Program in Applied Mathematics

The University of Arizona Program in Applied Mathematics

January 2021 Number XXI Greetings from the Chair, Program in Applied Mathematics

info. This significant change in the program tion; and it provides the opportunity to the curriculum was considered and approved incoming class to meet each other, program by a specially formed committee of Applied professors and staff. Dr. Colin Clark was in- Math faculty in 2019. The change was also strumental in smoothly running the Applied approved by the Graduate Committee of Mathematics component of the workshop. the Math Department in December of 2020, 5) We have continued the old tradition of con- and we expect the updated curriculum to ducting the Los Alamos – Arizona days, (res- be finalized in the UArizona course catalog urrected after a 15-year break) in 2019. This shortly -- in time for the start of the 2021-22 year the event was virtual (over zoom). Please academic year. check all the great talks by our students, b) The same committee of Applied Math professors and Los Alamos postdocs and fac- faculty has worked out respective ad- ulty, made available at https://appliedmath. justments in the program’s qualification arizona.edu/events/los-alamos-arizona-days. process. Our new qualification process We are also working on extending our is linked to the successful passing of six collaborations with other National Laborato- Dear Students, Alumni, Professors and exams (from 3 core courses) and it is mon- ries and Industry. In particular, in the fall of Friends of the Applied Math program at UA, itored and approved by three committees 2020, we hosted virtual visits for teams from 2020 was a difficult year for everybody, to (one per core course) each consisting of Lawrence-Livermore NL and from the Nevada say the least. However, and in spite of many six faculty. Absolute majority of our (now National Security Site. Many collaborations COVID-related obstacles, I am happy to report second year) students passed the qualifica- with Raytheon/Tucson and other companies good progress on a number of fronts. tion process successfully last May – which in Tucson, such as Critical Path, are ongoing. is good proof that the program continues to Those activities help to set up internships, 1) Our work on updating the program attract great students. fellowships and future employment oppor- curriculum and qualification process is tunities for our students. Five of our 1st year 2) Our admission numbers went up last year; almost complete: students had (virtual) summer internships 16 PhD students were admitted in 2020 (vs 10 with our National Lab and Industry partners a) 2019-2020 was the first -trial- year (two in 2019). We expect to maintain the numbers last summer. semesters) for the new edition of our three steadily, within the 12-18 range, in the coming core courses in Applied Mathematics: years. Our next recruitment event (virtual, due Theory, Methods and Algorithms. Content to COVID, utilizing both Zoom and GatherTown of the new courses is now up-to-date and platforms) is scheduled jointly with the Grad- CONTENTS balanced with the state-of-the-art in Ap- uate Program in Mathematics and Graduate Greetings from the Chair...... 1 plied Mathematics (which is significantly Interdisciplinary Program in Statistics & Data Obituary Tribute to Bob O’Malley...... 2 broader what it was 40 years ago, when the Science for February 28-March 1, 2021. program was created). Our AM core courses The Don Wilson Fund...... 3 combine traditional subjects in Applied 3) Thanks to efforts of the program steering Al Scott Lecture...... 4 Mathematics (such as Complex and Fou- committee, 45 new affiliate members and 2 rier Analysis, ODEs, PDEs and Variational new members across 28 Departments of UAr- New Program Calculus) with a number of more contem- izona were added to the list of the program’s Affiliate Profiles...... 4 faculty in 2020. The total number of UArizona porary subjects (Optimization, Control and Alumni Profiles...... 6 Elements of Data Science and Statistics for faculty affiliated with the program is now 113. Current Student Profiles...... 9 Inference and Learning). In 2019-20 and 4) The program joined forces with the De- 2020-21 academic years the courses were partment of Mathematics in setting up the News from Members led by Prof. Shankar Venkataramani (the- Integration workshop which we co-ran for the and Affiliates...... 12 ory), Prof. Mikhail Stepanov (algorithms) first time in the August of 2020. The work- Recent Graduates...... 13 and your humble servant (methods). Dr. shop, which we aim to continue annually, Colin Clark, the program Postdoctoral Fel- focuses on reviewing basic undergraduate News from Alumni...... 14 low, was helping the core instructors with mathematics that are critical for the students’ Current Student inter-course coordination (e.g. via recita- future success in the program; identifying Achievements...... 16 tions). See https://appliedmath.arizona. gaps in our students’ preparation for careers Incoming Class Fall 2020...... 17 edu/students/new-core-courses for more in Applied Mathematics that need atten- 1 Greeting (continued)

6) The new Applied Math Laboratory opened interruption via zoom. Moreover, a majority and the team have received an extension of its doors to the program students and fac- of the presentations made at the traditional the NIH training grant “Computational and ulty in February, 2020. The Lab is located in venues, and some temporary venues (such as mathematical modeling of biomedical sys- renovated office space on the 5th floor of the a working seminar in Applied Mathematics tems”. These two training grants are financing Physics and Atmospheric Science building. about Pandemics that we ran in April-June of 8 semesters in the 2020-21 academic year of This is a great location with an open space for 2020), are now recorded and posted online at our students’ Research Assistantships. We are individual work and discussions (equipped https://appliedmath.arizona.edu/events/sem- also expecting responses to a number of other with a sufficient number of tables, monitors inar-videos-fall-2020. grant submissions made on behalf of the and whiteboards), small-scale gatherings and 8) We continue to work on bringing new fund- program recently. also containing two rooms, e.g. suitable for ing to the program. Faculty of the program are I would like to thank all of you for your help small table-top experiments. key participants of the newly awarded NSF and support. Finally, I am especially grateful 7) The pandemic did not stop our program Research and Training Grant (RTG) in “Applied to Stacey and Keri working days and often colloquia and seminars. All of our regular Mathematics and Statistics for Data-Driven nights for keeping the program running. weekly activities have continued without Discovery”, led by Kevin Lin. Tim Secomb Sincerely Yours, Misha Chertkov Obituary tribute for Robert E. O’Malley Jr., 1939–2020 by Mark Kot (MS 1984), Professor, University of Washington

In 1973, Bob moved to the University of Ari- the Editor of the Book Reviews section of zona. In Tucson, Bob founded the Program in SIAM Review, a job he loved so much that Applied Mathematics in 1976. He also worked he continued in this role through 2014, five on singular perturbation problems in control years after his retirement. theory. Bob was a forceful advocate for applied I never got to know Bob at Arizona — he was mathematics at Arizona and was especially leaving just as I was arriving as a graduate supportive of young faculty. Many years later, student. He was, however, my neighbor and he (and I) would fondly reminisce about all colleague at the University of Washington for the wonderful people in Tucson. many years. I quickly learned four things about In 1981, Bob moved to Rensselaer Polytech- Bob: (1) He loved his work. He came into work, nic Institute, where he was Ford Foundation even after he retired, until the pandemic hit, Professor, Chairman of the Faculty, and Head and I had a better chance of running into Bob of a Department of Mathematical Sciences than any other colleague. Bob wrote his 2014 that emphasized applied mathematics and book on Historical Developments in Singular It is with great sadness that I report that Bob computer science. Many years later, in 1999, Perturbations after retiring, and he was working O’Malley, the founder of the Program in Ap- Bob’s colleagues at RPI hosted an O’Mal- on a new book on differential equations when plied Mathematics at the University of Arizona, ley-fest, a workshop on singular perturbations he passed away. (2) Bob loved books. He loved passed away December 31, 2020 at the age of 81. that brought some 60 mathematicians to Troy, reading them, writing them, reviewing them, Bob was born on May 23, 1939 and grew up in New York to celebrate Bob’s 60th birthday. and talking about them. His office was always Somersworth, New Hampshire. He began his At the end of 1990 and soon after a sabbatical to filled with stacks of books, dangerously so higher education at the University of New the Technical University of Vienna, Bob moved during his many years as Book-Review Editor Hampshire, where he earned a B.S. in Elec- to the Department of Applied Mathematics at for SIAM Review. (3) Bob loved the history of trical Engineering in 1960 and an M.S.in Math- the University of Washington. He served our mathematics. He loved reading and writing ematics in 1961. Bob then earned his Ph.D. in department as Chair, as Graduate Program about this history, and he often peppered his Mathematics in 1966 at Stanford University, Coordinator, and in many other ways, for many lectures with fascinating historical anecdotes. where he wrote a dissertation on two-parame- years. He retired in 2009, but he remained (4) Bob loved people. He always kept an open- ter singular perturbation problems under the active, as a Professor Emeritus, after that. door policy, and he would gladly drop whatever supervision of Gordon E. Latta. he was doing to talk with whomever entered Bob was extremely productive, and he received his office. Our graduate students loved Bob, and Bob had a long and illustrious career. After many honors. He was a member of the inaugu- many former students and colleagues would short appointments at the University of North ral class of fellows for both SIAM and for AMS, detour on their way through Seattle to visit Bob. Carolina, Bell Labs, the Courant Institute at and SIAM specifically cited Bob’s contributions He was a wonderful colleague, and he will be New York University, and the Mathematics to asymptotics and singular perturbations. He sorely missed. Research Center at the University of Wisconsin, authored four books, and Mathematical Reviews Bob returned to New York University in 1968, lists 161 publications for Bob. Bob’s funeral mass took place in St. James Cathe- where he worked with Joseph Keller and others. dral in Seattle on January 9, 2021. His son Patrick Bob then spent a year visiting the University of He was extremely active in SIAM. Bob was gave an especially eloquent tribute to how Bob’s Edinburgh. His lectures at these institutions President of SIAM from 1991 to 1992. He mathematics opened up the world for his family formed the basis for his book, Introduction to served as Vice President for Publications, on and how it also brought the world to their door. Singular Perturbations, published in 1974. many editorial boards, and as program chair Bob is survived by his wife Candy and by his for several meetings. In 2000, Bob became sons, Daniel, Patrick, and Timothy.

