Colloquium Archives for Academic Year 2018

Augmented reality in the estimation of small tail probabilitiesmall

When: Wed, September 5, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Benjamin Kedem (UMD) -

Aziz Lecture: Smooth random functions and smooth random ODEs

When: Wed, September 12, 2018 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Lloyd N. Trefethan (Oxford University)

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.

Dirac operators and Hecke algebras

When: Wed, September 19, 2018 - 3:15pm
Where: Chemical Engineering Room 2110

Speaker: Dan Ciubotaru (University of Oxford) -

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.

Scholze's Fields medal

When: Wed, September 26, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Michael Rapoport (UMD and University of Bonn) -

Modeling and Simulation of Asteroid-Generated Tsunamis

When: Wed, October 3, 2018 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Marsha Berger (NYU) -
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.

Topics in Markov chains

When: Fri, October 5, 2018 - 11:00am
Where: CSIC 2117

Speaker: Alan Frieze (CMU) -

(Special Applied Math Colloquium, Special time): Atomistic Simulation of Crystalline Defects [A Numerical Analysis Perspective]

When: Tue, October 9, 2018 - 11:00am
Where: Kirwan Hall 3206
Speaker: Christoph Ortner (University of Warwick) -
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.

Faculty Promotion Meeting

When: Wed, October 10, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Department meeting () -

Effective stability in quasi-periodic dynamics.

When: Fri, October 12, 2018 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Bassam Fayad (Universite de Paris) -
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

Faculty Promotion Meeting

When: Wed, October 17, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Department meeting () -

On traffic modeling and the Braess paradox

When: Fri, October 26, 2018 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Helge Holden (NTNU (Norwegian University of Science and Technology)) -

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)

(Special Applied Math Colloquium, Special time): Density fitting: Analysis, algorithm and applications

When: Tue, October 30, 2018 - 11:00am
Where: Kirwan Hall 3206

Speaker: Jianfeng Lu (Duke University) -
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.

Making mathematical videos

When: Wed, November 7, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Jeff Adams (UMD ) -
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.

-Meeting with the Dean Amitabh Varshney

When: Wed, November 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Department meeting () -


When: Wed, December 5, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Otis Chodosh (Princeton University) -