International Mathematical Union Courses

Probability Theory for Random Groups Arising in Number Theory

Explores probability theory for random groups in number theory, topology, and combinatorics. Covers moment problems, universality theorems, and distributions of class groups and Selmer groups.

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

Oscar Randal-Williams: Diffeomorphisms of Discs

Explore the mathematical intricacies of diffeomorphisms on discs with Oscar Randal-Williams in this insightful 45-minute lecture from the International Mathematical Union.

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

The History and Historiography of the Discovery of Calculus in India

Explore the evolution of calculus in India, from Āryabhaṭa to Mādhava's pioneering work, uncovering mathematical breakthroughs hidden in Sanskrit verses and examining historiographical aspects.

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

Theta Correspondence and the Orbit Method

Exploring theta correspondence and orbit method in representation theory, focusing on implications for unitary representations of classical groups and special unipotent representations.

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

Spin Systems with Hyperbolic Symmetry

Explore spin systems with hyperbolic symmetry, their origins, applications in probabilistic models, recent findings, and open questions in this advanced mathematical discussion.

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

Motivic Cohomology - Past, Present and Future

Explore motivic cohomology's evolution, recent developments, and future prospects in algebraic geometry, including cycles with modulus and Chow-Witt theory.

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

Evaluation Complexity of Algorithms for Nonconvex Optimization

Overview of global convergence rates and evaluation complexity for nonconvex smooth optimization methods, comparing steepest descent and Newton's method, and exploring benefits of higher-order regularization algorithms.

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

Surfaces via Spinors and Soliton Equations

Explore Weierstrass representation of surfaces, its relation to Willmore functional, and application to Davey-Stewartson II equation solutions with unique singularity patterns.

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

Analysis with Simple Lie Groups and Lattices

Explore advanced mathematical concepts focusing on simple Lie groups and lattices, delving into their analytical properties and applications in modern algebra and geometry.

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

Arithmetic Dynamics - A Survey

Explore arithmetic dynamics, a field merging number theory and algebraic geometry with dynamical systems, examining key problems and recent advancements in this emerging area of mathematics.

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

Classification of Gapped Ground State Phases in Quantum Spin Systems

Explore quantum spin systems and gapped ground state phases with Yoshiko Ogata's in-depth analysis of classification methods and theoretical frameworks.

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

Hodge Theory, Between Algebraicity and Transcendence

Explore recent advances in Hodge theory, comparing algebraic structures and bounding transcendence using o-minimal geometry. Gain insights into complex algebraic varieties and their applications.

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

Finite Approximations as a Tool for Studying Triangulated Categories

Explore finite approximations in triangulated categories, covering metrics, Fourier series, and surprising new results with applications in algebraic geometry and category theory.

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

Thomas Nikolaus: Frobenius Homomorphisms in Higher Algebra

Explore algebraic K theory, higher algebra, and Frobenius homomorphisms in topology and K theory with insights from Thomas Nikolaus.

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

Jennifer Hom: Homology Cobordism and Heegaard Floer Homology

Explore homology cobordism and Heegaard Floer homology, delving into manifolds, theorems, and chain complexes in this advanced mathematical lecture.

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