**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:** Quasiconformal uniformization of surfaces

**Abstract:** The uniformization theorem, one of the fundamental results of complex analysis, states that every simply connected Riemann surface is conformally equivalent to either the unit disk, the plane, or the sphere. In this talk, we discuss the problem of generalizing this result to metric spaces with minimal assumptions on their geometry. This research direction is motivated by connections to geometric group theory and complex dynamics, where such spaces arise naturally. In the metric space setting, the class of conformal mappings is quite restrictive, and it is natural to consider instead some notion of quasiconformal mapping. We give an overview of recent and ongoing work in this area.

**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.

Contact Dr. Benjamin Webb for details.

Click here to find out more

This seminar will occur every Wednesday at 11:00.