# July 2019 Prize Spotlight

Congratulations to the following members of the SIAM community who received awards at the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), 2019 International Conference on Scientific Computation and Differential Equations (SciCADE 2019), 15th International Symposium on Orthogonal Polynomials Special Functions and Applications (OPSFA 2019), and SIAM Conference on Applied Algebraic Geometry (AG19).

- Andrea L. Bertozzi - Ralph E. Kleinman Prize
- Maria J. Esteban - SIAM Prize for Distinguished Service to the Profession
- Steven Strogatz - George Pólya Prize for Mathematical Exposition
- Catherine Sulem - AWM-SIAM Sonia Kovalevsky Lecture
- Houman Owhadi - Germund Dahlquist Prize
- Elina Robeva - SIAM Activity Group on Algebraic Geometry Early Career Prize
- Thomas Bothner - Gábor Szegö Prize
- Joseph L. Hart - SIAM Student Paper Prize
- Michael Lindsey - SIAM Student Paper Prize
- Daniel Massett - SIAM Student Paper Prize

Congratulations to Margaret Wright, recipient of the John Von Neumann Prize, and Weinan E, recipient of the Peter Henrici Prize, who were also awarded at ICIAM 2019!

## Andrea L. Bertozzi - Ralph E. Kleinman Prize

The Ralph E. Kleinman Prize is awarded every two years to one individual for outstanding research or other contributions that bridge the gap between mathematics and applications. Work that uses high-level mathematics and/or invents new mathematical tools to solve applied problems from engineering, science, and technology is particularly appropriate. The award recognizes Bertozzi for her groundbreaking research in partial differential equations, image processing, numerical analysis, scientific computing, mathematical data science, and the application of mathematics to problems in the physical, life, and social sciences.

Andrea L. Bertozzi is Distinguished Professor of Mathematics and Mechanical and Aerospace Engineering at UCLA. Her expertise is in nonlinear partial differential equations and fluid dynamics. She also works in the areas of geometric methods for image processing, crime modeling and analysis, and swarming/cooperative dynamics.

Bertozzi completed all her degrees in mathematics at Princeton University. After postdoctoral work at the University of Chicago and Argonne National Laboratory, she joined the faculty of Duke University in 1995. In 2003, she joined the faculty of UCLA as a professor of mathematics. Since 2005, she has served as Director of Applied Mathematics, overseeing the graduate and undergraduate research training programs at UCLA. In 2012, she was appointed the Betsy Wood Knapp Chair for Innovation and Creativity. She was awarded a Simons Math + X Investigator Award in 2017, joint with UCLA's California NanoSystems Institute (CNSI). And in 2018, she was appointed Professor of Mechanical and Aerospace Engineering, in addition to her primary position in the UCLA Mathematics Department.

Bertozzi was awarded the AWM-SIAM Sonia Kovalevsky Lecture prize in 2009. She has been elected to the American Academy of Arts and Sciences and the U.S. National Academy of Sciences. She is a Fellow of the American Mathematical Society, the American Physical Society, and SIAM.

**Q:** *Why are you excited to be awarded this prize?*

**A:** It is a great honor to receive this prize, especially at the ICIAM meeting in Valencia. The Ralph E. Kleinman Prize epitomizes what I enjoy most about my research - discovering, developing new mathematics in parallel to new scientific work, and finding novel uses for high level mathematics in science.

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** I view mathematics as a language that describes the real world and which we can use to learn more about the world. Because mathematics is precise and descriptive, sometimes the framework from one area of science can be relevant for another research area. A common theme in my research is to make these connections and to advance new areas in applied mathematics, building on successes in very different application areas.

For example, shockwave theory was developed to study problems in gas dynamics. In the late 1990s, I worked on undercompressive shocks in thin film flow. My collaborators and I were able to explain new phenomena in coating flows – due to undercompressive waves. We were able to work out the details of the mathematics – it was beautiful and the only way to explain this bizarre behavior. Very recently we have found the same dynamics in “tears of wine”! This is a fun problem we have been working on. The work provides mathematical analysis of moving fronts often seen leading up to the tears of wine or wine legs phenomenon.

Another example is work I did in swarming and aggregation. We used ideas from incompressible fluid dynamics and also ideas from classical statistical mechanics from the mid-1900s – combining them to find all sorts of underlying rules for swarming patterns in two and three dimensions in nature. We also developed new mathematics for aggregation equations.

I also have been working on modeling crime dynamics using both PDEs and stochastic models. That was a completely undeveloped area when we got into it.