2 A Note on Bob O’Malley by Michael Tabor, Professor Emeritus, Head of the need for such a center as well as possible summer of 1976, and reported the results to Applied Mathematics GIDP (1992-2015) mechanisms for its formation. We believe Dr. Carter, Coordinator of Interdisciplinary When I arrived at the University of Arizona that a Center for Applied Mathematics at the Programs. As a result, President John Schaefer to become Head of Applied Mathematics in University of Arizona would provide a broadly appointed a University Committee on Applied 1992, I quickly learned about Bob’s central role based interdisciplinary program of high qual- Mathematics to “begin work on developing in starting the Program from colleagues who ity research and advanced study in applied an interdisciplinary program of research and were there at the time. With Bob’s passing, mathematics ... graduate education in applied mathematics and the fact that many others who were On March 13, 1976, Dr. Weaver reacted to the at the University of Arizona.” R.E. O’Malley involved have either retired or passed away, memo by forming an ad-hoc committee, con- was appointed Chairman of the University I thought it appropriate to record those early sisting of Professors D.G. Dudley, R.L. Ham- Committee and on October 28, 1976 issued days by sharing an extract from the 1991 Aca- blin, R.E. O’Malley (Chairman), M.L. Rosenz- invitations to join the program to 30 selected demic Program Review that tells the story: weig, A.R. Seebass, and M.O. Scully. In his faculty across a broad range on disciplines charge to the committee, Dr. Weaver stated: on campus. On December 10, 1976, Professor “The Program in Applied Mathematics at O’Malley announced that the degree program the University of Arizona had its beginnings If the Committee finds that such a program is needed ... and that we have the resources had received the approval of the Graduate with submission of a memo to Executive Vice Council and Regents and, with this action, the President Albert E. Weaver from Professors to make it a first-rate program, it should be reported to Dr. Carter. In this case, it should Program in Applied Mathematics was official- P.C. Fife, D.O. Lomen, R.E. O’Malley, H. Rund, ly established.” and A.R. Seebass, dated January 23,1976. In the recommend the general nature and character- memo, the professors wrote as follows: istic of the curriculum, the resources needed, By the time I had arrived in Arizona, Bob was the individuals who, or the departments already established at the University of Wash- We have been discussing the formation of a which, should be invited to participate, and ington. We would run into each from time to Center for Applied Mathematics with various in general delineate the proposed program time at conferences and SIAM meetings. He colleagues. Our discussions have lead us to in sufficient detail so that an estimate of the was always friendly and eager to hear news of the conclusion that there are many bene- cost, the needs, the student demand, the qual- the Program he had helped start. fits to be derived from such a center here. ity of the program, etc., can be made ... Consequently, we propose that you appoint Bob’s vision for a successful interdisciplinary an ad-hoc committee to advise you regarding The Committee accepted the charge from program aimed at solving real-world scientific Dr. Weaver, completed its study early in the problems lives on to this day.

Comments in Remembrance of Bob O’Malley By Alan Newell, Regents Professor, sciences and Dick Seebass, then an Associate unlikely to come. A second was the applied Mathematics Dean of the College of engineering, was key mathematics colloquium which attracted a “As I recall, it was key that Bob was supported to organizing that support although it was my huge following. For a while at least, it offered by Hanno Rund, then Chair of Mathematics. understanding and experience after I came an intellectual home for all those in the Uni- Hermann Flashka, Dave McLauglin, Jim Cush- here in 1981 that the support from Engineering versity whose work involved mathematical ing, Paul Fife were also very instrumental. But was widespread. I recall Bill Sears (a mentor thinking and models. I think the fundamental without Hanno it would have been difficult to for Dick Seebass) and Don Dudley as being idea that applied mathematics was rooted in get the whole thing going. (It should be also particularly enthusiastic supporters. Optics, science based research (and not just about noted that Ted Laetsch who became Chair and in particular Harry Barrett, and several of learning how to produce better algorithms after Hanno helped enormously by commit- the young guys there was also a staunch ally. for inverting matrices, popular in many other ting Mathematics to share its TA’s although One of the great successes of the program was schools at the time) was what separated the Arizona program from the rest. And Bob this was a year or two later.) Another crucial student quality as Arizona was able to attract ingredient in the beginning was the support a class of students who, without the flexibil- O’Malley certainly deserves credit for foster- of Engineering and many of the engineering ity offered by the program, would have been ing that approach despite the fact that his own research tended to be rather analytical.”

The Don Wilson Applied Mathematics Endowed Fund for Excellence

The Don Wilson Applied Mathematics Endowed group and helped train many of the Applied information about donating to the Don Fund for Excellence was established to honor Mathematics students who worked in that Wilson fund, the Michael Tabor Fellowship the memory of Don Wilson, a University of group. One of those students, Jack Hoppin Endowment, or the Applied Mathematics Arizona Research Professor in the College of (PhD 2003), and his wife Janna Murgia, made General Fund, please visit the following link: Optical Sciences, with the purpose of providing a generous gift to the Program that enabled the http://appliedmath.arizona.edu/program- support for the professional development of fund to be established. info/donate graduate students in the Program in Applied Due to the COVID-19 pandemic, no Don Mathematics. Dr. Wilson worked very closely Wilson travel awards were distributed in with Harry Barrett’s renowned medical imaging Spring or Fall semesters of 2020. For more

3 Al Scott Lecture Kevin Gomez (PhD 2020), Senior Research Engineer, Raytheon Missile Systems

Last Spring, I had challenges due to their rapid evolution. and evolutionary theory. presented the Al Specifically, these populations produce many I successfully defended two weeks before Scott prize lecture as beneficial mutations that concurrently at- giving the Al Scott prize lecture. Following the part of the applied tempt to spread. Competition among the mu- talk, I devoted time and energy to consid- math colloquia se- tant lineages results in the loss of beneficial er what I would do after graduation before ries. Dr. Alwyn Scott mutations whose lineages are driven extinct, starting my new position at Raytheon. The was a Professor at a phenomenon known as clonal interference. pandemic made it impossible for me to visit the University of Recently developed one-dimensional travel- family and friends back in California, as I Arizona, the founding director of the Center ing fitness waves had originally for Nonlinear Studies at Low Alamos Nation- in population planned. Lucki- al Lab, and a founding editor of Elsevier’s genetics have ly, I have always Nonlinear Phenomena Journal. Dr. Scott allowed signif- been a big fan was also known for his work on nonlinear icant advances of hiking, and systems in Biology, an area I came to appreci- in the study of Tucson is a ate more and more in my study of evolution asexual adapta- splendid place as a graduate student. I was honored to give tion with clonal if you are into the memorial lecture in remembrance of his interference. In that sort of remarkable career and contributions. my presentation, thing. I settled In my talk, I introduced a two-dimensional I discussed my for plans to visit traveling wave model that I developed to development of new trails and study trait evolution in large asexual popula- a two-dimen- subsequently tions. Natural selection often acts on multiple sional traveling wave and used the model to got my chance to reconnect with the natural traits at once, and genetic correlations be- show how clonal interference gives rise to world that I had grown to admire in my study tween traits help shape how traits evolve. This genetic interactions that resemble functional of evolution. I started my new position at topic has been studied extensively for quanti- constraints limiting the evolution of adaptive Raytheon in June of 2020. The change has tative traits in animal and plant populations. traits. The work was exciting and brought brought new challenges and opportunities Modeling trait evolution of large asexual pop- together my interests in stochastic processes into my life, and I am excited to see where my ulations such as microbes presents unique career takes me.

New Program Affiliate Profiles Laura Miller, Professor, Mathematics

Laura Miller joined particular, I am interested in how biological use of physical models to measure forces and the faculty of the structures have evolved to increase fluid flow velocities, and numerical simulations Department of transport and locomotion efficiency, the ways to understand the fluid dynamics of systems Mathematics at the in which fluid forces constrain biological that are difficult to approach experimentally. University of Arizona design, and the role of fluid dynamic forces These approaches complement each other in a in the fall of 2020. during development. My previous work has variety of ways. Measurements of morphology She is also an affil- focused on developing mathematical models and kinematics are used to set appropriate iate member of the and experiments to describe the pumping me- parameter values for simulations and physical Program in Applied chanics of embryonic and tubular hearts, fluid models. In many cases, physical models can Mathematics GIDP. transport through biological filtering layers, be used to study a large range of parameter Before joining the the fluid dynamics and structural mechanics values that would be difficult to investigate University of Arizona, she was a Professor in the of jellyfish swimming, and the aerodynamics numerically. Numerical simulations can be Departments of Mathematics and Biology at the of flight in the smallest insects. A central goal used to obtain detailed descriptions of flow University of North Carolina at Chapel Hill. She of my more recent work is to couple problems fields and to model biological systems with received an M.S. in Zoology from Duke Universi- in biological fluid dynamics to electrome- complicated mechanical properties. ty in 1999 and a Ph.D. in Mathematics from the chanical models of organs and organisms In terms of computational tools, the ma- Courant Institute in 2004. whose dynamics rely on environmental cues jority of my work has focused on using the I have used my training in both mathematics and neural activation through the action of immersed boundary method to solve the and biology to understand how organisms pacemakers. At the larger scale, I am develop- fluid-structure interaction problem of an elas- have adapted to their mechanical environ- ing models to quantify how the behavior of tic organ or organism in a viscous fluid. The ments. More specifically, I apply mathemati- small organisms can affect their long distance immersed boundary method provides a math- cal modeling, computational fluid dynamics, dispersal in air and water. ematical framework and numerical method and experimental fluid dynamics to reveal To study these problems, I have used a three- for solving the Navier-Stokes equations with the interactions between fluid forces and pronged approach that consists of measure- immersed elastic structures. Various fiber organ and organism form and function. In ments of morphology and kinematics, the models give the immersed boundary certain

