Infinite Dimensional and Stochastic Dynamical Systems and Their Applications Taking Stock

Institute for Mathematics IMA and its Applications 2012 2013

The Year in Review From the Director 1 2012-2013 Annual Program: Infinite Dimensional and Stochastic Dynamical Systems and Their Applications Taking Stock

2 Former IMA Postdoc John Voight The 2012–2013 Annual Thematic Program, which ended just a few Wins Selfridge Prize months ago, was on Infinite Dimensional and Stochastic Dynamical Systems. This was the third annual program on dynamical systems 3 Real-World Networking over a span of 20-plus years. The field is so big and so important that it made sense for the IMA to revisit the subject. Research in 3 New Directions Professor dynamical systems is active both within and outside of mathematics. Enrique Thomann Develops New Moreover, the field is also driven by the myriad of new applications and intersections with other areas of mathematics. Collaborations The first annual program in dynamical systems took place from 1989 to 1990. Even back then the organization of the program was 4 A Mathematical Celebration of Endre around application areas. The topics receiving attention then were chemical reactions, Szemerédi mathematical physics, physiology, and fluid flows. The overarching theme was the dynamical systems approach to these problems. 4 Kudos When dynamical systems returned to the IMA in 1997–1998, the focus was on emerging applications. Among the most important applications was mathematical biology. Other 5 MAXIMA REU Participants Win Big focus areas included the study of pattern formation. The activities on bio-related in San Diego applications that took place at the IMA during that year helped gel the mathematical biology community. The level of research in math biology exploded that year, and not 6 Ken Golden’s Research Is Improving long after that, the NSF founded the Mathematical Biosciences Institute at The Ohio Current Mathematical Models for State University. Global Warming Last year’s program had a different focus. This time the interplay between stochasticity and dynamical systems was explored in depth. The second half of the year was devoted 8 Was Pythagoras the First to Discover to applications. While many familiar areas were revisited—geophysical fluid dynamics Pythagoras’s Theorem? and biology—the ubiquitous component was randomness. The fact that uncertainty is everywhere in applications requires new mathematics. This was really highlighted in 9 IMA Holds Workshop on Career much of the discourse throughout the year. Options for Women in Mathematical What is rewarding to me is to see that many of the young researchers who spent time Sciences at the IMA in the previous two annual programs have become leaders in the field of dynamical systems; some were involved as organizers while others spoke at the workshops. 10 Green by Design It is also time for me to take stock of my role at the IMA. Last year, the IMA Board of Governors recommended that my initial appointment as director, which ran for five 11 Evolving Mean Field Game Theory years, beginning in July 2008, be renewed for another term. After much thought, I have Comes to the United States accepted the offer for a renewal but for a shorter two-year term. Therefore, I will be stepping down as director at the end of June 2015. Search for my successor is underway. 12 Outreach: New Science Buzz Kiosk But rest assured that I am not slipping into a lame duck director. I have much to do in at Science Museum of Minnesota; the next two years. Support for K-12 Math Modeling In March 2013, there was an NSF site visit to the IMA. As a result of the strong report by Program the site visit committee, we have been invited to submit a renewal proposal for funding. If awarded, the IMA’s funding will be secure until 2020. I have also made strides to increase the IMA’s international profile. We now have a very strong partnership with Korea. Three major universities in Korea are IMA Participating Institutions. Recently, the Korean National Institute for Mathematical Sciences established the Center for Applications of Mathematical Principles (CAMP). CAMP is modeled after the IMA so I was invited to give an inaugural address. It is very likely that the IMA will be collaborating with CAMP in the future. I am also exploring other collaborations in Asia. One area that I would like to do more is outreach. According to a 2010 report published by President Obama’s Council of Advisors on Science and Technology (PCAST), science, The Year in Review technology, engineering, and math (STEM) education is most successful when students develop personal connections with the ideas and excitement of STEM fields. The council Fiscal year recommended the creation of “opportunities for inspiration through individual and group July 1, 2012, to June 13, 2013 experiences outside the classroom.” To meet this challenge, the IMA is planning to offer Program year a week-long program in mathematical modeling for high-school students in partner- September 1, 2012, to June 30, 2013 ship with the University of Minnesota’s Mathematics Center for Educational Programs (MathCEP). Since this is an activity not currently funded by the NSF award, we are raising Institute for Mathematics money to support this effort. Our goal is to raise $50,000 to keep the program running for the next few years. I hope you will rise to our call for donations and give generously and its Applications IMA to this worthwhile effort. www.ima.umn.edu The work of the IMA would not be possible without the energy and support of our dedicated community. I want to take this opportunity to express my gratitude for all the contributions you have made over the years.

