BIMSA Courses

Lower Bound for the Genus of a Knot Using the Links-Gould Invariant

Delve into advanced knot theory and quantum link invariants, exploring how the Links-Gould polynomial provides improved lower bounds for Seifert genus calculations in topological mathematics.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Classification of SPT/SET Orders: Boundary-Bulk Relation and Higher Categories

Delve into advanced quantum physics concepts exploring symmetry protected topological orders and their classification through boundary-bulk relations and higher categorical mathematics.

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

Classification of Low-Rank Odd-Dimensional Modular Categories

Delve into the classification methods and properties of low-rank odd-dimensional modular categories, exploring their applications in quantum field theory and topological computation.

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

Spread Approximations and Intersection Problems

Explore the spread approximation method and its applications to intersection problems in combinatorics, including recent results on spanning trees, permutations, and forbidden sunflowers.

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

A Quick Trip to Knot Theory and Knot Data Analysis

Explore knot theory and its applications in data analysis with Professor Fengchun Lei, covering 3-manifold topology and topological data analysis concepts in this BIMSA Member Seminar.

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

对话安德鲁·怀尔斯 - 寻找问题是数学家最关键的能力

探索与安德鲁·怀尔斯的对话，了解数学家如何通过寻找问题来发展关键能力，以及这在数学研究中的重要性。

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

Lean Theorem Prover and Monoidal Category Theory

Explore Lean theorem prover's implementation of monoidal category theory in Mathlib, covering computer-verified mathematical formalization and metaprogramming for coherence theorems.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Markov Semigroups with Quantum Symmetry

Explore bimodule quantum Markov semigroups and their symmetry-preserving dynamics through von Neumann algebras, equilibrium states, and functional inequalities.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Homotopy Quantum Groups

Explore homotopy quantum groups and their role in describing symmetries of quantum field theories through the SymTFT paradigm, connecting higher categorical groups to topological spaces.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

Derived Equivalences from Invariant Theory

Explore derived equivalences in algebraic geometry through invariant theory, focusing on homological algebra and category theory applications to study varieties with insights from physics and noncommutative algebra.

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

Noncommutative Geometry of PGL(2,Cp) and KMS States

Explore noncommutative geometry on the Berkovich projective line, focusing on representation theory of groups acting on R-trees and the construction of cross-product C*-algebras and KMS states.

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

Vantage Points and Sign Patterns

Explore the mathematical study of ordering points in space based on their distances from vantage points, featuring an extension of sign pattern results with applications in discrete mathematics and computer science.

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

Topology of Complex Systems - Mathematical Modeling and GLMY Theory

Explore advanced topological theories and GLMY homology for analyzing high-order interactions in complex networks, with applications in disease research, microbiology, and materials science.

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

Understanding the KPZ Problem - A New Perspective on Random Geometry and Universal Statistics

Delve into the universal properties of random geometries and geodesics in the KPZ framework, exploring statistical mechanics, probability theory, and mathematical physics applications.

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

Double Affine Hecke Algebras Beyond Genus Zero

Delve into advanced mathematical concepts of Double Affine Hecke Algebras and their applications beyond genus zero, presented by mathematics expert Dr. Arthamonov.

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