Where: BPS 1250

Speaker: Ross Pinsky (Department of Mathematics, Technion) - http://www2.math.technion.ac.il/~pinsky/

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.

Where: BPS 1250

Speaker: Tom Chou (University of California, Los Angeles) - http://faculty.biomath.ucla.edu/tchou/

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.

Where: 1412 Toll Physics

Speaker: Frank Wilczek (MIT) - http://web.mit.edu/physics/people/faculty/wilczek_frank.html

Abstract: http://umdphysics.umd.edu/events/physicscolloquia.html#some-intersections-of-art-and-science

Where: BPS 1250

Speaker: Samy Tindel (Purdue University) - https://www.math.purdue.edu/%7Estindel/

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.

Where:

Speaker: UMCP Math () -

Where:

Speaker: () -

Where: Chem and Bio 0112

Speaker: Hold () - https://www-math.umd.edu/

Where:

Speaker: Held for Department Meeting (UMCP) - https://www-math.umd.edu/

Where:

Speaker: Held for Department Meeting (UMD) - https://www-math.umd.edu/

Where:

Speaker: Held for Department Meeting () - https://www-math.umd.edu/

Where: TBA

Speaker: Held for Department Meeting (UMD) -

Where: TBA

Speaker: Held (UMD) -

Where: Room 0112 in the Chemistry/Biochemistry Building

Speaker: Steve Zelditch (Northwestern University) - http://www.math.northwestern.edu/~zelditch/

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.

Where: CSIC 4122

Speaker: Alberto Bressan (Department of Mathematics, Penn State University) -

https://www.math.psu.edu/bressan/

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.

Where: Kirwan Hall 3206

Speaker: Shelemyahu Zacks (SUNY Binghamton) - http://www.math.binghamton.edu/shelly/

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.

Where: Kirwan Hall 3206

Speaker: Abdelmalek Abdesselam (University of Virginia) - http://people.virginia.edu/~aa4cr/

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.

Where: 3206 Kirwan Hall

Speaker: David Donoho (FFT Talk) (Stanford) - http://statweb.stanford.edu/~donoho/

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.

Where: Kirwan Hall 3206

Speaker: Kavita Ramanan (Division of Applied Mathematics, Brown University) - https://www.brown.edu/academics/applied-mathematics/kavita-ramanan

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.

Where: Kirwan Hall 3206

Speaker: Chris Jones (UNC) - http://www.unc.edu/math/Faculty/jones/

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.

Where: Kirwan Hall 3206

Speaker: Richard Schwartz (Brown University) - http://www.math.brown.edu/~res/

Where: MTH 0403

Speaker: Daniel Orr (Virginia Tech) - https://www.math.vt.edu/people/dorr/

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

interpretation.

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.

Where: Kirwan Hall 3206

Speaker: Dmitry Jakobson (McGill University ) - http://www.math.mcgill.ca/jakobson/

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.

Where: Kirwan Hall 3206

Speaker: Yan Guo (Division of Applied Mathematics, Brown University) - https://www.brown.edu/academics/applied-mathematics/yan-guo

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.

Where: Kirwan Hall 3206

Speaker: Karen Parshall (UVA) - http://people.virginia.edu/~khp3k/home.htm

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.

Where: Kirwan Hall 3206

Speaker: Held (UMD) -

Where: Kirwan Hall 3206

Speaker: Igor Krichever (Columbia) - http://www.math.columbia.edu/~krichev/

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.

Where: MTH 3206

Speaker: Indrid Daubechies (Duke University) - https://math.duke.edu/people/ingrid-daubechies

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.

https://www-math.umd.edu/research/kirwan-undergraduate-lectures.html

Where: Kirwan Hall 3206

Speaker: Indrid Daubechies (Duke) - https://math.duke.edu/people/ingrid-daubechies

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.