### Colloquium Archives for Academic Year 2020

#### Department Back to School & Tea

When: Fri, September 6, 2019 - 3:15pm
Where:

#### Faculty Meeting

When: Wed, September 11, 2019 - 3:30pm
Where:

#### Commutative harmonic analysis on noncommutative Lie groups(part of Conference in honor of John Benedetto)

When: Fri, September 20, 2019 - 4:30pm
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.

#### What's new with Mathematica and Wolfram|Alpha

When: Wed, September 25, 2019 - 3:15pm
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.

#### 2nd Annual Google Tech Talk

When: Wed, September 25, 2019 - 5:30pm
Where:
Speaker: Britt Hedenberg
University Programs Specialist

#### STAT Sem. Quantile Regression for Spectral Analysis of Time Series

When: Wed, October 2, 2019 - 3:15pm
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.

#### "Noether, Falconer, Mirzakhani, Kovalesky, and Me”

When: Thu, October 10, 2019 - 3:30pm
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.

#### Validity of Steady Prandtl Expansion

When: Wed, October 16, 2019 - 3:15pm
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.

#### Celestial surfaces

When: Wed, October 30, 2019 - 3:15pm
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.

#### Fluid-boundary interactions: transport, stratification and confinement effects

When: Fri, November 8, 2019 - 3:15pm
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.

#### WIM Alumni Series with Dr. Carolina Franco

When: Thu, November 14, 2019 - 2:00pm
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.

#### TBA

When: Fri, November 15, 2019 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Anthony Romano (US Naval Research Lab, DC) -

#### Discretizing Manifolds with Minimal Energy

When: Wed, November 20, 2019 - 3:15pm
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.

#### On the Hitchin fibration (first talk, Distriguished Lectures in Algebra and Number Theory)

When: Wed, December 4, 2019 - 3:15pm
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.

#### Length and volume in four-dimensional symplectic geometry

When: Fri, December 6, 2019 - 3:15pm
Where: Kirwan Hall 3206

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

Abstract:
Symplectic capacities are measurements of symplectic size. They are often defined as the lengths of certain periodic trajectories of dynamical systems, and so they connect symplectic embedding problems with dynamics. My talk will be about a certain family of symplectic capacities, called "ECH capacities". I will explain what ECH capacities are, and why they are useful for studying four-dimensional symplectic embedding problems. Then, I will explain a "volume formula", which recovers the volume of many symplectic 4-manifolds from the asymptotics of its ECH capacities. Finally, I will briefly discuss how to use this formula to obtain several dynamical results about surface diffeomorphisms and three-dimensional Reeb flows.

#### (Special Colloquium) (3/2)^n, linear cellular automata, and Apery-like sequences

When: Thu, December 12, 2019 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Hillel Furstenberg (Hebrew University, Israel) -
Abstract: Abstract: The sequence of integers { [(3/2)^n]} play a role in Waring's problem. This gave rise to the question of what can be said about the fractional parts of the sequence, or, for that matter, for the sequence {r^n mod 1} for any rational r > 1. This can be translated to the behavior of special orbits in a cellular automaton, and determining the entropy of the orbit closure. These questions can be answered for ""linear cellular automata" over a finite field. Over the reals similar considerations lead to "Apery-like sequences" which played a role in the proof of the irrationality of \zeta(3).

#### Some Applications of Statistics in Physics: quantized light, scattering, and tomography

When: Wed, February 12, 2020 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Zachary H. Levine (NIST) -
Abstract:
1. Intro. Physics and statistics (a) where theory and experiment meet, (b) divergent world views, (c) underlying probabilistic nature of the world: Bell's theorem and random number generation.
2. The calibration of a few photon detector. (a) What is a Transition Edge Sensor? What needs to be calibrated? (b) The K-means algorithm as maximum likelihood. (c) Adaptation of the K-means algorithm to Poisson statistics: a new maximum likelihood objective function: PIKA. (d) Application of PIKA to calibration of an attenuator at near-ideal quantum efficiency.
3. Monte Carlo and importance sampling: a rapid algorithm to determine scattering parameters for an optical medical phantom.
4. Tomography: (a) early application of a Bayesian method to integrated circuit interconnect tomography, (b) scattering, Monte Carlo and tomography: algorithmic developments - the moving expanding window and a hybrid standard and Forced-Fixed Detection Monte Carlo, (c) quantifying the uncertainty of the Response Evaluation Criteria in Solid Tumors (RECIST).

