IMA Institute for Mathematics and its Applications 2012 · IMAInstitute for Mathematics and its Applications 12012-2013 annual Program: infinite Dimensional and stochastic Dynamical

2013

2012

The Year in Review

IMA Institute for Mathematicsand its Applications

The 2012–2013 Annual Thematic Program, which ended just a few months ago, was on Infinite Dimensional and Stochastic Dynamical Systems. This was the third annual program on dynamical systems 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 dynamical systems is active both within and outside of mathematics. Moreover, the field is also driven by the myriad of new applications and intersections with other areas of mathematics.

The first annual program in dynamical systems took place from 1989 to 1990. Even back then the organization of the program was

around application areas. The topics receiving attention then were chemical reactions, mathematical physics, physiology, and fluid flows. The overarching theme was the dynamical systems approach to these problems.

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 focus areas included the study of pattern formation. The activities on bio-related 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 long after that, the NSF founded the Mathematical Biosciences Institute at The Ohio State University.

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 to applications. While many familiar areas were revisited—geophysical fluid dynamics and biology—the ubiquitous component was randomness. The fact that uncertainty is everywhere in applications requires new mathematics. This was really highlighted in much of the discourse throughout the year.

What is rewarding to me is to see that many of the young researchers who spent time 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.

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 years, beginning in July 2008, be renewed for another term. After much thought, I have 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. But rest assured that I am not slipping into a lame duck director. I have much to do in the next two years.

In March 2013, there was an NSF site visit to the IMA. As a result of the strong report by 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, technology, engineering, and math (STEM) education is most successful when students develop personal connections with the ideas and excitement of STEM fields. The council recommended the creation of “opportunities for inspiration through individual and group experiences outside the classroom.” To meet this challenge, the IMA is planning to offer a week-long program in mathematical modeling for high-school students in partner-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 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 to this worthwhile effort.

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

The Year in ReviewFiscal year

July 1, 2012, to June 13, 2013

Program year

september 1, 2012, to June 30, 2013

www.ima.umn.edu

From the Director

Taking Stock


1 2012-2013 annual Program: infinite Dimensional and stochastic Dynamical systems and Their applications

2 Former ima Postdoc John Voight Wins selfridge Prize

3 real-World Networking

3 New Directions Professor enrique Thomann Develops New collaborations

4 a mathematical celebration of endre szemerédi

4 Kudos

5 maXima reU Participants Win Big in san Diego

6 Ken golden’s research is improving current mathematical models for global Warming

8 Was Pythagoras the First to Discover Pythagoras’s Theorem?

9 ima Holds Workshop on career options for Women in mathematical sciences

10 green by Design

11 evolving mean Field game Theory comes to the United states

12 outreach: New science Buzz Kiosk at science museum of minnesota; support for K-12 math modeling Program

Peter Polacik, University of Minnesota, one of the annual program organizers, noted that the theory of infinite dimensional dynamical systems provides an effective way of studying and developing other mathematical theories, such as partial differential equations, delay differential equations, lattice dynamics, and stochastic processes.

Part of the impetus for this annual program, according to organizer Peter Bates, Michigan State University, was the recent development of tools for studying infinite-dimensional dynamical systems and the need to push this development further.

“Another aspect of the program is the focus on stochastic dynamics,” Bates notes. “The rapidly expanding field of stochastic dynamical systems, in both finite- and infinite-dimen-sional settings, promises to give some sense of predictability and order, even when realistic random perturbations are included.”

The theory of random dynamical systems and stochastic differential equations provides fundamental ideas and tools for the modeling, analysis, and prediction of complex phenomena; a large portion of the year was devoted to the theory and appli-cation of stochastic dynamics.

“All of these theories have seen a rapid growth and monu-mental progress in the last decades, both in their theoretical aspects and in the scope of their applications,” Polacik said. “This makes it extremely desirable to provide specialists with different backgrounds in infinite dimensional dynamical systems with a platform for an exciting exchange of ideas and insights into this vast research area, and the IMA is an ideal place to accomplish this goal,” he added.

A week-long tutorial launched the new program year, with the first workshop, Dynamical Systems in Studies of Partial Differential Equa-tions, beginning on September 24 and running through September 28, 2012. Throughout the year, the IMA hosted more than 40 long-term visitors and had 19 postdoctoral fellows in residence.

More information, including videos of the lectures, is available online at www.ima.umn.edu/2012-2013.

