Institute for Mathematics IMA and its Applications 2 016 2 017 The Year in Review From the Director

It has been almost organizing seminars, holding working please see ima.umn.edu/programs/annual six months since groups, and running tutorials. Many of the for program information. Participation in I assumed the long-term visitors toured the optics labs in these activities is strongly encouraged. directorship of the the University of Minnesota Department IMA, and this has of Electrical and Computer Engineering. New initiatives at the IMA been a time of rapid The timeliness of the theme was evident For 2017-18, we are beginning a multiyear change. We are from the buzz of activity in Lind Hall, collaboration in data science sponsored by charting a new course, featuring vibrant discussions that carried Target Corporation and Cargill, Inc. The and with it, new over to coffee breaks. grants fund six industrial postdocs, who sources of funding. At This past summer, we ran our second will spend half of their time working on the same time, we are continuing to apply Math-to-Industry Boot Camp which again projects directed by industrial scientists the basic principles that have served the generated a large number of applications and the other half at the IMA under faculty IMA so well over its 35-year history. I’m for the 32 spots. This six-week program for mentorship working on their research delighted to report that these efforts are Ph.D. students in mathematics provides program. Augmenting this program are succeeding, thanks in large part to the seeds the technical and interpersonal skills that semester-long focus periods that include sown by our prior director, Fadil Santosa. students need in order to transition into workshops, long-term visitors, and training But before we look ahead, I want to step industry, along with experience working in programs. Our first thematic program back and review a successful and exciting teams on industry-sponsored projects. Our begins this spring 2018 and will focus on 2016-2017 academic year at the IMA. third boot camp will run again this June. Spatial-Temporal Data Science. Plans We also held a number of hot topics for the fall 2018 semester are currently workshops, including Transdisciplinary Mathematics and Optics underway and will be announced in the Foundations of Data Science in September Since its founding in 1982, the IMA near future. 2016, which focused on the mathematical structured its programming around a central The IMA has had a long history of ties underpinnings in this growing field, and research theme each year that brought to industry, and we are excited by this novel Mathematical Modeling of 2D Materials in together leaders in the field. The 2016- and diversified funding model for the IMA. May 2017. 2017 year was the last such annual thematic These interactions also bring us closer program, focusing on Mathematics and to the mathematical challenges that are Optics and organized by Gang Bao, Shanhui A more responsive IMA bubbling up in the private sector. Fan, Graeme Milton, Shari Moskow and After the NSF’s decision to ramp In addition to the consortium, we are Michael Weinstein. It brought together down funding of the IMA, we decided to building further connections with the a diverse group of experimentalists, change format to a broader scope of yearly U.S. Department of Energy, exploring engineers, mathematicians, and physicists programming that could address the rapidly mathematical foundations of problems interested in emerging technologies arising evolving landscape of applied mathematics originating in the national labs. Finally, in optical science, including plasmonics, and to more directly address the needs of our Participating Organization program metamaterials, and advanced optical our academic and industrial partners. After remains vital to the IMA, providing imaging. The close connection between a call for proposals to the community, a numerous opportunities for support and theoretical scientists and experimentalists group of five major activities were formed, engagement at the IMA, and we continue created an exciting collaborative and many of these programs will run to explore new ways to deliver more value atmosphere throughout the year. through the spring and summer of 2018. to our partners. We selected six postdoctoral fellows While only half complete, they’ve already On behalf of the mathematical sciences to participate in the annual program. In provided valuable insights into effective community, I would like to express deep addition, several long-term visitors spent collaboration models. The major programs gratitude to Fadil for his vision and positive a semester or the entire year at the IMA, are listed on the back cover of this issue; energy over the last decade. In particular, his cultivation of connections to industry has laid the groundwork for future new directions. He will continue to impact activities as the director of special projects. 1 2016-2017 Annual Program Year The Year in Review Finally, having served as deputy director Fiscal year of the IMA for two years and now as 2 Collaboration July 1, 2016, to June 13, 2017 director, it has been striking how many 4 Public Lecture Series Program year colleagues have expressed their strong September 1, 2016, to June 30, 2017 5 ima Prize Winner affection for the IMA, especially in its 6 Hot Topics Workshops exploring www.ima.umn.edu ability to nurture the formative stages Cutting-Edge Research Areas of many careers. This sense of collective Institute for Mathematics ownership of the IMA remains a powerful 8 Data Science Fellowship IMA and its Applications force in the community and will help to 9 research Experience ensure that the IMA continues as a center 10 in Memoriam Hans Weinberger of excellence in the mathematical sciences. We look forward to a bright future. 10 support the IMA

