Uniform positivity of the Lyapunov exponent for monotonic potentials generated by the doubling map.

Speaker: 

Z. Zhang

Institution: 

Rice University

Time: 

Wednesday, March 15, 2017 - 12:00pm

Location: 

RH 340N

 

 

Abstract:  In this talk, we consider the one-dimensional discrete Schrodinger operators with potentials generated by the doubling map

on the unit circle. We show that if the potentials is monotonic, then the associated Lyapunov exponent is uniformly bounded away from zero for

all energies. This provides a second example of this kind after the trigonometric polynomials.

Central spectral gaps of the almost Mathieu operator.

Speaker: 

Igor Krasovsky

Institution: 

Imperial College, London

Time: 

Thursday, April 6, 2017 - 2:00pm

Location: 

RH 340P

Consider the almost Mathieu operator in the case of the critical coupling.

For rational frequencies p/q we obtain power-law bounds of the form 1/q^C

for the widths of the gaps close to the center of the spectrum. It follows that

these gaps remain open for the spectrum in the case of a certain class of Diophantine irrational frequencies.

Title: Universality for algorithms to compute the (extreme) eigenvalues of a random matrix

Speaker: 

T. Trogdon

Institution: 

UCI

Time: 

Thursday, March 16, 2017 - 2:00pm

Location: 

RH 340P

Abstract: The Toda lattice, beyond being a completely integrable dynamical system, has many important properties.  Classically, the Toda flow is seen as acting on a specific class of bi-infinite Jacobi matrices.  Depending on the boundary conditions imposed for finite matrices, it is well known that the flow can be used as an eigenvalue algorithm. It was noticed by P. Deift, G. Menon and C. Pfrang that the fluctuations in the time it takes to compute eigenvalues of a random symmetric matrix with the Toda, QR and matrix sign algorithms are universal. In this talk, I will present a proof of such universality for the Toda and QR algorithms and the power method.  This is joint work with P. Deift.

Absolutely continuous spectrum and the spectra of periodic approximants

Speaker: 

Yoram Last

Institution: 

Hebrew University

Time: 

Thursday, February 9, 2017 - 2:00pm

Location: 

RH 340P

We discuss relations between absolutely continuous spectrum of discrete one-dimensional
Schroedinger operators and the spectra of periodic approximants made by cutting and
repeating
finite pieces of the potential.

Sloshing, Steklov and corners

Speaker: 

Iosif Polterovich

Institution: 

Montreal

Time: 

Thursday, May 25, 2017 - 2:00pm

Host: 

Katya Krupchyk

The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.

 

Quantum Computing in Geometric Algebra Terms

Speaker: 

A Soiguine

Institution: 

Geometric Algebra Quantum Computing Initiative

Time: 

Thursday, October 13, 2016 - 2:00pm

Location: 

RH 340P

Following the Basil Hiley’s  long held belief (see, for example, B. J. Hiley, "Structure Process, Weak Values and Local Momentum," Journal of Physics: Conference Series, vol. 701, no. 1, 2016) that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of commonly used terms “state”, “observable”, “measurement” giving them a clear unambiguous definition. This concrete definition, along with complex planes variable in three dimensions, is quite natural in geometric (Clifford) algebra terms. It helps to establish a feasible language for the area of quantum computing.

Boundedness for the General Semilinear Duffing Equations via the Twist Theorem

Speaker: 

Daxiong Piao

Institution: 

Ocean University, China

Time: 

Thursday, September 8, 2016 - 2:00pm

Location: 

RH 340P

We consider the boundedness of all solutions for the periodic semilinear equation where the non-linear term does not necessarily satisfy the so called polynomial-like growth condition. Usually this condition is needed in the references about boundedness problems of semilinear Duffing equations. Two cases of resonance and non-resonance are considered respectively.

 

* Joint work with Yiqian Wang, Zhiguo Wang, Lei Jiao and Xiao Ma

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