Finally, in the last eight years I have been developing a lot of mathematics for graphical models in machine learning – building on a large body of work in continuum PDEs in Euclidean Space for things like motion by mean curvature and diffuse interface models and total variation. Many of these well-known problems in PDEs have graph analogues that can be developed to solve penalized graph cut problems for machine learning.

All of these works have involved collaborations with very talented mathematicians – both senior colleagues, students and postdocs, and a number of domain scientists including experimentalists.

**Q:** *What does your research mean to the public?*

**A:** Our work has various impacts at different levels. The highest profile work is on predictive policing. And this was an outgrowth of work spearheaded by a former postdoc in my group, George Mohler, who is now at Indiana University – Purdue University Indianapolis (IUPUI). The idea is to use self-exciting point process models for earthquakes and aftershocks to predict where new crimes are going to occur. Today this model, through a commercial software package known as PredPol, is used in over 50 cities worldwide and affects the lives of 1 in 33 Americans. Several of my students have worked on new aspects of these models.

I have many other works that are not commercial applications but provide ideas for new technologies perhaps in the future. One recent example is some rigorous analysis we did for a control theory model for a swarm of robotic bees that could be used to pollinate crops. The development of a fully automated robotic bee is still a work in progress. However we have some mathematics in place for the analysis of the coverage capability of such a control model, in terms of the bee’s sensing radius and the number of bees in the swarm. And that work builds on two other areas of mathematics – stochastic PDEs and optimal control. There are many other examples but these are a few highlights.

**Q:** *What does being a SIAM member mean to you?*

**A:** SIAM has had an overwhelming impact on my research at many levels and for over 30 years. I attend many conferences, have been an organizer of several meetings, organized many minisymposia at meetings, given several plenary talks, and have served on the SIAM Council. I have publications in seven SIAM Journals and have served on the editorial boards of four SIAM Journals (SIREV, SIMA, SIIMS, and MMS).

What I really admire about SIAM is the breadth of the organization both scientifically and also geographically. I have attended SIAM affiliated meetings in both Asia and Europe as well as many in the U.S. and on many topical themes.

## Maria J. Esteban - SIAM Prize for Distinguished Service to the Profession

SIAM awards its Prize for Distinguished Service to the Profession every year to an applied mathematician who has made distinguished contributions to the advancement of applied mathematics on the national or international level. SIAM recognizes Professor Esteban for her outstanding contributions to bringing together the mathematics communities in France, Europe, and the rest of the world and helping to bridge the gaps between theoretical mathematics and applications, including applications in industry. Her distinguished service to the community includes her presidencies of the Société de Mathématiques Appliquées et Industrielles (SMAI) and the International Council for Industrial and Applied Mathematics (ICIAM), her chairing of the Applied Mathematics Committee of the European Mathematical Society, her role as a founder and board member of the EU-MATHS-IN European network for industrial mathematics, and her membership of numerous international committees.

Maria J. Esteban is a French mathematician of Basque origin. She is currently senior researcher at CNRS (Centre National de la Recherche Scientifique) and holds a position at Université Paris-Dauphine. She did her undergraduate studies at the University of the Basque Country, in Bilbao. She moved to France to earn her PhD and, upon achieving this in 1981 at Université Pierre et Marie Curie, she decided to stay in France. Since then she has been a researcher at CNRS, holding various positions, first in what is now called Sorbonne Université and later at the Université Paris-Dauphine. Professor Esteban has been director of CEREMADE (the applied mathematics department of Université Paris-Dauphine), president of SMAI, and co-founder of EU-MATHS-IN (European Service Network of Mathematics for Industry and Innovation). She is president of ICIAM for the 2015-2019 term. Currently she is a member of several editorial boards, and has been for many years one of the two Editors-in-Chief of the *Annales of the Institut Henri Poincaré - Analyse Non Linéaire.* She has been an Associate Editor of the *SIAM Journal on Mathematical Analysis* and she is a Fellow of SIAM.

**Q:** *Why are you excited to be winning the SIAM Prize for Distinguished Service?*

**A:** It is a big honor to receive a SIAM Prize and this prize in particular. A large part of my activity in recent years has been devoted to community work, to work in associations and societies concerned with the applications of mathematics, and it is very nice to be recognized for this part of my activity. The recognition of not only my research but also of my community work makes me very happy.

**Q:** *Could you tell us a bit about the accomplishments that won you the prize?*

**A:** On one hand, my research work has been linked to the applications of mathematics. There is an important theoretical aspect to it, but I have also been involved in the study of fluid-solid interaction problems, and still more in the analysis of problems from quantum chemistry. My work in that area has not been entirely theoretical, but also involves developing algorithms that are efficient, stable, and rigorous.