4 desirable material properties relevant to many develop and test artificial heart valves, and ical simulations of flow around organisms scientific applications. Some examples of the tools that we provide should enable more and within organs. We will also 3D print these fiber models used in my work are linear and cardiovascular scientists and engineers to objects and place them inside flow tanks for torsional springs and beams, target points answer fluid-structure interaction questions comparison to simulation. I anticipate that for preferred motion, massive points, porous computationally. Our new method for treating some of these projects catalyze new research interfaces and volumes, and muscle fibers. the immersed boundary as a source or sink for directions in my group. This course will be The use of springs, torsional springs, beams, chemical concentrations should find many taught in Spring 2021 as MATH 481. and target points in the immersed boundary applications in biological problems including framework are now somewhat standard. The gas exchange in the lung, nutrient uptake by modeling challenge is to find the correct the gut and in filter feeding animals, and heat spring or beam model (or combination) with dissipation in a variety of organisms. the appropriate parameter values to describe I am currently designing an undergraduate the system of interest. Often new models and modeling course that will focus on organisms numerical methods are required to describe living within moving fluids and fluid flows porous tissues and muscles, and no one-size- through organs. The natural world is replete fits-all model is available. with examples of animals and plants whose Given the versatility of immersed boundary shape influences flow to their benefit. For methods, the potential impact of the research example, the shape of a maple seed generates performed by my group and our collaborators lift to allow for farther dispersal. The structure is quite broad. The results of numerical simu- of a pinecone helps it to filter pollen from lations of swimming and flying animals have the air. A falcon’s form during a dive reduces been used to inform the design of biologically drag and allows it to reach greater speeds. The inspired micro-air vehicles and autonomous design of heart valves minimizes turbulence underwater vehicles. Furthermore, it is ex- and increases the efficiency of pumping blood pected that the computational tools devel- throughout the body. In this course, students oped in our work may also drive innovations will develop semester long projects with the in medicine. For example, our results could goal of understanding how organisms deal the inform studies that aim to address basic sci- air and water around them and fluids within entific questions such as the fluid-structure them. Throughout the semester, students will interactions that drive the formation of the mathematically describe the shape of organs developing heart to studies that consider the and organisms using photogrammetry, 3D function of the lymphatic system. Immersed scanning, and computer aided design (CAD). boundary methods have already been used to We will use the resulting 3D objects in numer-

Joshua A. Levine, Associate Professor, Computer Science

Joshua A. Levine is an My research falls at the intersection of things sect?” forces one to solve an equation and associate professor that can be done visually with problems that do arithmetic using floating point precision. in the Department of benefit from applying interesting mathemat- Inevitably, there will be an edge case where Computer Science at ical frameworks. While my focus has evolved two infinitesimally close lines will require University of Arizona over time, these days I focus mostly on visu- special care to distinguish from two barely and an affiliate alizing data from physical simulations (e.g. overlapping lines. By comparison, topological member of the climate simulations, energy applications, as- tools rely on integer operations that ultimate- Applied Math GIDP. trophysics). Often, these datasets contain inter- ly improve robustness. Second, these methods Prior to starting at esting features that can be described through are naturally multiscale. This allows the anal- Arizona in 2016, he either geometric or topological properties. ysis chain to separate feature from noise and was an assistant professor at Clemson University Quite literally, I study techniques that help to provide both coarse-grained summaries and from 2012 to 2016, and before that a postdoctoral extract the “shape” of data, which in turn leads fine-grained investigation. Finally, especially research associate at the University of Utah’s SCI to properties we can show domain experts. for the domains I work with, we can compute Institute from 2009 to 2012. He is a recipient of To robustly compute shape-based features, I explicit features in the forms of data struc- the 2018 DOE Early Career award. He received rely on techniques in topological data analysis tures such as Reeb graphs and Morse-Smale his PhD in Computer Science from The Ohio State for visualization. In the past couple decades, complexes. These features can be embedded University in 2009 after completing BS degrees topological data analysis has provided a within the domain of the dataset and directly in Computer Engineering and Mathematics powerful tool set. There are multiple keys to visualized as proxies for the data. So it’s a win- in 2003 and an MS in Computer Science in its success. First, these methods are based on win-win for data analysis: we avoid computa- 2004 from Case Western Reserve University. algebraic topology, which provides a natural tional problems, we provide natural filters to His research interests include visualization, discretization of data that avoids many of the interact with data, and we can present these geometric modeling, topological analysis, mesh features using visualization. numeric precision errors of other techniques. generation, vector fields, performance analysis, For example, a geometric operation such My most active project (Analyzing Multifacet- and computer graphics. as computing “do two line segments inter- ed Scientific Data with Topological Analytics) 5 New Program Affiliate Profiles( continued) focuses on studying topological properties of less developed. Particularly, the tools that tell tions in combustion science and materials simulations that produce many simulation us about shape by analyzing topological prop- research. The same problems are also of outputs that need to be analyzed simulta- erties work great for one-at-a-time analysis, significant interest to the Department of En- neously. A great example of this is climate but do not yet address the use case of”many- ergy national laboratories, for which we have simulation. These multiphysics codes model at-a-time. Machine learning, on the other many close collaborations. The connections all aspects of climate -- spanning land, air, hand, works great for looking at distributions I have developed through the Program in and sea -- including temperature, pressure, of data. My research group has been asking Applied Math have already been fruitful, and humidity, precipitation, sea ice temperature, “how can we use machine learning to study I look forward to many opportunities to forge wind flow, ocean flow, and more. These codes the shape of many variables simultaneously?” new ones in the coming years. are enormously complex because they are Particularly, how can we study distributions trying to find the most accurate prediction of topological features and how can we learn possible of a huge chaotic system. the relationships that exist between these Topological data analysis already provides distributions? the tools we need to study any one aspect (e.g. Solving these problems is a great opportunity temperature). I want to develop new tech- for computer scientists and mathematicians niques that are suitable for analyzing combi- to work together closely with subject matter nations of aspects (e.g. what does air tempera- experts. A boon of being affiliated with the ture tell us about humidity combined with Applied Math program is we get to work at sea ice levels?). There is a huge opportunity this intersection. Besides the climate example here since both the mathematical frameworks described above, there are lots of stakeholders and the computational tools are somewhat here at UA who want to investigate applica-

Alumni Profiles Zhuocheng Xiao (PhD 2020) Swartz Postdoctoral Fellow, Courant Institute of Mathematical Sciences, New York University

The scientific career However, interest is just the start, and it never project was that one has to be ‘omnivorous’ is usually made up lasts long alone without reward. Nothing when working in such an interdisciplinary of the ‘dynamics’ provides a better reward than solving a little sci- field. Problems always emerge from unex- of self-motivation, entific problem by yourself. After that, one may pected aspects, and you are never entirely self-discipline, and find another one to solve, possibly larger. For prepared by your previous coursework. If peer pressure - at that, it is necessary to undergo rigorous training needed, one should keep absorbing new skills least it is true for me. to acquire a good sight of the field, as well as and information. I was first obsessed strong skills to dig into any potentially interest- Therefore, after MLMC, I decided to learn with computational ing problem. Coursework and exams assigned some ‘real’ neuroscience by working closely neuroscience with by UA applied math program were never big with experimentalists since I did not want to the elegance of deals to me as one of the ‘exam problem solvers’ play with ‘spherical brains in a vacuum’ my the mathematical (‘做题家,’ a self-mockery from many Chinese whole life. I joined Prof. Jean-Marc Fellous’ models and their potential to explain the students who received strict test-oriented lab in the Psychology Department (who is also complicated phenomena in our brains since education in childhood). Instead, my biggest affiliated with the applied math program) and my freshman year at Peking University (PKU). challenges during my PhD years were: started working on electrophysiological data Since then, my career goal has been posed as a A. Always leaving my safe zone for something from rat behavior experiments. My previous mathematician studying the brain. I was not familiar with, and illusions of animal experiments collapsed in ‘Do you think it fun?’ once said Prof. Louis B. Self-regulation when multitasking. the first minute I touched the data: Raw data Tao, my advisor in PKU, ‘If not, go tech compa- is never organized as wished for theoretical nies for higher salaries, or maybe Wall street if I did fine for A. I once did some pure theo- studies, and no analysis can be carried out you can. Don’t hesitate.’ Well, so far, I am still retical study in my undergraduate years with before some dull and time-consuming data fascinated by my research. My undergraduate Louis and thought that was the whole world processing. After that, one might develop a degree in biology and PhD training in applied about computational neuroscience. But my specific hypothesis from modeling think- math provide me a unique background. I first project in UA with Prof. Kevin Lin, my ad- ing, which worked perfectly on dataset 1. come up with views from the experimental viser in math, was with completely different On dataset 2, well, some issues popped up, side when looking at the mathematical mod- flavors: multilevel Monte-Carlo (MLMC) for but still tolerable. On dataset 3, oops, it went els. I can also process the information from a spiking networks. The goal was to provide a thousands of miles away. It was then time to neuroscience paper in a quantitative way for more efficient algorithm for simulations in decide: Should we go back to modify/discard modeling. In all, I play with my dog bone on computational neuroscience, and the project the hypothesis, or we can convince ourselves the eternal field between math and neurosci- involved simulations, estimations of statis- to proceed since dataset 3 was not recorded ence. That is my biggest motivation for now. tics, and heavy proofs ultimately. The most correctly, hence should be excluded? Such important thing I learned from Kevin and this problems occurred throughout my time in

6 the lab, and I found it impossible to keep my next summer.’ And my first reaction was like, Courant Institute and one from Center of Neu- hands ‘clean’ as if I was still doing pure theory. ‘WHAAAAT? At THIS moment?’ Kevin then ral Science). After an intense interrogation of On the other hand, I would never have a more explained the pros and cons: There were great my studies, they told me I was an excellent fit comprehensive understanding of computa- opportunities at that time since many great for the position. I was informed that my most tional neuroscience without these experienc- places were releasing postdoc positions for significant attracting point was my experienc- es and projects with Jean-Marc. computational neuroscience; Completing my es in those studies with completely different However, I did a much worse job for B. It is PhD work in 4 years was a little hurry, but not themes, exhibiting the potential to develop generally good to sort everything on one’s an unreachable goal; On the other hand, one complicated projects with skills from various plate by the degree of importance and ur- more year bought me a better possibility for fields. gency. However, just like many other PhD more papers, yet the postdoc market would be What could I say? I have been dreaming of students in many different areas, my life went unpredictable in 2020 (what an unintentional working in Courant since my freshman year into a mess when I faced more than three prophecy for covid-19!). at PKU. tasks simultaneously. Obtaining a PhD seems My mind was finally made, then overwhelmed The last few months in UA applied math to attract many procrastinators, including my- by peer-pressure soon after I started my ap- program were overwhelmed by paperwork: self. Instead of solving the most urgent issues plication. While I was still torturing (or being writing and revising in front of my desktop. I first and keep investing a consistent amount tortured by - both work) the data in Jean- missed seeing Kevin and Jean-Marc in person of time in the most important ones, I kept do- Marc’s lab, my old friends at PKU started to due to the pandemic, and I still haven’t got a ing first the ones I liked most and stalling the publish in the top journals, i.e., Cell, Nature, chance to take a photo with my PhD academic ones I disliked until the last moments. Being a etc. Looking back to my hopeless CV after dress. After graduation, I move to New York, slave to the deadlines, I also suffered from the congratulating my friends, I fell into panic and my postdoc life inevitably becomes multi- high pressure that I could have avoided, which inevitably. Though Kevin and Jean-Marc did a tasking again with even more tasks in parallel, often resulted in insomnia. lot to soothe my nervous emotion, I could not including projects based on my original ideas. The situation became much more intolera- help believing that the great institutes would But this time, I am much more prepared, not ble when I finally had to face peer pressure. not even review my materials, and nobody only by the PhD degree but also by the invalu- I started to seek a postdoc position last fall. I would care about my work, since I did so petty able training provided by UA applied math was writing one manuscript with Jean-Marc in computational neuroscience and wasted so program. There are lots of uncertainties in the and analyzing data for another project with much time doing different things. I literally future, but so far, I still find my academic life him and revising my MLMC paper at the same cried out one night, desperately scolding my- fun. To current students (including many of time. One day in September, Kevin sudden- self as a useless person, until my roommates my friends): You may sometimes doubt if your ly asked me, ‘Do you want to get a postdoc were disturbed. efforts are in vain during your journey pursu- next year? If so, let’s start preparing your I would never forget my postdoc interview ing your PhD, just like what I did. But trust me, applications now, as well as your graduation with my current advisors at NYU (one from they never are.