2016–2017 Annual PRogram

Workshops Mathematical and Physical Models of Nonlinear Optics Mathematics and Mathematical and Numerical Modeling in Optics Optical Imaging and Inverse Optics Problems Novel Optical Materials Optics and photonics are technologies that impact Emerging Topics in Optics society in a multitude of areas, including information and Other IMA Programs communications, imaging and sensing, healthcare, energy, Hot Topics Workshops manufacturing, and national security. September 14–16, 2016 • Transdisciplinary Foundations of Building upon impressive progress in fundamental optical science and in Data Science nanotechnology in recent years, optics and photonics have become drivers of May 16–19, 2017 • Mathematical technological innovation and economic growth. Modeling of 2D Materials The growing importance of the field is highlighted in the recent National Research Council report on Optics and Photonics: Essential Technologies for Special Events Our Nation, and the 2015 International Year of Light focused on raising global January 23–March 10, 2017 • IMA awareness of light-based technologies. Additionally, 2016 marked the 100th Data Science Fellowship anniversary of the The Optical Society. February 03, 2017 • Women in Data The field of optics and photonics encompasses the fundamental science of Science (WiDS) Conference light and its applications, and the long history of the field’s interactions with May 15, 2017 • Smart Urban mathematics covers topics ranging from ray optics to the classic theory of the Transportation Forum electromagnetic spectrum to the quantum nature of light. June 19–July 28, 2017 • Math-to- The IMA thematic program addressed a wide range of questions that have Industry Boot Camp II developed from the study of optical phenomena and connected mathematicians June 26–30, 2017 • IMA-MathCEP with the interdisciplinary community of scientists working in the field. Workshops Math Modeling Camp for High participants ranged from pure and applied mathematicians to physicists and School Students computer scientists. Workshop themes introduced participants to related June 29–July 01, 2017 • Recent applications, tools, and new techniques. Advances and Challenges in “The presence of many experts in the physics of optics and electromagnetics Discontinuous Galerkin Methods gave me an outstanding opportunity to gain an insight into the physical aspect of and Related Approaches themes related to my research. This will allow me to pay an increasing attention to July 24–August 11, 2017 • Industrial the physical properties of the models I analyze in my research,” said a Mathematical Mathematics Workshop and Clinic: and Numerical Modeling in Optics workshop participant. Collaboratively Tackling Emerging Problems in Industry The IMA thematic program also served to highlight the importance of topological insulators, a subject that was recognized by the 2016 Nobel Prize in August 14–18, 2017 • Phaseless Imaging in Theory and Practice: Physics, with talks on the topic arising at many of the workshops. Realistic Models, Fast Algorithms, “Not only did this introduce many mathematicians to the subject, but also and Recovery Guarantees the workshop on Novel Optical Materials served to forge links between people August 21–25, 2017 • Sage Days: working on topological insulators in mechanics and those working on it in optics,” Opening Workshop for a Year of said organizer Graeme Milton (). “That workshop also helped Coding Sprints forge links between people working on materials and inverse problems with ‘time- interfaces,’ or the material properties switch at given times, and people working Annual Program Organizers in the somewhat closely mathematically-related area of ‘hyperbolic materials’ that Gang Bao / Zhejiang University received attention due to their capacity for subwavelength resolution.” Shanhui Fan / Stanford University Mathematics and Optics was the 35th, and final, annual thematic program held Graeme Milton / University of Utah by the IMA, with more than 25 long-term visitors and 10 postdoctoral fellows Shari Moskow / Drexel University in residence. As one of the first two math institutes in the country, the IMA is Michael Weinstein / Columbia pleased to have set such high standards for how to run programs and workshops University of this scope. More information, including videos of the lectures, is available online at www.ima. umn.edu/2016-2017.

Year in Review • 1 Collaboration A Home Connection Originally from Minnesota, long-term visitor Aaron Welters (Florida Institute of Technology) came back home for the mathematics and optics program having long been aware of the IMA as a high- quality mathematical research institute.

Welters remembers his (University of Utah) and with IMA postdoc tion for our studies was to understand the first visit to the IMA Robert Viator. mechanisms that allow for simultaneous quite clearly as a 16-year- “With collaborators Graeme and magnetic Faraday rotation enhancement old coming to partici- Maxence, we continued our study of the and absorption suppression when the ferro- pate in the University of Dirichlet-to-Neumann (DtN) map for magnetic layer is highly lossy.” Minnesota Twin Family certain boundary-value problems for linear In addition to research, Welters organized Study. PDEs, such as Maxwell’s equations in the first half of the annual program seminar “I stood outside the bounded media and stratified media, using series with Peter Monk (University of Dela- offices of the IMA quite the important connection that had been Aaron Welters ware) and enjoyed all the social opportuni- amazed to be standing made recently with effective tensors in the ties that come with a long-term visit to the so close to mathematicians of such high theory of composites, for instance. We were IMA, such as tea time and group outings. caliber who were hard at work changing the especially interested in the applications of One particular highlight that Welters world with theorems,” he said. this connection to developing bounds and noted was bringing his 6-year-old son to Now a mathematician himself, Welters limitations on the DtN map in cloaking and see the IMA. was excited to be in residence at the IMA inverse problems.” “He pretend to do research in my office, with experts in his areas of research, namely “With Robert, we began a study on followed by pretending to be a student and the mathematical aspects of optics, such as the dissipative properties of electromag- then a teacher in a classroom, where he photonics and metamaterials. netic fields in stratified magnetic-dielec- lectured to me about mathematics at the “To be able to participate and contribute tric media. Our objective was to develop University of Minnesota,” he said. to such a fine program at the IMA was a deeper understanding of the interplay Then recalling his first visit to the IMA, professionally and personally something I between magnetism and dissipation in two- Welters thought about the passage of time. just couldn’t pass up,” he added. component composite systems in which “Coming back 20 years later to participate Welters dedicated much of his time one of the components is highly lossy. One in this mathematics and optics program, and effort during his fall semester visit to of the specific examples of the model we I now had an office within the offices of working with colleagues Graeme Milton considered was that of stratified photonic the IMA, and I was hard at work trying to (University of Utah) and Maxence Cassier crystals with lossy ferromagnetic layers and change the world with theorems,” he said. lossless dielectric layers. The main motiva-

Collaboration Annual Program Brings Back Former Postdoc Former IMA industrial postdoc Junshan Lin (Auburn University) came back for a year-long stay when his research interests in wave propagation and optics fit perfectly with the annual program.