Fadil Santosa Director 2012–2013 Annual PRogram Workshops

Dynamical Systems in Studies of Partial Differential Equations Random Dynamical Systems Infinite Dimensional Lattice and Nonlocal Dynamical Systems and Applications Theory and Applications of and Stochastic Stochastic PDEs Stochastic Modeling of the Oceans and Atmosphere Dynamical Systems Stochastic Modeling of Biological Processes and Their Applications Other IMA Infinite-dimensional dynamical systems is a vibrant Programs field of mathematical development and has become Hot Topics Workshop central to the study of complex physical, biological, June 11–14, 2013 Mathematical and and societal processes. Computational Challenges in the Control, Optimization, and Design of Energy-Efficient Peter Polacik, University of Minnesota, one of the annual program organizers, Buildings noted that the theory of infinite dimensional dynamical systems provides an effective way of studying and developing other mathematical theories, Special Events such as partial differential equations, delay differential equations, lattice August 1–3, 2012 dynamics, and stochastic processes. Fostering Mathematical Part of the impetus for this annual program, according to organizer Entrepreneurship—Creating Peter Bates, Michigan State University, was the recent development New Businesses for Impact of tools for studying infinite-dimensional dynamical systems and and Wealth the need to push this development further. September 5–7, 2012 “Another aspect of the program is the focus on stochastic International Workshop dynamics,” Bates notes. “The rapidly expanding field of on Complex Systems and stochastic dynamical systems, in both finite- and infinite-dimen- Networks sional settings, promises to give some sense of predictability and September 12–14, 2012 order, even when realistic random perturbations are included.” Mathematics and the Materials The theory of random dynamical systems and stochastic Genome Initiative differential equations provides fundamental ideas and tools for November 12-13, 2012 the modeling, analysis, and prediction of complex phenomena; Mean Field Games and a large portion of the year was devoted to the theory and appli- Applications cation of stochastic dynamics. November 29–December 1, 2012 “All of these theories have seen a rapid growth and monu- Third Abel Conference: A mental progress in the last decades, both in their theoretical Mathematical Celebration of aspects and in the scope of their applications,” Polacik said. Endre Szemerédi “This makes it extremely desirable to provide specialists with March 3–5, 2013 different backgrounds in infinite dimensional dynamical systems Career Options for Women in with a platform for an exciting exchange of ideas and insights into Mathematical Sciences this vast research area, and the IMA is an ideal place to accomplish June 3–7, 2013 this goal,” he added. Joint U.S.-Japan Conference A week-long tutorial launched the new program year, with the first for Young Researchers on workshop, Dynamical Systems in Studies of Partial Differential Equa- Interactions among Localized tions, beginning on September 24 and running through September 28, 2012. Patterns in Dissipative Throughout the year, the IMA hosted more than 40 long-term visitors and Systems had 19 postdoctoral fellows in residence. June 10–July 19, 2013 MAXIMA Interdisciplinary More information, including videos of the lectures, is available online at Research Experience for www.ima.umn.edu/2012-2013. Undergraduates June 17–28, 2013 Annual Program Organizers New Directions Short Course: Applied Statistics and Machine Peter Bates Martin Hairer Kening Lu Peter Polacik Wenxian Shen Michigan State University Warwick University Brigham Young University University of Minnesota Auburn University Learning

Year in Review • 1 Postdocs Past & Present Former IMA Postdoc John Voight Wins Selfridge Prize John Voight, a former IMA postdoc, now at the University of Vermont (UVM), recently received the Selfridge Prize. The prestigious award recognizes those individuals who have authored the best paper accepted for presentation at the Algorithmic Number Theory Symposium.

His reaction to Voight said he was drawn to the IMA UMN. He and Sperber worked together finding out he had by the breadth and depth of the institute’s on computing the zeta function of certain been chosen to receive proposed activities, the strong reputa- varieties over finite fields—a generating the prize? tions of both the IMA and the University function which records the number of solu- Shock and “utter of Minnesota (UMN), and the appeal of tions to a system of equations. One novel disbelief.” delving into algorithm and mathematical aspect of their work, according to Voight, is “I remembered software development research. that it considers those systems of equations back to the first time As a postdoctoral fellow during the IMA’s with few monomials, a topic that popped up I attended a meeting Thematic Year on Applications of Algebraic during an IMA workshop. John Voight of the Algorithmic Geometry, Voight said the highlight of his Their paper—“Computing zeta functions Number Theory visit was the interactions he had with the of nondegenerate hypersurfaces with few Symposium (ANTS) in 2002. I was other postdocs, staff, faculty, and visitors monomials”—has now been accepted to the completely overwhelmed by the level of during the year. LMS Journal of Computation and Mathematics. the wide-ranging talks and wondered if I According to Voight, the theory, design, would ever even have a paper accepted to and implementation of algorithms in arith- the conference! In fact, I almost did not There are so many problems metic geometry is a burgeoning area and submit my paper at all,” he said. to understand, so many there are many exciting applications of At the time, he was working on general- these methods to diverse fields. connections to be made. How izing some joint work with Matthew Green- After completing his fellowship at the berg, University of Calgary, to the case of can I rest when there are so IMA, Voight joined the Department of arbitrary class number, and it turned out to many mysteries to solve?” Mathematics and Statistics at UVM. His be much more difficult than he expected. research currently focuses on algorithms “For many months, I would compute “I feel very privileged to have participated for cohomological automorphic forms and Hecke matrices that were supposed to in the IMA year as it significantly broad- interrelates abstract theory and practical commute but did not. As the deadline ened my mathematical perspective,” Voight computation. Specifically, the explicit inves- approached, I began to despair, but then explained. tigation of the Langlands correspondence— they extended the deadline for a week! He said that in addition to being the deep connection between automor- Divine intervention, or so it seemed. After surrounded by pure mathematicians whose phic forms, algebraic groups, and Galois a few days, I resolved the issue and just in areas of research were adjacent to his own, representations—in both classical and novel time to meet the delayed submission date!” he was able to connect with individuals settings. Given this uneasy beginning, Voight said working in quite different fields—from Applications for his research include he was sure the award was a “mistake.” biology to chemistry to optimization and coding theory and cryptography. Of course, it was not a mistake, and signal processing, not to mention colleagues “Today, mathematicians recognize that Voight’s paper, “Computing automorphic working in industry. geometric properties often govern the forms on Shimura curves over fields with “I was particularly struck by methods behavior of arithmetic objects. Further- arbitrary class number,” published in Algo- in numerical algebraic geometry, which more, computational tools provide a means rithmic Number Theory, was awarded the can often find approximate solutions to to test conjectures and can sometimes Selfridge Prize from ANTS, the premier lengthy systems of equations when tradi- furnish partial solutions; at the same time, international forum for presentations on tional methods in computational algebra theoretical advances fuel dramatic improve- new research in computational number fail. This numerical approach has remained ments in computation,” he added. theory. in the back of my mind as I have pursued my Since receiving the Selfridge Prize, Voight However, it was only a handful of years research since leaving the IMA, and in the has also received the UVM College of Engi- ago that the now award-winning Voight was past couple of years, has come to the front neering and Mathematical Sciences Milt a postdoctoral fellow at the IMA. and proved to be directly useful,” he said. Silveira Award, an NSF Division of Math- His first visit to the institute was in the Throughout his fellowship, he was able ematical Sciences CAREER Award in the fall of 2006 by way of Australia, shortly to develop new connections with all of the amount of $400,000, and an NSA Young after completing his postdoc in the Magma other visitors who wanted to better under- Investigator’s Grant. Computer Algebra Group at the University stand applications of algebraic geometry. of Sydney. In fact, during his visit, a long-term collaboration was sparked with his mentor, Steven Sperber, a faculty member at

