Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium

Department Colloquium - Amie Wilkinson (University of Chicago)

Amie Wilkinson, University of Chicago

Friday, April 6th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Amie Wilkinson, University of Chicago

Title: Robust Mechanisms for Chaos

Abstract: What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics? In addressing this question, I will focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I will describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.

Amie Wilkinson (University of Chicago): Prof. Amie Wilkinson received her BA from Harvard and her Ph.D. from the University of California at Berkeley. After a post-doc at Harvard, she became a professor at North­ western University, where she stayed 13 years, before moving to the University of Chicago in 2012. Prof. Wilkinson is a leading researcher in ergodic theory and dynamical sys­ tems. Among other recognitions of her many achievements, she was an invited speaker at the International Congress of Mathematicians in 2010, was awarded the Satter Prize in Mathematics in 2011, and was elected a fellow of the AMS in 2014. Prof. Wilkinson has also been very active in public outreach, giving numerous public lectures, interviews, and recently publishing an article in the New York Times.

Fields Lecture Series - Amie Wilkinson (University of Chicago)

Amie Wilkinson, University of Chicago

Thursday, April 5th, 2018

Time: 5:30 p.m.  Place: Jeffery Hall 127

Speaker: Amie Wilkinson, University of Chicago

Title: The Mathematics of Deja Vu

Abstract: Dynamics is an area of mathematics concerned with the motion of spaces (" dynamical systems") over time. Dynamics has its roots in the late nineteenth century, when it was developed as a tool to understand physical phenomena, such as the motion of gas molecules in a box and planets around the sun. A simple and yet powerful concept in dynamics is that of recurrence. In everyday language, recurrence is the mathematical version of deja vu: a motion of a space is recurrent if, given enough time, it eventually returns to its original configuration (allowing for a small amount of error). In this talk, I will describe how mathematical results about recurrence can be used to answer surprisingly disparate questions, from the mixing and unmixing of two ideaI gases in a box, to deep properties of the prime numbers, to the discovery of exoplanets in nearby solar systems.

Amie Wilkinson (University of Chicago): Prof Wilkinson (University of Chicago) is a leading researcher in ergodic theory and dynamical systems. Among other recognitions of her many achievements, she was an invited speaker at the International Congress of Mathematicians in 2010, was awarded the Satter Prize in Mathematics in 2011, and was elected a fellow of the AMS in 2014. Prof Wilkinson has also been very active in public outreach, giving numerous public lectures, interviews, and recently publishing an article in the New York Times.

Department Colloquium - Mihai Nica (University of Toronto)

Mihai Nica, University of Toronto

Friday, March 23rd, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Mihai Nica, University of Toronto

Title: Phase transitions in random matrices and the spiked tensor model

Abstract: Given a matrix of noisy data, principal component analysis (PCA) can be viewed as "de-noising" technique that recovers the closest rank-one approximation. In certain matrix models, it is known that this procedure exhibits a phase transition: if the signal-to-noise ratio is below a critical value then PCA returns uninformative information. In this talk, we also consider a generalization of this problem to k-tensors (the matrix case corresponds to k=2). By studying the energy landscape of this model, we also find phase transitions akin to the matrix case. The proof of the results uses the Kac-Rice formula for the expected number of critical points of a random function and results about spiked random matrices. Based on joint work with Gerard Ben Arous, Song Mei and Andrea Montanari.

Department Colloquium - Laura DeMarco (Northwestern University)

Laura DeMarco, Northwestern University

Friday, March 2nd, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Laura DeMarco, Northwestern University

Title: Complex dynamics and arithmetic equidistribution

Abstract: About 5 years ago, Matt Baker and I formulated a conjecture about the dynamics of rational maps on P1, connecting geometry and arithmetic in the moduli space of such maps. My goal is to present recent progress on the conjecture, illustrating some of the main ideas appearing in proofs of special cases. One important special case includes a result about torsion points on elliptic curves, and I hope to discuss how this case can be related to dynamical stability and the Mandelbrot set.

Laura DeMarco (Northwestern University): Laura DeMarco received her Ph.D in Mathematics from Harvard University in 2002 under the supervision of Curtis McMullen. From 2002 to 2007, she was at he University of Chicago (as L.E. Dickinson Instructor from 2002 to 2005, and Assistant Professor from 2005 to 2007). From 2007 to 2014 she was at the University of Illinois at Chicago (as Assistant Professor from 2007 to 2009, Associate Professor from 2009 to 2012, and Professor from 2012 to 2014). In 2014, Prof DeMarco joined Northwestern University. Her awards include the NSF Postdoctoral Fellowship at the University of Chicago (2003-2006), the Sloan Foundation Research Fellowship (2008-2010), the NSF Career Award (2008-2013), the Simons Foundation Fellowship (2015-2016), and the Ruth LyttleSatter Prize (2017). In 2012, she became Fellow of the American Mathematical Society. Laura DeMarco is an Invited Speaker at the International Congress of Mathematicians in Rio de Janeiro in 2018. Her research interest include dynamical systems, complex analysis, and arithmetic geometry. She mainly focuses on the dynamics of rational maps on P1 and their moduli spaces.