Having been an IMA industrial postdoctoral cians provided novel mathematical analysis and computational fellow from 2011 to 2013, Lin already knew he modeling tools, which have the potential to solve the problems would enjoy the atmosphere of the IMA, where posed by physicists and engineers in the workshops,” Lin explained. visitors and postdocs are free to exchange ideas During the second half of the program year, Lin, along with and explore new research directions. Eric Bonneitier (Université Grenoble-Alpes) organized the annual He especially liked that IMA workshops are program seminar series. The subjects of the seminars ranged from interdisciplinary in nature and include partici- inverse and design problems in optics to numerical methods for pants across disciplines like mathematicians, electromagnetism, and other emerging topics in optics. physicists, and engineers. Lin also felt the “There is also a wonderful tutorial series on surface plasmonics Junshan Lin exchange of ideas and new developments among in graphene given by Tony Low (University of Minnesota, Twin the different disciplines injected new vitality to the field. Cities),” Lin added. “The talks always generated lively discussions; “For instance, physicists and engineers brought new mathemat- a group of us usually joined up for lunch together for further discus- ical problems and insights in several emerging topics in optics, such sion after each seminar. The talks also facilitated collaborations as the plasmonics and topological insulators, whereas mathemati- among several visitors.”

2 • Institute for Mathematics and its Applications Collaboration Developing a New Research Direction Former IMA industrial postdoc Nilima Nigam (Simon Fraser University) found the annual program workshops to be a near-perfect fit for her increasing interest in the mathematics of optics.

“I have been inter - ested in the analysis “I valued the deep scientific thought which clearly went into the and discretization of construction of the program and the collection of activities.” acoustic and electro- – Nilima Nigam magnetic scattering problems for several projects have her particularly excited. One is had many fruitful conversations, and he years,” she said. “More a collaboration with Jiguang Sun (Michigan suggested many interesting open problems. recently, my research Technological University) about eigenvalue I anticipate these will form an important interests have increas- Nilima Nigam problems. component of my research program over the ingly included eigen- “I met Jiguang Sun, who was visiting the next few years.” value problems, and I wanted to learn more IMA at the same time, and heard him give When asked about highlights of her visit, about novel application areas where these a wonderful talk about a fast method for Nigam noted the remarkable collection of arose.” locating eigenvalues for unusual problems,” people and activities that provide a unique Nigam knew about advances in optical Nigam said. “We chatted at the IMA coffee forum for mathematical exploration and materials and engineering, but was not sure break, and his work motivated me to revisit growth. about the mathematical and computational a very old eigenvalue problem in elasticity. “The scientific vibrancy at the IMA is research questions. She decided to take her I’d thought about this problem off and on incredible and intellectually inspiring,” she sabbatical at the IMA when it became clear for almost twenty years, but never had the said. “Where else could I have attended that she would not find another venue with time to work out the details.” public lectures, workshops, postdoctoral such concentrated expertise. Nigam and Sun made rapid progress, seminars, learned for hours from experts in “Nor (would I find) a forum for more with access to the University of Minnesota a new field, started several new collabora- casual mathematical interaction, which is libraries and computing services, and now tions, and found a quiet office to hammer my preferred way to develop collaborations,” have a couple manuscripts in preparation. out details in?” Nigam added. The other project that excites her stems “I’ve met people whose work I know and Nigam’s long-term visit during the from her interest in learning about optimiza- so many whose work I learned about for the spring semester proved fruitful in terms of tion problems arising in spectral geometry. first time,” Nigam continued. “I’ve come collecting new ideas for projects and starting “One of the world’s experts in the area, away with so many new mathematical ideas. collaborations, which she anticipates will Braxton Osting (University of Utah), was Without exaggeration, this visit to the IMA keep her busy for the next few years. Two another long-term visitor,” Nigam said. “We has changed my professional life—again!”

Lin had his own share of collaborations during his stay: nances in photonic crystals. The development of photonic struc- • With Hai Zhang (Hong Kong University of Science and tures with high quality factors, or low energy leakage, has significant Technology), he worked on mathematical studies of extraor- applications in physics and engineering, such as manufacture of dinary field enhancement in nanostructures. “We started by photonic chips, quantum information processing, and electron- looking at two-dimensional nano-slits structures and were photon interactions. Lin and Santosa’s collaboration actually began able to present quantitative analysis of electromagnetic field several years ago when they aimed to analyze, and eventually predict enhancement for the single nano slit and an array of nano or design, the energy leakage of such structures. slits. The study is a first step toward the understanding of the “In the beginning, we investigated a photonic structure that enormous enhancement that occurs in a rich collection of consists of a defect sandwiched between two finite periodic layers,” nanostructures, which we plan to explore next.” Lin said. “It is known that waves ‘trapped’ within the defect will • With David Nicholls (University of Illinois at Chicago) and eventually leak out of the structure. We studied the scattering Xiaobing Feng (University of Tennessee), he worked on fast resonances for the photonic structure and obtained an estimate numerical methods for wave propagation in random media. which says that the energy leakage rate is exponentially small in the “We proposed an efficient Monte Carlo–Transformed Field number of layers in the periodic sections.” Expansion (MC–TFE) method for the simulation of electro- “It was a fortuitous chance that we continued to chat on this magnetic wave scattering by random rough surfaces.” project when I was back at the IMA as a long-term visitor and Additionally, Lin collaborated with former IMA director Fadil started working on scattering resonances for the high-dimensional Santosa (University of Minnesota, Twin Cities) on scattering reso- photonic structures with defects.” Lin added.

Year in Review • 3 Public Lecture Series How Quantum Physics Democratized Music: A Meditation on Physics and Technology In May, Sir Michael Berry, a professor emeritus of physics at the University of Bristol, discussed how the connections between physics, technological invention, and aspects of human life that seem far removed from science are both unexpected and unexpectedly common.

