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Jones polynomial and knot transitions in Hermitian and non-Hermitian topological semimetals
Hermitian Topological semimetal Junction Transition
2023/1/4
Topological nodal line semimetals can host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this talk, I will show how to use the Jones polynomial (wh...
Basic references are Vogan’s notes on Sp(4, R): [?] (branching) and [?] (Hermitian forms). In fact these notes are largely a rewriting of [?] in more explicit atlas terms.
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
2015/8/17
This talk is about aspects of representation theory of padic
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...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. This conforms to the Lefschetz
principle which states that what is true for real groups is al...
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
2012/6/30
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Lehmer's conjecture Hermitian matrices Eisenstein and Gaussian integers Number Theory
2012/6/29
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least ...
Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrodinger Equations
Higher-order Schrodinger operators rescaled blow-up variables discrete real spectrum asymptotic behaviour nodal sets of solutions
2011/9/9
Abstract: A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.
The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
largest eigenvalue of real symmetric Hermitian and Hermitian self-dual random matrix rank one external source
2011/2/22
We consider the limiting location and limiting distribution of the largest eigenvalue in real
symmetric (β = 1), Hermitian (β = 2), and Hermitian self-dual (β = 4) random matrix models
with rank 1 e...
Metric operators for non-Hermitian quadratic su(2) Hamiltonians
Metric operators non-Hermitian quadratic su(2) Hamiltonians
2011/3/1
A class of non-Hermitian quadratic su(2) Hamiltonians that ful l an anti-linear symmetry is constructed. If unbroken this anti-linear symmetry leads to a purely real spectrum and the Hamiltonian can b...
Existence of Hermitian-Yang-Mills metrics under conifold transitions
Existence of Hermitian-Yang-Mills metrics conifold transitions
2011/1/21
We first study the degeneration of a sequence of Hermitian-Yang-Mills metrics with respect to a sequence of balanced metrics on a Calabi-Yau threefold ˆX that degenerates to the balanced metric c...
Existence of approximate Hermitian-Einstein structures on semi-stable bundles
Existence of approximate Hermitian-Einstein semi-stable bundles
2011/1/19
The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact K¨ahler manifold X. It is shown that, if E is semistable,then Donaldson’s functional is bo...
Products of Independent Non-Hermitian Random Matrices
Products Independent Non-Hermitian Random Matrices
2011/2/24
For fixed m > 1, we consider m independent n×n non-Hermitian random matrices X1, . . . ,Xm with i.i.d. centered entries with a finite (2 + )-th moment, > 0. As n tends to infinity, we show that the...
Geometric Realizability of Covariant Derivative Kähler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds
Geometric Realizability Covariant Derivative Kä hler Tensors Pseudo-Hermitian
2011/2/25
The covariant derivative of the K¨ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which s...
Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
Solvable Pseudo-hermitian Many-particle Quantum Systems Isospectral Deformation
2011/3/2
A class of non-Dirac-hermitian many-particle quantum systems admit-ting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems...
Two families of maximal curves which are not Galois subcovers of the Hermitian curve
maximal curves generalized GK curves Galois coverings
2011/1/20
We show that the generalized Giulietti-Korchm´aros curve and the maximal curve with equation x q2 − x = y (qn+1)/(q+1) defined over F q2n, for n 3 odd and q 3, are not Galois subcovers...