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In this talk I will introduce some basic concepts in higher category and some details of the construction in the first talk. I will introduce crossed modules and the example of strict 2-representation...
For a compact 3-manifold M with arbitrary (possibly empty) boundary, we give a parametrization of the set of conjugacy classes of boundary-unipotent representations of π1(M) into SL(n, C). Our param...
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W . We construct a one parameter family of flat connections ∇κ on h with values in any finite–dimensional g–moduleV...
This article, a continuation of [HRo], constructs the Satake parameter for any irreducible smooth J-spherical representation of a p-adic group, where J is any parahoric subgroup. This parametrizes s...
The Atlas of Lie Groups and Representations is a project in representation theory of real reductive groups. Themain goal of the atlas computer software, currently under development, is to compute the ...
The purpose of this paper is to give a finite algorithm for computing the set of irreducible unitary representations of a real reductive Lie group G. Even before explaining the nature of the algorithm...
Let E be an elliptic curve over the rationals that does not have complex multiplication. For each prime `, the action of the absolute Galois group on the `-torsion points of E can be given in terms of...
Much of the material in this talk was presented at the conference in honor of Roger Howe. The slides are available at http://math.mit.edu/conferences/howe/program.php The theme of the talk is to n...
This talk is about aspects of representation theory of p􀀀adic groups that parallel real groups. In the case of real groups, the results refer to J. Adams, P. Trapa, M. vanLeuwen, W-L. Yee a...
This talk is about aspects of representation theory of p􀀀adic groups that parallel real groups. This conforms to the Lefschetz principle which states that what is true for real groups is al...
We introduce the category of set-theoretic representations of a matched pair of groupoids. This is a monoidal category endowed with a monoidal functor f` to the category of quivers over the common b...
We present Las Vegas algorithms for constructive recognition and constructive membership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} for some m > 0, in their natural representatio...
We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are fou...
Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathb...

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