Infinite Dimensional and Stochastic Dynamical Systemsand TheiR applicaTions

infinite-dimensional dynamical systems is a vibrant field of mathematical development and has become central to the study of complex physical, biological, and societal processes.

Workshops dynamical systems in studies of partial differential equations

Random dynamical systems

lattice and nonlocal dynamical systems and applications

Theory and applications of stochastic pdes

stochastic Modeling of the oceans and atmosphere

stochastic Modeling of Biological processes

other ima Programs hoT Topics WoRkshop

June 11–14, 2013 Mathematical and computational challenges in the control, optimization, and design of energy-efficient Buildings

special evenTs

august 1–3, 2012 Fostering Mathematical entrepreneurship—creating new Businesses for impact and Wealth

september 5–7, 2012 international Workshop on complex systems and networks

september 12–14, 2012 Mathematics and the Materials Genome initiative

November 12-13, 2012 Mean Field Games and applications

November 29–December 1, 2012 Third abel conference: a Mathematical celebration of endre szemerédi

march 3–5, 2013 career options for Women in Mathematical sciences

June 3–7, 2013 Joint U.s.-Japan conference for Young Researchers on interactions among localized patterns in dissipative systems

June 10–July 19, 2013 MaXiMa interdisciplinary Research experience for Undergraduates

June 17–28, 2013 new directions short course: applied statistics and Machine learning

annual program organizers

peTeR BaTes michigan state University

2012–2013 Annual Program

MaRTin haiReR Warwick University

keninG lU Brigham young University

peTeR polacik University of minnesota

WenXian shen auburn University

year in review • 1

2 • institute for mathematics and its applications

H i s r e a c t i o n t o f inding out he had been chosen to receive the prize?

Shock and “utter disbelief.”

“ I r e m e m b e r e d back to the first time I attended a meeting of the Algorithmic N u m b e r T h e o r y

Symposium (ANTS) in 2002. I wa s completely overwhelmed by the level of the wide-ranging talks and wondered if I would ever even have a paper accepted to the conference! In fact, I almost did not submit my paper at all,” he said.

At the time, he was working on general-izing some joint work with Matthew Green-berg, University of Calgary, to the case of arbitrary class number, and it turned out to be much more difficult than he expected.

“For many months, I would compute Hecke matrices that were supposed to commute but did not. As the deadline approached, I began to despair, but then they extended the deadline for a week! Divine intervention, or so it seemed. After a few days, I resolved the issue and just in time to meet the delayed submission date!”

Given this uneasy beginning, Voight said he was sure the award was a “mistake.”

Of course, it was not a mistake, and Voight’s paper, “Computing automorphic forms on Shimura curves over fields with arbitrary class number,” published in Algo-rithmic Number Theory, was awarded the Selfridge Prize from ANTS, the premier international forum for presentations on new research in computational number theory.

However, it was only a handful of years ago that the now award-winning Voight was a postdoctoral fellow at the IMA.

His first visit to the institute was in the fall of 2006 by way of Australia, shortly after completing his postdoc in the Magma Computer Algebra Group at the University of Sydney.

Voight said he was drawn to the IMA by the breadth and depth of the institute’s proposed activities, the strong reputa-tions of both the IMA and the University of Minnesota (UMN), and the appeal of delving into algorithm and mathematical software development research.

As a postdoctoral fellow during the IMA’s Thematic Year on Applications of Algebraic Geometry, Voight said the highlight of his visit was the interactions he had with the other postdocs, staff, faculty, and visitors during the year.

“I feel very privileged to have participated in the IMA year as it significantly broad-ened my mathematical perspective,” Voight explained.

He said that in addition to being surrounded by pure mathematicians whose areas of research were adjacent to his own, he was able to connect with individuals working in quite different fields—from biology to chemistry to optimization and signal processing, not to mention colleagues working in industry.

“I was particularly struck by methods in numerical algebraic geometry, which can often find approximate solutions to lengthy systems of equations when tradi-tional methods in computational algebra fail. This numerical approach has remained in the back of my mind as I have pursued my research since leaving the IMA, and in the past couple of years, has come to the front and proved to be directly useful,” he said.

Throughout his fellowship, he was able to develop new connections with all of the other visitors who wanted to better under-stand applications of algebraic geometry.

In fact, during his visit, a long-term collaboration was sparked with his mentor, Steven Sperber, a faculty member at

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.

UMN. He and Sperber worked together on computing the zeta function of certain varieties over finite fields—a generating function which records the number of solu-tions to a system of equations. One novel aspect of their work, according to Voight, is that it considers those systems of equations with few monomials, a topic that popped up during an IMA workshop.

