneity 3 actions, and examining conjectures about reading topological ellipticity from quotient spaces.

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

Combings, Local-to-Global Properties and Divergence

Explore geometric and analytic viewpoints in group theory, focusing on boundaries, asymptotic cones, combings, and divergence functions, with insights on dichotomies under non-positive curvature assumptions.

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

Using Currents to Represent Steenrod Powers

Explore how currents on spheres can geometrically represent Steenrod powers, with applications in quantitative topology and space classification using cohomology operations.

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

Using Currents to Represent Cohomology - Lightning Talk

Explore visual representations of cohomology and operations using currents, with special focus on geometric representations of Steenrod powers.

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

Analytically One Dimensional Planes and CLP

Explore the connection between conformal dimension and analytically one-dimensional planes in this mathematical research talk, linking Laakso diamond spaces to Poincaré inequalities on two-dimensional spheres.

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

Mean Curvature Flow in ℝ³ and the Multiplicity One Conjecture

Explore recent advances in mean curvature flow mathematics, including the solution to the Multiplicity One Conjecture and progress on understanding singularity formation in evolving surfaces.

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

Lipschitz Rigidity for Scalar Curvature

Explore the extremality and rigidity phenomena of lower scalar curvature bounds on spin Riemannian manifolds, focusing on Lipschitz rigidity generalizations and connections between spin geometry and quasiconformal mappings.

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