2 • Institute for Mathematics and its Applications New Directions Real-World Networking New Directions Paolo Codenotti applied for a postdoctoral Professor Enrique fellowship at the IMA because the timely theme of the annual program—the Thomann Develops Mathematics of Information—aligned with his work on creating mathematical models New Collaborations for large-scale networks. Enrique Thomann has been a regular visitor

“I am particularly interested in to the IMA over the course of his career as a randomly generating networks that workshop attendee. ‘look like’ real-world networks, such as the internet, social networks, biological It just so happened that he was looking for networks (e.g., protein-protein interac- an opportunity to take a sabbatical where tion networks). One of the main reasons research was active and collaborations would this is useful is to detect anomalies. thrive. It was around this same time that he Something is anomalous if it is different found out about the IMA’s New Directions from what we expect, but in order to program. The topic of the year—Infinite Paolo Codenotti define ‘what we expect’ precisely, we need Dimensional and Stochastic Dynamical a random model.” Systems and Their Applications—was aligned Applications for his work range from creating more precise with his research, but one that he wanted to directions and more adaptive Twitter feeds to trying to find Enrique Thomann learn more about. mutations in genes that are involved in diseases. “In particular, the topic that I was curious During his stay, Codenotti was extremely active with the about, and that one that I learned the most about, was stochastic IMA’s outreach activities—from the Minnesota State Fair to PDEs,” he explained. During his visit, he and other long-term visi- the University of Minnesota’s homecoming events—rallying tors and postdoctoral fellows at the IMA worked to understand the other postdocs to planning activities for the students. how small noise perturbations propagate through systems of fluid “I find math very exciting, and I want to get other people mechanics. excited about it as well. I think it is one of our duties as scien- “What I am most proud of is the collaboration—that really tists to share our discoveries with everyone. I personally always started from nothing—that developed during my visit. This is a enjoy talking about math,” he said. substantial investment of time for me and the area is very inter- Codenotti headed to the University of Michigan in spring esting. There are opportunities for taking this technology to 2013 to work with Karem Sakallah’s group in the Electrical different areas and to collaborate with different people. This area Engineering and Computer Science Department. Currently, has a very steep learning curve, so being on sabbatical and able to use Codenotti works as a software engineer at Google, Inc. these months to jump into research was a big advantage,” he said. According to Thomann, although the highlight of his visit was the collaboration, he noted that he was also impressed by the third Abel Conference in celebration of Endre Szemerédi. “I attended the conference and it completely blew me away. It was one of the best conferences that I have ever attended. The quality of the speakers was excellent—it was very intense. It was just on another level. The mathematics was extremely inspiring and the conference represented a remarkable series of lectures,” said Thomann. The IMA is currently accepting applications for its New Direc- tions Research Professorships. Like Thomann, participants will spend an academic year immersed in the thematic program at the IMA, where they learn new mathematics and applications, connect their research with important problems, and establish new contacts and collaborations. IMA support, in the form of a subcontract to the home institution, will be for up to 50% of 2014-2015 salary with Codenotti (far right) explains the concept of cryptography, using the Jefferson a maximum of $50,000 for the entire nine- to 12-month visit. Wheel Cipher to kids at the UMN Science and Family Fun Fair. If you are interested in visiting the IMA during the 2014-2015 year on Discrete Structures: Analysis and Applications or the 2015-2016 year on Control Theory and its Applications, please apply online. Applications are due by February 2014.

Year in Review • 3 Third Annual Abel Conference A Mathematical Celebration of Endre Szemerédi The IMA’s third annual Abel Conference—a collaboration between the Norwegian Academy of Sciences and Letters and the IMA—was held in honor of Endre Szemerédi.

Szemerédi received the Abel Prize in 2012 for his It is no wonder then that the conference was the fundamental contributions to discrete mathematics largest to date with more than 100 participants gath- and theoretical computer science. He is a permanent ered from across the globe. Opening with an introduc- research fellow at the Alfréd Rényi Institute of Math- tion given by University of Minnesota Provost Karen ematics, Hungarian Academy of Sciences, in Buda- Hanson, the conference lasted three days with talks pest. He also serves as the New Jersey professor of that included Hillel Furstenberg (Hebrew Univer- computer science at Rutgers University. sity) who presented on “A Szemeredi-type theorem Szemerédi is described as a mathematician with for non-amenable groups,” Terence Tao (University of exceptional research power whose influence on California, Los Angeles) on “Arithmetic and algebraic today’s mathematics is immeasurable. Many of his regularity lemmas,” and Avi Wigderson (Institute for results have generated research for the future and Advanced Study) on “Points, lines, and ranks of design have laid the foundations for new directions in math- matrices.” ematics. He has published more than 200 papers in a According to organizer Joel Spencer, Szemerédi’s career spanning five decades. approach to mathematics is through discrete mathematics. He worked on asymp- totically large discrete objects, such as graphs and subsets of the integers. By moving toward infinite limit objects, his results have been recast in terms of dynamical systems and Fourier analysis. This conference saw a synthesis of these diverse methodologies.” The IMA gratefully acknowledges the generous support of IBM Research, Microsoft, and the University of Minnesota for this annual conference series.

KUDOS

Michael Levitt, a professor of structural In 2013, Anna C. Gilbert was named biology at the Stanford University School the recipient of the Society for Industrial of Medicine, was recently awarded the 2013 and Applied Mathematics (SIAM) Ralph Nobel Prize in Chemistry for his work in Kleinman prize. The award is given to protein folding. Levitt shares the prize with one individual annually for outstanding Martin Karplus (University of Strasbourg) research, or other contributions, that and Arieh Warshel (University of Southern bridge the gap between mathematics and California). The winners found a new way applications. Gilbert was recognized for for computers to model proteins and their her creative and deep contributions to the interactions in the human body. Levitt was mathematics of signal processing, data an organizer of the 2007-2008 IMA Annual Thematic Program on analysis, and communications. “Her bold and interdisciplinary the Mathematics of Molecular and Cellular Biology. He and Patrice work combines techniques from computer science, harmonic Koehl (University of California, Davis) organized a tutorial on the analysis, and probability in the best traditions of the Kleinman mathematics of proteins, including three hour-long lectures. Levitt, Prize,” cited the awards committee. In addition, Gilbert has been Ken Dill (University of San Francisco), and Sorin Istrail (Brown invited to speak at the International Congress of Mathematicians University) were responsible for the very successful workshop on in Korea in 2014. Gilbert, a professor of mathematics at the Univer- protein folding held that same year. The IMA is grateful to Levitt sity of Michigan, has been a regular visitor to the IMA since 1994. for his contributions to the IMA and congratulates him on this She has served an organizer and as a member of the institute’s momentous achievement. Board of Governors.

