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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：2-representations and 2-vector bundles
2 向量丛 群论
2023/4/13
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topology optimization via implicit neural representations
隐式 神经表示 拓扑优化
2023/4/24
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On constructions of Lax representations: some examples
松弛表示 构造 非线性数学物理方程 KdV方程
2023/4/24
著名数学家Peter Lax 在1968年将重要的非线性数学物理方程---KdV方程表示为一个算子方程， 即给出了KdV方程的Lax表示或Lax对。Lax对在孤立子理论的发展中扮演者重要角色，可以看成是研究可积系统的出发点。但如何构造一个给定非线性系统的Lax表示却是非常困难的问题。本报告在概述Lax表示历史的基础上，以Boris Kupershmidt提出的两个非线性发展型方程为具体例子，介绍L...
SURFACE GROUP REPRESENTATIONS TO SL(2, C) AND HIGGS BUNDLES WITH SMOOTH SPECTRAL DATA
SURFACE GROUP SL(2, C) HIGGS BUNDLES SPECTRAL DATA
2015/12/17
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...
CASIMIR OPERATORS AND MONODROMY REPRESENTATIONS OF GENERALISED BRAID GROUPS
CASIMIR OPERATORS MONODROMY REPRESENTATIONS GENERALISED BRAID GROUPS
2015/10/14
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...
TIME-FREQUENCY AND TIME-SCALE CANONICAL REPRESENTATIONS OF DOUBLY SPREAD CHANNELS
TIME-FREQUENCY TIME-SCALE CANONICAL REPRESENTATIONS DOUBLY SPREAD CHANNELS
2015/9/29
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...
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
2015/9/29
Goldman gratefully acknowledges partial support by NSF grants
DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research
Award from the General Research Board of the University of
Maryland in Fa...
On Lipschitz Inversion of Nonlinear Redundant Representations
Lipschitz Inversion Nonlinear Redundant Representations
2015/9/29
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...
Invariant functions on Lie groups and Hamiltonian flows ofsurface group representations
Lie groups Hamiltonian flows
2015/9/29
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...
Topological components of spaces of representations
representations Topological components
2015/9/29
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...
CHARACTERISTIC CLASSES AND REPRESENTATIONS OF DISCRETE SUBGROUPS OF LIE GROUPS
CHARACTERISTIC CLASSES REPRESENTATIONS
2015/9/29
(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 ...
ON SATAKE PARAMETERS FOR REPRESENTATIONS WITH PARAHORIC FIXED VECTORS
SATAKE PARAMETERS PARAHORIC
2015/9/29
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...