Where: Kirwan Hall 3206

Speaker: Benjamin Kedem (UMD) - https://www.math.umd.edu/~bnk/

Abstract: https://drive.google.com/file/d/0B3jYat5x6nNJbzhRSEJiNVhzQ3FBQnotRHFpcVlpUTQ0X1U4/view?usp=sharing

Where: Kirwan Hall 3206

Speaker: Lloyd N. Trefethan (Oxford University)

https://people.maths.ox.ac.uk/trefethen/

Abstract: What is a random function? What is noise? The standard answers are nonsmooth, defined pointwise via the Wiener process and Brownian motion. In the Chebfun project, we have found it more natural to work with smooth random functions defined by finite Fourier series with random coefficients. The length of the series is determined by a wavelength parameter lambda. Integrals give smooth random walks, which approach Brownian paths as lambda shrinks to 0, and smooth random ODEs, which approach stochastic DEs of the Stratonovich variety. Numerical explorations become very easy in this framework. There are plenty of conceptual challenges in this subject, starting with the fact that white noise has infinite amplitude and infinite energy, a paradox that goes back in two different ways to Einstein in 1905.

Where: Chemical Engineering Room 2110

Speaker: Dan Ciubotaru (University of Oxford) - https://www.maths.ox.ac.uk/people/dan.ciubotaru

Abstract: I will explain the construction and main properties of Dirac operators for representations of various Hecke-type algebras (e.g., Lusztig's graded Hecke algebra for p-adic groups, Drinfeld's Hecke algebras, rational Cherednik algebras). The approach is motivated by the classical Dirac operator which acts on sections of spinor bundles over Riemannian symmetric spaces, and by its algebraic version for Harish-Chandra modules of real reductive groups. The algebraic Dirac theory developed for these Hecke algebras turns out to lead to interesting applications: e.g., a Springer parameterization of projective representations of finite Weyl groups (in terms of the geometry of the nilpotent cone of complex semisimple Lie algebras), spectral gaps for unitary representations of reductive p-adic groups, connections between the Calogero-Moser space and Kazhdan-Lusztig double cells. I will present some of these applications in the talk.

Where: Kirwan Hall 3206

Speaker: Michael Rapoport (UMD and University of Bonn) - http://www.math.uni-bonn.de/ag/alggeom/rapoport

Where: Kirwan Hall 3206

Speaker: Marsha Berger (NYU) - https://cs.nyu.edu/berger/

Abstract:

Four years ago, an asteroid with a 20 meter diameter exploded in the

atmosphere over Chelyabinsk, Russia, causing injury and damage 20

kilometers away but no deaths. We are studying the question of what

would occur if such an airburst happened over the ocean. Would the

blast wave generate a tsunami that could threaten coastal cities far away?

We begin with several simulations of tsunami propagation from

asteroid-generated airbursts under a range of conditions. We use the

open source software package GeoClaw, which has been successful in

modeling earthquake-generated tsunamis. GeoClaw uses a basic model of

ocean waves called the shallow water equations (SWE). We then present a

simplified one dimensional model problem with an explicit solution in

closed form to understand

some of the unexpected results.

The SWE model however may not be accurate enough for airburst-generated

tsunamis, which have shorter length and time scales than

earthquake-generated waves. We extend our model problem to the

linearized Euler equations of fluid mechanics to explore the effects of

wave dispersion and water compressibility. We end with a discussion of

suitable models for airburst-generated tsunamis, and speculate as to

appropriate tools to study the more serious case of an asteroid that

impacts the water.

Where: CSIC 2117

Speaker: Alan Frieze (CMU) - https://www.math.cmu.edu/~af1p/

Abstract

Where: Kirwan Hall 3206

Speaker: Christoph Ortner (University of Warwick) - https://warwick.ac.uk/fac/sci/maths/people/staff/christoph_ortner/

Abstract: A common problem of atomistic materials modelling is to determine properties of crystalline defects, such as structure, energetics, mobility, from which

meso-scopic material properties or coarse-grained models can be derived (e.g.,

Kinetic Monte-Carlo, Discrete Dislocation Dynamics, Griffith-type fracture

laws). In this talk I will focus on one the most basic tasks, computing the

equilibrium configuration of a crystalline defect, but will also also comment on

free energy and transition rate computations.

A wide range of numerical strategies, including the classical supercell method

(periodic boundary conditions) or flexibe boundary conditions (discrete BEM),

but also more recent developments such as atomistic/continuum and QM/MM hybrid schemes, can be interpreted as Galerkin discretisations with variational crimes, for an infinite-dimensional nonlinear variational problem. This point of view is effective in studying the structure of exact solutions, identify approximation parameters, derive rigorous error bounds, optimise and construct novel schemes with superior error/cost ratio.

Time permitting I will also discuss how this framework can be used to analyse

model errors in interatomic potentials and how this can feed back into the

developing of new interatomic potentials by machine learning techniques.

Where: Kirwan Hall 3206

Speaker: Department meeting () -

Where: Kirwan Hall 3206

Speaker: Bassam Fayad (Universite de Paris) - https://webusers.imj-prg.fr/~bassam.fayad/

Abstract: A natural question in smooth dynamics is to measure the

escape time of orbits from the neighborhood of invariant sets such as

fixed points or invariant submanifolds.

KAM theory asserts that a quasi-integrable real analytic Hamiltonian

system has in general a large measure set of invariant tori on which

the dynamics is quasi-periodic.

We show that these invariant tori are usually doubly exponentially

stable and not more than double exponentially stable. Double

exponential stability refers to the fact that a point starting at

distance r from the invariant torus remains within distance 2r during

a time that is doubly exponential in some power of 1/r. Similar

results are obtained for general elliptic equilibria of Hamiltonian

flows.

Where: Kirwan Hall 3206

Speaker: Department meeting () -

Where: Kirwan Hall 3206

Speaker: Helge Holden (NTNU (Norwegian University of Science and Technology)) - https://www.ntnu.edu/employees/holden

Abstract: We will discuss models for vehicular traffic flow on networks. The models

include both the Lighthill-Whitham-Richards (LWR) model and Follow-the-Leader (FtL) models.

The emphasis will be on the Braess paradox in which adding a road to a traffic network

can make travel times worse for all drivers.

In addition, we will present a novel proof how FtL models approximate the LWR model in

case of heavy traffic.

If time permits, we will discuss a novel model for multi-lane traffic.

The work is joint with N.H. Risebro (Oslo) and R. Colombo (Brescia)

Where: Kirwan Hall 3206

Speaker: Jianfeng Lu (Duke University) - https://services.math.duke.edu/~jianfeng/

Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Stefan Steinerberger, Kyle Thicke, and Lexing Ying.

Where: Kirwan Hall 3206

Speaker: Jeff Adams (UMD ) - https://www.math.umd.edu/~jda/

Abstract: I have been teaching a flipped class (applied linear

algebra), for which I have made a set of videos, which the students

watch before class. In class we have a general discussion: I answer

questions about the video, go over homework problems, etc. I have also

used this method to make a video in other conventionally taught

classes on days that I am absent.

In this talk I will give a brief report on my experience flipping

classes, and then demonstrate how I make the videos, using an

interactive pen/tablet display and video capture software.

Where: Kirwan Hall 3206

Speaker: Department meeting () -

Where: Kirwan Hall 3206

Speaker: Otis Chodosh (Princeton University) - https://web.math.princeton.edu/~ochodosh/