Associate ProfessorDaniel Tubbenhauer

I am currently working on aspects of 2-representation theory and its applications in cryptography and machine learning, properties of (weighted) KLRW algebras, growth rates in representation theory, dualities in representation theory and I am always interested in a challenge.

My latest research fields include:

• 2-representation theory ("the representation theory of the 21th century"). Ingredients.
  (Modular) representation theory, categorical algebra, (higher) category theory, group and semigroup theory.
• Knot homologies, topological quantum field theories, Lie theory and geometry. Ingredients.
  Low-dimensional topology, representation theory, quantum Lie theory, quantum or string physics, homological algebra.
• Modular representation theory, in particular of Lie algebras and Lie groups. Ingredients.
  Representation theory, Lie theory, diagrammatics, Soergel bimodules.
• Diagrammatic representation, especially, their diagrammatic presentations and properties such as cellularity. Ingredients. Classical algebra, monoidal categories, diagram categories, combinatorics.
• Representation theory of monoids and cryptography, when looking at bounds or growth rates of simple representations. Ingredients. Green's cell theory (Green's relations), monoidal categories, diagram categories.
• Representation theory and machine learning, when looking at equivariant neural networks. Ingredients: Representation theory in piecewise linear.

Please find more information on my personal website: http://www.dtubbenhauer.com/

My research aligns with the Faculty of Science Research Strengths - Data and Decisions, Understanding the Universe, Fundamental Laws of Nature, Complex Systems."