4 • Institute for Mathematics and its Applications Research experience for Undergrads MAXIMA REU Participants Win Big in San Diego MAXIMA, an intensive 12-student, six-week research experience for undergraduates (REU) in interdisciplinary mathematics, is funded by a three-year NSF REU grant and the IMA.

During the REU, students work in teams of four on open research “Design of Laser Beams in GRIN Media for Profile Transforma- problems in applied mathematics posed by University of Minnesota tion and Selective Resonance” was a joint effort by students Philip (UMN) faculty members. Each team is advised by a Macalester Burnham (Villanova University), Delani Cele (Ithaca College), College Mathematics, Statistics, and Computer Science faculty Hyunmoon Kim (Princeton University), and Tim Moon (Rice member and mentored by a postdoctoral fellow at the IMA. University). The program is designed to allow students to experience the The third MAXIMA research team was mentored by Macalester excitement of doing research that is relevant to another field. By Computer Science professor Shilad Sen. His group, who presented the end of the summer, each team produces a written report, an “The Lifecycle of Wikipedia Editors,” consisted of Alexander oral presentation, and a research poster. Bristol (University of Massachusetts, Amherst), Mary-Katherine Two posters submitted by MAXIMA teams received an Huffman (Virginia Polytechnic Institute and State University), Outstanding Presentation Award at the Mathematical Association Nathan Leech (Macalester College), and Guanyu Wang (University of America (MAA) Undergraduate Student Poster Session at the of Iowa). 2013 Joint Mathematics Meetings in San Diego, sponsored by the American Mathematical Society (AMS) and MAA. The session showcased the work of more than 500 undergraduate students. The top 15% of posters, as judged by mathematicians at the conference, received the Outstanding Presentation Award. “I am really impressed that our students stood out in this group of talented peers,” said mentor Andrew Beveridge. “They worked hard, developed some lovely results, and executed in the moment. It’s a pleasure working with them and watching their research develop.” Winners included Rosalie Carlson (Harvey Mudd College), Claire Djang (Oberlin College), Stephen Ragain (Pomona College), and Maxray Savage (Macalester College) for their project entitled “Pursuit-Evasion in Polygonal Environments: When Can Two Cops Win?”

Andrew Beveridge (second from left) with the 2013 MAXIMA participants.

Former IMA industrial postdoc Former IMA postdoc Arthur Szlam was Vasileios Maroulas (2008–2010, Lock- recently awarded a two-year Sloan Foun- heed Martin) received the Leverhulme dation Research Fellowship. The award Trust Visiting Fellowship from the Univer- seeks to “stimulate fundamental research sity of Bath in Great Britain. He will by early-career scientists and scholars of serve as a visiting faculty member in the outstanding promise.” The award is given Department of Mathematical Sciences to 126 researchers each year in recognition at the University of Bath from October 1, of “distinguished performance and a unique 2013, until June 30, 2014. He was one of the potential to make substantial contributions two awardees honored with fellowships to their field.” Currently a faculty member at through a university-wide competition. Maroulas is currently the City College of the City University of New York, Szlam focuses an assistant professor in the Department of Mathematics at the his research on computational harmonic analysis. According to University of Tennessee. In addition, his research will be supported Szlam, there has been much progress lately on the object detection by the Simons Foundation Collaboration Grant for 2013–2018. and recognition problems in computer vision. Many, or even most, of the successful methods use sparsity, encouraging transformations as a component, he explained. His current work focuses on trying to understand if this sparsity is causally important for solving these problems, and if so, what about them makes the sparsity important.

Year in Review • 5 Public Lecture Series Ken Golden’s Research Is Improving Current Mathematical Models for Global Warming Ken Golden is not your “average” mathematician. While he holds a Ph.D. in mathematics and teaches three or four days a week at the University of Utah, he also spends a good deal of his time in the polar regions, studying sea ice—frozen sea water—and the way it moves and melts.

According to Golden, conducting field Papanicolaou, a professor at NYU at the work is essential to developing relevant time, was teaching a class on random media mathematics in this area. and composite materials. “Sea ice is complicated—it does all sorts “I have to admit that the moment I first of things that you wouldn’t necessarily saw ‘percolation theory’ described at the expect. It’s one thing to sit in your office, blackboard, I thought of the brine phase in but it’s another thing to go down there and sea ice,” he said. “As I look back now, it was see it for yourself,” he explained. precisely what was needed to revolutionize Notably, he has made 16 voyages to the the study of sea ice and its transport proper- polar regions. He’s been interested in sea ties,” Golden said. ice since he was in high school, studying at Golden’s second published paper included the Institute for Arctic and Alpine Research a figure of these brine inclusions coalescing at the University of Colorado, Boulder, and connecting up to form pathways, which through an NSF summer science training was actually an example of percolation— program, as well as at NASA/Goddard when fluid can move through a porous during his senior year of high school. solid—although he didn’t know it yet. While a freshman at Dartmouth College, “The moment I saw George lay out he began working with Steve Ackley on radar mathematical percolation theory, I was like propagation in sea ice, gauging its thickness, ‘Oh, brine and ice, just like the figure I put and went on his first Antarctic expedition in my paper.’ Again, I had no idea this was during his senior year. important.” Other scientists had found that if the Then, in 1994, Golden was in Antarctica radar antenna is situated one way, you get a for his second trip out when he saw sea water big signal back from the ice-water interface, percolating up and flooding the surface. but if you turn it 90 degrees, then the return “Literally, in one instant, I knew—that’s almost vanishes. “By analyzing sea ice as a percolation!” he remembers. composite material and looking at its effec- And he spent the next few years studying tive electromagnetic properties, I was able this mystery. As it turns out, he had discov- to explain this phenomenon and develop ered the on/off switch for fluid flow in sea some of the first basic treatments of sea ice ice. This “switch” is critical to melt pond as a composite,” Golden said. This work led evolution and snow-ice formation—key to his second published paper, “Modeling of processes that help us to understand the role anisotropic electromagnetic reflection from of sea ice in the climate system. sea ice,” in the Journal of Geophysical Research. “It took about 10 years to play out in terms After Golden received his B.A. degree in of the mathematics, of actually bringing mathematics and physics at Dartmouth, he that one idea to fruition,” Golden said. “We planned to pursue a Ph.D. degree in math- published this paper in Science in 1998, and ematics from New York University (NYU). it was probably six, seven years down the Golden thought he would follow a more road that the sea ice world began to realize classical path for a mathematician—perhaps the effects. It affected everything. It sort studying differential geometry or quantum of explained all these processes that they field theory—because he wanted to be a had wondered about for a long time. It was “serious” mathematical physicist—and they a critical advance when the field work and don’t study sea ice. the theoretical math came together and, But then he encountered George Papani- ultimately, had a big impact.” colaou and that all changed.

