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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...
Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing tre...
We show that for every nonelementary representation of a surface group into SL(2, C) there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the d...
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...
In [11] we parametrized boundary-unipotent representations of a 3-manifold group into SL(n; C) using Ptolemy coordinates, which were inspired by A-coordinates on higher Teichmuller space due to Foc...
The Ptolemy coordinates for boundary-unipotent SL(n; C)-representations of a 3-manifold group were introduced in [7] inspired by the A-coordinates on higher Teichmuller space due to Fock and Goncha...
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...
A general technique for the generation of canonical channel models and demonstrate the application of the technique to time-frequency and time-scale integral kernel operators is developed. As an examp...
In this note we show that reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”) can be performed using Lipschitz continuous maps. Specifically we show that whe...
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes of representat...
Let S be a closed oriented surface of genus g > 1 and let ~r denote its fundamental group. Let G be a semisimple Lie group. The purpose of this paper is to investigate the global properties of the s...
(For convenience we shall henceforth assume that n is torsionfree: by Selberg's lemma [12] this may be accomplished by replacing TT by a subgroup of finite index. This insures that M is a compact ...
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...

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