Their paper—“Computing zeta functions of nondegenerate hypersurfaces with few monomials”—has now been accepted to the LMS Journal of Computation and Mathematics.

According to Voight, the theory, design, and implementation of algorithms in arith-metic geometry is a burgeoning area and there are many exciting applications of these methods to diverse fields.

After completing his fellowship at the IMA, Voight joined the Department of Mathematics and Statistics at UVM. His research currently focuses on algorithms for cohomological automorphic forms and interrelates abstract theory and practical computation. Specifically, the explicit inves-tigation of the Langlands correspondence—the deep connection between automor-phic forms, algebraic groups, and Galois representations—in both classical and novel settings.

Applications for his research include coding theory and cryptography.

“Today, mathematicians recognize that geometric properties often govern the behavior of arithmetic objects. Further-more, computational tools provide a means to test conjectures and can sometimes furnish partial solutions; at the same time, theoretical advances fuel dramatic improve-ments in computation,” he added.

Since receiving the Selfridge Prize, Voight has also received the UVM College of Engi-neering and Mathematical Sciences Milt Silveira Award, an NSF Division of Math-ematical Sciences CAREER Award in the amount of $400,000, and an NSA Young Investigator’s Grant.

John Voight

There are so many problems to understand, so many connections to be made. how can i rest when there are so many mysteries to solve?”


It just so happened that he was looking for an opportunity to take a sabbatical where research was active and collaborations would thrive. It was around this same time that he found out about the IMA’s New Directions program. The topic of the year—Infinite Dimensional and Stochastic Dynamical Systems and Their Applications—was aligned with his research, but one that he wanted to learn more about.

“In particular, the topic that I was curious about, and that one that I learned the most about, was stochastic PDEs,” he explained. During his visit, he and other long-term visi-tors and postdoctoral fellows at the IMA worked to understand how small noise perturbations propagate through systems of fluid mechanics.

“What I am most proud of is the collaboration—that really started from nothing—that developed during my visit. This is a substantial investment of time for me and the area is very inter-esting. There are opportunities for taking this technology to different areas and to collaborate with different people. This area has a very steep learning curve, so being on sabbatical and able to use 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 a maximum of $50,000 for the entire nine- to 12-month visit.

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.

“I am particularly interested in randomly generating networks that ‘look like’ real-world networks, such as the internet, social networks, biological networks (e.g., protein-protein interac-tion networks). One of the main reasons this is useful is to detect anomalies. Something is anomalous if it is different from what we expect, but in order to define ‘what we expect’ precisely, we need a random model.”

Applications for his work range from creating more precise directions and more adaptive Twitter feeds to trying to find mutations in genes that are involved in diseases.

During his stay, Codenotti was extremely active with the IMA’s outreach activities—from the Minnesota State Fair to the University of Minnesota’s homecoming events—rallying the other postdocs to planning activities for the students.

“I find math very exciting, and I want to get other people excited about it as well. I think it is one of our duties as scien-tists to share our discoveries with everyone. I personally always enjoy talking about math,” he said.

Codenotti headed to the University of Michigan in spring 2013 to work with Karem Sakallah’s group in the Electrical Engineering and Computer Science Department. Currently, Codenotti works as a software engineer at Google, Inc.

Real-World NetworkingPaolo codenotti applied for a postdoctoral fellowship at the ima because the timely theme of the annual program—the mathematics of information—aligned with his work on creating mathematical models for large-scale networks. enrique Thomann has been a regular visitor

to the ima over the course of his career as a workshop attendee.

Paolo codenotti

enrique Thomann

New Directions

New Directions Professor Enrique Thomann Develops New Collaborations

codenotti (far right) explains the concept of cryptography, using the Jefferson Wheel cipher to kids at the UmN science and Family Fun Fair.

In 2013, Anna C. Gilbert was named the recipient of the Society for Industrial and Applied Mathematics (SIAM) Ralph Kleinman prize. The award is given to one individual annually for outstanding research, or other contributions, that bridge the gap between mathematics and applications. Gilbert was recognized for her creative and deep contributions to the mathematics of signal processing, data

analysis, and communications. “Her bold and interdisciplinary work combines techniques from computer science, harmonic analysis, and probability in the best traditions of the Kleinman Prize,” cited the awards committee. In addition, Gilbert has been invited to speak at the International Congress of Mathematicians in Korea in 2014. Gilbert, a professor of mathematics at the Univer-sity of Michigan, has been a regular visitor to the IMA since 1994. She has served an organizer and as a member of the institute’s Board of Governors.