Rather than flowing one way—from physics long after the physics was first formulated. to gadgets—the connections form an But physicists don’t always aim to make intricate web, linking all aspects of human their work applicable; they instead strive to culture. explain and theorize about things observed Berry’s first example of the connections in the world. For example, understand- between physics and technology related ing why gold is the color that it is means back to the title of his lecture—music. He understanding the interaction of light with contended that the arrival of the compact the electrons in the crystal structure of disc (CD) player should not be perceived as the material—and using mathematics to a discrete invention, but one that stretched predict the interaction. It turns out the back to 1917 and Albert Einstein’s ideas long, detailed calculation requires quantum about quantum physics and the processes relativity. by which atoms absorb and emit light. It was “Isn’t it remarkable that to understand the concept of stimulated emission that led this color that has so fascinated and beguiled to the invention of the laser, a component human beings for thousands of years requires critical for the CD player. for its understanding this other unexpected “It was unimaginable in 1917 by Einstein connection between the two great physics that in 1958—40 years later—his quantum theories of the 20th century: the physics physics ideas would lead to the creation of of the fast, or relativity, and the physics of this pure, bright light,” Berry said. “And it the small, which is quantum mechanics,” was unimaginable in 1958 by the physicists First one-twentieth of quantum revival time. Image Berry said. who invented the laser that in 1982, engi- from Michael Berry. To complete the web of connections, neers would use it to reproduce music.” Berry talked about examples where new While acknowledging that the CD player According to Berry, Leon Lederman, technology leads to new physics, such as needed the connections between physics, winner of a Nobel Prize for Physics in 1988, with quantum revivals, or the periodic recur- engineering, mathematics, business, finance, has claimed that at least a third of the gross rence of the quantum wave function. The advertising, and music itself to be successful, national product of industrialized countries equations look complicated, but with the Berry stated that the device is still simply a is the result of the direct application of help of computers, the mathematics can be quantum physics machine. And since the quantum mechanics. Without understand- brought to life as an image, such as the one CD player made music digital, portable, ing quantum theory, there would not have that accompanies this article which shows and convenient, “it’s not an exaggeration to been, among other things, microelectronics, the first one-twentieth of a revival time. say that quantum physics has democratized biotechnology, or diagnostic radiography, as Public Lectures, continued next page music,” he said. new technologies often don’t appear until

2016-2017 Public Lecture Series

February 2017 March 2017 Gunther Uhlmann / University of Washington Anna Gilbert / University of Michigan Inverse problems arise in all fields of science and Eighth Annual Arnold Family Lecture technology, where information is obtained about In the 1940s, several economists in the U.S. an object from a set of observed measurements. Public Health Service devised a cost-saving Taking human vision as an example, our method known as pooling designs to examine brains construct a detailed, 3-D map from groups of drafted soldiers for disease in a single measurements of scattered light that reach our test. These designs—and the more general retinas. Thus, solving inverse problems can problem of testing large populations of items— reveal what is hidden. But can objects be made became known as combinatorial group testing. invisible? Fascination with this subject includes Greek mythology and This lecture demonstrated the usefulness of group testing with a simple science fiction like Star Trek and Harry Potter. This lecture explored magic trick, described some modern applications of group testing in several inverse problems and then described a simple and powerful genetics, and then illustrated several group testing designs that come proposal for achieving invisibility, the so-called transformation optics, from error-correcting codes, which are used to transmit information so and other progress that has been made in the last decade. that a decoding algorithm can detect and correct errors.

4 • Institute for Mathematics and its Applications IMA Prize in Mathematics and its Applications Jianfeng Lu Awarded the 2017 IMA Prize in Mathematics and its Applications In September 2017, the IMA Prize in Mathematics and its Applications was awarded to Jianfeng Lu, an associate professor in the Department of Mathematics at Duke University, with secondary appointments in the departments of chemistry and physics.

Lu received this recognition for his contri- standing that helps “It has been my long-term goal to help butions in applied analysis, computational improve the existing build stronger and tighter connections mathematics, and applied probability, in approaches.” between applied mathematics with theo- particular for problems from physics, chem- Lu credits his Ph.D. retical chemistry and materials science,” Lu istry, and material sciences. The strength of advisor, Weinan E noted. “Oftentimes this leads to fascinating his research is combining advanced math- (Princeton Univer- challenges from the mathematical point of ematical analysis and algorithmic tools with sity) for teaching him view and calls for new development on the a deep understanding of problems from to always look for math side.” science and engineering. challenges outside Since receiving his Ph.D. eight years ago, “More specifically, I am interested in the existing bound- Lu’s list of about 100 peer-reviewed publi- understanding essential mathematical tools Jianfeng Lu aries of applied math- cations demonstrates his broad expertise and ideas behind the approximation and ematics and to never in terms of models, computational tools, numerical methods developed to deal with be afraid of learning and working in unfa- and rigorous techniques. Lu is currently complex chemical and materials systems miliar territories. focusing on numerical algorithms for high modeled at physical levels ranging from “My research and career paths have dimensional problems (either classical quantum mechanics to atomistic models also been majorly influenced by other or quantum) arising from these areas by to continuum mechanics,” Lu explained. mentors and collaborators, including Ingrid drawing and further developing tools from Research on the frontiers of mathematics Daubechies (Duke University), Shi Jin other areas of applied mathematics. in other fields has been quite fruitful for (University of Wisonsin, Madison), Robert “I hope this research direction will lead to him. Some of Lu’s major research achieve- Kohn (New York University), Jonathan fruitful interactions and cross-fertilization ments include ground-breaking contribu- Mattingly (Duke University), Felix Otto between various disciplines,” he said. tions to electronic structure models, multi- (Max Planck Institute for Mathematics The IMA Prize in Mathematics and its scale methods, rare events, and quantum in the Sciences), Eric Vanden-Eijnden Applications is awarded annually to a math- molecular dynamics. His most recent (New York University), Michael Weinstein ematical scientist who is within 10 years of contribution on the mathematical under- (Columbia University), and Lexing Ying having received his or her Ph.D. degree. standing of surface hopping algorithms (Stanford University),” Lu added. “They The award recognizes an individual who has generated enormous excitement in the taught me various aspects of applied and has made a transformative impact on the quantum chemistry community. computational mathematics.” mathematical sciences and their applica- “I have always been curious about the Collaborations with his Duke colleagues tions. The prize can recognize either a single latest scientific breakthroughs in other outside the math department, including notable achievement or acknowledge a body science and engineering disciplines,” Lu Thomas Barthel (physics), Volker Blum of work. The prize consists of a certificate said. “Most of my research is driven by curi- (materials science), David Dunson (statis- and a cash award of $3,000. Funding for osity in trying to understand the models and tics), Jungsang Kim (electrical engineering), the IMA Prize in Mathematics and its numerical tools that physicists, chemists, Henry Pfister (electrical engineering), and Applications is made possible by generous and materials scientists have developed and Weitao Yang (chemistry), bring him new donations of friends of the IMA. trying to develop a mathematical under- challenges and opportunities to research.

