Where:

Where:

Where: Kirwan Hall 3206

Speaker: Fulvio Ricci (Scuola Normale Superiore, Pisa) -

In harmonic analysis on noncommutative groups one often encounters subalgebras of $L^1$, characterized by appropriate invariance properties of its elements, which are commutative. For such an algebra $A$, the Gelfand theory, called "spherical" in this context, can present various degrees of similarity with Fourier analysis on abelian groups, depending on the nature of the involved groups.

In the context of Lie groups with polynomial volume growth, investigation on numerous examples has shown that the spherical transform maps Schwartz functions in $A$ bijectively to Schwartz functions on the Gelfand spectrum, appropriately embedded into some $\mathbb{R}^n$ space.

The open question is how general this property is. In this talk we give a short account of the state of the art on this problem.

Where: Kirwan Hall 3206

Speaker: Andrew Dorsett (Wolfram Research, Inc) -

Abstract: This will be a lecture/demonstration on the latest developments

in Mathematica and Wolfram|Alpha, and how they can be of use to

mathematicians.

Where:

Speaker: Britt Hedenberg

University Programs Specialist

careers.google.com/students

Where: Kirwan Hall 3206

Speaker: Ta-Hsin Li (IBM T. J. Watson Research Center) - http://www.research.ibm.com/people/t/thl

Abstract:

Quantile regression is a powerful tool that extends the capability of the traditional least-squares

apparatus by focusing on the behavior of the data at different quantiles instead of the mean. This talk gives an overview of some recent advances in quantile regression for spectral analysis of time-series data. In particular, it discusses a new type of periodogram, called the quantile periodogram, which is constructed from quantile regression with harmonic (trigonometric) regressors; it explains the theoretical underpinning of the quantile periodogram in relation with the spectrum of level-crossing processes, it demonstrates, with both simulated and real data, the capability of the quantile periodogram in offering a richer view than the one provided by the ordinary periodogram; and finally, it discusses possible extentions of the methodology.

Where: Kirwan Hall 3206

Speaker: Shelby Wilson (Department of Biology, UMD) - http://biology.umd.edu/shelby-wilson.html

Abstract: My mathematical journey has been shaped and molded by some incredible women in the mathematical sciences. This begins with my grandmother, mathematician and educator, Etta Falconer, and continues with a network of women who I have grown to admire greatly. In this talk, I will highlight my journey to becoming a “Mathematical Biologist” and the women (and men) who helped me get here. I will discuss how my childhood love of mathematics came together with my interest in medicine to create a career path that I am passionate about.

Where: Kirwan Hall 3206

Speaker: Yan Guo (Brown University) - http://www.cfm.brown.edu/people/guoy/home.html

Abstract: Abstract: In a joint work with Sameer Iyer, the validity of steady Prandtl layer expansion is established in a channel. Our result covers the celebrated Blasius boundary layer profile, which is based on uniform quotient estimates for the derivative Navier-Stokes equations, as well as a positivity estimate at the flow entrance.

Where: Kirwan Hall 3206

Speaker: Janos Kollar (Princeton University) - https://web.math.princeton.edu/~kollar/

Abstract. We outline the recent completion of a program, started by Kummer

and Darboux, to describe all surfaces that contain at least 2 circles

through every point.

Where: Kirwan Hall 3206

Speaker: Roberto Camassa (University of North Caroline at Chapel Hill) - https://amath.unc.edu/?people=roberto-camassa

Abstract: Arguably some the most interesting phenomena in fluid dynamics, both from a mathematical and a physical perspective, come from the interplay between a fluid and the boundary of its domain. This talk will present recent analytical, numerical and experimental results that illustrate boundary effects in various setups. For an ideal Euler fluid under gravity, smooth contact of material surfaces with horizontal boundaries may persist until loss of regularity occurs. For fluids with a diluted passive or an active scalar, diffusion in the presence of impermeable boundaries further adds to the complexity of the dynamics. In the passive case, such as that of a neutrally buoyant chemical solute transported by the flow in a duct or pipe, the interplay with the cross sectional geometry of the pipe can shape the solute distribution downstream from a release location. In the active case, e.g., when a diluted scalar alters the local density of a fluid under gravity, boundary orientation with respect to gravity can lead to hydrostatic imbalances, which can give rise to self-induced flows with remarkable consequences.