Peter D. Miller (PhD 1994) Professor, University of Michigan Ann Arbor

Speedway for the last year. But what was by far in a suitable asymptotic limit. The rogue wave the best was the intermediate period where I problem is rooted in physics but the analysis had a great apartment just north of River on 1st involves lots of beautiful mathematics. I want Avenue with a view of the Tucson Mountains to explain how I got involved in these kinds of and the arroyos in between. I had a little hiba- problems and what happened to me along the chi grill on the balcony (is that even safe? I’m way. It started when I was a student in Tucson. pretty sure it was not allowed.). I really got a lot out of the coursework during My current research interests include all the first few years in the program. So many aspects of nonlinear wave theory, especially things just clicked. The main courses at the those connected with integrable systems, and time were “Principles of Analysis” taught by analysis applied to related problems also in the Hermann Flaschka, “Methods of Applied Math” fields of special functions and mathematical taught by Alan Newell and Marty Greenlee, and physics. I have a particular interest in asymp- “Numerical Analysis” taught by Bruce Bayly. I totic analysis problems; if a small parameter was certain that the teachers of these courses Peter Miller at the Mackinac Bridge in is going to zero somewhere, I’m there! As an were meeting together weekly to conspire northern Michigan, 2004. example, in recent work with Deniz Bilman about introducing the same topics simultane- and Liming Ling, we studied rogue waves of ously from three different perspectives, and I first came to Tucson in 1989 for my PhD after increasingly large amplitude and showed that while I don’t know for sure whether that was getting my bachelor’s from Southern Method- in the limit the rogue wave achieves a universal the case, it is what I prefer to believe, because it ist University, and I graduated in 1994. I lived form that is given by a particular nonlinear gave the material a cohesive appearance that I in different parts of town in those 5 years, for special function solving equations in the Pain- really appreciated then and still do today. After instance staying near Glenn and Campbell levé-III hierarchy. It is an example of a ``uni- the first year and the exams, I remember taking for the first year, and in an apartment behind versal wave pattern’’ that emerges either in the course in PDE and pulling all-nighters on what used to be called Reay’s Ranch Market on different problems or from different initial data the homework sets with classmates at a Den-

7 Alumni Profiles (continued) ny’s-like place on Campbell Ave. that has since papers on this topic, but actually the whole first, because I thought of myself as an applied morphed into Yoshimatsu. math department at Arizona was teeming with mathematician (of course) and this job was not In my first year, I also took a special top- experts in this area. As my interests developed, even in a mathematics department! I felt a little ics course on “Excitable Media” taught by I started talking with other faculty members, better when I learned that the Optical Scienc- Al Scott and Art Winfree. In talking with Al and ultimately I ended up writing my disser- es Centre shared a building with the Applied Scott I found out that he was interested in tation with Dave Levermore as my advisor, Mathematics department, although after I the quantum theory of nonlinear oscillators, although I learned equally much from Nick arrived down under I quickly learned that this which really sounded interesting to me as I had Ercolani and Al Scott as I did from Dave. I think was poorly named as it was really a department always found quantum mechanics to be a fasci- of the three of them equally as my advisors in of folks working in surfactant chemistry. But nating subject. We used to meet in his office to graduate school. in the Optical Science Centre there was a lot of informally discuss things, and sometimes later The mid-1990’s were a very difficult time to be soliton theory going on, which made me happy Al would put a paper in my mailbox to read if it on the job market. The iron curtain had fallen and feel at home. Shortly after I arrived in Can- was relevant to our discussions. One day when just a few years earlier, and the market was berra, so did Ole Bang coming from Denmark, I looked in my mailbox I saw a preprint of his flooded with very highly-qualified academics and it was a treat to work in the same depart- with some computations of the spectrum for from the former Soviet Union who were free ment with somebody I had known from before the “N=2” sector of a coupled system of quan- to seek employment overseas for the first and with whom I had already some common tum oscillators, and there was a sticky note on time. I remember receiving advice from my scientific interests. We ended up writing the paper that said “Would you like to try this mentors that it might be necessary to wait out several papers together. I had lots of projects in for N=3?” I took this as both a the time I spent in Canberra, some challenge and an invitation more mathematical and some quite to participate in research, and applied, but all very interesting. it was the gateway drug for Another aspect of my time in Can- me. As it turned out, the N=3 berra was that I was able to develop case was tractable by similar what has become a lifelong interest methods but required sub- in jazz music. I was a little curious stantially more computation. before then (that time with Al Scott In the end one could make in Copenhagen had something to plots of the energy spectrum do with it) but in the mid 1990’s partitioned according to a there was a book you could down- momentum coordinate, and I load for free from the proto-in- really liked those plots because ternet that was called “The Jazz they showed a discretized Improvisation Primer”, and with form of the band-gap structure some PhD students and colleagues that I had seen in solid-state we decided to go through this thing physics books, except now in detail together. Ultimately, we it was coming from my own formed a small band that we called computations. “The Light-Headed Trio” (there At that time, Al Scott spent Left to right: Connie Schober (PhD 1991); Alvaro Islas (MS 1992); Annalisa were 9 of us, obviously; and did you half of his time in Tucson and Calini (PhD 1994); Brenton LeMesurier; and Peter Miller (PhD 1994). catch the pun on optics?). We all the other half in Copenhagen, learned an enormous amount, and Denmark, at the Danish Technical Universi- the wave, and that it would be important to we even were able to get some chances to play keep an affiliation with an institution --- -re in public around town (that’s an advantage of ty. In the spring of 1992 I went with him to Denmark. While there, I had the opportunity gardless of whether I could be paid --- in order living in a smaller city!). Some of us still talk to visit the University of Salerno in Italy with to have a base for future applications. I think about “getting the band back together”. Al, and to speak there in a seminar about the in the end after sending out many applica- When my position was coming to an end in project we were working on together. It was tions I had two positive reactions, but actually Canberra, I found two opportunities almost si- my first time giving a talk, and I was nervous, it is enough to have just one! That becomes multaneously: a research fellowship at Monash but it went well. While staying in Copenhagen the door to your future. University further south in Melbourne, and for the rest of the semester and summer, I got For me, that door opened to the remote a membership at the Institute for Advanced to know lots of great people, many of whom Southern hemisphere, and a job in the Opti- Study in Princeton. I was torn, because I saw I have continued to maintain some sort of cal Sciences Centre at the Australian National the IAS membership as a great opportunity, contact with to this day. For instance, Ole Bang University in Canberra. I still remember especially as a stepping stone to a permanent was a graduate student at DTU whom I met the day I went in to see Dave, after thinking position in the US; but I also had come to love then; later our paths crossed more substan- about my options and coming to a decision living in Australia and wanted to go further tially on the other side of the planet when we to accept the job offer in Canberra. As I with that. However, it worked perfectly, be- worked as postdocs in the same department walked into his office, he simply asked: “So, cause I was able to negotiate a delayed starting (more about that soon). are you off to see the wizard?” date for the Monash fellowship until after the Another subject that I first learned about from Moving to Australia after graduate school program at IAS was scheduled to finish. Al Scott was soliton theory and integrable in Tucson turned out to be one of the best So next I moved from Canberra to Princeton, systems. Al had written some of the earliest decisions I ever made! I was a little hesitant at for a year. I lived on Einstein Drive! One of the