6 • Institute for Mathematics and its Applications We can now make the This impact continues today, as key the volume of ice by a significant amount. statement that we have lost discoveries from Golden’s research are These are real effects that need to be under- over half of the summer Arctic being used to improve current mathemat- stood and incorporated into these models,” ical models for climate change. Golden said. sea ice pack.…Our climate According to Golden, one of the biggest Today, Golden’s group is working on really is changing and it’s unknowns in the climate world is the sea ice mathematically understanding processes significant.” pack’s albedo (the ratio of reflected sunlight that determine the evolution of these to incident sun light), which is a critical melt ponds and ice-albedo feedback. For parameter in climate models. example, Danny Feltham of the Center pond issue, and other key processes that “Ice-albedo feedback is one of the key for Polar Observation and Modeling at the were not incorporated into previous models. driving mechanisms helping to melt the ice, University of Reading, one the foremost The previous generation of global climate particularly in the Arctic, at a very fast rate. applied mathematicians working on sea models have predicted general declines Ice and snow reflect most of the incoming ice modeling today, and his group have of summer Arctic sea ice over the 21st solar radiation whereas melt water on the developed fairly detailed numerical models century. However, according to Golden, the surface of the ice or the open ocean absorbs of melt pond evolution, and one of the key observed losses have significantly outpaced it. The ice protects the ocean below, but if ingredients is Golden’s results on percola- the predictions of these models. that ice is gone or you’ve got melt pools tion theory applied to the study of fluid “We are losing ice really fast. The 21-year on the surface, that radiation is absorbed, flowing through porous sea ice. average of the September minimum sea which melts the ice even further. The more “Ultimately they are using mathematical ice extent from 1979 to 2000 was about it melts, the more the solar radiation is results to build more accurate models. 7 million square kilometers. But now, the absorbed, which means the more you melt They’re working to finally parameterize record minimum over the satellite era was the system,” he explained. melt ponds into global climate models,” he set on September 13, 2012, when the ice Golden noted that this is a very impor- explained. They develop computationally extent on that day was about 3.4 million tant nonlinear feedback effect that was not efficient methods of incorporating melt square kilometers. We can now make the properly incorporated into most existing pond evolution into much larger-scale statement that we have lost over half of the climate models. models. summer Arctic sea ice pack. There’s obvi- “If you don’t properly incorporate ice- These advances will help to improve the ously something very serious happening albedo feedback and melt ponds into these sea ice component of global climate models here. Our climate really is changing and it’s [climate] models, you can overestimate by having much more rigorous representa- significant,” he added. tions of this ice-albedo feedback, the melt

2012-2013 Public Lecture Series

October 2012 December 2012 February 2013 April 2013 Kristin Lauter / Microsoft Research Andrew Hodges / University David Mumford / Brown Kenneth Golden / University Kristin Lauter, manager of Micro- of Oxford University of Utah soft Research’s Cryptography Author of Alan Turing: The Award-winning mathematician In September 2012, the area Group, presented “Private Data, Enigma, Andrew Hodges, Univer- David Mumford presented a series of the Arctic Ocean covered by Public Computation” for the fourth sity of Oxford, lectured on the life of vignettes of actual math from sea ice reached its lowest level annual Arnold Family Lecture. and work of Alan Turing, whose Babylon, Vedic India, Han China, ever recorded in more than three During her talk, Lauter explored short and extraordinary life had Baghdad, and Kerala (India) to decades of satellite measure- internet-based services that are great consequences for modern illustrate how rich the full picture ments. While global climate hosted in the Cloud at large—e- computers, the philosophy of of mathematical origins is and models generally predict sea ice mail, back-up storage, electronic mind, and the outcome of the how the idiosyncrasies of each declines over the 21st century, the medical records— and how many Second World War. Hodges’ talk culture profoundly altered the math precipitous losses observed so far of these services currently rely illustrated the way that Turing they developed. Mumford, Brown have significantly outpaced most on trusting the Cloud provider to seized on a great range of math- University, has been awarded a projections. During his lecture, maintain confidentiality of private ematical ideas and turned them Fields Medal, the Shaw Prize, Golden discussed how mathemat- data and to assure integrity of data into world-changing discoveries. the Steele Prize for Mathematical ical models of composite materials and computation. Lauter discussed Exposition, Wolf Prize, and the and statistical physics are used to solutions based on emerging tools National Medal of Science. study key sea ice processes and from cryptography to prevent and advance how sea ice is repre- mitigate these problems. sented in climate models.

Year in Review • 7 Public Lecture Series Was Pythagoras the First to Discover Pythagoras’s Theorem? According to Brown University mathematician David Mumford, the answer to the question is an emphatic “No!”

