Colloquium Archives for Academic Year 2016

A natural probabilistic model on the integers and its relation to Dickman-type distributions and Buchstab’s function

When: Wed, September 7, 2016 - 3:15am
Where: BPS 1250
Speaker: Ross Pinsky (Department of Mathematics, Technion) -
Abstract: For each natural number N, let p_N denote the nth prime number, and let Omega_N denote the set of positive integers all of whose prime factors are less than or equal to p_N. Let P_N denote the probability measure on Omega_N for which P_N(n) is proportional to n. This measure turns out to have some very useful and interesting properties which are related to the theory of additive arithmetic functions.
After recalling and discussing briefly some seminal results of this theory, such as those of Erdos-Wintner, Kac-Erdos and Hardy-Ramanujan, we will investigate P_N more closely. This will lead us to the Dickman function and "smooth" numbers, which are numbers without large prime factors, and to the Buchstab function and "rough" numbers, which are numbers without small prime factors. These two functions satisfy differential-delay equations. We obtain a new representation of the Buchstab function.

Path integral-based inference of PDEs and bond energies and mobility in Dynamic Force Spectroscopy

When: Fri, September 16, 2016 - 3:15pm
Where: BPS 1250
Speaker: Tom Chou (University of California, Los Angeles) -
Abstract: A Bayesian interpretation is given for regularization terms for parameter functions in inverse problems. Fluctuations about the extremal solution depend on the regularization terms - which encode prior knowledge - provide quantification of uncertainty. After reviewing a general path-integral framework, we discuss an application that arises in molecular biophysics: The inference of bond energies and bond coordinate mobilities from dynamic force spectroscopy experiments.

Prange Prize Lecture: Some Intersections of Art and Science

When: Tue, September 20, 2016 - 4:00pm
Where: 1412 Toll Physics
Speaker: Frank Wilczek (MIT) -

Introduction to rough paths techniques and applications

When: Wed, September 21, 2016 - 3:15pm
Where: BPS 1250
Speaker: Samy Tindel (Purdue University) -
Abstract: The so-called rough paths theory can be seen as a technique which allows to define very general noisy differential systems with a minimum amount of probability structure.
I will first give an introduction and some motivation for this area of research, and also highlight some of the main applications to stochastic differential equations and stochastic partial differential equations. Then I’ll try to explain the main mechanisms behind the rough paths method. I will eventually give some results about noisy differential systems which can be achieved from the rough paths perspective.

Held for department meeting

When: Fri, September 23, 2016 - 3:15pm
Speaker: UMCP Math () -

Held for department meeting

When: Wed, September 28, 2016 - 3:15pm
Speaker: () -

Held for department meeting

When: Fri, October 14, 2016 - 3:15pm
Where: Chem and Bio 0112
Speaker: Hold () -

Held for department meeting

When: Wed, October 19, 2016 - 3:15pm
Speaker: Held for Department Meeting (UMCP) -

Held for department meeting

When: Fri, October 21, 2016 - 3:15pm
Speaker: Held for Department Meeting (UMD) -

Held Department

When: Wed, October 26, 2016 - 3:15pm
Speaker: Held for Department Meeting () -

Held For Department Meeting

When: Mon, November 7, 2016 - 3:15pm
Where: TBA
Speaker: Held for Department Meeting (UMD) -

Held for Dept. Meeting

When: Wed, November 30, 2016 - 3:15pm
Where: TBA
Speaker: Held (UMD) -

Local and Global Harmonic Analysis

When: Fri, December 2, 2016 - 3:15pm
Where: Room 0112 in the Chemistry/Biochemistry Building
Speaker: Steve Zelditch (Northwestern University) -
Abstract: Harmonic analysis is about eigenfunctions of the Laplacian on Riemannian manifolds. It begins with Fourier analysis on Euclidean space or tori and proceeds to other metrics and manifolds. Local Harmonic analysis is about the analysis of eigenfunctions on `small balls' of radius equal to a few hundred wavelengths. Global Harmonic analysis uses the wave equation and geodesic flow. A well-known case is quantum chaos, which studies the effect of ergodicity of the geodesic flow on the structure of eigenfunctions. This talk is about recent results on nodal sets of eigenfunctions obtained by both local and global methods.

Modeling traffic flow on a network of roads (Aziz Lecture)

When: Fri, December 9, 2016 - 3:15pm
Where: CSIC 4122
Speaker: Alberto Bressan (Department of Mathematics, Penn State University) -
Abstract: The talk will present various PDE models of traffic flow on a network of roads. These comprise a set of conservation laws, determining the density of traffic on each road, together with suitable boundary conditions, describing the dynamics at intersections.
While conservation laws determine the evolution of traffic from given initial data, actual traffic patterns are best studied from the point of view of optimal decision problems, where each driver chooses his/her departure time and the route taken to reach destination. Given a cost functional depending on the departure and arrival times, a relevant mathematical problem is to determine (i) global optima, minimizing the sum of all costs to all drivers, and (ii) Nash equilibria, where no driver can lower his own cost by changing departure time or
route to destination.
Several results and open problems will be discussed.