8 things I liked the best from this year was that I movie spoke to me, I guess. many different regular seminars so there is overlapped there with a good friend from high When I was working at Monash University, I always something interesting to learn about. A school whom I hadn’t really seen since then took a night-school class in the Japanese Stud- substantial fraction of our faculty consists of and who had also become a (pure) mathemati- ies Centre on that campus, and that is where postdocs who continually add energy to the de- cian. Another important thing that happened I met my wife! So that is really the most import- partment. One of my longest-standing collabo- to me during that year in Princeton was that I ant thing that happened to me during all of that rators, Jinho Baik, is also a professor here, and began a collaboration with Ken McLaughlin, time back and forth across the Pacific Ocean. we run a weekly seminar on integrable systems whom I had met at a conference when we were and random matrix theory. The commitment both students and whose father had been the During the first year of the fellowship, I got of our department to applied mathematics as a very person who had recruited me to Tucson the call from Ann Arbor. So, I negotiated a de- subdiscipline is evidenced by a new Michigan for my PhD! Working with Ken really opened layed starting date to let me finish two years of Center for Applied and Interdisciplinary Math- up a whole new toolbox of mathematical meth- the fellowship in Melbourne. Then in August ematics (MCAIM), that sponsors seminars and ods for me. Some of the tools I first learned of 2000 I moved to Michigan, where I have colloquia as well as conferences and short and during that year in Princeton are still my go-to lived ever since. In 2005 another alumnus long-term visitors. techniques in many situations, and I have of the Arizona GIDP in Applied Mathematics came to work at Michigan: Aaron King (PhD In the past 20 years a lot has happened. I got continued to collaborate with Ken on several to teach versions of the courses I remem- projects since then. 1999), who also worked with Al Scott. Aaron and I are both still here; just a few weeks ago bered from Tucson to new classes of graduate While I was at IAS, I took the opportunity to he spoke in our Applied and Interdisciplinary students, and I have had the chance to see how apply for permanent positions around the US. Mathematics seminar (over Zoom - there’s a they react to the material and learn about what One of the interviews I got was at the Univer- pandemic going on), and it was my great plea- they think is the most interesting. For five sity of Michigan, where they were building a sure to introduce him. years I got to direct Michigan’s own graduate program in applied mathematics. I really liked program in Applied and Interdisciplinary the feel of Ann Arbor when I visited, although I really like living in Michigan. The Great Mathematics, and I’m proud of the students it snowed during my visit late in the spring Lakes are, well, great. The proximity of Ann who’ve graduated from our program. I’ve semester. (As a person used to living in some Arbor to Lakes Erie and Huron has a mitigat- had the chance to write lots of papers on lots warmer climates, I have gotten used to this ing effect on the winter weather (although for of interesting topics with lots of interesting once-jarring phenomenon since then.) The people living on the western side of the state, co-authors, and a few books too. I’ve mentored wheels of bureaucracy turned slowly, so a job proximity to Lakes Michigan and Superior has my own PhD students and even more post- offer did not come immediately, but that was the opposite effect). In the summer, Ann Ar- docs (for those of you looking toward the job OK with me because I had a research fellowship bor hosts an annual summer festival with lots market, Michigan hires lots of postdocs every waiting for me back in Melbourne. of free outdoor entertainment over a three- year- please apply). week period as well as an annual Art Fair that So, I got back on the big plane and returned to brings artists from all over the world to show It has been 25 years since I moved away from Australia. My fellowship there let me work on off their works. Every Labor Day weekend we Tucson after graduating. But I’ve been back my own research without other obligations, so have the Detroit Jazz Festival, which is the many times to visit since then, even spending I made rapid progress on the circle of problems biggest free jazz (i.e., jazz that you don’t have parts of two sabbaticals there. The influence that I had been discussing with Ken McLaugh- to pay to listen to, not necessarily the oeuvre that the people, the living and working envi- lin back in Princeton. The only downside to of Ornette Coleman) festival in the world. ronment, and my studies at the time have had such a position is that some days you work on me throughout this phase of my career has hard but can’t prove a darn thing. On those days I also like very much working at the University been monumental. The real gem in Tucson I felt a little jealous of friends and colleagues of Michigan. Our mathematics department is isn’t to be found at the Gem Show, but at the who had more traditional positions and who huge, so there is a lot of variety of expertise intersection of 6th St. and Santa Rita Ave., in could earn a sense of daily accomplishment around. Like Arizona, applied mathematicians the building shaped like a multiplication sign from teaching and service duties when the work side-by-side with pure mathematicians and its more recent nearby outposts. math doesn’t flow. But “Galaxy Quest” had just in the same department, and we have a culture of collegiality that also reminds me of Tucson. With other Arizona alumni at the ICIAM Con- come out at that time, and the catchphrase ference in Valencia, Spain, 2019. “Never give up; never surrender” from that Since we are a large department, there are Current Student Profiles Jessica Pillow (5th Year Student)

During the summer of 2015, I did an REU (Re- enough to present our work at several confer- University of Arizona’s Program in Applied search Experience for Undergraduates) at the ences the following school year, which was Mathematics. Florida Institute of Technology. The research my senior year at Rhodes College in Mem- I did NOT realize just how hard the first year of was on a particular inverse PDE problem, and phis, TN. The summer made me realize that I the program would be! The math was difficult, eight weeks flew by as I studied functional wanted to continue studying and researching the homework was endless, teaching under- analysis and coded up numerical meth- mathematics, so I applied to several graduate graduates added a whole new challenge, and ods. I had a great experience with full-time schools and was very happy when I received then being far away from home for the first mathematical research, and I was even lucky the news that I had been accepted to the time made it that much harder. Between the

9 Current Student Profiles( continued)

research project, I was hooked. tion, which preserves edges. Tikhonov and The project focuses on developing new tech- TV regularization should not both be applied niques to deblur images, specifically images to the same pixel, so we enforce regulariza- captured by high-energy X-ray machines tion-based partitioning of the blurred, noisy during material science experiments conduct- image. We have developed such a method ed at the NNSS. Deblurring is formulated as based on statistical properties of the image; a deconvolution problem, which is ill-posed however, it requires a high level of involve- in the presence of noise. Reconstructions ment from the user. We hope to automate can be obtained by Tikhonov regularization; this process in the future, perhaps by imple- however, this method requires one to choose menting machine learning techniques. the value of a parameter that serves as a Now, after two-and-a-half years of research tradeoff between smoothing and fidelity to and two summer internships with the NNSS, the data. By assuming a Gaussian distribution I am wrapping up the project and writing my on the added noise, the issue of choosing the dissertation. My research advisors are Matti parameter’s value can be avoided by using a Morzfeld (now at UCSD), Matt Kupinski (UA Bayesian framework and letting the unknown Optics), Marylesa Howard (NNSS), and Jesse parameter be a random variable. By assuming Adams (NNSS). As I now spend most days certain prior information on the underlying writing my dissertation, I often stop and image, we construct a posterior distribution, think how lucky I am to have been included which in this case is a distribution of all in such an extraordinary group of scientists. start of the program in August 2016 and when possible image reconstructions for the given Thank you for everything. I am also thankful I passed the qualifying exam in January 2018, corrupted image. The optimal deblurred for this five-year chapter of my life in Tucson. I had thoughts of quitting the program at least image is the estimated mean of the posterior. In particular, during this time I came out as a fifty times. I’m glad I held on, though, because Samples are drawn from the posterior using member of the LGBTQ+ community, met Liz in September 2018, Matti Morzfeld asked me a Gibbs sampler, a Markov chain Monte Carlo (the love of my life), and married her just last if I wanted to join him and his collaborators at (MCMC) method. year. Tucson has been an amazing home to us, the Nevada National Security Site (NNSS) on a My work extends this statistical process of and we’ve had many adventures hiking and fully funded research project. One of his stu- deblurring by assuming each pixel in the trail running in the mountains. As my time dents who had been working with the NNSS image requires its own regularization value. in Tucson comes to an end, I want to thank (now AM alumnus, Jesse Adams, 2019) was Therefore, the balancing act between the everyone in the applied math program for graduating soon, and Matti wanted to contin- effects of regularization and fidelity to the welcoming me in over four years ago and for ue his working relationship with the lab by data is varied throughout the image. My work your continued support and encouragement. I bringing on a new graduate student. When also incorporates the use of another common feel lucky to have been a part of this program, I first met with Matti to discuss the possible technique—Total Variation (TV) regulariza- and I’m looking forward to the next chapter.

Alberto Acevedo (4th Year Student)

Quantum mechanics is the field of physics scheme or algorithm. Indeed, quantum com- used to study the properties and/or dynam- putation cannot exist without the existence ics of molecular systems, atomic systems , of quantum coherences, and it is therefore nanoscale material and so much more. Of of great importance that to understand how particular interest to quantum information these coherences are formed, how robust they scientist, amongst other things, is the study are and how they evolve in time. of quantum decoherence which is focuses In the beginnings of quantum theory physicist on the dynamical behavior of the so-called where content with so called “collapse” models coherences exhibited by a quantum systems. of decoherence where the superposition nature There is a one to one correlation between of any given quantum states were completely these quantum coherences and the “super po- wiped out after a measurement. An example sition” principle so one may think of them as is the famous double slit experiment in which being relatively the same phenomenon. These a beam of electrons is shot through a double coherences are not just curiosities but are also slit onto a subsequent detector wall/pad. If the fundamental in any quantum computation

10 beam of electrons remained undisturbed one there should be a link between this “classi- puters. My ANL project set the stage for what I observes a diffraction pattern on the barrier cal” reality and the quantum one that says would be doing the following summer during situated after the double slit but if disturbed that a quantum state may be in a superposi- the corona virus pandemic from the comfort by some measuring mechanism, e.q. photons, tion. It turns out that there is, and the link is of my house. During the summer of 2020 I then one would witness only a projection of essentially decoherence theory. It turns out received and internship from IPAM which was the slit as expected classically. Now, it turns out that a quantum system as described above to take place in Sendai Japan but COVID-19 that if the intensity of the measurement device decoheres to a state known as a “Spectrum happened and I had to work from home. is diminished gradually, we can continuously Broadcast Structure” which gives us al of the Lucky for me I got to implement my knowl- go from the two-fringe case to the diffraction statistical information about the state that of edge of quantum variational methods on a case. This observation already hinted at a more the particle that our n observers monitoring, new problem. This time I was working on the subtle dance between quantum coherence and minus the superposition. n-body problem but with focus on optimiz- the environment the quantum system evolves Aside, from my research and course work at ing an MCMC ( Markov-Chain Monte Carlo) in. It wasn’t until models invoking the appro- the UofA I have had the pleasure of complet- approach for estimating ground state energies priate Markovian-master equations for the ing two summer internships. of quantum systems. Attached is an image of study of quantum open systems that we began an MCMC simulation used to approximate the to really grasp origin of “decoherence”, i.e. the Summer 2019 I worked at Argonne national probability density function of a system of decay of quantum coherences due to environ- lab for the computational science department two fermionic particles in a potential well. mental influences. on several molecular dynamics’ projects. Us- ing variational methods that utilized a novel Currently I am finishing my coursework and With my advisor Dr. Janek Wehr I have had the framework, qiskit, manufactured by IBM for commencing on the work which will eventual- privilege of studying the rich field of quan- quantum computation using quantum com- ly turn into my PhD dissertation. Wish me luck! tum decoherence via the study of quantum open systems. More recently we have been interested in the study of compound quantum open systems, i.e. we study multiple open systems at the same time and analyze their dynamics in parallel. An example would be the state of some semi-classical particle and n conglomerates of scattered photons each with a trajectory terminating in the retina of a human observer. In such a system the particle is assumed quantum, and of course the photons will be quantum as well. We undoubtably know that anytime we see something in some room anyone other person in the same room facing the observed object should see the same thing, i.e. same configuration, and so