Szemerédi received the Abel Prize in 2012 for his fundamental contributions to discrete mathematics and theoretical computer science. He is a permanent research fellow at the Alfréd Rényi Institute of Math-ematics, Hungarian Academy of Sciences, in Buda-pest. He also serves as the New Jersey professor of computer science at Rutgers University.

Szemerédi is described as a mathematician with exceptional research power whose influence on today’s mathematics is immeasurable. Many of his results have generated research for the future and have laid the foundations for new directions in math-ematics. He has published more than 200 papers in a career spanning five decades.

third Annual Abel conference

A Mathematical Celebration of Endre SzemerédiThe 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.

It is no wonder then that the conference was the largest to date with more than 100 participants gath-ered from across the globe. Opening with an introduc-tion given by University of Minnesota Provost Karen Hanson, the conference lasted three days with talks that included Hillel Furstenberg (Hebrew Univer-sity) who presented on “A Szemeredi-type theorem for non-amenable groups,” Terence Tao (University of California, Los Angeles) on “Arithmetic and algebraic regularity lemmas,” and Avi Wigderson (Institute for Advanced Study) on “Points, lines, and ranks of design matrices.”

According to organizer Joel Spencer, Szemerédi’s approach to mathematics is through discrete math-

ematics. He worked on asymp-totically large discrete objects, such as graphs and subsets of the integers. By moving toward infi-nite 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.

Michael Levitt, a professor of structural biology at the Stanford University School of Medicine, was recently awarded the 2013 Nobel Prize in Chemistry for his work in protein folding. Levitt shares the prize with Martin Karplus (University of Strasbourg) and Arieh Warshel (University of Southern California). The winners found a new way for computers to model proteins and their interactions in the human body. Levitt was

an organizer of the 2007-2008 IMA Annual Thematic Program on the Mathematics of Molecular and Cellular Biology. He and Patrice Koehl (University of California, Davis) organized a tutorial on the mathematics of proteins, including three hour-long lectures. Levitt, Ken Dill (University of San Francisco), and Sorin Istrail (Brown University) were responsible for the very successful workshop on protein folding held that same year. The IMA is grateful to Levitt for his contributions to the IMA and congratulates him on this momentous achievement.

KUDoS

Former IMA postdoc Arthur Szlam was recently awarded a two-year Sloan Foun-dation Research Fellowship. The award seeks to “stimulate fundamental research by early-career scientists and scholars of outstanding promise.” The award is given to 126 researchers each year in recognition of “distinguished performance and a unique potential to make substantial contributions to their field.” Currently a faculty member at

the City College of the City University of New York, Szlam focuses his research on computational harmonic analysis. According to Szlam, there has been much progress lately on the object detection 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.

Former IMA industria l postdoc Vasileios Maroulas (2008–2010, Lock-heed Martin) received the Leverhulme Trust Visiting Fellowship from the Univer-sity of Bath in Great Britain. He will serve as a visiting faculty member in the Department of Mathematical Sciences at the University of Bath from October 1, 2013, until June 30, 2014. He was one of the two awardees honored with fellowships

through a university-wide competition. Maroulas is currently an assistant professor in the Department of Mathematics at the University of Tennessee. In addition, his research will be supported by the Simons Foundation Collaboration Grant for 2013–2018.


research experience for Undergrads

MAXIMA REU Participants Win Big in San DiegomaXima, 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 problems in applied mathematics posed by University of Minnesota (UMN) faculty members. Each team is advised by a Macalester College Mathematics, Statistics, and Computer Science faculty member and mentored by a postdoctoral fellow at the IMA.

The program is designed to allow students to experience the excitement of doing research that is relevant to another field. By the end of the summer, each team produces a written report, an oral presentation, and a research poster.

Two posters submitted by MAXIMA teams received an Outstanding Presentation Award at the Mathematical Association of America (MAA) Undergraduate Student Poster Session at the 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?”

“Design of Laser Beams in GRIN Media for Profile Transforma-tion and Selective Resonance” was a joint effort by students Philip Burnham (Villanova University), Delani Cele (Ithaca College), Hyunmoon Kim (Princeton University), and Tim Moon (Rice University).

The third MAXIMA research team was mentored by Macalester Computer Science professor Shilad Sen. His group, who presented “The Lifecycle of Wikipedia Editors,” consisted of Alexander Bristol (University of Massachusetts, Amherst), Mary-Katherine Huffman (Virginia Polytechnic Institute and State University), Nathan Leech (Macalester College), and Guanyu Wang (University of Iowa).

andrew Beveridge (second from left) with the 2013 maXima participants.


