International Mathematical Union Courses

Numerical Stability of Algorithms at Extreme Scale and Low Precisions

Explore numerical stability in extreme-scale computing and low-precision arithmetic, focusing on error bounds, blocked algorithms, and probabilistic analysis for matrix computations.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Tianyi Zheng- Asymptotic Behaviors of Random Walks on Countable Groups

Explore asymptotic behaviors of random walks on countable groups, covering Kesten's theorems, entropy, and applications to group theory and graph analysis.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Fractal Uncertainty Principle and Quantum Chaos

Explore quantum chaos and fractal uncertainty principle in wave equations, with applications to eigenfunctions, Schrödinger equation, and hyperbolic surfaces. Gain insights beyond classical/quantum correspondence.

• YouTube
• 47 minutes
• On-Demand
• Free Video

New Trends in Nonlinear Optimization

Explore new trends in nonlinear optimization, including gradient methods, quasi-Newton techniques, and approaches for constrained problems, with a focus on recent developments and efficient algorithms.

• YouTube
• 46 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video