Where: Kirwan Hall 3206

Speaker: Carolina Franco (U.S. Census Bureau) -

Abstract: Dr. Franco received her PhD in Applied Mathematics at the University of Maryland under the advisement of Dr. Abram Kagan. Her thesis focused primarily on the asymptotic properties of semi-parametric estimators. She is now working as a Research Mathematical Statistician at the Center for Statistical Research and Methodology (CSRM) at the U.S. Census Bureau where she works on small area estimation and sampling. Her talk will include an overview of her academic and professional journey, as well as time for Q&A.

Where: Kirwan Hall 3206

Speaker: Anthony Romano (US Naval Research Lab, DC) -

Where: Kirwan Hall 3206

Speaker: Ed Saff (Vanderbilt University) - https://my.vanderbilt.edu/edsaff/

Abstract: Minimal discrete energy problems arise in a variety of scientific contexts---such as crystallography, nanotechnology, information theory, and viral morphology, to name but a few. Our goal is to analyze the structure of configurations generated by optimal (and near optimal) N-point configurations that minimize the Riesz s-energy over a bounded surface in Euclidean space. The Riesz s-energy potential is simply given by 1/r^s, where r denotes the distance between a pair of points; it is a generalization of the familiar Coulomb potential. We show how such potentials and their minimizing point configurations are ideal for use in sampling surfaces (and even generating a "near perfect" poppy-seed bagel). Connections to the recent breakthrough results by M. Viazovska et al on best-packing and universal optimality in 8 and 24 dimensions will be discussed.

Where: Kirwan Hall 3206

Speaker: Bao-Chau Ngo (University of Chicago) - https://www.math.uchicago.edu/~ngo/

Abstract (for all three talks): Simpson's non-Abelian Hodge theory stipulates a diffeomorphism between the moduli space of flat connections on a smooth projective variety and the moduli space of semi-stable Higgs bundles with trivial Chern classes. The main feature of the moduli space of Higgs bundles is the Hitchin map calculating the characteristic polynomial of the Higgs field. Over a curve, the structure of the Hitchin map is fairly well understood as an abelian fibration with degeneration. When the base field is a finite field, counting points on the Hitchin fibration allows us to connect the geometry of the Hitchin fibration with orbital integrals and the trace formula. This interplay between geometry and harmonic analysis has been very fruitful for understanding both sides of the story, and in particular, it gave rise to a proof for the fundamental lemma. I will give an account of this interplay in my first lecture.

In the second lecture, I want to discuss the theory of non-archimedean integration on the Hitchin fibration due to Groechenig, Wyss and Ziegler. Surprisingly, calculating nonarchimedean integrals is not exactly the same as counting points and this approach gives another proof of the fundamental lemma, and this discrepancy sheds yet new lights on the theory of endoscopy. The proof is also more elementary in the sense that it does not use the theory of perverse sheaves.

In my third lecture, I want to report on a completely different development on the moduli space of Higgs bundles. In joint work with T.H. Chen we started exploring the structure of the Hitchin map for the moduli space of Higgs bundles over higher-dimensional varieties, which raises interesting questions on the geometry of commuting varieties.

Where: Kirwan Hall 3206

Speaker: Daniel Cristofaro-Gardiner (UCSC) - https://dancg.sites.ucsc.edu/

Where: Kirwan Hall 3206

Speaker: Bhargav Bhatt (University of Michigan, Ann Arbor) - http://www-personal.umich.edu/~bhattb/

Where: Kirwan Hall 3206

Speaker: Henry Segerman (Oklahoma State University) - https://math.okstate.edu/people/segerman/

Abstract: I'll talk about my work in mathematical visualization:

making accurate, effective, and beautiful pictures, models, and

experiences of mathematical concepts. I'll discuss what it is that

makes a visualization compelling, and show many examples in the medium

of 3D printing, as well as some work in virtual reality and spherical

video. I'll also discuss my experiences in teaching a project-based

class on 3D printing for mathematics students.

Where: Kirwan Hall 3206

Speaker: Lexing Ying (Stanford University) - https://web.stanford.edu/~lexing/

Where: Kirwan Hall 3206

Speaker: Spring Dynamics Conference (TBA) -

Where: Kirwan Hall 3206

Speaker: Martin Hairer (Imperial College, London, UK) - https://www.imperial.ac.uk/people/m.hairer