According to Golden, conducting field work is essential to developing relevant mathematics in this area.

“Sea ice is complicated—it does all sorts of things that you wouldn’t necessarily expect. It’s one thing to sit in your office, but it’s another thing to go down there and see it for yourself,” he explained.

Notably, he has made 16 voyages to the polar regions. He’s been interested in sea ice since he was in high school, studying at the Institute for Arctic and Alpine Research at the University of Colorado, Boulder, through an NSF summer science training program, as well as at NASA/Goddard during his senior year of high school.

While a freshman at Dartmouth College, he began working with Steve Ackley on radar propagation in sea ice, gauging its thickness, and went on his first Antarctic expedition during his senior year.

Other scientists had found that if the radar antenna is situated one way, you get a big signal back from the ice-water interface, but if you turn it 90 degrees, then the return almost vanishes. “By analyzing sea ice as a composite material and looking at its effec-tive electromagnetic properties, I was able to explain this phenomenon and develop some of the first basic treatments of sea ice as a composite,” Golden said. This work led to his second published paper, “Modeling of anisotropic electromagnetic reflection from sea ice,” in the Journal of Geophysical Research.

After Golden received his B.A. degree in mathematics and physics at Dartmouth, he planned to pursue a Ph.D. degree in math-ematics from New York University (NYU). Golden thought he would follow a more classical path for a mathematician—perhaps studying differential geometry or quantum field theory—because he wanted to be a “serious” mathematical physicist—and they don’t study sea ice.

But then he encountered George Papani-colaou and that all changed.

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.

Papanicolaou, a professor at NYU at the time, was teaching a class on random media and composite materials.

“I have to admit that the moment I first saw ‘percolation theory’ described at the blackboard, I thought of the brine phase in sea ice,” he said. “As I look back now, it was precisely what was needed to revolutionize the study of sea ice and its transport proper-ties,” Golden said.

Golden’s second published paper included a figure of these brine inclusions coalescing and connecting up to form pathways, which was actually an example of percolation—when fluid can move through a porous solid—although he didn’t know it yet.

“The moment I saw George lay out mathematical percolation theory, I was like ‘Oh, brine and ice, just like the figure I put in my paper.’ Again, I had no idea this was important.”

Then, in 1994, Golden was in Antarctica for his second trip out when he saw sea water percolating up and flooding the surface.

“Literally, in one instant, I knew—that’s percolation!” he remembers.

And he spent the next few years studying this mystery. As it turns out, he had discov-ered the on/off switch for fluid flow in sea ice. This “switch” is critical to melt pond evolution and snow-ice formation—key processes that help us to understand the role of sea ice in the climate system.

“It took about 10 years to play out in terms of the mathematics, of actually bringing that one idea to fruition,” Golden said. “We published this paper in Science in 1998, and it was probably six, seven years down the road that the sea ice world began to realize the effects. It affected everything. It sort of explained all these processes that they had wondered about for a long time. It was a critical advance when the field work and the theoretical math came together and, ultimately, had a big impact.”

This impact continues today, as key discoveries from Golden’s research are being used to improve current mathemat-ical models for climate change.

According to Golden, one of the biggest unknowns in the climate world is the sea ice pack’s albedo (the ratio of reflected sunlight to incident sun light), which is a critical parameter in climate models.

“Ice-albedo feedback is one of the key driving mechanisms helping to melt the ice, particularly in the Arctic, at a very fast rate. Ice and snow reflect most of the incoming solar radiation whereas melt water on the surface of the ice or the open ocean absorbs it. The ice protects the ocean below, but if that ice is gone or you’ve got melt pools on the surface, that radiation is absorbed, which melts the ice even further. The more it melts, the more the solar radiation is absorbed, which means the more you melt the system,” he explained.

Golden noted that this is a very impor-tant nonlinear feedback effect that was not properly incorporated into most existing climate models.

“If you don’t properly incorporate ice-albedo feedback and melt ponds into these [climate] models, you can overestimate

the volume of ice by a significant amount. These are real effects that need to be under-stood and incorporated into these models,” Golden said.

