The AWM Distinguished Colloquium series is being established in Spring 2021 in celebration of the 50th anniversary of the founding of the Association for Women in Mathematics. The series will comprise three colloquium talks this spring and will continue thereafter with one colloquium per semester.

## Spring 2023

**Speaker:** Anna Wienhard (Maz Planck Institute)**When:** Wednesday, March 15 2023 at 3:15 p.m.**Where:** Kirwan Hall 3206**Abstract:** Hight Rank Teichmüller Spaces

Classical Teichmüller space describes the space of conformal structures on a given topological surface. It plays an important role in several areas of mathematics as well as in theoretical physics. Due to the uniformization theorem, Teichmüller space can be realized as the space of hyperbolic structures, and is closely related to discrete and faithful representations of the fundamental group of the surface into PSL(2,R), the group of isometries of the hyperbolic plane. Higher rank Teichmüller spaces generalize many aspects of this classical theory when PSL(2,R) is replaced by other Lie groups of higher rank, for example the symplectic group PSp(2n, R) or the special linear group PSL(n, R). In this talk I will give an introduction to higher rank Teichmüller spaces and their properties. I will also highlight connections to other areas in geometry, dynamics and algebra.

#### About the Speaker

Anna Wienhard is the Direcot of the Max Planck Institute for Mathematics in Leipzig and currently a member of the Institute for Advanced Study in Princeton. She earned her Ph.D. from the Rheinische Friedrich-Wilhelms University of Bonn in 2004 and has since held positions at the University of Basel, the University of Chicago, Princeton University, and Ruprecht-Karls University of Heidelberg. Her research covers Lie theory, representation vanities, and geometric structures on manifolds, as well as applications of geometry and topology to data science and natural sciences. Her work has been recognized with a Sloan Fellowship, and ICM invitation, and prestigious Consolidator and Advanced grants from the European Research Council. She is a Fellow of the American Mathematical Society and Scientific Chair of the Heidelberg Laureate Forum Foundation.

## Fall 2023

**Speaker:** Emily Riehl (Johns Hopkins)**When:** Friday, October 6, 2023 at 3:15 p.m.**Where:** Kirwan Hall 3206**Abstract:** Path Induction and the Indiscernibility of Identicals

Mathematics students learn a powerful technique for proving theorems about an arbitrary natural number: the principle of mathematical induction. This talk introduces a closely related proof technique called "path induction," which can be thought of as an expression of Leibniz's "indiscernibility of identicals": if x and y are identified, then they must have the same properties, and conversely. What makes this interesting is that the notion of identification referenced here is given by Per Martin-Löf's intensional identity types, which encode a more flexible notion of sameness than the traditional equality predicate in that an identification can carry data, for instance of an explicit isomorphism or equivalence. The nickname "path induction" for the elimination rule for identity types derives from a new homotopical interpretation of type theory, in which the terms of a type define the points of a space and identifications correspond to paths. In this homotopical context, indiscernibility of identicals is a consequence of the path lifting property of fibrations. Path induction is then justified by the fact that based path spaces are contractible.

#### About the Speaker

Emily Riehl is a professor in the department of mathematics at Johns Hopkins University. She earned her Ph.D. from the University of Chicago in 2011. Before Johns Hopkins, she was a Benjamin Peirce Postdoctoral Fellow at Harvard until 2015. She is a category theorist, and her research covers higher homotopy theory and homotopy type theory. She has published four influential textbooks in her research area. Her work has been recognized with AWM-Birman Research Prize in Topology and Geometry. She is a Fellow of the American Mathematical Society and she is a Simons Fellow in 2022.

## Spring 2022

**Speaker:** Lillian Peirce (Duke University)**When:** Wednesday, April 20, 2022 at 3:15 p.m.**Where:** Online Zoom**Abstract:** Counterexamples for Generalizatons of the Schrödinger Maximal Operator

In 1980 Carleson posed a question: how “well-behaved” must an initial data function be, to guarantee pointwise convergence of the solution of the linear Schrödinger equation? After progress by many authors, this was recently resolved (up to the endpoint) by a combination of two celebrated results: one by Bourgain, whose counterexample construction for the Schrödinger maximal operator proved a necessary condition, and a complementary result of Du and Zhang, who proved a sufficient condition. In this talk we describe a study of Bourgain’s counterexamples, from first principles. Then we describe a new flexible number-theoretic method for constructing counterexamples, which opens the door to studying convergence questions for many more dispersive PDE’s. Along the way we’ll see why no mathematics we learn is ever wasted, and how the boundary from one mathematical area to another is not always clear.