Hannah Kravitz (5th year student) action between the edges by assuming that a pulse of light is sent through a network of the solution exists only at the nodes and is interconnected waveguides. Only certain transferred instantaneously to other nodes frequencies resonate and in certain parts of via the connecting edges. However, in many the network. These lasing networks can be applications (lasers, water flow, gas flow, etc.) tailored and enhanced to achieve a desired the transmission is not instantaneous, and so configuration. Mathematically, this process the travel of information along the edges must can be represented by an eigenvalue problem be taken into consideration. This necessitates (the eigenvalues of the wave equation corre- the construction of a special type of network spond to lasing frequencies and the eigenso- called a metric graph, a network in which lutions to the light waves along the wave- the notion of physical distance is defined on guides). Thus, if the eigenvalues of the wave each edge. Even though there are numerous equation can be found for a given graph, one engineering applications, the mathematics of can predict the behavior of the network laser. PDEs on metric graphs is still in its infancy. I Interestingly, some eigensolutions are zero am excited to be conducting my research in nearly everywhere, with the entirety of their Networks are all around us, from city water this rapidly developing field. energy existing only on a localized shape. I grids to social media connections to the The current focus of my research is the study study these network systems from both an design of lasers. A network is made up of a of the wave equation on connected, finite eigenvalue perspective and a time-dependent series of points (nodes) and the connections metric graphs. One application of particular numerical finite difference once. between them (edges). In the past, modeling interest to me is the design and construc- I feel very fortunate for the opportunities of partial differential equations (PDEs) on tion of lasing networks. In this type of laser, the Program in Applied Mathematics has networks has primarily focused on inter- 11 Current Student Profiles( continued) afforded me. The interdisciplinary nature to be refined yet again in the coronavirus-era their desired career, or even just an obsta- of the program has encouraged me to share to accommodate online learners. It has been cle to overcome in order to continue on the my research and collaborate with experts in quite challenging to continue to implement path toward earning their degree. Therefore, optical science, public health, and mathemat- active learning online, but so far, my students when teaching non-math-major courses, I ics. I attended the SIAM (Society for Industrial and I have found success with Zoom breakout include applications to science and business, and Applied Mathematics) Workshop on rooms, polls, and online forums. One of my fun mnemonics (songs, memes, etc.) to help Network Science in Utah in 2019 and was able primary goals as a mathematics instructor is students remember concepts, and the use of to discuss the latest trends in network theory to make math accessible to students who lack smaller building blocks to build up to more research with other researchers who share my mathematical confidence. Lack of confidence difficult concepts. I have had many students passion. I also had an opportunity to present a in their mathematical ability keeps many tell me that they hated math until they took poster at the virtual Los Alamos Days 2020, in students from pursuing STEM careers entirely. my class. Hearing that I have turned former which I was able to interact with and present Most students taking an introductory math “math haters” into “math tolerators” is enough my work to researchers at a national lab. course do not plan to be mathematicians and to get me through even the toughest semes- In addition to my research, I have spent much instead see mathematics as a tool to use in ters of graduate school. of my time at the University of Arizona developing my skills as an educator. I have taught a range of classes from Business Calculus to Ordinary Differential Equations and have been able to refine my teaching philosophy and improve my teaching skills throughout my five years here. By attending teaching seminars, working with experienced educators in the Math Department, and through sheer trial-and-error, I have developed an active-learning style of teaching in which I keep lectures to a minimum and instead focus on work- sheets in which students work together to solve problems. Of course, this approach had

News from Members and Affiliates

Bredas, Jean-Luc (Chemistry and Biochem- Breiger, Ronald (School of Sociology) “Extreme and Inconsistent: A Case-Oriented istry) Top 5 Recent Publications: 1) 1165. 5 Publications in 2020: 1) Basov, Nikita, Regression Analysis of Health, Inequality, and “Nucleation-Elongation Dynamics of Two-Di- Ronald Breiger, and Iina Hellsten. 2020. Poverty.” Socius: Sociological Research for a mensional Covalent Organic Frameworks”, H. “Socio-Semantic and Other Dualities.” Poetics Dynamic World 6 (January): 1–13. https://doi. Li, A. M. Evans, I. Castano, M.J. Strauss, W.R. 78 (1): 1–12. https://doi.org/10.1016/j.poet- org/10.1177/2378023120906064. Dichtel, and J.L. Brédas, Journal of the Amer- ic.2020.101433. 2) Dabkowski, Matthew F, ican Chemical Society, 142, 1367-1374 (2020). Neng Fan, and Ronald Breiger. 2020. “Finding Chesson, Peter (Ecology 2) 1167. “Understanding Charge Transport Globally Optimal Macrostructure in Multi- and Evolutionary Biology) in Donor/Acceptor Blends from Large-Scale ple Relation, Mixed-Mode Social Networks:” Became Regents Professor Device Simulations Based on Experimental Methodological Innovations 13 (3): 1–17. effective January 2021. Film Morphologies”, H.Y. Li, G. Sini, J. Sit, A.J. https://doi.org/10.1177/2059799120961693. 3) Moule, and J.L. Brédas, Energy & Environmen- Mützel, Sophie, and Ronald L. Breiger. 2020. Lemoine, Derek (Dept of Economics, Eller tal Science, 13, 601-615 (2020). 3) 1168. “Struc- “Duality beyond Persons and Groups: Culture College) Published in 2021 “The Climate Risk tural and Electronic Impact of an Asymmetric and Affiliation.” Oxford Handbook of Social Premium: How Uncertainty Affects the Social Organic Ligand in Diammonium Lead Iodide Networks, edd. Ryan Light and James Moody. Cost of Carbon.” Journal of the Association of Perovskites”, S. Silver, S.N. Xun, H. Li, J.L. Bré- Oxford University Press. https://global.oup. Environmental and Resource Economists 8 das, and A. Kahn, Advanced Energy Materials, com/academic/product/the-oxford-hand- (1): 27–57. https://doi.org/10.1086/710667. 1903900/01-06 (2020). 4) 1171. “Organic Solar book-of-social-networks-9780190251765?c- Parent, Bernard (Aerospace and Mechan- Cells Based on Non-fullerene Small-Molecule c=us&lang=en&# 4) Pachucki, Mark C., and ical Engineering) My lab won two grants Acceptors: Impact of Substituent Position”, T. Ronald L. Breiger. 2020. “Network Theories.” this year: 1) Preliminary Estimates of Plasma Wang and J.L. Brédas, Matter, 2, 119-135 (2020). Cambridge Handbook of Social Theory, vol Properties in Hypersonic Boundary Layers 5) 1174. “Modulation of Broadband Emissions 2: Contemporary Theories and Issues, ed. Using CFD: The objective of this study was to in Two-Dimensional ⟨100⟩-Oriented Rud- Peter Kivisto. Cambridge University Press. gain a better understanding of plasma effects dlesden−Popper Hybrid Perovskites”, J. Yin, https://www.cambridge.org/core/books/ in vehicle boundary layers at hypersonic R. Naphade, L. Gutierrez Arzaluz, J.L. Brédas, cambridge-handbook-of-social-theory/8E- speeds. The study compared the results of O.M. Bakr, and O.F. Mohammed, ACS Energy 4225D618E166517A206DAEB09EA560 5) Ram- two CFD codes (CFDWARP and LEMANS) in Letters, 5, 2149-2155 (2020). botti, Simone, and Ronald L. Breiger. 2020. modeling plasmas including plasma sheath

12 effects. Additional analysis activities included in Communications (Volume: 38, Issue: 7, several probabilistic representations of the investigating plasmas at lower Mach numbers July 2020), 2) Muhammad Taqi Raza, Fatima evolution of a quantum system, leading to via sublimation of the ablation layer partly Muhammad Anwar, Dongho Kim, and Kyu- fascinating questions in both mathematics composed of cesium. Resulting data genera- Han Kim, “FERRET: Fall-back to LTE Microser- and physics. Here is the webpage with the tion was used to estimate how plasmas can vices for Low Latency Data Access” in USENIX description of the fellowship: https://www. effect radio communication and electron HotEdge, 2020. simonsfoundation.org/grant/simons-fel- transpiration cooling. Sponsor: Raytheon lows-in-mathematics/ Missiles and Defense. Duration: May 2020 Wehr, Jan (Mathematics) just received a — December 2020. Project funding: 45K. 2) message from the Simons Foundation that Xubin Zeng (Hydrology and Atmospheric Advanced Aerocapture System for Enabling my proposal, Mathematics of open quantum Science) Received the 2021 Charles Franklin Faster-Larger Planetary Science & Human Ex- systems, to the Simons Fellows in Mathe- Brooks Award for Outstanding Service to the ploration Missions: This is phase 1 of a NASA matics program has been recommended for Society from the American Meteorological Innovative Advanced Concept (NIAC) Project. funding. This will enable me to spend the Society. The citation reads “For skillful and The “Advanced Aerocapture System” consists academic year 2021/22 working on mathemat- effective service in senior leadership roles of using MHD forces — instead of control ical problems of quantum theory. This work that has materially improved the Society’s surfaces — to guide and control a capsule en- involves two graduate students from the Ap- meetings and other activities.” tering Mars’s and Neptune’s atmosphere. The plied Mathematics program: Dustin Keys and University of Arizona’s role in this project is Alberto Acevedo. My research will be on open Zhang, Chicheng (Computer Science) Pub- to perform simulations using CFDWARP of the quantum systems. It will be done in collabora- lished in the NeurIPS 2020 conference this coupling between the plasma flow surround- tion with three physics groups: at the institute year: 1) Crush Optimism with Pessimism: ing the capsule, the plasma sheaths near the of Photonic Science in Barcelona (Spain), at Structured Bandits Beyond Asymptotic electrodes, and the Lorentz forces generated Ecole Normale Superieure in Lyon (France) Optimality. Kwang-Sung Jun (also affiliate by the electromagnet. Sponsor: NASA Langley and at the Center for Theoretical Physics in member of the applied math program) and Research Center. Duration: September 2020 — Warsaw (Poland). I will be studying quantum Chicheng Zhang. 2) Efficient Contextual May 2021. Project funding: 125K. systems interacting with their environment Bandits with Continuous Actions. Maryam with a particular focus on quantum measure- Majzoubi, Chicheng Zhang, Rajan Chari, Raza, Taqi (Management Information ment. The influence of the environment can Akshay Krishnamurthy, John Langford, Systems, Eller College) Two Publications: 1) be modeled as quantum noise, leading to a and Aleksandrs Slivkins. 3) Efficient Active Muhammad Taqi Raza, and Songwu Lu, “Un- description of open quantum systems known Learning of Sparse Halfspaces with Arbitrary interruptible IMS: Maintaining Users Access as quantum Langevin equations. Mathemati- Bounded Noise. Chicheng Zhang, Jie Shen, During Faults in Virtualized IP Multimedia cal theory of these equations, which has been and Pranjal Awasthi. Subsystem”, in IEEE Journal on Selected Areas created by Hudson and Parthasarathy provides