Department Colloquium - Catherine Pfaff (UC-Santa Barbara)


Catherine Pfaff, UC-Santa Barbara

Friday, February 16th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Catherine Pfaff, University of California-Santa Barbara

Title: A Nielsen-Thurston Inspired Story of Iterating Free Group Automorphisms and Efficiently Deforming Graphs

Abstract: While many fundamental contributions to the study of outer automorphisms of free groups date back to the early 20th century, the real explosion of activity in the eld came with two much more recent developments: the denition by Culler and Vogtmann of the deformation space of metric graphs on a surface, namely Outer Space, and the development by Bestvina, Feighn, and Handel of a train track theory for outer automorphisms of free groups. The explosion was a result of a new ability to study free group outer automorphisms using generalizations of techniques developed to study surface homeomorphisms (mapping classes) via their action on the deformation space of metrics on the surface (Teichmuller space). In our talk, we focus specically on a Nielsen-Thurston inspired story jointly studying: 1) outer automorphism conjugacy class invariants obtained by iteratively applying the automorphisms and 2) geodesics in Culler-Vogtmann Outer Space.

Catherine Pfaff, (University of California-Santa Barbara): Catherine Pfa obtained her Ph.D. in Mathematics from Rutgers University in 2012 under the supervision of Lee Mosher. Dr. Pfa was Postdoctoral Research Fellow at the Universite d'Aix-Marseille (2013-2014) and at the Universitat Bielefeld (2014-2015). Since 2015, she is Ky Fan Visiting Assistant Professor at the University of California, Santa Barbara. Catherine Pfa's research focuses on geometric group theory and geometric topology. In particular, she studies the outer automorphism group of the free group and Outer Space from a mapping class group perspective.

Department Colloquium - Qiang Zeng (Northwestern University)

Qiang Zeng, Northwestern University

Wednesday, February 14th, 2018

Time: 3:30 p.m.  Place: Jeffery Hall 234

Speaker: Qiang Zeng, Northwestern University

Title: Replica Symmetry Breaking for Mean Field Spin Glass Models

Abstract: In statistical physics, the study of spin glasses was initialized to describe the low temperature state of a class of magnetic alloys in the 1960s. Since then spin glasses have become a paradigm for highly complex disordered systems. Mean eld spin glass models were introduced as an approximation of the physical short range models in the 1970s. The typical mean eld models include the Sherrington- Kirkpatrick (SK) model, the (Ising) mix p-spin model and the spherical mixed p-spin model. Starting in 1979, the physicist Giorgio Parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking (RSB), which allowed him to predict a solution for the SK model by breaking the symmetry of replicas innitely many times at low temperature. This is known as full-step replica symmetry breaking (FRSB). In this talk, we will show that Parisi's FRSB prediction holds at zero temperature for the more general mixed p-spin model. As a consequence, at positive temperature the level of RSB will diverge as the temperature goes to zero. On the other hand, we will show that there exist two-step RSB spherical mixed spin glass models at zero temperature, which are the rst examples beyond the replica symmetric, one-step RSB and FRSB phases. This talk is based on joint works with Antonio Aunger (Northwestern University) and Wei-Kuo Chen (University of Minnesota).

Qiang Zeng (Northwestern University): Qiang Zeng obtained his Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign in 2014 under the supervision of Marius Junge and Renming Song. From 2014 to 2015 he was a Postdoctoral Fellow at Harvard University. In 2015, Dr. Song was a Postdoctoral Fellow at the Mathematical Sciences Research Institute in Berkeley, California. Since 2016, he is Boas Assistant Professor at Northwestern University in Evanston, Illinois. Qiang Zeng works at the interfaces of probability, functional analysis and mathematical physics. His main topic of study is noncommutative probability and spin glasses.

Department Colloquium - Brad Rodgers (University of Michigan)

Brad Rodgers, University of Michigan

Monday, February 12th, 2018

Time: 4:30 p.m.  Place: Jeffery Hall 234

Speaker: Brad Rodgers, University of Michigan

Title: Some Applications of Random Matrix Theory to Analytic Number Theory

Abstract: In this talk I'll survey some of the ways that ideas originating from the study of random matrices have had an impact on analytic number theory. I hope to discuss in particular: 1) the statistical spacing of zeros of the Riemann zeta function, and what this spacing has to say about arithmetic, 2) a resolution of conjectures of Saari and Montgomery about the distribution of Rudin-Shapiro polynomials, using a connection to random walks on compact groups, and 3) recent work on the de Bruijn-Newman constant; de Bruijn showed that the Riemann hypothesis is equivalent to the claim that this constant is less than or equal to 0, and I will describe recent work showing the constant is greater than or equal to 0, conrming a conjecture of Newman. This includes joint work with J. Keating, E. Roditty-Gershon, and Z. Rudnick; and with T. Tao.

