International Mathematical Union Courses

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

Enhancing Markov Chain Monte Carlo Sampling Methods with Deep Learning

Explore advanced techniques combining Markov Chain Monte Carlo sampling with deep learning, focusing on importance sampling, normalizing flows, and non-equilibrium methods for enhanced efficiency in high-dimensional problems.

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

Corinna Ulcigrai - Dynamics and Arithmetics of Higher Genus Surface Flows

Explore dynamics of higher genus surface flows, examining discrete systems, arithmetic conditions, and ergodic integrals. Gain insights into mixing, shearing, and local linearization techniques.

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

Julia Boettcher- Graph and Hypergraph Packing

Explore graph and hypergraph packing, Latin squares, and randomness in mathematics with Julia Boettcher's insightful lecture on combinatorial structures.

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

Floer Cohomology and Birational Geometry

Explore Floer cohomology applications in birational geometry, including McKay correspondence and quantum cohomology of Calabi-Yau manifolds.

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

On the Brumer-Stark Conjecture and Refinements

Exploration of the Brumer-Stark conjecture and its refinements, covering group rings, class groups, and related conjectures in algebraic number theory.

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

Jelani Nelson- Forty Years of Frequent Items

Explore forty years of frequent items algorithms, from classic approaches to modern techniques, including turnstile streaming, heavy hitters, and local differential privacy.

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

Composing and Decomposing Surfaces in R^n

Explore surface decomposition in R^n, Lipschitz functions, nonorientability, and their applications in mathematics, with insights on the Heisenberg group.

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

George Willis, Pierre-Emmanuel Caprace - A Totally Disconnected Invitation to Locally Compact Groups

Explore topological groups, focusing on locally compact and totally disconnected types. Discover recent advances in theory, simple groups, local structure, and comparisons with linear groups.

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

Anna Sfard- The Long Way From Mathematics to Mathematics Education- How Educational Research

Explore the conceptualization of mathematics as narrative creation and its impact on education through a researcher's personal journey and theoretical insights.

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

Bhargav Bhatt: Algebraic Geometry in Mixed Characteristic

Explore recent developments in algebraic geometry over p-adically complete commutative rings, covering prismatic cohomology, semistable reduction, and Kodaira vanishing in mixed characteristic.

• YouTube
• 1 hour
• On-Demand
• Free Video

Deep Neural Networks via Monotone Operators

Explore deep equilibrium models, their theoretical foundations, and applications in machine learning, including guaranteed convergence and robustness in neural networks.

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