Public Lectures, continued

“There is a cliché that a picture is worth a The unexpected can also happen when these pictures and seen what would happen, thousand words, but it remains true that an translating equations into images. When so this is a quantum phenomenon,” Berry equation is a more economical representa- plotting the whole history of a quantum explained. “And my computer is a quantum tion summarizing infinitely many pictures. revival instead of only part of it, the image device, so quantum physics helps me do But economy and worth are not the same displays quantum carpets woven by extreme quantum physics.” thing. And the extreme compactness of interference, or an art-like pattern of over- Recorded public lectures are available on the equations can cause a loss of immediate lapping diagonal lines. IMA website at ima.umn.edu/public-lecture. understanding and communication which “We wouldn’t have thought of under - pictures can remedy,” Berry said. standing (all the lines) if we hadn’t drawn

Year in Review • 5 Hot Topics Workshop Exploring Cutting-Edge Research Areas IMA hot topics workshops continue to investigate emerging mathematical and scientific questions while gathering those with diverse backgrounds to strengthen interdisciplinary connections.

Transdisciplinary Foundations of Data Science As diverse and high-volume data sets have become more easily generated and stored in many scientific and business applica - tions, interest in research pertaining to data science has risen in both academia and industry. However, according to workshop organiz- er Gilad Lerman (University of Minnesota, Twin Cities), the foundations of data science as a field are far from developed, and it is difficult for practitioners to develop reliable models from data and for the public to trust Transdisciplinary Foundations of Data Science the models derived from big data. “More specific challenges include univer- sality versus domain expertise, casual infer- This will help me with the teaching that reproducibility and generalizability of ence, limits of predictability, non-station- of data science-related courses results are important to demand. arity of practical settings, guaranteeing “There was an inspiring discussion and and my independent research.” successful heuristics such as deep learn- talk by Daniel Goroff (Alfred P. Sloan Foun- ing, and building data science as its own – Workshop participant dation) on the possible use of differential domain,” Lerman said. privacy as a way to improve reproducibility,” The hot topics workshop in September Foundational considerations included Lerman added. brought together researchers from academia scientific methods (such as reproducibility The workshop also had several group and industry in three core areas of exper- of results), mathematical (such as perfor- discussions, which covered the challenges tise: mathematics, statistics, and computer mance guarantees, probabilistic estimates, and open problems facing researchers, science. The talks surveyed discipline- and generalization bounds), statistical (such curriculum development in data sciences, specific perspectives, results, and knowledge as causal inference, uncertainty quantifica- and effective interaction between industry gaps as part of a larger exploration into tion, and post modal selection inference), and academia. A particularly important how these perspectives could be integrated and computing (such as computational discussion revolved around building effec- and moved into a transdisciplinary, holistic complexity of problems, scalable algorithms, tive data science centers, as many of the approach to data science and its founda- and resource trade-offs). Lerman noted participants have been involved in helping tions. that one such outcome was the agreement build a center or program at their home universities. One workshop participant noted that “I finally found a way to start learning about data science and thinking about a research program.” t io n s: Lerman, who is also director of the IMA Data Science Lab, said “the University of Minnesota data science activities and curric- ulum development were strongly affected by the discussions and talks.” t io n ” Smart Urban Transportation Forum t “Ve h icle- o-Ve icle C omm un ica The rapid increase in urban populations, the surge of online retailing sales, and the rising concerns of climate change all call for a more safe, efficient, and clean urban transportation system. In May, the IMA hosted a one-day forum for experts to offer I mage f rom NHT SA re p or R ea d i n ess o f V2V Tec hn ology App lica

6 • Institute for Mathematics and its Applications their perspectives on the design, planning, Mathematical Modeling of and operation of the next generation urban transportation system. 2D Materials According to organizers Qie He (Univer- The hot topics workshop held in May sity of Minnesota, Twin Cities) and Anton was the first to focus on the mathematical Klegweyt (Georgia Institute of Technology), modeling and computing aspects of 2D a, T w i n C t ies) the increasing popularity of ride-sharing and materials, which are a class of nanomateri- ride-hailing companies already significantly als that are only one or two atoms thick affects the way people commute, and the and behave as two-dimensional structures. arrival of self-driving cars, communicat- Despite being so miniscule, these materi- ing cars, non-gasoline powered cars, such als possess the remarkable properties of as electric cars, and connected vehicles is being exceptionally strong, lightweight, expected to change the landscape of urban flexible, and excellent conductors of heat transportation systems dramatically over and electricity. the next 10 years. There has been an extraordinary level of