Telegraph process with elastic boundary

When: Wed, January 25, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Shelemyahu Zacks (SUNY Binghamton) -
Abstract: A particle moves on the real line starting at the origin. It moves up for a random length of time at velocity V(t)=1. At that point it moves down at velocity V(t)=-1, for a random
time. This alternately renewal process is a basic Telegraph process. The first time the particle returns to the origin it is absorbed with probability p or reflected up with probability 1-p. If the particle is reflected a new renewal cycle starts.
We develop the distribution of cycle length and its moment. The distribution of the time till absorption and its moments.

A toy model for three-dimensional conformal probability

When: Wed, February 1, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Abdelmalek Abdesselam (University of Virginia) -
Abstract: The use of hierarchical or dyadic toy models is a common theme in analysis. The basic idea is to replace the real line by the leafs of an infinite tree. In harmonic analysis for instance, this can be done by replacing Fourier series with Walsh series. Results such as the Carleson-Hunt Theorem are still nontrivial in the hierarchical (Walsh)
setting but they come in a cleaner form than in the Euclidean (Fourier) setting, thus allowing one to focus
on the essential difficulties. I will present an elementary introduction to a similar hierarchical toy model for the simplest conformal quantum field theory in three dimensions. The latter corresponds to the critical scaling limit of the Ising model with long-range interactions. It has also been the subject of very recent investigations by physicists from the area known as the conformal bootstrap. The most elegant formulation of this toy model is in terms of
p-adic numbers but my talk should be accessible to a wider audience with no prior knowledge of p-adics nor conformal quantum field theory.

Accelerating Multidimensional NMR Spectroscopy by Compressed Sensing of Hypercomplex FTs

When: Fri, February 17, 2017 - 3:15pm
Where: 3206 Kirwan Hall
Speaker: David Donoho (FFT Talk) (Stanford) -
Abstract: Multidimensional NMR (MDNMR) experiments are an important tool in physical chemistry, but can take a long time, in some cases weeks, to conduct. At first glance, the application looks ideal for compressed sensing because the object to be recovered is sparse and the under-sampled measurements are made in the 'Fourier' domain. Actually, MDNMR is not covered by the existing compressed sensing literature. First, the 'Fourier' domain is not the classical one, but involves the so-called hypercomplex Fourier transform. Second, random undersampling is not a really sensible option, because of the structure of the actual experiment. In this talk I will review this background and review recent work with Hatef Monajemi, Jeffrey Hoch and Adam Schuyler, where we find that the now traditional structures -- for example Gaussian phase transitions, which are thought to be universal -- don't accurately describe the sparsity-undersampling relation. We will derive an accurate description with we think novel and interesting structure. Based on joint work with Hatef Monajemi, Jeffrey Hoch and Adam Schuyler.

Tails of Random Projections

When: Wed, March 1, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Kavita Ramanan (Division of Applied Mathematics, Brown University) -
Abstract: The interplay between geometry and probability in high-dimensional spaces is a subject of active research. Classical theorems in probability theory such as the central limit theorem and Cramer’s theorem can be viewed as providing information about certain scalar projections of high-dimensional product measures.   In this talk we will describe the behavior of random projections of more general (possibly non-product) high-dimensional measures, which are of interest in diverse fields, ranging from asymptotic convex geometry to high-dimensional statistics.   Although the study of (typical) projections of high-dimensional measures dates back to Borel, only recently has a theory begun to emerge, which in particular identifies the role of certain geometric assumptions that lead to better behaved projections.   We will review past work on this topic, including a striking central limit theorem for convex sets, and show how it leads naturally to questions on the tail behavior of random projections and large deviations on the Stiefel manifold.   

What is the Role of Applied Mathematics in the Era of Big Data?

When: Fri, March 10, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Chris Jones (UNC) -
Abstract: Data is (are) big these days. The area has taken root in computer science and even statisticians are playing catch-up, despite data being their natural objects of study. Do we, as applied mathematicians, have a place at the table? I will argue that the answer lies in how we place models and observations within the scientific enterprise. The issue is relevant throughout advanced mathematics, from the gateway college courses to the frontiers of research and I will develop a perspective based on thinking about what the proliferation of data means for our teaching as well as our research.


When: Tue, March 14, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Richard Schwartz (Brown University) -

Quiver Hall-Littlewood functions and Kostka-Shoji polynomials

When: Wed, March 29, 2017 - 3:15pm
Where: MTH 0403
Speaker: Daniel Orr (Virginia Tech) -
Abstract: Hall-Littlewood symmetric functions and their transition coefficients
with Schur functions, the Kostka-Foulkes polynomials, have multiple
realizations in representation theory, geometry, and combinatorics.
These realizations reveal deep properties such as the positivity of
the Kostka-Foulkes polynomials.