#### About the Speaker

Lillian Pierce is Leonardy Professor of Mathematics at Duke University. She graduated as valedictorian from Princeton University in 2002 and won a Rhodes scholarship to study at Oxford, where she earned her Master’s degree. Pierce earned her Ph.D. from Princeton in 2009. Her research combines harmonic analysis and number theory. Pierce has been awarded a Presidential Early Career Award in Science and Engineering, a Sloan Research Fellowship, the AWM Sadosky Prize, and the Birman Fellowship for Women Scientists; she was named a Fellow of the American Mathematical Society in 2021. Pierce is the co-founder and Editor-in-Chief of the new journal “Essential Number Theory.”

## Fall 2022

**Speaker:** Melanie Wood (Harvard University)**When:** Canceled Wednesday, November 2, 2022 at 3:15 p.m.**Where:** Kirwan Hall 3206**Abstract:** Finite Quotients of 3-Manifold Groups

It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and H_1,...,H_n finite groups, does there exist a 3-manifold group with G as a quotient but no H_i as a quotient? We answer all such questions. To prove non-existence, we prove new parity properties of the fundamental groups of 3-manifolds. To prove existence of 3-manifolds with certain finite quotients but not others, we use a probabilistic method, by first proving a formula for the distribution of the fundamental group of a random 3-manifold, in the sense of Dunfield-Thurston. This is joint work with Will Sawin.

#### About the Speaker

Melanie Matchett Wood is Radcliffe Alumnae Professor at Harvard University. Her research in number theory centers on the distribution of number fields and the probabilistic features of their fundamental structures. As a high school student in Indiana and undergraduate at Duke University, she broke through barriers in the realm of mathematics competitions by becoming the first woman named to the US International Mathematics Olympiad team, on which she won silver medals in 1998 and 1999, and the first woman to be named a Putnam Fellow. She won the Alice T. Schafer Prize, a Gates Cambridge Scholarship, and the Morgan Prize, among other honors. She earned her Ph.D. at Princeton University in 2009 with advsior M. Bhargava. She has since held positions at Stanford, the University of Wisconsin, and UC Berkeley, and has been distinguished with a Clay Liftoff Fellowship, a Sloan Fellowship, the AWM-Microsoft Research Prize in Algebra and Number Theory, an ICM Special Lecture invitation, and the NSF Waterman Award, among many other honors.

## Spring 2021

**Speaker:** Gigiliola Staffilani (MIT)**When:** Wednesday, February 17, 2021 at 3:00 p.m.**Where:** Online Zoom**Abstract:** Waves: Building Blocks inWaves: Building Blocks inNature and in Mathematics

In this talk I will first give a few examples of wave phenomena in nature. Then I willIn this talk I will first give a few examples of wave phenomena in nature. Then I willexplain how, in order to understand these phenomena, mathematicians use toolsfrom many different areas of mathematics, such as Fourier analysis, harmonicanalysis, dynamical systems, number theory, and probability. I will also giveexamples of the beautiful interaction between the “concrete" and the “abstract,” andhow these interactions constantly advance the boundaries of research.

#### About the Speaker

Gigliola Staffilani is Abby Rockefeller Mauze Professor of Mathematics at MIT.Gigliola Staffilani is Abby Rockefeller Mauze Professor of Mathematics at MIT.She has previously held positions at the Institute for Advanced Study, Stanford,Harvard, and Brown Universities. She graduated from the Universitá di Bolognain 1989 and obtained her Ph.D. from the University of Chicago in 1995.Staffilani is a Fellow of the American Academy of Arts and Sciences, theMassachusetts Academy of Sciences, and the American Mathematical Society.She has held fellowhips from the Sloan, Guggenheim, and Simons foundations.Her research concerns harmonic analysis and partial differential equations,including the Korteweg–de Vries equation and the Schrödinger equation.