“Associated changes in infrastructure research activity on the electronic, optical, u l C azea x (U n i v ersi t y o f M nn eso Pa are needed to facilitate these new types and mechanical properties of 2D materials of vehicles,” Klegweyt explained. “This in the materials science community. Inter- creates a chicken-and-egg dilemma—the est in the mathematics community has Visualization of a 2D heterostructure car designers would like to know what the recently emerged with the goal of devel - infrastructure of the future will be like, but oping rigorous foundations and efficient the infrastructure designers need to know and accurate computational methods. The “[Most valuable was] meeting how the cars of the future will work.” major challenge addressed by this workshop and hearing many different The recent advent of new technologies was the modeling and computation of the approaches and perspectives in computer vision, telecommunication, mechanical and electronic properties of and auto industries and new transportation 2D materials. to the problems in our field. The business models also provide enormous “One of the main themes explored from mix of experimental, theoretical, opportunities. the perspective of physics, materials science, and mathematical physics was “One long-standing challenge is the traffic and mathematics was the mechanical relax- extremely interesting.” congestion caused by the mismatch between ation of 2D heterostructures into Moire growing travel demand and existing infra- patterns of commensuration and incom- – Workshop participant structure capacities,” He said. “Some recent mensuration, and models for the effect of developments to address this challenge this relaxation on electronic properties,” However, only one decade after the include intelligent traffic signals making use said workshop organizer Mitchell Luskin discovery of graphene, a host of other 2D of massive data from roadside and vehicular (University of Minnesota, Twin Cities). materials with semiconducting or insulating sensors, as well as a multi-modal transit Other new challenges have arisen over the behavior have since been discovered. system including bike and car sharing.” years to address the inhomogeneity of real “Even more exciting and promising is the The forum brought together a diverse 2D materials, which have ripples, defects, possibility of interleaving these materials to group of speakers, panelists, and partici- boundaries, and incommensurability. create stable structures with any combina- pants from industry, national labs, govern- “These aspects lead to challenges in tion of desired electronic, optical, magnetic, ment agencies, and academia to promote parametrizing tight-binding coefficients and thermal properties with atomic-scale communication and collaboration on for physical graphene and in the modeling features,” Luskin said. interdisciplinary research related to urban and computation of electronic properties,” Workshops related to this topic will transportation. A wide variety of disciplines Luskin added. “Thus, modeling the elec- be held in winter/spring 2018 under the were also represented, including computer tronic properties of 2D materials depends “Multiscale Mathematics and Computing science, operations research, civil engineer- on accurate modeling of their mechanical in Science and Engineering” program. See ing, industrial and systems engineering, properties. www.ima.umn.edu/2017-2018.3 for more mechanical engineering, mathematics, and The explosion of scientific and technolog- details. public policy. ical interest in 2D materials was sparked by Participants were able to learn about the 2004 isolation of freestanding graphene emerging issues, new research, and the sheets. However, workshop organizer types of technologies being developed in and speaker Efthimios Kaxiras (Harvard the transportation field. University) noted that “graphene, despite “The panel discussion at the end (of its exciting and unique properties, has its the day) demonstrated the potential for limitations, mostly due to the absence of rich discussion between practitioners and a band gap which is a necessary feature in researchers,” said a forum participant. most optical and electronic applications.”

Year in Review • 7 data science Learning Data Science at the IMA To help meet the burgeoning needs of industry in data analytics, and to create career pathways for young mathematical scientists, the IMA held a Data Science Fellowship this past winter to prepare Ph.D. students near graduation and recent postdoctoral mathematicians to become successful data science professionals.

The seven-week program trained participants in the basic techniques and tools in data science and provided the opportunity to work in teams on real-world industrial projects proposed by partner companies. The six selected fellows arrived with varied back- grounds—from low-dimensional topology and partial differential equations to scientific computing to combinatorics, probability, and numerical analysis— and while many of them had computing experi- ence, there was limited exposure to data science. The fellowship served as a way to bridge the gap in knowledge between graduate school and working in industry while providing a demonstrable skill set in data science for employers. “I’m looking to start a career in data science, but Data Science Fellows I come from a background in theoretical math with only occasional experience working with real-world data,” said Gavin King, a fifth-year graduate student This fellowship gave me the opportunity at the University of Wyoming. “During my graduate training, my interest in data to create a demonstrable skill set to show science and machine learning grew ‘by the second,’ employers that I have the knowledge to be but I had lots of questions about the field and the successful in a data career.” best approach to handle some machine learning prob- – melissa Davidson lems,” added Olabanji Shonibare, a recent graduate from Michigan Technological University. The program began with two weeks of instruc- effectively, developing “storytelling” using quantita- tion on basic skills by Daniel Kaplan, a professor tive findings, and recognizing that some data are of mathematics, statistics, and computer science at nonsense and contain little information. Macalester College. The small size of the program “We were given the opportunity to learn not only let participants interact closely with Kaplan and how to analyze data, but how to present it in an former IMA Director Fadil Santosa for help, advice, easily consumable fashion,” said Melissa Davidson, and feedback. a graduate from the University of Notre Dame. The remaining weeks of the fellowship were “Presenting data in a way that everyone can under- devoted to working on real-world projects provided stand is very powerful.” by Ford, New Frontier Data, Corning, 3M, and Alter- “I learned the pipeline of a data science project native Strategies Advisors on topics related to data if given a raw data set—how to start from it, how to wrangling, machine learning, predictive analytics, clean data, perform basic data analysis, and tell stories natural language processing, and sentiment analysis. from data, how to apply machine learning algorithms, This included analyzing glass data and building and how to deal with clients,” added Xiao Wang, a models to predict properties of glass; examining the fifth-year graduate student from University of Illinois results of an owner survey to study capacity loss of at Urbana-Champaign. the Tesla Model S battery; evaluating municipal bond The fellowship also assisted participants with trading activities and building a model to predict building their career paths by helping them seek higher trading prices in the future; and analyzing employment in industry and inviting professionals Comcast consumer reviews to determine patterns working in data science to talk about their jobs. that would improve customer service strategies. All six fellows left the program with promising job Over the course of seven weeks, the fellows leads, with three now having found employment with received several valuable lessons: learning to speak DST Systems, Starkey Hearing Technologies, and the language of their clients, using visualization tools Anheuser-Busch InBev.

8 • Institute for Mathematics and its Applications research experience Math-to-Industry Boot Camp This summer program returned for its second year to give 32 graduate students from across the country the training and skills needed to work in industry.