The other part of my activity is related to my community work. I started by being involved in SMAI, the French Society for Applied and Industrial Mathematics. There I occupied several positions and finally became its president in 2009-2012. After that I became actively involved in the European Mathematical Society Applied Mathematics Committee, and I chaired that in 2012-2013. I also participated in the creation of the EU-MATHS-IN Foundation, whose aim is to coordinate and stimulate activities related to the industrial applications of mathematics at the European level. Finally, in 2015 I became president of ICIAM, and I will stay there until the fall of 2019.

**Q:** *What does your work and service mean to the public?*

**A:** By leading organizations concerned with the applications of mathematics, I believe I serve society, since mathematics is key in most of the innovative processes that will change society in the future. I have always tried to convey this message to the general public via public lectures and publications that help people, including young students and teachers, to understand the value of mathematics. I aim to motivate the young to study science in general and mathematics in particular.

**Q:** *What does being a SIAM member mean to you?*

**A:** SIAM is the largest organization in applied mathematics in the world, the one with the largest number of members. Being part of it is a natural and, at the same time, a very important choice. It is an excellent source of information about the community and new research and projects. I have always been proud of being a member of SIAM. Whenever I am asked to serve on SIAM prize committees, SIAM conference program committees, or SIAM journal editorial boards, I have done that with pleasure and pride.

## Steven Strogatz - George Pólya Prize for Mathematical Exposition

The George Pólya Prize for Mathematical Exposition is awarded every two years to an outstanding expositor of the mathematical sciences. The prize may be awarded for a specific work or for the cumulative impact of multiple expository works that communicate mathematics effectively. The work may range from popular accounts of mathematics and mathematical discovery, from pedagogy to systematic organization of mathematical knowledge.

The award recognizes Strogatz for his extensive and brilliant works conveying the fascination and the impact of mathematics to the general public through numerous books, newspaper and magazine articles, and radio, television, web, and video appearances, and for his important and influential textbook on nonlinear dynamics and chaos.

Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He works in the areas of nonlinear dynamics and complex systems, often on topics inspired by the curiosities of everyday life. He studied at Princeton University, Cambridge University, and Harvard University and taught at Massachusetts Institute of Technology before moving to Cornell University in 1994. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for *The New York Times* and *The New Yorker* and has been a frequent guest on *Radiolab* and *Science Friday*. He is the author of several books: *Nonlinear Dynamics and Chaos*, *Sync*, *The Calculus of Friendship*, and *The Joy of x*. His most recent book is *Infinite Powers: How Calculus Reveals the Secrets of the Universe*.

**Q:** *Why are you excited to win the George Pólya Prize for Mathematical Exposition?*

**A:** George Pólya was a great writer, teacher, and communicator of mathematics, as well as a very creative mathematician. It's a tremendous thrill to receive a prize that honors his legacy.

**Q:*** Could you tell us a bit about the work that won you the prize?*

**A:** For as long as I can remember, I've been captivated by a mathematical view of nature, so applied mathematics felt irresistible. I also love thinking about math itself, and always try to understand it as clearly and simply (and often, as visually) as possible. At the beginning of my career those twin passions (for applications and simplicity) were mainly channeled into my research and teaching. More recently I've been trying to share those passions with a wider audience.

**Q:*** What does your work mean to the public? *

**A:** I hope that my work helps to convey the joy of math. Different things bring joy to different people, so I try a bit of everything, like telling the stories of how math was invented and discovered, or showcasing its beautiful puzzles and patterns, or highlighting its mysterious power to make sense of the world.

**Q:*** What does being a SIAM member mean to you?*

**A:** It means feeling at home and being with my people!

## Catherine Sulem - AWM-SIAM Sonia Kovalevsky Lecture

The Association for Women in Mathematics (AWM) and SIAM award the Sonia Kovalevsky Lecture annually to an individual in the scientific or engineering community whose work highlights the achievements of women in applied and computational mathematics. The 2019 award recognizes Sulem for her contributions in the area of nonlinear analysis and partial differential equations, specializing in the topic of singularity development in solutions of the nonlinear Schrödinger equation (NLS), on the problem of free surface water waves, and on Hamiltonian partial differential equations. Her book on the NLS is the central and most highly cited reference monograph in the field. Her continuing work on the problem of water waves, their time evolution, and their approximation by model dispersive equations is opening new territory, both in studies of wave propagation and in the analysis of the Euler equations.