On February 27, 2013, in a public lecture at the mathematics was developed for different reasons in Institute for Mathematics and its Applications at the different cultures. Whereas in Babylonia algebraic University of Minnesota, Mumford showed how ancient “word” problems were posed seemingly just for fun, the cultures, including the Babylonians, Vedic Indians, and Nine Chapters on Computational Methods, consid- Chinese, all proved the beloved formula long before the ered the Chinese equivalent of Euclid’s Elements, was Greeks. He argued that the theorem is ultimately the compiled in about 180 BCE for very practical applica- rule for measuring distances on the basis of perpendic- tions—among them Gaussian elimination for solving ular coordinates. This comes up naturally in calculations systems of linear equations, which the Chinese carried of land area for purposes like taxation and inheritance. out using only counting rods on a board. Riemann He further suggested that the Greeks’ love of formal sums grew naturally out of the necessity for estimating proof may have contributed to the Western belief that volume. Mumford suggested that Vedic Indians even they discovered what Mumford calls the “first nontrivial pondered problems of limit in integral calculus. mathematical fact.” Contrary to Western historical belief, Mumford Along with Pythagoras’s theorem, showed, the West did not always lead in mathematical Mumford discussed the discovery discovery. Apparently, the origins of calculus sprang and use of algebra and up totally independently in Greece, India, and China. calculus in ancient Original concepts included area and volume, trigonom- cultures. One of etry, and astronomy. Mumford considers the year 1650 a his key points turning point, after which mathematical activity shifted is that deep to the West. Mumford’s presentation runs counter to current texts on the history of mathematics, which often neglect discoveries occurring outside the West. He showed that purposes for which mathematics is pursued can be very culturally dependent. Nevertheless, his talk points to the fundamental fact that the mathematical experience has no inherent cultural boundaries. Mumford, a professor emeritus in the Division of Applied Mathematics at Brown University, has worked predominantly in the area of algebraic geometry and is a leading researcher in pattern theory. Mumford received a Fields Medal in 1974; his more recent awards include the Shaw Prize (2006), the Steele Prize for Mathematical Exposition (2007), the Wolf Prize (2008), and the National Medal of Science (2010).

This article was originally published in SIAM News and was written by Anna Barry. Barry, a postdoctoral fellow at the Institute for Mathematics and its Applications at the University of Minnesota, followed up on her coverage of David Mumford’s IMA lecture with an interview. The full article and interview is available online at www.siam.org/news/news. php?id=2067.

8 • Institute for Mathematics and its Applications special Workshop IMA Holds Workshop on Career Options for Women in Mathematical Sciences From March 3 to March 5, 2013, the IMA brought together women from all across the United States for the special workshop on Career Options for Women in Mathematical Sciences.

Organizers Georgia Benkart (University of Wisconsin-Madison), Erica Klampfl (Ford Motor Company), Irina Mitrea (Temple Univer- sity), Evelyn Sander (George Mason University), and Cheri Shakiban (University of St. Thomas and IMA) gathered more than 80 participants for the three-day workshop that focused on professional opportunities for women working in the mathematical sciences. As a coorganizer, Mitrea said she was “thrilled” at the opportunity to expose a new generation of women in mathematics to some of her own role models and mentors. She said the workshop was really able to gather an “an amazing group of women mathematicians.” Speakers, panelists, and discussion leaders represented women in industry, academia, and government labs. Mitrea noted that the event’s success was a direct result of those involved: “We had an enthusiastic group of women graduate students and postdocs with tremendous potential, who will play a major role in shaping the future of our profession and a group of women mathematicians at various stages of their careers, ready to share experiences and give practical advice,” Mitrea said. Throughout the workshop, panel discussions covered the interviewing process and the principles of negotiation. Workshop participants We had an enthusiastic group of women graduate students included graduate students and Ph.D.s in the and postdocs with tremendous potential, who will play a early stages of their post-graduate careers. On major role in shaping the future of our profession...” Monday, participants were also able to present posters on their research. “What a great community of women you brought together,” said workshop speaker Kathryn Leonard, an associate professor of mathematics at California State University, Channel Islands. Photos and videos of the presentations are available on the IMA’s website at www.ima.umn. edu/2012-2013/SW3.3-5.13. The event was sponsored by the IMA and the Association for Women in Mathematics (AWM).

Year in Review • 9 Hot Topics Workshop Green by Design

In June 2013, the IMA John Burns (Department of Mathematics, aerospace engineers, and mathematicians Virginia Polytechnic and State University), all sitting in a room learning the language, held a well-attended Satish Narayanan (United Technologies gathered together looking at the same types Hot Topics Workshop Corporation), and Chai Wah Wu (IBM) of problems,” Burns said. on the Mathematical and served as organizers. Participants from There are incentives to greener building both industry and academia came together practices. First, it saves money. According Computational Challenges around this topic because both sides are to workshop organizers, buildings consume in the Control, Optimization, highly interested in developing solutions to 40% of the energy in the United States and designing and operating more energy-effi- they produce 40% of the greenhouse gases. and Design of Energy- cient buildings. The workshop connected “If you can make the buildings 50% more Efficient Buildings. attendees from across a spectrum of disci- efficient, that’s equivalent to taking all the plines, including mathematicians, engineers, cars and trucks off the highway. The scope of scientists, and students in different stages this is so huge for both energy independence of their careers all working on the same and greenhouse gas emissions. In terms of problems. the impact, it’s huge,” explained Burns. According to organizer Burns, “The work- There is still a lot of opportunity for more shop was timely because of the emphasis on sophisticated mathematical control tech- energy consumption and efficiency. Over niques. However, according to organizers, the last 10 years, a lot of fairly modern, this industry is still pretty low-tech. sophisticated tools have gone into some “In a building like this [Lind Hall, Univer- fairly simple buildings and really reduced sity of Minnesota], 84% of all the energy energy consumption. Simple tools that deal used is due to how you use the building. with more complex buildings are the state It’s like a control problem. The dynamics of the art. You need to be able to take these change from day to day, hour to hour,” modern mathematical tools and scale them Burns explained, adding another level of to larger buildings.” complexity to this layered and challenging “The IMA was a good place to do this issue of creating and maintaining greener because people come from all over the buildings. world—hard core engineers, electrical engineers, civil engineers, mechanical engineers,

10 • Institute for Mathematics and its Applications Short Course Evolving Mean Field Game Theory Comes to the United States

Mean field game theory—a branch of game theory—was created in 2006 by Jean-Michel Lasry and Pierre-Louis Lions. Lions, along with Pierre Cardaliaguet and Panagiotis Souganidis, organized a special two-day short course on this topic in November 2012.