As in the first year, the six-week boot camp was divided into two parts: technical training and team-based, hands-on projects. Instructors from the University of Minne- sota School of Mathematics and Depart- ment of Industrial and Systems Engineering and from the local colleges of Macalester College and the University of St. Thomas taught students about probabilistic and stochastic modeling, optimization theory, and programming. Updates to the training portion of the 2017 boot camp included adding in the section on optimization theory and spend- ing more time teaching statistics. These Participants engage in a team-building activity technical changes were incorporated to match the skills needed for the projects and after consulting industrial scientists about the kinds of skills they look for in job candidates and employees. The soft skills training was refined to focus on team dynamics, effectiveness, and communica- 2017 Math-to-Industry Boot Camp participants tion. Students also learned essential skills for giving presentations geared toward a which were real-world problems posed that may not be optimal but are effective non-technical audience. by industry scientists. Industry mentor and (2) being able to convey that informa- “It’s not something that you’re trained Thomas Grandine (Boeing), with the help tion in a useful and concise way. for in mathematics because in school of another senior technical fellow at Boeing, “I think, on both of these points, there you’re trying to give seminars, but if you’re posed a problem related to machine tool is just a remarkable transformation that working in a company, you have a different and robot calibration through kinematic happens in the six weeks,” Spirn said. audience than an academic audience,” said analysis. “There is no doubt that these students IMA Director Daniel Spirn. “The graduate students discovered a bug can quickly learn the skills and gain the The project work that followed in the in his software that had been in place for technical acumen to do well on the techni- second half of the boot camp allowed over 15 years,” Grandine explained. “The cal side for these projects,” Spirn contin- students to utilize their new skills and accli- fact that his software still worked in spite of ued. “It’s more the comfort level of getting mate to teamwork. The first project allot- this error meant that there was something used to working and thinking in a different ted students one week to work on a small- deep going on with the mathematics in the way. They have to get used to not finding scale, open-ended problem posed by IMA application, and the graduate students were the most optimal result, as we’re taught in directors. One project involved generating able to figure it out after a few days.” math, but finding the result quickly enough a product or an app based on specific cell- After the boot camp, Grandine’s and that’s effective enough for the industry phone data. The assigned team devised an colleague fixed the bug in his software, and, mentor to be satisfied.” app that measures certain fitness activities equipped with the insight provided by the The results and positive experiences using machine learning and signal process- graduate students, was able to put a soft- seen with the boot camp have led the ing in a novel way. An unexpected result of ware enhancement plan in place. IMA to create a BIG, or business, industry, this project is that the team is working to “We are currently working through this and government, Internship Network to bring their product to market. plan and hope to have the upgraded capabil- support the development of similar gradu- The entrepreneurial aspect is “not some- ity in place in 2018,” Grandine said. “This ate training programs. The IMA will serve thing that many of them thought was possi- new capability will improve the rapidity as a hub to share resources, information, ble with a math degree,” Spirn noted. with which Boeing can calibrate machine and connections to industry among the Students were also able to make an imme- tools and robots.” network, which aims to serve a geographi- diate impact through their second projects, There are two key ways the IMA director- cally distributed audience. ship is gauging the success of students in the boot camp: (1) being able to find good technical results in a short period of time

Year in Review • 9 In Memoriam Support the IMA The IMA Remembers Thanks to Corporate Supporters Hans Weinberger The IMA thanks 3M, Cargill, C.H. The IMA expresses its sadness at the passing of its founding Director Hans Wein- Robinson, Eaton, Medtronic, Microsoft Research, and Target for providing funds berger, a professor emeritus in the School of Mathematics at the University of that support research, workshops, visitors, Minnesota, on Friday, September 15, 2017 in Durham, North Carolina. and social activities. Weinberger was an integral part of the IMA proposal created in response to the National Science Foundation’s request for proposals to establish a Mathematical Sciences Research Institute in 1979. Along with George Sell and Willard Miller, both Honor Roll of Contributors math professors from the University of Minnesota, they envisioned a mathematics September 1, 2016 to August 31, 2017 institute that would be bold and look outward from the core of mathematics toward applications. Its goal was to bring mathematicians and scientists together to focus on The IMA values and honors each and every gift, and thanks you for your interdisciplinary problems from academia and industry, creating new research that continuing and generous support. would have an impact on the science and enrich mathematics. Weinberger served as the IMA’s first director from 1982 to 1987. Under his leader- Donations to the Hans Weinberger Fund ship, the IMA quickly became known for cutting-edge scientific programs, a collab- support a variety of programs and activities. orative atmosphere, and as a training ground for postdoctoral researchers. During his $1,000 - $2,500 tenure, Weinberger was very engaged in scientific life at the IMA, attending lectures Jacobus Family Foundation and collaborating with visitors and postdocs. His presence at these lectures usually Peter Rejto meant that the toughest and most penetrating questions were asked. Scott Spector & Kathleen Pericak-Spector While well known for his contributions to the analysis of partial differential $200 - $500 equations, especially eigenvalue problems, Weinberger turned his attention to math- Tryphon Georgiou Balaji Gopalakrishnan ematical biology later in his career. He remained active in research throughout his Junshan Lin life and authored several papers after his retirement in 1998. Weinberger was elected Jose A. Orozco Rodriguez a member of the American Academy of Arts and Sciences in 1986 and was in the Paul Sacks Ivar Stakgold inaugural class of the American Mathematical Society Fellows in 2012. “In spite of his impressive accomplishments, Hans was the most modest and acces- $20 - $150 sible person one could ever meet,” said former IMA Director Fadil Santosa. “He was Henry Adams Robert D. Albright Jr & Carolyn Albright generous with his time and his ideas. He will be sorely missed.” Peter Baxendale In 2009, the IMA established the Hans Weinberger IMA Fund in his honor. The Aycil Cesmelioglu fund continues to support programs and activities that strengthen the IMA’s mission. Paul Constantine Isabel K. Darcy Douglas P. Dokken Leonardo Espin Robert Krasny Robert Kohn Barbara Lee Keyfitz Anna Mazzucato Michael A. Savageau John Voight Shinya Watanabe