Catherine Sulem is currently Professor of Mathematics at the University of Toronto. She received her Doctorat d'État from the Université de Paris-Nord in 1983 and held a CNRS position at the École Normale Supérieure in Paris before coming to the University of Toronto in 1990. Together with Pierre-Louis Sulem, she wrote the monograph, *The Nonlinear Schrödinger Equation: Self-Focusing Instability and Wave Collapse*, which first appeared in 1999. She was awarded the Krieger-Nelson Prize of the Canadian Mathematical Society (CMS) in 1998, and was elected Fellow of the Royal Society of Canada in 2015. Sulem was elected an Inaugural Fellow of the American Mathematical Society (AMS) in 2013, and of the CMS in 2018. She has served on the editorial boards of several journals, including *Canadian Journal of Mathematics* (1999–2005), *SIAM Journal on Mathematical Analysis* (2001--2010), and *Proceedings of the AMS* (since 2013).

**Q:** *Why are you excited to be awarded the AWM-SIAM Sonia Kovalevsky Lecture?*

**A:** SIAM has been a fruitful venue for my interaction with applied mathematicians over many years. The Sonia Kovalevsky Lectureship is of special significance to me. The Cauchy-Kovalevsky theorem was among the first and deepest theorems I studied when I entered the field of PDEs as a graduate student, and I have used it extensively in my work.

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** I work on nonlinear partial differential equations that model wave propagation arising in physical contexts such as fluid dynamics, nonlinear optics, and plasma physics. The main PDEs involved are the nonlinear Schrödinger equation and related systems, and the water wave equations which describe the motion of the free surface of a body of fluid under the influence of gravity and surface tension. My research has focused on qualitative properties of solutions such as singularity formation, stability of solitary waves, and long-time behavior dynamics.

Together with my long-time collaborator Walter Craig (who sadly passed away in January 2019), I used the Hamiltonian character of the water wave problem discovered by Zakharov (1968) to propose a formulation of the water wave equations that involves the Dirichlet-Neumann operator and its expansion associated to the fluid domain. This approach is currently used in theoretical studies and derivation of models in asymptotic regimes, as well as for high-order numerical simulations.

Throughout my career, I have benefited from fruitful collaborations with many researchers whom I thank warmly.

**Q:*** What does your research mean to the public?*

**A:** The study of water waves has important applications in oceanography and coastal engineering. It is central to the prediction of key features of ocean waves and currents (under both regular conditions and in extreme events) and of their effect on weather and climate.

In many regions of the world, oceans are stratified by density into distinct layers due to temperature or salinity variation and they support internal waves. These are often generated by tides. Internal waves can influence measurements of currents and undersea navigation and they present a potential hazard for offshore platforms. Mixing associated with large amplitude nonlinear internal waves can significantly affect biogeochemical processes.

**Q:** *What does being a SIAM member mean to you?*

**A:** SIAM provides an excellent environment to learn about the latest progress in applied mathematics and to develop collaborations. I have been a member of SIAM and of the SIAM Activity Groups on Analysis of PDEs and on Nonlinear Waves and Coherent Structures for many years. I regularly participate in SIAM conferences and particularly appreciate the large spectrum of theoretical and applied topics presented.

## Houman Owhadi - Germund Dahlquist Prize

The Germund Dahlquist Prize is awarded every two years to one individual for original contributions to the numerical solution of differential equations and numerical methods for scientific computing. The individual must have, at the award date, no more than 18 years (full time equivalent) of involvement in mathematics since receiving their Ph.D.

The 2019 award recognizes Owhadi for his varied, original, and deep work in areas of computational mathematics that include homogenization, stochastic differential equations, game theoretic approaches to numerical analysis, stochastic variational integrators, and uncertainty quantification. His substantial contributions to these challenging topics have had great impact in the broad fields of scientific computing, practical numerical methods, and machine learning.

Houman Owhadi is Professor of Applied and Computational Mathematics and Control and Dynamical Systems in the Department of Computing and Mathematical Sciences of the California Institute of Technology. He earned a M.Sc. from the École Polytechnique in France in 1994 and was a high-ranking civil servant in the Corps des Ponts et Chaussées (the corps for bridges and highways) until 2001. He earned his Ph.D. in probability theory from the École Polytechnique Fédérale de Lausanne in 2001 under the supervision of Gérard Ben Arous. He returned to France to join the CNRS in the same year, following a postdoc at Technion-Israel Institute of Technology. He moved to the California Institute of Technology in 2004. He currently serves as an associate editor of *SIAM Journal on Numerical Analysis*, *SIAM/ASA Journal on Uncertainty Quantification*, the *International Journal for Uncertainty Quantification*, the *Journal of Computational Dynamics*, and *Foundations of Data Science*.