Recent Graduates

Kevin Gomez, (PhD, Spring 2020) is currently a Senior Research Engineer at Raytheon Missile Systems, Tucson, AZ. Travis Harty (PhD, Fall 2020) is currently searching for opportunities in industry. Zhuocheng Xiao (PhD, August 2020) is currently a Swartz Postdoctoral Fellow, Courant Institute of Mathematical Sciences, New York University. Kenneth Yamamoto (PhD, August 2020) is currently an NSF- RTG Postdoctoral Visiting Professor, Department of Mathematics, Southern Methodist University (SMU), Dallas, TX. John McKinnon (MS, May 2020) is currently a graduate student in the Atmospheric Sciences PhD program, University of AZ. Kathryn Stefanko (MS, May 2020) is currently an Educator at Numerade. Jessica Zanetell (MS, May 2020) is currently faculty at North Yarmouth Academy, Maine.

13 News from Alumni

It has been a crazy year, and I really look on Quantum Chaos yet he couldn’t get through forward to getting vaccinated and being able to the first chapter of any QFT canon—started a travel again - hopefully sometime soon. program of learning QFT by, first, “taking QED Beauregard, Matthew (PhD 2008) was recent- seriously”, which meant trying to do the obvi- ly appointed as the interim chair of the Depart- ous thing for him (and for me and anyone else ment of Physics, Engineering and Astronomy I can easily relate to), namely write down and at Stephen F. Austin State University. solve the dynamical equations of motion for certain straightforward initial value problems Coombs, Daniel (PhD 2001) spent a lot of related to it. In doing so he finally started to 2020 thinking about mathematical modelling understand QFT and realized a lot of the para- applied to the covid-19 epidemic in Canada, phernalia associated with it is not only option- and how to communicate projections from al, but it some ways historically accidental and models effectively. This has included giving even misleading and obfuscating. Meanwhile advice about modelling to the provincial and Justin Peatross from BYU physics informed me Amir, Orna (PhD 1999) Five years ago I started federal public health agencies, and the federal a decade or so ago that there does not exist an working at Google in Israel where I have lived science advisor’s office, as well as talking to unimpeachable classical theory describing how since graduation. Initially I led the Data Science a lot of journalists. It has been an interesting a charged particle interacts with its own field. and Product Analytics group at Waze which year but not one that I want to repeat. Cheers, (“Classical” here means non-quantum mechan- grew over the years from 12 to 20+ people. It Dan Coombs ical, whether or not relativistically correct.) was exciting managing at this larger scale and This seemed ludicrous to me so I supposed that also solving problems with data and algorithms Garcia Naranjo, Luis (PhD 2007) is now an something closer to a “theory of everything” that improved the Waze App, an app I loved associate professor at the Mathematics De- should work, even if it amounted to using too using on my commute and travels. After 3 years partment “Tullio Levi-Civita” at the University big a gun. QED seemed to be that bazooka, so of mostly managing though I missed working of Padua in Italy. I used funds for a “Special Year in Quantum more hands on and developing models and Glasgow, Scott Optics” in 2011 to invite several big names in algorithms. In those years there were so many (PhD 1993) that area to BYU to give relevant talks. In doing advancements in the area of Machine Learning so I met (and became mesmerized with) Rainer that I felt could really help improve the product I hope each of Grobe, and ultimately co-authored a paper so I started a new smaller Machine Learning you can click on with him in 2012 (on the “Phi-4” QFT Model), team working on improving Waze’s estimated the link below along with BYU alumnus Sebastian Acosta. time of arrival (ETA) algorithm as well as other and see what we (Mesmerized: for example, Rainer gave a talk interesting drive related ML features. Ultimate- believe is one of in the BYU physics auditorium--standing room ly my team and I were able to improve the Waze my more import- only--in which he had the students and faculty ETA algorithm by a mix of simple algorithms ant contributions laughing out loud most of the hour yet learning and some sophisticated deep learning models, to physics, namely a “time-resolved” analysis new things with most every sentence. I was the both of which were very satisfying. of scattering of a photon off of an electron— Compton Scattering. (If you read the abstract, MC and he answered my final question before Having spent that time learning Python and intro and conclusion you should understand I could finish it, by belting out “42!”. The audi- new modeling techniques and working mostly the main novel claims of this work.) All but two ence erupted once more into laughter.) as an individual contributor I started missing of my papers in the last 20 years have had some Since then Rainer produced a paper in Physical having a substantial management role, which sort of support by the NSF, and this one and its Review Letters—the Inventiones Mathemat- brought me to my latest position as a lead logical predecessor in 2016 regard Quantum icae of physics—drumming up interest in and Data Science manager in the Growth and Electrodynamics (QED), what Feynman called the above kind of obvious approach to QFT, Notifications Team at Google. The group is re- “the crown jewel of physics,” this because it is namely to go ahead and try to solve obvious sponsible for ensuring that Google sends high the only nontrivial physical theory in which initial value problems, and our BYU group has quality notifications to its users. It has been its predictions are verified by experiment followed that direction of trying to continue to fascinating working with teams across Google’s to no less than ten significant digits. In case take things seriously (or literally, if you like). various apps to understand their needs in com- you want to know more: https://link.aps.org/ In doing so we have not kept up with Rainer municating with their users and working to doi/10.1103/PhysRevA.102.062203 and his army of post-docs in volume, with improve notification quality for Google users. Like a lot of students of physics I was intimi- their 7 to 10 papers a year, but in our last two I started my current role/adventure 2 months dated by Quantum Field Theory, QED arguably publications we have taken things even more into the new reality of working from home, the beginning, this because the usual introduc- literally than we think he and his people were with all or part of my family working/learning tions to it seem to rely on a lot more than just able, for example by discovering certain ways from home, depending on the local restric- a deep and thorough knowledge of Quantum of computing finitely with massless particles tions. My two boys, Aviv and Gal who are in Mechanics (my PhD thesis is effectively a (genuine photons) rather than with vanishing- high school and junior high respectively are treatise on QM), but rather on that plus some ly small but still massive approximations to now doing hybrid learning, and my husband sort of almost religious acceptance of certain such. (Something like division by the mass of mostly works from his office. Besides my “day axiom-like propositions such as the Feynman the particle arises in those dynamical theories.) job” at Google I have also been able to spend rules, which, together with certain perturba- Thus, we believe we’re keeping up with a cer- some time mentoring women in and outside tion series with infinite coefficients arising tain mandate that Henry Eyring seemed to hint of Google to start careers or take on more chal- from them, seemed (infinitely) unmotivated at a few years ago, namely that of producing lenging roles in Computer Science, Math and and hard to swallow. A German researcher high quality if not also quantity of work. Data Science. Rainer Grobe from the University of Illinois By the way the classical problem of how to with similar misgivings—his PhD thesis was 14 account for a charged particle interacting with via Double Application of the Divergence help me every day in this new field. I’ve even its own field is, we believe, completely solvable Theorem”, submitted for publication in IEEE been able to do a little statistical consulting for now, albeit by taking into account lessons Trans. on Antennas and Propagat. 2) J. Rivero, F. my company, which I’ve really enjoyed. learned for the larger, enveloping theory of Vipiana, D. R. Wilton, and W. A. Johnson, Eval- Uribe, Guillermo (PhD 1993) after 28 years of QED. Rainer has made progress there and about uation of MOM Reaction Integrals Applying the full-time work and 36 years of total commit- the only thing missing is how to do such with Divergence Theorem, URSI GASS, Rome, Italy ment to the University of Arizona, I retired on large numbers of such particles, ultimately August 29-September 5, 2020. June 30, 2020. My last year was productive. I then countenancing issues like those arising in Kilen, Isak (PhD 2017) published a paper in co-authored two papers on effectiveness of ac- various of the many-body problems. PRL this year: Propagation Induced Dephasing tive learning techniques in STEM courses, one Hardesty, Quintina (MS 2010) while at in Semiconductor High-Harmonic Generation - through the Math department and the other in Raytheon, had 3 submissions for Raytheon PRL Vol 125, 2020. collaboration with the College of Engineering. Intellectual Property where one was selected Love, David (PhD 2013) has a new position at I taught three courses during the year, two of as a trade secret and another for an innovation American Express as Manager, Chat Bot Devel- which ran during the fateful Spring 2020, in award. Since then, I have moved to Huntsville, opment, New York City, NY. the middle of the pandemic. My experience in AL to work as a Test Team Manager for SAIC. On technology helped the staff develop strategies the path to get my PE License in Industrial and Lyttle, David (PhD 2013) earlier this year to support faculty and students adapt to online Systems Engineering, I was recently certified started a job as a computational biologist, (do- teaching and learning. ing research on the human gut microbiome, as an Engineer-in-Training (EIT) in Texas and Washburn, Ammon (PhD 2018) will become working on getting certified as an EIT in Ala- i.e. poop science, haha) for Finch Therapeutics in Boston, MA. a Vice President of the projections pillar of bama. I have been happily divorced for a year Corporate Treasury at Goldman Sachs, Salt Lake and have spent the time focusing on my boys, Mercado, Gema (PhD 1999) was the Secretary City, UT. I will be in charge of automating and moving to Alabama and training to compete at of Education in the local government of the validating our liquidity projections. In Gold- the 2022 USA Weightlifting National Masters state I lived, Zacatecas, Mexico from September man, there are only five titles: Analyst to As- Championship in Salt Lake City, UT. 2016 to August 2020. Now, I’m taking a break sociate to VP to Managing Director to Partner. Hunke, Elizabeth (PhD 1994) This year, was until this following December to catch up with Just for context, around 20% or so of Goldman an author on two papers that received “Top a bunch of family matters. In January I might employees are VPs. Downloaded Paper for 2018-2019” awards, from go back to my academic job in the local Univer- sity where I am a math Professor. Williams, Katie (PhD 2016) was elected Pres- Journal of Geophysical Research: Atmospheres ident of Women In Bio for the 2022 term (she and Journal of Advances in Modeling Earth Rossi, Lou (PhD 1993) In August, completed will be President-Elect in 2021). Women In Bio Systems, and the Los Alamos National Labo- a successful term at Chair of the Department (WIB) is a non-profit organization comprised ratory (LANL) Fellows awarded her their Prize of Mathematical Sciences at the University of of 13 active chapters in the United States and for Leadership. In addition to leading the CICE Delaware. My plans to enjoy a sabbatical were Canada along with over 2500 members. WIB Consortium and serving as LANL’s program thwarted again when I was named Dean of the aims to promote the professional advancement manager for the Department of Energy (DOE) Graduate School and Vice Provost for Graduate of women in STEM. Office of Science Biological and Environmental and Professional Education. I still find time Research Division’s portfolio in Earth and En- to solve mathematical problems involving vironmental Systems Sciences, Elizabeth also plankton and flow down tree bark. Last year, I took on a new role leading Earth System Model enjoyed a brief visit with Michael Shelley (PhD Development for DOE’s Integrated Coastal 1985) where he is doing amazing work in com- Modeling project, whose goal is a robust, pre- putational biology at the Flatiron Institute in dictive understanding of coastal evolution that NYC. Tammy and I still have great memories of accounts for the complex, multiscale interac- the Program in Applied Mathematics where we tions among physical, biological, and human met. Our daughter just completed her degree systems. Check out her article in SIAM News in mathematics and computer science, and our (Oct 2020) for more information about her sea son has chosen to similarly major in mathe- ice modeling work: https://sinews.siam.org/ matics and computer science. Details-Page/the-challenges-and-opportunities-of-one-size-fits-all-sea-ice-models. Soneson, Joshua (PhD 2005) Our son (with Subok Park, PhD 2004) is now 10 and doing Johnson, William (PhD 1978) moved to the well with distance learning. Subok is still mountains about 20 miles from Los Alamos to working at FDA and I left FDA in favor of a job be close to my son and his family. I continue to at Johns Hopkins University Applied Physics consult remotely for Sandia National Laborato- Laboratory as a “senior acoustics modeling en- ries and do some technical work with friends. gineer.” I took a virtual walk through the UofA Here are 2 journal papers and one meeting that campus the other day using Google Streetview. we have. There are others but I am no lon- I really miss Tucson and the open spaces of ger trying to keep track of all of them as I am the American West. Hope to visit when the reaching 70 shortly. 1) D. R. Wilton, J. Rivero, pandemic is over. F. Vipiana, W. A. Johnson, ”Evaluation of static Integrals on Triangular Domains”, 10.1109/ Stockbridge, Rebecca (PhD 2013) is now an ACESS.2017.DOOI IEEE ACCESS Android developer at Detroit Labs. While I am no longer directly involved in mathematical Alex Young (PhD 2017) and J. Rivero, F. Vipiana, D. R. Wilton, W. A. John- research, the skills gained from the Program son, “Evaluation of 6-D Reaction Integrals Katie Williams (PhD 2016) 15 Current Student Achievements