**Speaker:** Sommer Gentry (US Naval Academy) **When:** Wednesday, March 24, 2021 at 3:00 p.m.**Where:** Online Zoom**Abstract:** People who volunteer as living kidney donors are often incompatible with their intended recipients. Kidney paired donation matches one patient and his or her incompatible donor with another pair in the same situation for an exchange. The lifespan of a transplant depends on the immunologic concordance of donor and recipient. We represent the patient-donor pairs with an undirected, edge-weighted graph and formulate the problem in terms of integer programming. I will propose an edge weighting of G which guarantees that every matching with maximum weight also has maximum cardinality, and also maximizes the number of transplants for an exceptional subset of recipients, while favoring immunologic concordance.

#### About the Speaker

Sommer Gentry is a Professor of Mathematics at the United States Naval Academy, and is also on the faculty of the Johns Hopkins University School of Medicine. She has a B.S. in Mathematical and Computational Science and an M.S. in Operations Research, both from Stanford University, and a Ph.D. in Electrical Engineering and Computer Science from MIT. She designed matching optimization methods used for nationwide kidney paired donation registries in both the United States and Canada, and is now redistricting liver sharing boundaries to help reduce geographic disparities in transplantation. Her work has attracted the attention of major media outlets including Time Magazine, Reader’s Digest, Science, the Discovery Channel, and National Public Radio. Gentry has received the MAA’s Henry L. Alder award for distinguished teaching and was named the Naval Academy’s 2021 recipient of the Class of 1951 Civilian Faculty Excellence in Research award.

**Speaker:** Kathryn Mann (Cornell University)**When:** Wednesday, April 21, 2021 at 3:15 p.m.**Where:** Kirwan Hall 3206**Abstract:** Dynamics in dimensions 1 and 3

Suppose you have a group of transformations of a space. If you know something about individual transformations, can you extrapolate to say something global about the whole system? The paradigm example of this is an old theorem of Hölder: if you have a group of homeomorphisms of the real line and none of them fixes a point, then the group is abelian and the whole system is conjugate to an action by translations. My talk will be an illustrated introduction to this family of problems, including some recent joint work with Thomas Barthelmé that gives a new such result about groups acting on the line. As an application, we use this to prove rigidity results for a different, fascinating family of dynamical systems, Anosov flows in dimension 3.

#### About the Speaker

Kathryn Mann is an Assistant Professor of Mathematics at Cornell University. She has previously held positions at UC Berkeley and Brown University. She graduated from the University of Toronto in 2008 with degrees in Mathematics and Philosopy and obtained her Ph.D. from the University of Chicago in 2014. Her research has been recognized with the Mary Ellen Rudin Young Researcher Award, the AWM's Joan and Joseph Birman Research Prize in Geometry and Topology, and the Wroclaw Mathematical Foundation's Kamil Duszenko Award. She has held a CAREER grant from the NSF and a Sloan Fellowship. She studies fundamental questions about groups actions on manifolds, including rigidity of homeomorphism and diffeomorphism groups of manifolds.

## Fall 2021

**Speaker:** Maria Emelianenko (George Mason University)**When:** Wednesday, December 8, 2021 at 3:15 p.m.**Where:** Kirwan Hall 3206**Abstract:** Entropy and random walks in materials, biology and quantum information science

What do mathematics, materials science, biology and quantum information science have in common? It turns out there are many connections worth exploring. In this talk, I will focus on graphs and entropy, starting from the classical mathematical constructs and moving on to applications. We will see how the notions of graph entropy and KL divergence appear in the context of characterizing polycrystalline material microstructures and predicting their performance under mechanical deformation, while also allowing to measure adaptation in cancer networks and entanglement of quantum states. We will discover unified conditions under which master equations for classical random walks exhibit nonlocal and non-diffusive behavior and discuss how quantum walks may allow to realize the coveted exponential speedup.

#### About the Speaker

Maria Emelianenko is Professor and Chair of Mathematics at George Mason University. She earned her B.S. in Computer Science and Mathematics from Moscow State University in 1999 and her Ph.D. in 2005 from Pennsylvania State University. She subsequently held a postdoctoral position at the Center for Nonlinear Analysis at Carnegie Mellon University. For her work in numerical computation and scientific computing, she was awarded an NSF CAREER grant in 2011, a Mason Emerging Researcher Award in 2013, and the Penn State Alumni Society Early Career Award in 2014. She is a member of the US National Committee for Theoretical and Applied Mechanics. Her research specialties include the study of grain growth and Voronai tesselations.