**Q: ***Why are you excited to be awarded the Germund Dahlquist Prize?*

**A: **Germund Dahlquist was an outstanding applied mathematician and human being, so I feel honored and humbled by the decision of the selection committee and by the nomination of my peers. I think that numerical approximation, statistical inference and learning have a lot to contribute to each other, so the increased attention that this prize might bring to this interface is exciting.

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** In our earlier efforts on uncertainty quantification, my collaborators and I worked on calculus enabling computation with finite information in infinite dimensional spaces of measures and functions, on the robustness/brittleness of inference and on adversarial decision rules. Our research on homogenization and differential equations was focused on interplays between non-separated scales, geometry and noise.

My recent research has been focused on the interface between numerical approximation, statistical inference, and learning, which are intimately connected through the shared purpose of making estimations with partial information. The study of their connections is not new; it can be traced back to Henri Poincaré, Arthur Sard, F. M. Larkin, to Bayesian numerical analysis, and information-based complexity and is currently reemerging in probabilistic numerics/scientific computing. My collaborators and I have looked at these connections from a game/decision theoretic perspective motivated by the idea that they might not just be objects of curiosity but could constitute a pathway to simple solutions to fundamental problems in both areas, that is, in the areas of numerical analysis/approximation and statistical inference. For examples, fast solvers can be obtained by turning the process of computing with partial information into one of playing repeated adversarial games against the missing information, and the Green's function of an elliptic operator defines a Gaussian process whose conditioning on non-adapted (e.g. Haar) wavelets produces operator adapted wavelets. In another example, identifying the conditional correlation of Gaussian processes with scalar products between variational splines produces a simple proof of the screening effect observed in inference/geostatistics. Moreover, in learning theory, kernels with good generalization properties can be designed by bootstrapping numerical approximation errors from data, and pattern recognition problems can be solved as statistical numerical approximation problems through their reformulation as mode decomposition/recomposition problems.

**Q: ***What does your research mean to the public?*

**A: **As a society we tend to underestimate risk and it is critical to use adversarial approaches in safety studies with competing interests. Adversarial approaches also play an important role in robustness assessments and in learning. For example, addressing the brittleness of machine learning algorithms under adversarial perturbations is essential to the safety of their everyday implementation. Considering minimax numerical approximations as adversarial games establishes a natural connection between inference and approximation which can be used to guide the process of discovery in scientific computing (e.g. of fast solvers, which are everywhere in scientific computing and of increasing importance in data sciences) and offer some insights on mechanisms that might be at play in learning. The underlying mechanisms supporting such connections transfer to learning models from data and to numerous problems in applied sciences requiring modeling over hierarchies of levels of complexity.

**Q:** *What does being a SIAM member mean to you?*

**A:** It means being part of a vibrant and inspiring community. I am very grateful for it.

## Elina Robeva - SIAM Activity Group on Algebraic Geometry Early Career Prize

The prize recognizes Robeva for her highly innovative contributions to the analysis of tensors, especially for major advances in the theory of orthogonally decomposable tensors. She received the award and delivered her lecture, “Orthogonal Tensor Decomposition,” on July 10, 2019.

The SIAM Activity Group on Algebraic Geometry (SIAG/AG) awards the SIAG/AG Early Career Prize every two years to an outstanding early career researcher in the field of algebraic geometry and it applications for distinguished contributions to the field in the three calendar years prior to the award year. The contributions must be contained in a paper or papers in English in peer-reviewed journals.

Elina Robeva is currently a Statistics Instructor and an NSF Postdoctoral Fellow in Mathematics at Massachusetts Institute of Technology. At Stanford University, she earned a B.S. in Mathematics with Honors and Distinctions in 2011 and received several awards, including the Dean’s Award for Academic Accomplishment. She completed her Ph.D. in 2016 at the University of California Berkeley under the supervision of Bernd Sturmfels, and her doctoral thesis, “Decomposing Matrices, Tensors, and Images,” won the Bernard Friedman Memorial Prize in Applied Mathematics.

Robeva’s research is focused on studying statistical models that depict complex interactions between random variables. Such models are often given by nonlinear algebraic constraints. Her research utilizes tools from algebraic geometry and combinatorics to answer statistical and optimization questions such as inference, model selection, model equivalence, and non-parametric density estimation.

**Q:** *Why are you excited to be awarded the prize?*

**A:** It is a great honor for me to have been awarded the SIAG/AG Early Career Prize. The activity group on algebraic geometry is a vibrant community performing interdisciplinary research applied to fields outside of mathematics such as biology, statistics, quantum physics, chemistry, and computer science. I am deeply honored that my work was chosen for the award, considering the very high-quality research produced by the members of our activity group.

