This series consists of talks in the area of Mathematical Physics.
In this talk, intended for a broader audience, I promise to use techniques only at the level of university calculus. While staying at this level, our goal will be to learn conceptual lessons for categorification of quantum group invariants of knots and 3-manifolds, also known as the Witten-Reshetikhin-Turaev (or WRT) invariants. In particular, we will introduce new q-series invariants of 3-manifolds that have integer powers and integer coefficients and, if time permits, discuss their various constructions and properties. The talk is based on several papers with D. Pei and/or P. Putrov, C.
Abstract TBA
The cobordism hypothesis gives a functorial bijection between oriented
n-dimensional fully local topological field theories, valued in some
higher category C, and the fully dualizable object of C equipped with
the structure of SO(n)-fixed point. In this talk I'll explain recent
works of Haugseng, Johnson-Freyd and Scheimbauer which construct a
Morita 4-category of braided tensor categories, and I'll report on joint
work with Brochier and Snyder which identifies two natural subcategories
TBA
In this talk I will describe joint work in progress with Andre Henriques to construct examples of Graeme Segal's functorial definition of 2d chiral conformal field theory. While Segal's definition originated in the 1980's, constructive aspects of the theory continue to be challenging, especially with regard to higher genus surfaces. I will motivate and introduce Segal's definition, and describe a new approach to constructing examples using von Neumann algebras.
Recently, Roland van der Veen and myself found that there are sequences of solvable Lie algebras "converging" to any given semi-simple Lie algebra (such as sl(2) or sl(3) or E8). Certain computations are much easier in solvable Lie algebras; in particular, using solvable approximations we can compute in polynomial time certain projections (originally discussed by Rozansky) of the knot invariants arising from the Chern-Simons-Witten topological quantum field theory.
I will give a brief survey of the study of decomposable Specht modules for the symmetric group and its Hecke algebra, which includes results of Murphy, Dodge and Fayers, and myself. I will then report on an ongoing project with Louise Sutton, in which we are studying decomposable Specht modules for the Hecke algebra of type $B$ indexed by `bihooks’.
Let be a complex semisimple algebraic group of adjoint type and the wonderful compacti
In this talk, I'd like to explain how quantum integrability and (q-deformed) W-algebraic structure arise from the moduli space of quiver gauge theory. It'll be also shown that our construction gives rise to a new family of W-algebras.
Quiver varieties, as introduced by Nakaijma, play a key role in representation theory. They give a very large class of symplectic singularities and, in many cases, their symplectic resolutions too. However, there seems to be no general criterion in the literature for when a quiver variety admits a symplectic resolution. In this talk, I will give necessary and sufficient conditions for a quiver variety to admit a symplectic resolution. This result builds upon work of Crawley–Boevey and of Kaledin, Lehn and Sorger. The talk is based on joint work with T. Schedler.