BIMSA Courses

Intersections of Hypergraphs: Discrepancy and Anticoncentration

Explore the discrepancy of hypergraph pairs, examining Bollobás and Scott's conjecture with counterexamples for k>2 and related results on edge statistics in hypergraphs of moderate density.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Frame Matroids with a Distinguished Frame Element

Explore the characterization of 3-connected frame matroids with a fixed element in their frame, including graphical representations and recognition algorithms.

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

Long Cycle in the Percolated Cube

Explore the mathematical proof of a long-standing conjecture about percolated hypercubes, showing they typically contain cycles of length at least (1-ε)2^d when p>C/d.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Chromatic Threshold via Combinatorial Convexity, and Beyond

Explore the connection between chromatic threshold in extremal combinatorics and the (p,q)-theorem in discrete geometry, with insights on bounded complexity graphs and density conditions.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Symmetry-Resolved Entanglement in AdS and BCFT

Explore the refinement of entanglement entropy in theories with global conserved charges, examining symmetry-resolved entanglement in AdS3/CFT2, equipartition properties in U(1) Kac-Moody symmetry, and BCFT techniques.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Symmetries: From Groups to Tensor Categories

Explore the evolution of symmetry in mathematics, from traditional Group Theory to modern tensor categories, and how these concepts help explain states of matter and recent developments in condensed matter physics.

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

Quantum Symmetry in Multigraphs

Explore quantum symmetry in multigraphs, extending established concepts from simple graphs to finite multigraphs within compact quantum groups, with applications in quantum information theory and noncommutative mathematics.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

2D CFTs and Dual Description of Deformed Integrable Sigma Models

Delve into quantum field theories through screening charges, exploring dual descriptions of 2D sigma models and their integrable deformations with applications to O(N) and OSp(N|2m) theories.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Wreath-like Product Groups and Their von Neumann Algebras: W*-superrigidity and Outer Automorphism Groups

Delve into wreath-like product groups and their von Neumann algebras, exploring W*-superrigidity and outer automorphism groups with Adrian Ioana, who presents groundbreaking research on property (T) groups.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Problems, Methods, and Applications in Lipschitz Global Optimization

Explore problems, methods, and applications in Lipschitz global optimization with Distinguished Professor Yaroslav Sergeev, covering adaptive partition strategies, zero-crossing points, safe optimization, and numerical infinities.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Zero-Sum Sequences in Algebraic Combinatorics

Explore the mathematical theory of zero-sum sequences and their applications in algebraic combinatorics, from group permanents to cyclic sieving phenomena and coding theory.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

The Classification of Fusion 2-Categories

Delve into advanced mathematical concepts of fusion 2-categories, their classification using braided fusion categories, and applications in quantum field theories through expert insights and theoretical frameworks.

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

From Segal's Sewing to Pseudo-q-Traces and Back

Delve into advanced vertex operator algebra theory, exploring connections between Segal's sewing construction, pseudo-q-traces, and torus conformal blocks in quantum field theory mathematics.

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

Operator Algebra Approach for Topological Pauli Stabilizer Codes in Two Dimensions

Delve into operator algebra methods for analyzing 2D topological Pauli stabilizer codes, exploring anyon types, fusion rules, and braiding statistics for quantum error correction and fault-tolerant computing.

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

Commutative Algebras in Braided Monoidal Categories and Rigidity

Delve into advanced mathematical concepts of commutative algebras, exploring their behavior in braided monoidal categories and examining rigidity conditions in vertex operator algebras.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video