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** The research for which I won the prize concerns the study of tensor decompositions. Like matrix decompositions, tensor decompositions are extremely useful for working with data -- they can be used for uncovering hidden information about the data, as well as for storing the data in a very efficient way. One type of tensor decomposition, called CP-decomposition, simply expresses a given tensor (or multi-dimensional array) as a sum of several rank-1 tensors. Unlike matrix decompositions, the tensor CP-decomposition is computationally hard to find. Furthermore, tensor eigenvectors are also hard to find, and the set of tensors of given low rank is not closed, which poses problems for the low-rank approximation problem. My research focused on studying a subclass of tensors called orthogonally decomposable tensors. The orthogonality structure for these tensors alleviates all of the above problems. They can be decomposed efficiently, their eigenvectors can be found efficiently, in fact, we can give a formula for them, and the set of such tensors is closed and can be described by a very nice set of quadratic equations. Being able to solve these problems is a very important development, and I am excited to look for other structure (different from orthogonality) that allows us to do so.

**Q:** *What does your research mean to the public?*

**A:** Being able to decompose subclasses of tensors allows us to solve interesting real-world problems. For example, given a corpus of documents, we can recover the set of topics that gave rise to them (such as politics, science, sports, etc.), and we can find the most common words for each topic. Or, given a database of lots of people's genomes, we can tell how different populations, which lived far apart for a while, have been intermixed at different points in time.

**Q:** *What does being a SIAM member mean to you?*

**A:** Being a SIAM member gives me the opportunity to be part of a community performing cutting edge research which develops mathematical tools for solving problems in all areas of science. What I like most about SIAM are the top-notch journals as well as the high-quality conferences such as the SIAM Annual Meeting and the SIAG/AG biennial meetings. The SIAM conferences are the conferences that are always on my calendar, and I am always excited to be part of them as both a speaker and a minisymposium organizer.

## Thomas Bothner - Gábor Szegö Prize

^{ }International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 2019), held July 22-26, 2019 in Hagenberg, Austria. He received the award and gave his Gábor Szegö Prize talk, “What is…a Riemann-Hilbert Problem,” on July 24, 2019. The SIAM Activity Group on Orthogonal Polynomials and Special Functions (SIAG/OPSF) awards the Gábor Szegö Prize every two years to one individual in their early career for outstanding research contributions in the area of orthogonal polynomials and special functions, as evidenced in a publication in English in a peer-reviewed journal. The recipient will have no more than 10 years involvement in mathematics since PhD, allowing for breaks in continuity.

The award recognizes Bothner for his truly brilliant contributions to the recent advances in Riemann-Hilbert techniques at the boundary between the theory of special functions and applications to mathematical physics. The award is based on Bothner’s paper, “Transition Asymptotics for the Painlevé II Transcendent,” published in the *Duke Mathematical Journal* in 2017.

Thomas Bothner received his PhD in mathematics from Purdue University under the supervision of Alexander Its in 2013. After that he held postdoctoral positions at the Centre de Recherches Mathématiques Montréal and at the University of Michigan Ann Arbor. In September 2018, he joined the Department of Mathematics at King’s College London as a Lecturer in Analysis.

**Q:** *Why are you excited about winning this prize?*

**A:** It is a great pleasure and honor to receive the 2019 Gábor Szegö Prize. I am a junior researcher in the field and such a distinction will serve as a major motivational boost for my upcoming work.

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** My recent work focuses on problems in random matrix theory that display intimate connections to the theory of exactly solvable models in statistical mechanics and the field of integrable differential equations. Central to this work is the application of asymptotic methods, special functions, and orthogonal polynomials. In particular, the work recognized by the 2019 Gábor Szegö Prize enabled a unified asymptotic description of certain Painlevé functions. These special functions play a dominant role in modern mathematical physics. For instance, they can be used in the modeling of slow combustion fronts that spread somewhat randomly over a paper when you burn one of its sides.

**Q:** *What does your research mean to the public?*

**A:** Returning to the burnt paper, the statistical fluctuations of such an interface growth model are governed by the Kardar-Parisi-Zhang (KPZ) equation. This iconic equation has presented mathematicians with serious challenges over the past 30 years, some of which were resolved by Martin Hairer who was in turn awarded the Fields Medal in 2014 for his outstanding contributions. My own results are much more modest: they helped people working on stochastic PDEs and in probability theory to uncover and understand previously unknown properties of solutions to the KPZ equation. In some sense, we now have a better understanding of the spread of certain firelines.

**Q:** *What does participation in SIAM mean to you?*

**A:** I greatly value SIAM’s activity groups and related conferences. For instance, OP-SF NET, the electronic news net of SIAG/OPSF, is a valuable source for updates on preprints, books, and meetings. I look forward to it in my mailbox every month.