Abrams, Ruby (4th Year Student) participated Division of Fluid Dynamics “on-demand ses- West LASE conference at the Moscone center in a remote summer internship at LANL XCP/ sion”, online, November 22-24, 2020 “Machine in San Francisco, CA., and presented during EEP division attempting to answer the question Learning Statistical Geometry of Turbulence”. the Vertical External-Cavity Surface-Emitting “Why do earthquakes look like explosions?” Kravitz, Hannah (5th Year Student) was Lasers (VECSELs) X subconference. My talk, and I passed my oral comprehensive exam! :) named the ARCS Foundation’s Kathryn John- Microscopic modeling of transverse non-equi- Deeny, Sheldon (2nd Year Student) spent ston West Scholar for the 2020-2021 school librium dynamics in mode-locked VECSELs, this past summer as an intern at Nevada year. This award consists of a scholarship was published in the conference proceedings. National Security Site (or MSTS Inc, a contrac- from ARCS, a supplemental cash award and Puente, Patricia (2nd Year Student) has tor) based out of Las Vegas. I worked for the travel grant from the Graduate College, and an been working in collaboration with Dr. Laura Signal Processing and Applied Math (SPAM) opportunity to represent the University of Ari- E Condon from the Hydrology and Atmo- group under Dr’s Marylesa Howard and Dan zona and present my research at an upcoming spheric Sciences Department to present the Champion (former UA math alum). This is virtual poster presentation. I was also given an work titled Identifying Patterns in Long Term the same organization that Jessica Pillow opportunity to present a virtual poster titled Streamflow Variability and Predictability (5th year student) is working and doing her “Eigenvalue Problem for the Wave Equation in the Upper Colorado River Basin using a dissertation with. with Applications to Random Network Lasers” Nonlinear Dynamics Approach. I presented Hyett, Criston (2nd Year Student) remotely at Los Alamos Arizona Days in May 2020. this work in an eLightning poster session attended a summer 2020 internship at LANL, Luca, Sarah (2nd Year Student) attended titled Uncertainty Analysis in Hydrology and CCS-2, mentor Daniel Livescu. Presented at APS the Woods Hole Marine Biological Laboratory Water Quality at the American Geophysical (MBL) virtual workshop on Brains, Minds and Union (AGU) Fall Meeting on December 14, Machines August 10-21, 2020. 2020. Although no travel was necessary, I was funded by Dr. Condon to cover the conference Luna, Kevin (5th Year Student) In January registration and AGU membership fees. 2020, presented a conference paper titled “The Role of Fluctuating Dissipative Fluxes Toner, Brian (2nd Year Student) Over the in the Receptivity of High-Speed Reacting Summer of 2020, interned remotely for the Binary Mixtures to Kinetic Fluctuations” at US Food and Drug Administration (FDA) in the the AIAA (American Institute of Aeronautics Division of Imaging, Diagnostics, and Soft- and Astronautics) 2020 SciTech Forum in ware Reliability (DIDSR). I explored how Deep Orlando, Fl. 2) In November, 2020 presented Convolutional Neural Networks could be used a poster titled “Accelerating GMRES with Deep in classification tasks to reduce the amount Learning in Real-Time” at SC20 (The Inter- of recalls for mammogram screenings. Will be national Conference for High Performance presenting a poster on the research in Febru- Computing, Networking, Storage, and Anal- ary, 2021 at the SPIE Medical Imaging Con- ysis; Also known as Supercomputing) that ference (most likely virtual, but still possibly was held virtually this year. This poster was a in San Diego) titled “Classification of round “Best Research Poster” nominee meaning that lesions in dual-energy FFDM using a convolu- it was in the top 4 out of 71 accepted posters. I tional neural network. Simulation study.” also gave a corresponding talk at a session for Woodward, Michael (3rd Year Student) In best poster finalists. 3) In January, 2020 was a January, 2020 gave a poster presentation titled funded participant of the 2020 Winter Work- “Hypersonic Boundary Layer Flows, Transi- shop on Optimization, Differential Equations, tion prediction, and Reduced Order Models” and Data Analysis held at UC San Diego. 4) at the 3rd annual Physics Informed Machine Over the summer and Fall 2020, I interned at Learning conference in Sante Fe NM. In No- the National Energy Research Scientific Com- vember, 2020 presented a talk titled “Machine puting Center (NERSC) at Lawrence Berkeley Learning of Reduced Lagrangian Models for National Laboratory. I worked on developing Turbulence” at the APS-DFD (American Physi- and implementing a methodology to acceler- cal Society - Division of Fluid Dynamics), and ate PDE-based simulations with deep learning in December, 2020 published an AIAA (Ameri- in real-time. 5) In April 2020, was awarded a can Institute of Aeronautics and Astronautics) Department of Defense (DOD) Science, Mathe- conference paper titled “Direct Numerical matics, And Research For Transformation De- Simulations of Laminar-Turbulent Transi- fense Scholarship Program award which will tion for Transonic Boundary Layers”. Was fund me for two years and provide guaranteed also awarded the Physics Informed Machine employment placement at a DoD lab. Learning conference student travel grant McLaren, Sam (5th Year Student) in January supporting my attendance and travel to Sante 2020, published an article titled Microscopic Fe, NM. Over the summer 2020, interned at modeling of transverse modeling of trans- Los Alamos National Labs in the Computer, verse mode instabilities in mode-locked Computational and Statistical Sciences Divi- vertical external-cavity surface-emitting la- sion where we worked on developing machine sers in the Applied Physics Letters journal. In learning algorithms of reduced Lagrangian February, 2020 attended the 2020 Photonics models for Turbulence.

16 Incoming Class Fall 2020 Program in Applied Mathematics, University of Arizona

Nick Bagley Alyssa Burritt Jalen Cates Eonho Chang Cornell University University of Cincinnati University of Alabama, Tuscaloosa UC Santa Cruz

Alex Christensen Bao Do Robert Ferrando Dunia Fernandez University of Arizona Columbus State University, GA City University of New York Montclair State University

Addie Harrison Fiona McCann Matthew McCaskey Erica Papke Wake Forest University University of Massachusetts, Appalachian State University Mercer University, Macon, GA Amherst

Marta Sowinski Vianella Spaeth Dan Van Boxel CUNY - Hunter College Embry-Riddle Aeronautical Purdue University University – Daytona

17 This newsletter is published annually by the Program in Applied Mathematics

The University of Arizona PO Box 210089 Tucson, AZ 85721-0089 appliedmath.arizona.edu Phone: 520-621-2016 Fax: 520-626-5048

Michael (Misha) Chertkov Chair Stacey LaBorde Program Coordinator, Sr. Keri Oligmueller Graduate Coordinator To submit articles or news items, contact: [email protected]