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Principal Investigator
Principal Investigator
My research is at the interaction between representation theory, low dimensional topology and symplectic topology. I am working on topological models for quantum invariants, such as (coloured) Jones and (coloured) Alexander polynomials and Witten-Reshetikhin-Turaev invariants. The aim of this research direction is to create a framework for discovering topological information which is behind these quantum invariants, given by geometrical categorifications or asymptotics when the colour tends to infinity. I am also interested in non-semisimple quantum invariants and TQFT's coming from the representation theory of super quantum groups.
Key words: Low dimensional topology, quantum topology, geometric representation theory, symplectic topology, categorifications.
Team member
Team member
My research interests are centred around algebraic and geometric topology, including:
configuration spaces of various kinds,
moduli spaces of manifolds,
monopole moduli spaces,
surface braid groups, loop braid groups, mapping class groups (their representation theory, lower central series, ...),
polynomial functors,
group-completions of topological monoids,
multi-crossing numbers of knots and links,
"big" mapping class groups (mapping class groups of infinite-type surfaces),
connections of any of the above to other parts of mathematics.
Team member
Team member
My research interests lie primarily in the field of algebraic geometry. So far, I have mainly focused on questions concerning the moduli theory of coherent sheaves on algebraic varieties.
Team member
Team member
I am a quantum topologist in the math department at Texas State University interested in the interplay between low-dimensional topology and quantum link invariants.
Research interests: Knot theory, quantum topology, 3-manifolds.
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