## Joseph L. Hart - SIAM Student Paper Prize

*SIAM Journal on Scientific Computing*in 2017. Hart co-authored the paper with Alen Alexanderian and Pierre A. Gremaud while he was a student at North Carolina State University. He will be recognized and present his paper at the 2020 SIAM Annual Meeting held jointly with CAIMS. SIAM Student Paper Prize winners receive their awards and present their papers at the SIAM Annual Meeting. Due to the ICIAM Congress, SIAM did not hold an annual meeting in 2019.

The SIAM Student Paper Prize recognizes outstanding scholarship by students in applied mathematics and computing as evidenced in a paper accepted for publication in a SIAM journal. The Student Paper Prize is awarded annually to the student authors of the most outstanding papers accepted by a SIAM journal within the three years preceding the nomination deadline. The award is based solely on the merit and content of the candidate’s contribution to the paper. Up to three prizes are awarded.

Joseph (Joey) Hart is a Postdoctoral Appointee at Sandia National Laboratories. He received his Ph.D. in applied mathematics from North Carolina State University in December 2018 under the direction of Pierre Gremaud. His research interests span various aspects of uncertainty quantification, computational science, and high performance computing. He is particularly interested in developing and applying uncertainty quantification methodologies for large scale applications.

**Q:** *Why are you excited about winning the SIAM Student Paper Prize?*

**A:** SIAM is an extraordinary organization that has facilitated many excellent opportunities for me throughout graduate school. I consider the SIAM Student Paper Prize to be one of the highest honors an applied mathematics graduate student may receive. I am thankful to SIAM, as well as to my advisor and mentors with whom I have been privileged to work.

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** The research provides a rigorous mathematical framework and computationally efficient algorithm to analyze the sensitivity of stochastic models to uncertain parameters. Variance based sensitivity analysis of uncertain parameters in deterministic models has been used by researchers across a variety of fields. This work provides foundational analysis to extend the methodology from deterministic models (such as ordinary and partial differential equations) to stochastic models (such as stochastic differential equations and Monte Carlo simulations).

**Q:** *What does your research mean to the public?*

**A:** Stochastic models are gaining popularity and replacing their deterministic counterparts in a variety of applications. Two common examples are chemical reaction networks and biological systems. Analyzing the influence of parametric uncertainty in stochastic models provides a modeler valuable insight into the underlying mechanisms which drive dynamics in the system.

**Q:** *What does being a SIAM member mean to you?*

**A:** I became familiar with SIAM through my Student Chapter at NCSU. SIAM has provided me with numerous opportunities to interact with leaders from the applied mathematics community and serve the community in a variety of ways. Being a SIAM member means being part of an international community which facilitates extraordinary research and service that impacts not only our community but society as a whole.

## Michael Lindsey - SIAM Student Paper Prize

*SIAM Journal on Mathematical Analysis*in 2017. He will be recognized and present his paper at the 2020 SIAM Annual Meeting held jointly with CAIMS. SIAM Student Paper Prize winners receive their awards and present their papers at the SIAM Annual Meeting. Due to the ICIAM Congress, SIAM did not hold an annual meeting in 2019.

The SIAM Student Paper Prize recognizes outstanding scholarship by students in applied mathematics and computing as evidenced in a paper accepted for publication in a SIAM journal. The Student Paper Prize is awarded annually to the student authors of the most outstanding papers accepted by a SIAM journal within the three years preceding the nomination deadline. The award is based solely on the merit and content of the candidate’s contribution to the paper. Up to three prizes are awarded.

Michael Lindsey is an NSF Postdoctoral Fellow at the Courant Institute of Mathematical Sciences, New York University. He completed his undergraduate studies at Stanford University and earned his Ph.D. in applied mathematics at the University of California Berkeley in August 2019.

**Q :**

*Why are you excited about winning the SIAM Student Paper Prize?*

**A:** It's really an honor to receive this prize. Working on this paper was a formative experience for me, and it is quite gratifying to see the work recognized in this way.

