# October Prize Spotlight: Sean Lawley, Jiawang Nie, Aretha Teckentrup, and Alex Townsend

Congratulations to these four SIAM members who were recently awarded the SIAM Activity Group on Life Sciences Early Career Prize, SIAM Activity Group on Linear Algebra Best Paper Prize, SIAM Activity Group on Uncertainty Quantification Early Career Prize, and SIAM Activity Group on Linear Algebra Early Career Prize, respectively.

**Sean Lawley, SIAM Activity Group on Life Sciences Early Career Prize**

Sean Lawley of the University of Utah received the SIAM Activity Group on Life Sciences Early Career Prize on August 7, 2018 at the 2018 SIAM Conference on the Life Sciences (LS18) in Minneapolis, Minnesota. The award recognizes Lawley for his significant contributions to the analysis of stochastic phenomena in biology, particularly his recent fundamental work on diffusion processes subject to switching boundaries.

The SIAG/LS Early Career Prize is awarded every two years to one individual in their early career, in the field of mathematics applied to the life sciences, for distinguished contributions to the field in the three calendar years prior to the award year. The prize was awarded for the first time at LS18.

Sean Lawley is currently an assistant professor in the Department of Mathematics at the University of Utah. He completed his Ph.D. in mathematics from Duke University in 2014 and held a postdoctoral position at the University of Utah for two years. He specializes in the analysis and application of stochastic processes to biological problems.

**Q:** *Why are you excited to be winning the SIAG/LS Early Career Prize?*

**A:** I am honored to receive this prize, and I am very pleased that the work I’ve done with collaborators is being highlighted. It is an exciting time to be working on stochastics in biology, and I hope that this field will continue to grow.

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

**A:** My research is at the interface of stochastics and biology. Initially prompted by biological questions, I have analyzed diffusion processes in randomly switching environments. Mathematically, these models take the form of either random partial differential equations or stochastic differential equations in a random environment. One salient feature of these models is that they combine multiple levels of randomness interacting across spatial and temporal scales. Studying these systems has uncovered new mathematical phenomena and stimulated new questions in stochastic analysis, many of which we are actually just beginning to answer.

In addition, we have applied this modeling paradigm to diverse biological systems, including biochemical reaction kinetics, volume transmission in the brain, and insect respiration. In some of these applications, we are excited that the mathematics is revealing unexpected biological features that appear to be quite important.

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

**A:** Broadly speaking, my research is part of a much larger effort to use mathematical analysis and other quantitative methods to answer biological questions. Indeed, technological advances now allow life scientists to make measurements and observations that were previously impossible, and quantitative techniques are essential to synthesize and understand this new data. Importantly, biological problems are driving innovations and advancements in mathematics, and so the relationship between the fields is truly reciprocal.

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

**A:** SIAM has connected me to a broad community of applied mathematicians. In addition to sharing my work, this connection has enabled me to discover new problems and applications, learn new mathematical methods, and forge collaborations.

**Jiawang Nie, SIAM Activity Group on Linear Algebra Best Paper Prize**

The SIAG/LA Best Paper Prize is given every three years to the author or authors of the most outstanding paper, as determined by the selection committee, on a topic in applicable linear algebra in the four calendar years preceding the award year.

The award recognizes Nie for his paper, “Generating Polynomials and Symmetric Tensor Decompositions,” *Foundations of Computational Mathematics* (2017), in which he develops theoretical results and an innovative, mathematically elegant, computationally efficient algorithm for symmetric tensor decompositions, with potential for impact on applications. Nie accepted the award and presented his talk, “Generating Polynomials and Symmetric Tensor Decompositions,” on May 7, 2018.

Jiawang Nie earned a bachelor's degree from Xi'an Jiaotong University, a master's degree from the Chinese Academy of Sciences, and his Ph.D. from the University of California, Berkeley. He is currently a full professor of mathematics at University of California, San Diego. He has received a Hellman Fellowship (2009), NSF CAREER Award (2009), INFORMS Young Researcher Prize (2014), and Kalman Visiting Fellowship (2015). He was a Tucker Prize Finalist in 2009. Nie’s research focuses on tensor computation, truncated moment problems, polynomial optimization, and their applications in science and engineering. He is particularly interested in tensors, polynomials, semi-definite programming, and the sum of squares.

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

**A:** The past winners are world leading experts in the field of linear algebra. I am deeply honored to be joining the list of winners. The prize is not only encouraging for me, but also for my colleagues who are working on tensors. I am extremely grateful to the people who appreciate my work.

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

**A:** For symmetric tensors of a given rank, there exist linear relations of recursive patterns among their entries. These relations can be represented by generating polynomials. My research introduces generating polynomials as a new tool for computing symmetric tensor decompositions.

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

**A:** A matrix is a basic tool for traditional scientific computing. It models scientific problems that are "linear". I would like to view tensors as a tool for modern computational mathematics. Tensors can model scientific problems that are "multi-linear" or "non-linear". They have broad applications in computer graphics and vision, image and signal processing, machine learning, data science, etc.

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

**A:** I have been constantly, actively participating in SIAM conferences and publishing in SIAM journals. The SIAM conferences give valuable opportunities for scientists of different backgrounds to meet, discuss, communicate, and collaborate. The SIAM journals publish first rate, novel, important research results. SIAM provides excellent, great services to various areas of applied mathematics.