The majority of the research being criteria and where this criteria is partly the reduced system), others remain obscure conducted in this field has taken place in determined by the choices of all the other and challenging. All of this makes mean field Europe, thus the IMA was pleased to offer agents, according to Cardaliaguet. games a very exiting topic,” he said. this intense program with the experts in the For example, he said, one can think about Mean field game theory is an important field as a means of sparking interest in this traffic congestion—each agent wants to and evolving area of mathematics. It’s useful burgeoning field here in the United States. go as fast as possible from one position to for applications in many domains of human Like all game theory, it is a set of concepts, another, but his velocity depends on the sciences and also serves to trigger many new mathematical tools, theorems, simulation other agent’s behavior. classes of mathematical problems. methods, and algorithms intended to help “More specifically, mean field game theory Organizers noted that the time was right specialists (economists [micro or macro], is the study of limits (when they exist) of for a workshop on this area in light of the sociologists, engineers, architects, urban stochastic differential games when the extremely high speed of development of planners) model situations where agents number of players goes to infinity,” Lasry mean field game mathematical tools and make decisions strategically. Mean field explained. applications. Mean field games has triggered games are extremely useful for applications Although, mean field game theory has many new classes of mathematical prob- in many domains of the human sciences. long been studied and developed for use lems. Examples to date, according to Lasry, Lasry said that, at a very general level, mean in practical applications, from economics are the study of forward/backward coupled field games use a variety of mathematical and finance to the dynamics of crowds, Hamilton-Jacobi-Bellman (HJB) equation/ tools for contexts in which there are so many according to Cardaliaguet, this is just a Fokker-Planck (FP) PDEs (an extension of players that individual strategies depend starting point, and many applications the HJB and FP theories); the theory of a only on the statistical average of other remain to be discovered. new subclass of hyperbolic PDE systems, agents strategies. “At the level of theoretical aspects, mean called “monotone systems”; stochastic PDE Moreover, mean field games are modeled field games have reached a point where approach of mean field game equilibrium; by a class of systems of partial differential many interesting issues are identified, but new algorithmic ideas in statistics; and equations (PDEs), whose solutions provide not yet solved. If some points are well engineering theory. an understanding of the behavior of infi- understood (e.g., existence/uniqueness for nitely many agents in a world where each agent is individually optimizing his own

Organizers Pierre-Louis Lions, Panagiotis Souganidis, and Pierre Cardaliaguet

Year in Review • 11 Outreach Science Buzz Kiosk at Science Museum of Minnesota

The IMA partnered with the Science Museum of Minnesota to create a Science Buzz kiosk, an informational and interactive exploration station housed in the museum’s front lobby. The kiosk featured activities for kids to explore the Traveling Salesman Problem (TSP), with a map of Minnesota for illustrating the challenge of planning the shortest route while visiting several specific cities along the way, as well as a hands-on activity for making TSP art, where kids could take their photo at the booth to create their very own TSP portrait. IMA Director Fadil Santosa said that working with the Science Museum of Minnesota has been a rewarding experience. “We wanted to reach out to kids and show them that math can be fun and interesting. We rarely get to reach this audience, and it’s fundamental that we show the next generation that math is behind a lot of We rarely get to reach really interesting things from computer this audience, and it’s design to weather prediction. By allowing fundamental that we show them to interact with this hands-on exhibit, we hope to demonstrate the value of math the next generation that in a fun and engaging way,” explained IMA math is behind a lot of Director Fadil Santosa. really interesting things The IMA’s Science Buzz kiosk was from computer design to housed at the Science Museum through the fall. A grand total of 15,241 TSP images were weather prediction.” generated on the kiosk camera. Overall, the —Fadil Santosa collaboration was a huge success!

Support for K-12 Math Modeling Program

Since 2008, the IMA’s Community Relations Committee (CRC) has worked to raise funds in order to support programs and activities beyond those accounted for by our National Science Foundation award. After a successful campaign in 2012, the CRC would like to continue its goal of raising $50,000 to support the institute’s K-12 outreach initiatives. For the first time, the IMA participated in the University of Minnesota’s program, Exploring Careers in Engineering and Physical Science (ECEPS), hosting activities for high school students over one week in the summer of 2013. Following successful survey results, the IMA has decided to launch our own program, modeled after our Mathematical Modeling in Industry Workshop for Graduate Students program, which was established in 1992. The current math modeling program supports students as they work in teams on a real-world problem under the guidance of a mentor and will be adapted for high-schoolers with an affinity for mathematics. Please support the IMA as we continue to reach our goal of $50,000 toward K-12 outreach. To make a donation, please visit www.ima.umn.edu/giving/funds.html.

Students from the IMA’s week-long session at the University of Minnesota’s ECEPS program.