**Q: ***Could you tell us a bit about the research that won you the prize?*

**A:** The paper advances an approach to solving certain optimal transport problems. In optimal transport, the goal is to figure out how to move a given distribution of 'stuff' (the source distribution) to a desired target distribution in a way that minimizes a total moving cost. For ‘stuff,’ one could substitute 'mass,' 'probability,' 'goods,' etc., depending on the situation. I will use 'mass' from now on. Now for a certain important class of optimal transport problems, a solution can be obtained by a solving a partial differential equation called a Monge-Ampère equation, which encodes the constraint that our transport map actually ends up moving the given source distribution to the desired target distribution. At any particular location, there are two ways that this could fail to happen: the map could excessively *compress* mass (yielding a distribution that is too dense in some place), or it could excessively *expand* mass (yielding a distribution that isn't dense enough in some place). But it turns out, as we observed in the paper, that if the map doesn't over-compress mass *anywhere*, then it can't over-expand it anywhere either; otherwise you would end up with less mass than you started with! This observation has significance because it means that you can tell how far away you are from solving the Monge-Ampère equation by penalizing excessive compression only. In fact the penalty function for this excessive compression is convex for special target distributions, and we describe how the more general setting can be reduced to this special one. As a result our Monge-Ampère equation can be solved by convex optimization. A large part of the paper then consists of proving that discretization of the optimization problem will yield appropriate results. We also demonstrate the approach in practice with some numerical examples.

**Q:** *What does your research mean to the public?*

**A:** Though optimal transport is a lively field that is by no means limited to the perspective of Monge-Ampère equations, this perspective has arisen in diverse areas such as optical design, meteorology, and (recently) machine learning (where optimal transport is used to compare probability distributions). In addition to advancing a solution for certain optimal transport problems, the paper suggests an appealing perspective on the Monge-Ampère equation that may be of further interest in such applications.

**Q:** *What does being a SIAM member mean to you?*

**A:** I really appreciate the role of SIAM journals and conferences in the applied math community, and in fact I'm one of the leaders of the SIAM Student Chapter at UC Berkeley. This role has given me the opportunity to get to know other graduate students in applied math, which I have certainly enjoyed.

## Daniel Massatt - SIAM Student Paper Prize

*Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal*in 2017. Massatt co-authored the paper with Mitchell Luskin and Christoph Ortner while he was a student at the University of Minnesota. He will be recognized and present his paper at the 2020 SIAM Annual Meeting held jointly with CAIMS. SIAM Student Paper Prize winners receive their awards and present their papers at the SIAM Annual Meeting. Due to the ICIAM Congress, SIAM did not hold an annual meeting in 2019.

The SIAM Student Paper Prize recognizes outstanding scholarship by students in applied mathematics and computing as evidenced in a paper accepted for publication in a SIAM journal. The Student Paper Prize is awarded annually to the student authors of the most outstanding papers accepted by a SIAM journal within the three years preceding the nomination deadline. The award is based solely on the merit and content of the candidate’s contribution to the paper. Up to three prizes are awarded.

Daniel Massatt is a Martin H. Kruskal Instructor in the Department of Statistics at the University of Chicago. He graduated with a B.S. and M.A. (2013) in mathematics from UCLA, and received his Ph.D. in mathematics from the University of Minnesota under the direction of Professor Mitchell Luskin in 2018. He studied the electronic structure of incommensurate 2D materials, focusing on important fundamental observables such as the density of states and conductivity from real space and momentum space perspectives. Currently his research interests are in topological insulators and incommensurate 2D materials.

**Q:** *Why are you excited about winning the SIAM Student Paper Prize?
*

**A:** I am very excited to have won the SIAM Student Paper Prize. It is a prestigious recognition of a very interesting line of work that I am working on with Mitchell Luskin, Christoph Ortner, and several other collaborators in both mathematics and physics. I think this work is a strong case of successful interdisciplinary work between mathematics and physics in a cutting-edge topic.

**Q:** *Could you tell us a bit about the research that won you the prize?
*

**A:** This work focuses on understanding the electronic behavior of 2D materials stacked in such a way that they form incommensurate or aperiodic structures because of lattice mismatch or rotation between different 2D materials. The possible incommensurate stacking formations create a wide parameter space, allowing one to tune and optimize the desired electronic and optical properties. Our work focuses on modeling and developing numerical methods to predict the electronic behavior for the possible system configurations and to thus guide selection of configurations for experiment. The incommensurate structure posed significant mathematical and physical questions, leading us to work closely with the group of Professor Efthimios Kaxiras in the Applied Physics Department at Harvard University.

**Q:** *What does your research mean to the public?
*

**A:** Our research gives a new framework for studying incommensurate materials that has led to the development of efficient and accurate numerical methods that are able to compute the electronic density of states and other electronic properties in previously inaccessible parameter regimes. This work thus provides a tool-set to approach and study incommensurate material problems, which is a hot topic in the physics and materials science community with multiple potential applications.

**Q:** *What does being a SIAM member mean to you?*

**A:** I am very glad to be part of the SIAM community. There is a variety of benefits and access to scientific material, but particularly I appreciate the strong mathematical community.