#### Why Leadership: Its Appeal & Challenges- Women in Math Alumni Series

When: Thu, February 20, 2020 - 4:00pm
Where: Kirwan Hall 1311

Speaker: Amanda Galante (Johns Hopkins University Applied Physics Laboratory)
Abstract: Dr. Amanda Galante graduated in 2012 from the Applied Mathematics, Statistics, and Scientific Computation Ph.D. program at UMD-College Park as an advisee of Dr. Doron Levy. She is currently working at the Johns Hopkins University Applied Physics Laboratory. She will give a talk center on her life at APL and her journey both pre and post-graduation, followed by a Q&A session.

#### Prismatic cohomology and applications (Note: Special time)

When: Wed, February 26, 2020 - 3:00pm
Where: Kirwan Hall 3206

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

Abstract: Prismatic cohomology is a cohomology theory in p-adic geometry that was developed recently (in joint works with Morrow and Scholze). I'll give a high level overview of what this theory was designed to accomplish, and spend the rest of talk explaining a few concrete applications (to questions in algebraic geometry, commutative algebra, and, time permitting, algebraic topology).

#### Artistic mathematics: truth and beauty

When: Wed, March 4, 2020 - 3:15pm
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.

#### Algorithmic solutions to Diophantine problems

When: Wed, March 11, 2020 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Brian Lawrence (University of Chicago) - http://math.uchicago.edu/~brianrl/

Abstract: A basic problem in number theory is to find all integer (or rational) solutions to a system of polynomial equations. This class of problem, known as Diophantine problems, includes many questions of traditional interest. In 1900, Hilbert asked whether there is a general algorithm to solve all such problems; work of Matiyasevich and others shows that such an algorithm does not exist. The prospects are much better when the system has only one degree of freedom -- the solution set is a curve. In 1983, Faltings proved Mordell's conjecture, showing that a curve of genus at least 2 has only finitely many rational points. Since then, significant progress has been made toward a general algorithm. I will give an overview of the subject, including recent developments.

#### Solving inverse problems with machine learning (Aziz Lecture)

When: Wed, April 1, 2020 - 3:15pm
Where: Kirwan Hall 3206

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

Abstract: This talk is about some recent progress on solving inverse problems using deep learning. Compared to traditional machine learning problems, inverse problems are often limited by the size of the training data set. We show how to overcome this issue by incorporating mathematical analysis and physics into the design of neural network architectures. We first describe neural network representations of pseudodifferential operators and Fourier integral operators. We then continue to discuss applications including electric impedance tomography, optical tomography, inverse acoustic/EM scattering, seismic imaging, and travel-time tomography.

#### TBA

When: Wed, April 8, 2020 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Tim Healey (Cornell University) - https://math.cornell.edu/timothy-j-healey

#### TBA

When: Thu, April 16, 2020 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Spring Dynamics Conference (TBA) -

#### Taming Infinities (Aziz Lecture)

When: Wed, April 22, 2020 - 3:15pm
Where: Kirwan Hall 3206

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

Abstract: Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! What's worse, this doesn't just happen for some exotic theories, but in the standard theories describing some of the most fundamental aspects of nature. Various techniques, usually going under the common name of “renormalisation” have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will tip our toes into some of the conceptual and mathematical aspects of these techniques and we will see how they have recently been used in probability theory to study equations whose meaning was not even clear until now.

#### TBA (Moved to later semester)

When: Wed, May 6, 2020 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Paolo Aluffi (Florida State University) - https://www.math.fsu.edu/~aluffi/