BIMSA Courses

Rigidity of the Category of Local Modules in Braided Monoidal Categories

Delve into advanced mathematical concepts exploring rigidity of local module categories, braided monoidal categories, and their applications in vertex operator algebra representations.

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

Perfect Modular Categories of Low Dimension

Delve into advanced mathematical concepts of modular categories, exploring solvability conditions for Frobenius-Perron dimensions and their applications in quantum symmetry theory.

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

Modular Data of Non-Semisimple Modular Categories

Explore the extension of modular tensor category theory to non-semisimple cases, focusing on SL(2,Z)-representation and rank finiteness through factorizable ribbon Hopf algebras.

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

Invisible SL_n-skeins in Quantum Knot Theory

Explore the mathematical theory of invisible SL_n-skeins in 3D manifolds, examining their unique properties when parameter q is a root of unity, through symmetric polynomials in n variables.

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

Fusion Rules of Edge Excitations in Topological Order

Delve into boundary excitations in topological orders, exploring fusion rules, half-linking numbers, and their connections to the Verlinde formula through both Abelian and non-Abelian examples.

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

Hopf Algebras of Dimension p^2 in Positive Characteristic p

Delve into advanced mathematical concepts of Hopf algebras in positive characteristic p, exploring nonsemisimple structures and their dimensional properties through recent research findings.

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

Mining for Modular Data from Congruence Representations

Explore how modular data can be reconstructed from SL(2,Z) congruence representations in modular fusion categories, with applications in mathematics and physics.

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

2-Character Theory of Finite 2-Groups

Explore advanced mathematical concepts in 2-character theory, representation theory of finite 2-groups, and their connections to topological quantum field theory through rigorous theoretical frameworks.

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

Local Modules in Braided Fusion 2-Categories

Delve into advanced mathematical concepts of local modules, braided fusion 2-categories, and Lagrangian algebras, exploring their role in topological boundaries and quantum symmetry theory.

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

Constructing Modular Tensor Categories Using Hopf Algebras

Delve into advanced mathematical concepts of modular tensor categories and their construction through Hopf algebras, focusing on ribbon factorizable structures and representation theory.

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

Braided Zestings of Verlinde Modular Categories and Their Modular Data

Delve into advanced mathematical concepts of braided zesting in modular categories, exploring quantum groups, fusion categories, and their applications in quantum computing theory.

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

Weak Hopf Symmetry Behind the 2D Topological Phases

Delve into advanced quantum physics concepts exploring weak Hopf symmetry and its relationship to 2D topological phases, string-net models, and lattice gauge theory through mathematical frameworks.

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

Factorization Homology in Topological Quantum Field Theory

Explore factorization homology's role in organizing TQFT observables, understanding its construction with chain complexes and n-manifolds, and discovering its applications in quantum topology.

• YouTube
• 2 hours 20 minutes
• Self-Paced
• Free Video

Concrete C*-Dynamical Systems and SL2(Z)-Actions on Rotation Algebras

Delve into C*-dynamical systems through SL2(Z)-actions on rotation algebras, exploring classification theory, crossed products, and explicit computation of Elliott's invariants for irrational rotation algebras.

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

Weak Hopf Symmetry and Quantum Double Model Theory

Delve into quantum symmetry theory through weak Hopf algebra extensions, exploring anyonic systems, symmetry breaking, and quantum double models with applications in topological quantum field theories.

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