**Aretha Teckentrup, SIAM Activity Group on Uncertainty Quantification Early Career Prize**

The SIAG/UQ Early Career Prize is awarded every two years to an individual in their early career for outstanding research contributions in the field of uncertainty quantification in the three calendar years prior to the award year. The 2018 award recognizes Teckentrup for her seminal contributions to the extension of the multilevel Monte Carlo approach to random PDEs and to Monte Carlo Markov chain settings. This was the first award of the prize. Teckentrup accepted her award and gave her lecture, “Multilevel Markov Chain Monte Carlo Methods for Uncertainty Quantification,” on April 19, 2018.

Aretha Teckentrup received her Ph.D. from the University of Bath in 2013, and held postdoctoral positions at Florida State University and the University of Warwick before joining the University of Edinburgh in 2016 as a Lecturer in Mathematics of Data Science. Her research interests are in uncertainty quantification and data science, at the interface of numerical analysis, statistics and machine learning. She is especially interested in the theoretical underpinnings of algorithms and approximations.

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

**A:** Being awarded the SIAG/UQ Early Career Prize is certainly a great motivational boost. Uncertainty quantification is a very active area of research, and it is a great honor to have my work acknowledged as notable contributions.

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

**A:** The research is about the development and analysis of multilevel sampling methods, with a particular focus on complex simulation tasks involving partial differential equation models. In these types of applications, multilevel methods drastically reduce the computational effort required by cleverly using a hierarchy of increasingly complex computational models. As well as being able to apply these methods in a wide range of scenarios, it is important to have a theoretical foundation explaining why these methods work.

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

**A:** Many day-to-day simulation tasks, such as numerical weather prediction and oil reservoir simulation, are already extremely time consuming on their own. Including the effect of uncertainties, due to, for example, incomplete knowledge of model parameters, adds further complexity to the undertaking, and can quickly become infeasible. Using the multilevel methods we helped develop, however, this can be done without significantly increasing the computational effort, leading to more accurate forecasts and predictions with the same computational budget.

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

**A: **SIAM is a great platform to keep up to date with events and developments in my research field, and to connect with like-minded researchers.

**Alex Townsend, SIAM Activity Group on Linear Algebra Early Career Prize**

The SIAG/LA Early Career Prize is awarded every three years to a post-Ph.D. early career researcher in the field of applicable linear algebra for outstanding contributions to the field within six years of receiving the Ph.D. or equivalent degree as of January 1 of the award year.

The 2018 award was the first award of the prize. It recognizes Townsend for his significant contributions to a broad range of linear algebra topics that includes low-rank matrices, orthogonal polynomials, and spectral methods.

Alex Townsend is currently an assistant professor at Cornell University in the Mathematics Department. Prior to Cornell, he was an Applied Math Instructor at MIT (2014-2016) and a DPhil student at the University of Oxford (2010-2014). He was awarded a second-place Leslie Fox Prize in numerical analysis in 2013 for his work with Sheehan Olver on the ultraspherical spectral method and a first-place Leslie Fox Prize in 2015 for his work on fast transforms.

Townsend's research focuses on spectral methods, low-rank techniques, orthogonal polynomials, and fast transforms. He is interested in analyzing and developing numerical algorithms for computing with functions, differential equations, and triangulated geometries. He particularly enjoys turning classical mathematical ideas such as Gaussian elimination, asymptotics of special functions, and Zolotarev numbers into modern numerical tools.

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

**A:** I am greatly honored to receive the inaugural SIAG/LA Early Career Prize and join the future researchers on that list. The prize is a fantastic opportunity for the field of applicable linear algebra to promote the work of its early career researchers. I am grateful to the people who nominated me.

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

**A:** My research focuses on the algorithmic and theoretical development of spectral methods, low-rank techniques, and orthogonal polynomials. Often these topics are fruitful to combine. For example, spectral methods are a class of spectrally-accurate techniques for solving differential equations that traditionally lead to dense and ill-conditioned linear systems. By using recurrence relationships between ultraspherical polynomials, Sheehan Olver and I derived the ultraspherical spectral method that often leads to almost banded and well-conditioned matrices. The structure of almost banded matrices is banded plus low-rank and this can be exploited to derive an adaptive QR procedure that provides an optimal complexity and order-adaptive solver for linear ordinary and partial differential equations.

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

**A:** I, together with colleagues from across the world, have combined our algorithmic ideas to develop exploratory and order-adaptive algorithms for solving a broad range of computational problems with global spectral methods. There are now three established open source software systems that allow users to seamlessly compute with functions and solve differential equations: Chebfun (led by Nick Trefethen and written in MATLAB), ApproxFun (led by Sheehan Olver and written in Julia), and Dedalus (led by Geoff Vasil and written in Python). These computing environments are being used in computational fluid dynamics (CFD) simulations and computational astronomy.

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

**A:** I have been a member of SIAM since I was a graduate student. I professionally benefit from the activities of SIAM by attending SIAM organized conferences, by publishing in SIAM journals, and by reading SIAM blogs and news. SIAM is a professional association whose activities help me keep up-to-date with the wider research landscape of applied mathematics, build academic collaborations, and assimilate my ideas.