Donations to the Eugene B. Fabes IMA Directorship Fund support an endowed IMA directorship. $4,000 Kahn Brothers, LLC—in memory of Donald Kahn

Donations to the Arnold Family Fund support the IMA’s public outreach efforts. $50 - $100 Douglas P. Dokken Shuanglin Shao Zhu Wang

Hans Weinberger

10 • Institute for Mathematics and its Applications Board of Governors IMA Partners Christian Borgs The IMA is a partnership of the National Science Foundation, the University of Minnesota, and a broad Microsoft Research consortium of affiliated universities, government laboratories, and corporations. Affiliation brings many 01/01/2014–12/31/2018 benefits to members, including access to research, influence over the IMA’s agenda, collaboration within Suncica Canic the IMA’s network, and opportunities to participate in workshops, short courses, and tutorials. University of Houston 01/01/2015–12/31/2019 Institutions Corporations Arizona State University University of Delaware Corning Incorporated Margaret Cheney Colorado State University University of Houston ExxonMobil Colorado State University Georgia Institute of Technology University of Illinois at Urbana- Ford Motor Company 01/01/2015–12/31/2019 Indiana University Champaign Honeywell Amir Dembo Iowa State University University of Iowa IBM Stanford University Korea Advanced Institute of Science University of Kansas Los Alamos National Laboratory 01/01/2012–12/31/2017 and Technology (KAIST) University of Kentucky Medtronic Michigan State University University of Maryland Bjorn Engquist Microsoft Research University of Texas, Austin Michigan Technological University University of Michigan Mitsubishi Electric Research 01/01/2013–12/31/2017 Mississippi State University University of Minnesota – Twin Cities Laboratories National Institute for Mathematical University of North Carolina National Institute of Standards and Irene Fonseca Sciences (NIMS) Technology Carnegie-Mellon University Greensboro Ohio State University Sandia National Laboratories 01/01/2014–12/31/2018 University of Notre Dame Pennsylvania State University University of Pittsburgh Schlumberger-Doll Thomas Grandine Pohang University of Science and University of Tennessee Siemens The Boeing Company Technology (POSTECH) University of Wisconsin – Madison 01/01/2012–12/31/2017 Portland State University University of Wyoming Purdue University Erica Zimmer Klampfl Wayne State University Ford Motor Company Seoul National University Worcester Polytechnic Institute 01/01/2013–12/31/2017 Texas A&M University Zhejiang University University of Central Florida Karin Remington Computationality, Inc. University of Chicago 01/01/2015–12/31/2019

David B. Shmoys 01/01/2015–12/31/2019 2016–2017 Postdoctoral Fellows Postdoctoral Employment, 2016-2017 Yang Wang Shelvean Kapita, 2016 Ph.D., University of Delaware Romeo Awi, Hampton University Hong Kong University of Science and Technology Wei Li, 2016 Ph.D., University of Michigan Rohit Gupta, Michigan State University 01/01/2014–12/31/2018 Shixu Meng, 2016 Ph.D., University of Delaware Mark Hubenthal, Amazon Natalie Sheils, 2015 Ph.D., University of Washington Shelvean Kapita, University of Georgia Incoming Board of Governors Members Robert Viator, 2016 Ph.D., Louisiana State University Wei Li, Louisiana State University Kaushik Bhattacharya Haitao Xu, 2016 Ph.D., University of Massachusetts Shixu Meng, University of Michigan California Institute of Technology Amherst Natalie Sheils, University of Minnesota, Twin Cities 01/01/2018–12/31/2022 Robert Viator, Southern Methodist University Martin Lacasse Industrial Postdoctoral Fellows Haitao Xu, Huazhong University of Science and ExxonMobil Mark Hubenthal, 2012 Ph.D., University of Washington Technology 01/01/2018–12/31/2022 Zhou Zhou, Doron Levy University of Maryland 01/01/2018–12/31/2022

Lois Curfman McInnes Argonne National Laboratory Credits Writer/editor: Rebecca Malkovich 01/01/2018–12/31/2022 Designer: Dawn Mathers Photography: iStock; Rebecca Malkovich Cynthia Phillips Sandia National Laboratories 01/01/2018–12/31/2022

IMA Directors and Staff Institute for Mathematics Daniel Spirn, Director IMA and its Applications Benjamin Brubaker, Deputy Director Katherine Dowd, Assistant Director The Institute for Mathematics and its Applications connects scientists, engineers, and mathematicians in order to address scientific and technological challenges in a collaborative, engaging environment, devel- Ines Foss, Accounting Supervisor oping transformative, new mathematics and exploring its applications, while training the next generation Shawn Golley, Database Applications Developer of researchers and educators. It receives major funding from the National Science Foundation and the Georgia Kroll, Workshop Coordinator University of Minnesota. Rebecca Malkovich, Communications Coordinator Sam Richter, Executive Accounts Specialist The University of Minnesota is an equal opportunity educator and employer. The University’s mission, Chad Sullivan, Systems Administrator carried out on multiple campuses and throughout the state, is threefold: research and discovery, teaching and learning, and outreach and public service.

This publication/material is available in alternative formats upon request. Direct requests to Georgia Kroll, workshop coordinator, at [email protected].

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Institute for Mathematics IMA and its Applications July 2017– August 2018 Major Programs for 2017-18

PROGRAMS Industrial Mathematics: Collaboratively Tackling Emerging Problems in Industry Innovative Statistics and Machine Learning in Precision Medicine Modeling, Stochastic Control, Optimization, and Related Applications Multiscale Mathematics and Computing in Science and Engineering SageMath Coding Sprints

www.ima.umn.edu/programs/annual