12 • Institute for Mathematics and its Applications Board of Governors IMA Partners

Peter W. Bates The IMA is a partnership of the National Science Foundation, the University of Minnesota, and a broad Michigan State University, 2009–2013 consortium of affiliated universities, government laboratories, and corporations. Affiliation brings many Rene Carmona benefits to members, including access to research, influence over the IMA’s agenda, collaboration within the Princeton University, 2011–2015 IMA’s network, and opportunities to participate in workshops, short courses, and tutorials. David Chock University of Michigan, 2009–2013 Institutions Amir Dembo Arizona State University The University of Iowa Wayne State University Stanford University, 2012-2016 Colorado State University University of Central Florida Worcester Polytechnic Institute Bjorn Engquist Georgia Institute of Technology University of Chicago Zhejiang University University of Texas, Austin, 2013–2017 Indiana University University of Delaware Corporations Robert Ghrist University of Houston Iowa State University Corning Incorporated University of Pennsylvania, 2009–2013 University of Illinois at Urbana- Korea Advanced Institute of Science Boeing Company, The Thomas Grandine and Technology (KAIST) Champaign Eaton Corporation The Boeing Company, 2012–2016 Michigan State University University of Kansas ExxonMobil Alice Guionnet Michigan Technological University University of Kentucky Massachusetts Institute of Technology, 2013–2017 Ford Motor Company Mississippi State University University of Maryland General Motors Thomas Yizhao Hou Northern Illinois University University of Michigan California Institute of Technology, 2010–2014 Honeywell Pohang University of Science and University of Minnesota, Twin Cities Trachette L. Jackson Technology (POSTECH) IBM University of Michigan, 2012–2016 University of North Carolina, Portland State University Greensboro Lawrence Livermore National Erica Zimmer Klampfl Laboratory Purdue University University of Notre Dame Ford Motor Company, 2013–2017 Los Alamos National Laboratory Rice University University of Pennsylvania Richard M. Murray Medtronic California Institute of Technology, 2011–2015 Seoul National University University of Pittsburgh Sandia National Laboratories Texas A&M University University of Tennessee Douglas W. Nychka Schlumberger-Doll National Center for Atmospheric Research, The Ohio State University University of Wisconsin, Madison Siemens 2011–2015 The Pennsylvania State University University of Wyoming Dana Randall Georgia Institute of Technology, 2010–2014 Panagiotis E. Souganidis 2012-2013 Postdoctoral Fellows University of Chicago, 2010–2014 Anna Barry, 2012 Ph.D., Boston University Nitsan Ben-Gal, 2010 Ph.D., The Weizmann Institute of Science Community Relations Committee Renato Calleja, 2009 Ph.D., McGill University Juraj Foldes, 2009 Ph.D., Vanderbilt University Lockwood Carlson Nathan Glatt-Holtz, 2008 Ph.D., Indiana University Carlson Consulting Group Xingye Kan, 2012 Ph.D., Illinois Institute of Technology Henry Cohn Ji Li, 2012 Ph.D., Brigham Young University Microsoft Research Rui Peng, 2012 Ph.D., Memorial University of Newfoundland Katherine Cramer Geordie Richards, 2012 Ph.D., University of Toronto IMA Yannan Shen, 2012 Ph.D., University of Massachusetts Anastacia Quinn Davis Industrial Postdoctoral Fellows University of Minnesota Krystal Taylor, 2012 Ph.D., University of Rochester John Dexheimer Zhu Wang, 2012 Ph.D., Virginia Polytechnic Institute and State University First Analysis Randy Jacobus Postdoctoral Employment, 2013 ASA Brendan Ames, California Institute of Technology Renato Calleja, Georgia Institute of Technology Donald Kahn University of Minnesota Paolo Codenotti, Google, Inc. Nathan Glatt-Holtz, Virginia Polytechnic Institute and State University Roger Lui, chair Xin Liu, Clemson University Worcester Polytechnic Institute Shiqian Ma, Chinese University of Hong Kong Willard Miller Geordie Richards, University of Rochester University of Minnesota Yannan Shen, University of Texas, Dallas William Pulleyblank Divyanshu Vats, Rice University United States Military Academy Teng Zhang, Princeton University Susan Rydell Metropolitan State University Fadil Santosa Credits Writer/editor: Amanda Baumann IMA Designer: Dawn Mathers Ridgway Scott Photography: iStock, Amanda Baumann, Ken Golden, Science Museum of Minnesota University of Chicago Carlos Tolmasky Cargill Institute for Mathematics IMA Directors and Staff IMA and its Applications Fadil Santosa, Director Jiaping Wang, Deputy Director The Institute for Mathematics and its Applications connects scientists, engineers, and mathematicians in Luca Capogna, Associate Director order to address scientific and technological challenges in a collaborative, engaging environment, devel- Chehrzad Shakiban, Associate Director oping transformative, new mathematics and exploring its applications, while training the next generation of researchers and educators. It receives major funding from the National Science Foundation and the Katherine Cramer, Chief of Staff University of Minnesota. Eve Raymond, Office Supervisor Georgia Kroll, Workshop Coordinator The University of Minnesota is an equal opportunity educator and employer. The University’s mission, Holly Pinkerton, Housing/Visa Coordinator carried out on multiple campuses and throughout the state, is threefold: research and discovery, teaching Ines Foss, Accounting Supervisor and learning, and outreach and public service. Sam Richter, Accountant Amanda Baumann, Communications Coordinator This publication/material is available in alternative formats upon request. Direct requests to Georgia Kumsup Lee, Systems Manager Kroll, workshop coordinator, at [email protected]. Brian Hayden, Database Applications Programmer Chad Sullivan, Assistant Systems Manager © 2013 Regents of the University of Minnesota. All rights reserved. Institute for Mathematics Nonprofit Org. and its Applications 400 Lind Hall U.S. Postage 207 Church Street, SE PAID Minneapolis, MN 55455 Twin Cities, MN www.ima.umn.edu Permit No. 90155

Workshops Probabilistic and Extremal Combinatorics September 8–12, 2014 Discrete Structures: Additive and Analytic Combinatorics Analysis and Applications September 29–October 3, 2014 Geometric and Enumerative Combinatorics September 2014–June 2015 November 10–14, 2014

Convexity and Optimization: Theory and Applications February 23–27, 2015 Determinism versus Randomization in Computation March 16–20, 2015 (at Georgia Institute for Technology) Information Theory and Concentration Phenomena April 13–17, 2015 Graphical Models, Statistical Inference, and Algorithms (GRAMSIA) May 18–22, 2015 Analytical Tools in Probability and Applications June 22–26, 2015 (at the Euler Institute)

Organizing Committee Sergey Bobkov / University of Minnesota Jerrold Griggs / University of South Carolina Penny Haxell / University of Waterloo Michel Ledoux / University of Toulouse Benny Sudakov / ETH, Zurich University of California, Los Angeles Prasad Tetali / Georgia Institute of Technology 14 • Institute for Mathematics and its Applications