**Title:** Universal Series and Strange Duality

**Abstract:** The Hilbert scheme of points parametrizes unordered tuples of points on a complex surface. Generating series associated to Hilbert schemes are often decompose nicely into products of certain “universal” series. In this talk, I will introduce Hilbert schemes and explain the relevant generating series. Finally, I will say how a “strange duality” conjecture (coming from moduli spaces of vector bundles) suggests a surprising relationship between some of these series and discuss some recent progress in proving this relationship.

**Title:** Symbolic coding for geodesic flow in negative curvature

**Abstract:** Symbolic codings allow us to encode a complicated dynamical system — the geodesic flow — by a simpler model system, thereby proving a number of strong theorems. In this talk I’ll discuss how these codings show up for geodesic flows on negatively curved spaces. Then I will discuss some applications of this coding machinery to problems in geometric group theory, in particular to the amenability problem. This talk is based on joint work with Jean-Francois Lafont and Daniel Thompson.

**Title:** Communities in Networks

**Abstract:** Networks are all around us, from online social networks to business relationships to family and friends. The patterns in these connections control the way that information, ideas, and diseases spread across a population. In many cases, these processes are strongly influenced by the large-scale organization of nodes into groups. As such, the algorithmic detection of tightly-connected groups of nodes, known as communities, has become a prominent method for studying various networks across different disciplines. Examples discussed in this talk include online social networks, political data, and features of pathogenic E.coli. No previous knowledge about networks will be assumed.

**Bio:** Peter Mucha is a Professor of Mathematics and Applied Physical Sciences at the University of North Carolina at Chapel Hill. Born in Texas and raised in Minnesota, Dr. Mucha moved east to attend college at Cornell University where he majored in Engineering Physics. After a Churchill Scholarship studying in the Cavendish Laboratory at Cambridge with an M.Phil. in Physics, he returned to the States to continue his studies at Princeton with an M.A. and Ph.D. in Applied and Computational Mathematics. Following a postdoctoral instructorship in applied mathematics at MIT, and a tenure-track assistant professorship in Mathematics at Georgia Tech, he moved to UNC-Chapel Hill, where he has served as chair of the Department of Mathematics, the founding chair of the Department of Applied Physical Sciences, and is the current Director of the Chairs Leadership Program at the Institute for the Arts & Humanities. His awards include a DOE Early Career PI award and NSF CAREER award. At UNC, he was recognized with a Bowman and Gordon Gray Distinguished Term Professorship for excellence in undergraduate teaching and he was named to the inaugural cohort of the Outstanding Postdoc Mentor Award. Dr. Mucha’s research includes a variety of topics in the mathematics of networks, including network representations of data, community detection, and modeling dynamics on and of networks. His group’s activities are fundamentally interdisciplinary, applying tools of network analysis and data science in collaborations across the mathematical, physical, life, and social sciences.

**Title:** Stochastic cascade solutions of the Navier-Stokes equations.

**Abstract:** Branching processes were used by McKean in 1975 to study the KPP-Fisher equation. His ideas were robust enough to apply to a larger class of semilinear parabolic equations. In 1997, Le Jan and Sznitman used similar ideas for the Navier-Stokes equations. They introduced a class of stochastic cascade solutions. Since then, the theory of cascade solutions has been quite fruitful, producing further insights on the uniqueness/nonuniqueness of solutions. Cascade solutions can also be defined for various toy models of the Navier-Stokes equations, for example the alpha-Riccati equation and the complex Burgers equation. In this talk, I will present some history and recent results of cascade solutions, with applications to the Navier-Stokes equations.

**Title:** Structure in complex networks

**Abstract:** A core challenge in data science is obtaining a principled understanding of the structure of empirical data. The particular case of complex network data is increasingly important and particularly challenging due, for example, to dependencies among samples and lack of obvious spatial structure. I will discuss recent advances on this problem, including new data models, approximation theorems, scalable algorithms, and applications. These advances apply to data with a number of different structures, such as community structure, core-periphery structure, temporality, and multiplexity. The analytic and algorithmic tools are drawn from a variety of fields, such as metallurgy, compressed sensing, and statistics. Applications include image segmentation, counterterrorism, neuroscience, and genealogy.

Please join us this Thursday, October 24th, 2019, as Pace Nielsen receives the Distinguished Teaching Award from the Savage Foundation. The award will be presented by David and Carolyn Wright and will be followed by a lecture by Dr. Nielsen on “Mathematical Paradoxes.”

Every Thursday, the Department of Mathematics invites math professionals from all around the country to present about how they use math in their careers. Join us every Thursday at 4:30 in 1170 TMCB to learn about these cool companies!

**September**

12: *Focus on Math:* Dana Richards

19: Internship Panel

26: Mike Bastian, Expedia

**October**

3: Tyler Folkman, Branded Entertainment Network

10: Scott Porter, The NPD Group

17: Eric Ringger, Zillow

24: Savage Teaching Award presented by David & Carolyn Wright

31: *Focus on Math*: Steve Butler, Iowa State University

**November**

7: Ashley Duncan, The Art of Problem Solving

14: Kerk Phillips, Congressional Macroeconomic Analysis Division

21: *Focus on Math*: Carol Meyers, Lawrence Livermore National Laboratory

**December**

5: Matthew Webb, Goldman Sachs

12: Alexandra Greenwood Hurst, Qualtrics

**Optimizing the Enterprise: My Career at a National Laboratory **

Are you curious as to the kind of work that is done at a national laboratory? Have you heard of the field of operations research, or are you interested in learning about how it is applied to real problems? In this talk I will give a brief introduction to the field of operations research, as well as describing the kinds of math I have used in my 13 years at Lawrence Livermore National Laboratory. The talk will give a broad perspective across several application areas, including nuclear stockpile modeling, counterterrorism, energy grid modeling, and (most recently) improving the efficiency of operations at my own laboratory. These projects span a range of time frames, sponsors, and team sizes, and hopefully will give a flavor of the diverse work that is done at a national laboratory. This talk is intended for undergraduates or anyone interested in applications of math in the real world.

Carol Meyers is a mathematician and associate program leader for nuclear weapons enterprise evaluation and planning at Lawrence Livermore National Laboratory. Her expertise is in the areas of integer and linear programming optimization, decision theory, cost analysis, schedule analysis, and risk analysis. She manages a suite of efforts modeling the enterprise at different scales, including stockpile, workforce, infrastructure, and cost models. She is the original architect of the Stockpile Transformation Optimization Requirements Model (STORM) code, which is currently used to evaluate potential courses of action for stockpile planning in the Department of Energy. Previously she led an effort to port the PLEXOS power market modeling software to run on high-performance computers, in conjunction with industrial partners. She also co-leads the New Moms’ Group at LLNL. She holds a BA in math from Pomona College and a Ph.D. in Operations Research from the Massachusetts Institute of Technology.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Contact Dr. Jared Whitehead for details.

Contact Dr. Mark Kempton for details.