Brad Rodgers (University of Michigan): Brad Rodgers obtained his Ph.D. in Mathematics from the University of California, Los Angeles in 2013 under the supervision of Terence Tao. From 2013 to 2015 he held a postdoctoral position at the Institut fur Mathematik at the Universitat Zurich. Since 2015, he is a Postdoc Assistant Professor at the University of Michigan. Dr. Rodgers's awards include the AMS-Simons Travel Grant (2013-2016) and a NSF research grant (2017-2020). His research interests include random matrix theory, analytic number theory. In particular, he focuses on the interaction of these disciplines with analysis, probability, and combinatorics.

Department Colloquium - Daniel Le (University of Toronto)

Daniel Le, University of Toronto

Friday, February 9th, 2018

Time: 3:30 p.m.  Place: Jeffery Hall 234

Speaker: Daniel Le, University of Toronto

Title: The geometry of Galois representations

Abstract: The arithmetic of number fields can be profitably studied through the representation theory of their absolute Galois groups. These representations exhibit a number of elegant and surprising phenomena, most famously the quadratic reciprocity law. Many of these phenomena are explained by the modularity conjecture of Langlands that all Galois representations come from modular forms. Startling progress towards this conjecture began with Taylor and Wiles's study of Galois deformation spaces. We give a construction of local models for some Galois deformation spaces coming from geometric representation theory, and describe some applications to modularity conjectures and congruences between modular forms. Much of what we discuss is joint work with Bao Le Hung, Brandon Levin, and Stefano Morra.

Department Colloquium - Jory Griffin (Queen’s University)

Jory Griffin

Friday, February 2nd, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Jory Griffin, Queen’s University

Title: The Lorentz Gas – Macroscopic Transport from Microscopic Dynamics

Abstract: The Lorentz Gas is microscopic model for conductivity in which a point particle representing an electron moves through an infinite array of scatterers representing the background medium. On the macroscopic scale the dynamics can instead be modelled by the linear Boltzmann transport equation, an irreversible equation where motion of particles appears to be stochastic. How can these two pictures be reconciled? Can we 'derive' the macroscopic picture from the microscopic one? I will talk about the solution to this problem as well as its quantum mechanical analogue where much less is currently known.

Jory Griffin (Queen's University): Jory Griffin received his Ph.D. in Mathematics from the University of Bristol in 2017 under the supervision of Jens Marklof. He recently joined the Department of Mathematics and Statistics at Queen's University as a Coleman Postdoctoral Fellow. Dr. Grin's research focuses on Mathematical Physics, specifically in the quantum propagation of wave packets in the presence of scatterers.

Department Colloquium - Milian Derpich (USM, Valparaiso, Chile)

Milan Derpich

Friday, January 26th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Milian Derpich, Universidad Técnica Federico Santa Maria, Valparaiso, Chile

Title: The Differential Entropy Gain Created by Linear Time-Invariant Systems

Abstract: The differential entropy of a continuous-valued random variable quantifies the uncertainty associated with the latter, and plays a crucial role in many fundamental result of Information Theory. This talk will discuss how the differential entropy rate of a random process exciting a discrete-time linear time invariant (LTI) system relates to that of the random process coming out of it. First, an apparent contradiction between existing results characterizing the difference between these two differential entropy rates, referred to a 'differential entropy gain', will be exposed. It will then be shown how and when these results can be reconciled, presenting a geometric interpretation as well as novel results which quantify the differential entropy gain introduced by LTI systems. Finally, some of the implications of these results will be illustrated for three different problems, namely: the rate-distortion function for non stationary processes, an inequality in networked control systems, and the capacity of stationary Gaussian channels.

Milan S. Derpich (Universidad Tecnica Federico Santa Maria, Valparaiso, Chile): Milan S. Derpich received the 'Ingeniero Civil Electronico' degree from Federico Santa Maria Technical University, in Valparaso, Chile in 1999. Dr. He then worked by the electronic circuit design and manufacturing company Protonic Chile S.A. between 2000 and 2004. In 2009 he received the PhD degree in electrical engineering from the University of Newcastle, Australia. He received the Guan Zhao-Zhi Award at the Chinese Control Conference 2006, and the Research Higher Degrees Award from the Faculty of Engineering and Built Environment, University of Newcastle, Australia, for his PhD thesis. Since 2009 he has been with the Department of Electronic Engineering at UTFSM, currently as associate professor. His main research interests include rate-distortion theory, networked control systems, and signal processing. He has just started a sabbatical one-year visit to the Department of Mathematics and Statistics in Queen's University, Canada, as a visiting professor.

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