Dr Travis Scrimshaw

Lecturer in Maths

Mathematics
Faculty of Science
t.scrimshaw@uq.edu.au
+61 7 336 56134

Overview

Research Interests

  • Combinatorial Representation Theory
    The study of symmetries of physical systems is a cornerstone of modern algebra, and representation theory is writing these as matrices. However, the solutions and study of these matrices can still remain complicated as there often remains an infinite number of choices. We translate the linear algebra into manipulating discrete objects, we can reinterpret problems into pictures and counting certain sets, such as the number of cut a hexagon into triangles.

Qualifications

  • Doctor of Philosophy, University of California

Publications

View all Publications

Available Projects

  • 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.

View all Available Projects

Publications

Featured Publications

Journal Article

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • 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.