Kashiwara's Crystals And Generalizations

Quantum groups are important objects in various aspects of mathematical physics, such integrable systems. Representations of quantum groups have nice bases called crystal bases, which allows us to translate problems in representation theory into a combinatorial framework called (Kashiwara) crystals. Crystals have appeared in a diverse set of mathematical topics, including geometry, probability theory, and statistical mechanics. A recent trend has been to generalize these to other applications, such as Lie superalgebras.

There are many questions available for honours, Masters, and PhD students in crystals and releated fields, including algebraic combinatorics, representation theory, and algebraic geometry. I am happy to talk about any of these subjects to find a project that interests you.