Fri, 27 May 2022

16:00 - 17:00
N4.01

Deconfining N=2 SCFTs

Matteo Lotito
(University of Massachusetts)
Further Information

It is also possible to join online via Microsoft Teams.

Abstract

In this talk I will describe a systematic approach, introduced in our recent work 2111.08022, to construct Lagrangian descriptions for a class of strongly interacting N=2 SCFTs. I will review the main ingredients of these constructions, namely brane tilings and the connection to gauge theories. For concreteness, I will then specialize to the case of the simplest of such geometrical setups, as in the paper, even though our approach should be much more general. I will comment on some low rank examples of the theories we built, that are well understood by (many) alternative approaches and conclude with some open questions and ideas for future directions to explore.

Thu, 21 Oct 2021
14:00
Virtual

Randomized Methods for Sublinear Time Low-Rank Matrix Approximation

Cameron Musco
(University of Massachusetts)
Abstract

I will discuss recent advances in sampling methods for positive semidefinite (PSD) matrix approximation. In particular, I will show how new techniques based on recursive leverage score sampling yield a surprising algorithmic result: we give a method for computing a near optimal k-rank approximation to any n x n PSD matrix in O(n * k^2) time. When k is not too large, our algorithm runs in sublinear time -- i.e. it does not need to read all entries of the matrix. This result illustrates the ability of randomized methods to exploit the structure of PSD matrices and go well beyond what is possible with traditional algorithmic techniques. I will discuss a number of current research directions and open questions, focused on applications of randomized methods to sublinear time algorithms for structured matrix problems.

--

A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact @email.

Fri, 24 Jan 2020

16:00 - 17:00
L1

Nonlinear Waves in Granular Crystals: From Modeling and Analysis to Computations and Experiments

Panos Kevrekidis
(University of Massachusetts)
Further Information

The Mathematical Institute Colloquia are funded in part by the generosity of Oxford University Press.

This Colloquium is supported by a Leverhulme Trust Visiting Professorship award.

Abstract

In this talk, we will provide an overview of results in the setting of granular crystals, consisting of spherical beads interacting through nonlinear elastic spring-like forces. These crystals are used in numerous engineering applications including, e.g., for the production of "sound bullets'' or the examination of bone quality. In one dimension we show that there exist three prototypical types of coherent nonlinear waveforms: shock waves, traveling solitary waves and discrete breathers. The latter are time-periodic, spatially localized structures. For each one, we will analyze the existence theory, presenting connections to prototypical models of nonlinear wave theory, such as the Burgers equation, the Korteweg-de Vries equation and the nonlinear Schrodinger (NLS) equation, respectively. We will also explore the stability of such structures, presenting some explicit stability criteria for traveling waves in lattices. Finally, for each one of these structures, we will complement the mathematical theory and numerical computations with state-of-the-art experiments, allowing their quantitative identification and visualization. Finally, time permitting, ongoing extensions of these themes will be briefly touched upon, most notably in higher dimensions, in heterogeneous or disordered chains and in the presence of damping and driving; associated open questions will also be outlined.

Thu, 13 Feb 2020

16:00 - 17:30
L3

Nonlinear Schrödinger PDEs and Some Applications in Atomic and Optical Physics

Professor Panos Kevrekidis
(University of Massachusetts)
Abstract

Nonlinear generalizations of the Schrödinger equation are of wide applicability to a range of areas including atomic and optical systems, 
plasma physics and water waves.  In this  talk we revisit some principal excitations in atomic and optical systems (such as Bose-Einstein condensates and photo-refractive crystals), namely dark solitonic fronts in single-component systems, and dark-bright waves in multi-component systems. Upon introducing them and explaining their existence and stability properties in one spatial dimension, we will extend them both in the form of stripes and in that rings in two-dimensions, presenting an alternative (adiabatic-invariant based) formulation of their stability and excitations. We will explore their filamentary dynamics, as well as the states that emerge from their transverse (snaking) instability. Then, we will consider these structures even in three dimensions, in the form of planar, as well as spherical shell wave patterns and generalize our adiabatic invariant formulation there. Finally, time permitting, we will give some glimpses of how some of these dynamical features in 1d and 2d generalize in a multi-orbital, time-dependent quantum setting.

Thu, 30 May 2013

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

The FEAST eigenvalue algorithm and solver with new perspectives for first-principle electronic structure calculations

Professor Eric Polizzi
(University of Massachusetts)
Abstract
FEAST is a new general purpose eigenvalue algorithm that takes its inspiration from the density-matrix representation and contour integration technique in quantum mechanics [Phys. Rev. B 79, 115112, (2009)], and it can be understood as a subspace iteration algorithm using approximate spectral projection [http://arxiv.org/abs/1302.0432 (2013)]. The algorithm combines simplicity and efficiency and offers many important capabilities for achieving high performance, robustness, accuracy, and multi-level parallelism on modern computing platforms. FEAST is also the name of a comprehensive numerical library package which currently (v2.1) focuses on solving the symmetric eigenvalue problems on both shared-memory architectures (i.e. FEAST-SMP version -- also integrated into Intel MKL since Feb 2013) and distributed architectures (i.e. FEAST-MPI version) including three levels of parallelism MPI-MPI-OpenMP.

\\

\\

In this presentation, we aim at expanding the current capabilies of the FEAST eigenvalue algorithm and developing an unified numerical approach for solving linear, non-linear, symmetric and non-symmetric eigenvalue problems. The resulting algorithms retain many of the properties of the symmetric FEAST including the multi-level parallelism. It will also be outlined that the development strategy roadmap for FEAST is closely tied together with the needs to address the variety of eigenvalue problems arising in computational nanosciences. Consequently, FEAST will also be presented beyond the "black-box" solver as a fundamental modeling framework for electronic structure calculations.

\\

\\

Three problems will be presented and discussed: (i) a highly efficient and robust FEAST-based alternative to traditional self-consistent field

(SCF) procedure for solving the non-linear eigenvector problem (J. Chem. Phys. 138, p194101 (2013)]); (ii) a fundamental and practical solution of the exact muffin-tin problem for performing both accurate and scalable all-electron electronic structure calculations using FEAST on parallel architectures [Comp. Phys. Comm. 183, p2370 (2012)]; (iii) a FEAST-spectral-based time-domain propagation techniques for performing real-time TDDFT simulations. In order to illustrate the efficiency of the FEAST framework, numerical examples are provided for various molecules and carbon-based materials using our in-house all-electron real-space FEM implementation and both the DFT/Kohn-Sham/LDA and TDDFT/ALDA approaches.

Subscribe to University of Massachusetts