International Mathematical Union Courses

Aaron Pixton- The Double Ramification Cycle

Explore divisorial conditions, dual graphs, and tautological generators in algebraic geometry. Gain insights into computing DR(A) and multiplying Hain's formula.

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

Character Estimates for Finite Simple Groups and Applications

Explore character estimates for finite simple groups and their applications in various mathematical problems, including mixing times, Waring's Problem, and conjectures by Ore and Thompson.

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

Real Gromov-Witten Theory

Survey of recent developments in real Gromov-Witten theory, covering construction challenges, structural results, and connections to physics. Explores moduli spaces, invariants, and enumerative geometry.

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

Cynthia Dwork: The Mathematics of Privacy

Explore the mathematics of privacy with Cynthia Dwork, covering differential privacy, data analysis techniques, and advanced concepts in privacy-preserving algorithms.

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

Ehud Friedgut- KKL’s Influence on Me

Explore KKL theorem, hypercontractivity, graph properties, isoperimetric inequalities, and intersecting families in this mathematical journey through influential concepts and applications.

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

Thomas Vidick - Connes Embedding Problem, Tsirelson’s Problem, and MIP* = RE

Explore the connections between operator algebras, quantum correlations, and computational complexity in this advanced mathematical lecture on recent breakthroughs in theoretical physics and computer science.

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

The Mathematics of Artificial Intelligence

Explore the mathematical foundations of AI, its impact on problem-solving in mathematics, and the challenges in developing reliable AI systems. Gain insights into generalization, explainability, and AI applications in inverse problems and PDEs.

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

The Motion of Hybrid Zones - And How to Stop Them

Explore mathematical models of hybrid zones in population genetics, including deterministic approximations, curvature flow, and probabilistic proofs, with applications to invasions and blocking.

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

Variety of Fractional Laplacians

Explore various types of fractional Laplacians, their properties, and applications in mathematical analysis through proofs, comparisons, and counterexamples.

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

Oded Regev: The Reverse Minkowski Theorem

Explore the Reverse Minkowski Theorem, its applications, and open questions in lattice theory with mathematician Oded Regev in this insightful mathematical lecture.

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

Enlargements - A Bridge Between Maximal Monotonicity and Convexity

Explore connections between maximally monotone operators and convex functions through enlargements, offering insights into variational problems and new distance measures for point-to-set maps.

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

Alexander Efimov: On the K-Theory of Large Triangulated Categories

Explore Grothendieck groups, categorical localization, and continuous K-theory in large triangulated categories. Delve into higher algebraic K-theory, negative K-theory, and dualizable DG categories.

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

Kenji Nakanishi - Global Dynamics Around and Away From Solitons

Explore global dynamics of nonlinear dispersive PDEs, focusing on solitons in Klein-Gordon and Schrödinger equations. Analyze stability, multi-soliton interactions, and open questions in soliton behavior.

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

Allen Knutson- Schubert Calculus and Quiver Varieties

Explore Schubert calculus, quiver varieties, and their connections through puzzle rules, Yang-Baxter equations, and representation theory in this advanced mathematics lecture.

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

Statistical Inverse Problems and PDEs: Progress and Challenges

Explore statistical inverse problems and PDEs, covering Bayesian approaches, computational challenges, and mathematical guarantees for algorithms in high-dimensional settings.

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