I will discuss joint work with Mark Shimozono in which we define a
family of Hall-Littlewood functions for any quiver. Our functions form
a basis for a tensor power of symmetric functions over a field with
several parameters, one for each arrow in the quiver. For the Jordan
quiver, with a single vertex and single loop arrow, our functions are
the usual (modified) Hall-Littlewood functions. For a cyclic quiver
with more than one vertex, they are modified versions of functions
defined by Shoji. The general quiver Hall-Littlewood functions are
defined via creation operators and also admit a geometric

We conjecture that the quiver Hall-Littlewood functions are
Schur-positive for arbitrary quivers. In the context of cyclic quivers
we propose an explicit combinatorial formula for the multiparameter
Kostka-Shoji polynomials, which were introduced and studied recently
by Finkelberg and Ionov.

Quantum ergodicity for ray-splitting (branching) billiards

When: Fri, March 31, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Dmitry Jakobson (McGill University ) -
Abstract: After giving an overview of Quantum Ergodicity results on
compact Riemannian manifolds with ergodic geodesic flow (due to
Shnirelman, Zelditch, Colin de Verdiere and others), we discuss joint
work with Yury Safarov and Alex Strohmaier, which concerns the
semiclassical limit of spectral theory on manifolds whose metrics have
jump-like discontinuities. Such systems are quite different from
manifolds with smooth Riemannian metrics because the semiclassical
limit does not relate to a classical flow but rather to branching
(ray-splitting) billiard dynamics. In order to describe this system we
introduce a dynamical system on the space of functions on phase space.
We prove a quantum ergodicity theorem for discontinuous systems. In
order to do this we introduce a new notion of ergodicity for the
ray-splitting dynamics. If time permits, we outline an example
(provided by Y. Colin de Verdiere) of a system where the ergodicity
assumption holds for the discontinuous system.
We end with a list of open problems.

Steady Prandtl theory over a moving plate

When: Wed, April 5, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Yan Guo (Division of Applied Mathematics, Brown University) -
Abstract: Let the Reynolds' number be sufficiently large. Prandtl boundary layer theory connects the Euler theory for ideal inviscid fluids and the Navier-Stokes theory for viscous fluids near a rigid boundary. Consider a steady flow over a moving boundary. We review recent work to prove the validity of Prandtl layer theory, which states that a Navier-Stokes flow can be approximated by an Euler flow and a Prandtl layer flow.

Sit Up and Take Note: European Mathematicians in 1920s America

When: Fri, April 7, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Karen Parshall (UVA) -
Abstract: American mathematics was experiencing growing pains in the 1920s. It had looked to Europe at least since the 1890s when many Americans had gone abroad to pursue their advanced mathematical studies. It was anxious to assert itself on the international---that is, at least at this moment in time, European---mathematical scene. How, though, could the Americans change the European perception from one of apprentice/master to one of mathematical equals? How could Europe, especially Germany but to a lesser extent France, Italy, England, and elsewhere, come fully to sense the development of the mathematical United States? If such changes could be effected at all, they would likely involve American and European mathematicians in active dialogue, working shoulder to shoulder in Europe and in the United States, and publishing side by side in journals on both sides of the Atlantic. This talk will explore one side of this “equation”: European mathematicians and their experiences in the United States in the 1920s.

Held for Department

When: Wed, April 19, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Held (UMD) -

A discrete analog of the Novikov-Veselov hierarchy and its applications

When: Wed, April 26, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Igor Krichever (Columbia) -
Abstract: Spectral theory of the 2D Schrodinger operator on one energy level pioneered by Novikov and Veselov developed over the years is still full of open problems. In the talk I will present recent progress in this area and its application to a wide range of problems, including characterization of Prym varieties in algebraic geometry and the solution of a
sigma SO(N) model in mathematical physics.

Mathematics for art investigation (Kirwan Undergraduate Lecture)

When: Thu, April 27, 2017 - 4:00pm
Where: MTH 3206
Speaker: Indrid Daubechies (Duke University) -
Abstract: Mathematical tools for image analysis increasingly play a role in helping art
historians and art conservators assess the state of conservation of paintings,
and probe into the secrets of their history. The talk will review several case
studies, Van Gogh, Gauguin, Van Eyck among others.

Surfing Wavelets

When: Fri, April 28, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Indrid Daubechies (Duke) -
Abstract: Wavelets provide a mathematical tool that emerged in the 1980s from a synthesis of ideas in mathematics, physics, computer science and engineering. They are now used in a wide range of mathematical applications, and provide a mathematical way to "zoom in" on details, without losing track of the large picture. The talk will describe some of the essential features of the approach, and illustrate with examples.