Today, Golden’s group is working on mathematically understanding processes that determine the evolution of these melt ponds and ice-albedo feedback. For example, Danny Feltham of the Center for Polar Observation and Modeling at the University of Reading, one the foremost applied mathematicians working on sea ice modeling today, and his group have developed fairly detailed numerical models of melt pond evolution, and one of the key ingredients is Golden’s results on percola-tion theory applied to the study of fluid flowing through porous sea ice.

“Ultimately they are using mathematical results to build more accurate models. They’re working to finally parameterize melt ponds into global climate models,” he explained. They develop computationally efficient methods of incorporating melt pond evolution into much larger-scale models.

These advances will help to improve the sea ice component of global climate models by having much more rigorous representa-tions of this ice-albedo feedback, the melt

We can now make the statement that we have lost over half of the summer arctic sea ice pack.…our climate really is changing and it’s significant.”

pond issue, and other key processes that were not incorporated into previous models.

The previous generation of global climate models have predicted general declines of summer Arctic sea ice over the 21st century. However, according to Golden, the observed losses have significantly outpaced the predictions of these models.

“We are losing ice really fast. The 21-year average of the September minimum sea ice extent from 1979 to 2000 was about 7 million square kilometers. But now, the record minimum over the satellite era was set on September 13, 2012, when the ice extent on that day was about 3.4 million square kilometers. We can now make the statement that we have lost over half of the summer Arctic sea ice pack. There’s obvi-ously something very serious happening here. Our climate really is changing and it’s significant,” he added.

ocToBer 2012

kristin lauter / microsoft research

Kristin lauter, manager of micro-soft research’s cryptography group, presented “Private Data, Public computation” for the fourth annual arnold Family lecture. During her talk, lauter explored internet-based services that are hosted in the cloud at large—e-mail, back-up storage, electronic medical records— and how many of these services currently rely on trusting the cloud provider to maintain confidentiality of private data and to assure integrity of data and computation. lauter discussed solutions based on emerging tools from cryptography to prevent and mitigate these problems.

DecemBer 2012

andrew hodges / University of oxford

author of Alan Turing: The Enigma, andrew Hodges, Univer-sity of oxford, lectured on the life and work of alan Turing, whose short and extraordinary life had great consequences for modern computers, the philosophy of mind, and the outcome of the second World War. Hodges’ talk illustrated the way that Turing seized on a great range of math-ematical ideas and turned them into world-changing discoveries.

FeBrUary 2013

david Mumford / Brown University

award-winning mathematician David mumford presented a series of vignettes of actual math from Babylon, Vedic india, Han china, Baghdad, and Kerala (india) to illustrate how rich the full picture of mathematical origins is and how the idiosyncrasies of each culture profoundly altered the math they developed. mumford, Brown University, has been awarded a Fields medal, the shaw Prize, the steele Prize for mathematical exposition, Wolf Prize, and the National medal of science.

aPril 2013

kenneth Golden / University of Utah

in september 2012, the area of the arctic ocean covered by sea ice reached its lowest level ever recorded in more than three decades of satellite measure-ments. While global climate models generally predict sea ice declines over the 21st century, the precipitous losses observed so far have significantly outpaced most projections. During his lecture, golden discussed how mathemat-ical models of composite materials and statistical physics are used to study key sea ice processes and advance how sea ice is repre-sented in climate models.

2012-2013 Public Lecture Series



Public Lecture Series

Was Pythagoras the First to Discover Pythagoras’s Theorem?

On February 27, 2013, in a public lecture at the Institute for Mathematics and its Applications at the University of Minnesota, Mumford showed how ancient cultures, including the Babylonians, Vedic Indians, and Chinese, all proved the beloved formula long before the Greeks. He argued that the theorem is ultimately the rule for measuring distances on the basis of perpendic-ular coordinates. This comes up naturally in calculations of land area for purposes like taxation and inheritance. He further suggested that the Greeks’ love of formal proof may have contributed to the Western belief that they discovered what Mumford calls the “first nontrivial mathematical fact.”

Along with Pytha gora s ’s theorem, Mumford discussed the discovery

and use of a lgebra and ca lculus in ancient

cultures. One of his key points

is that deep

according to Brown University mathematician David mumford, the answer to the question is an emphatic “No!”

mathematics was developed for different reasons in different cultures. Whereas in Babylonia algebraic “word” problems were posed seemingly just for fun, the Nine Chapters on Computational Methods, consid-ered the Chinese equivalent of Euclid’s Elements, was compiled in about 180 BCE for very practical applica-tions—among them Gaussian elimination for solving systems of linear equations, which the Chinese carried out using only counting rods on a board. Riemann sums grew naturally out of the necessity for estimating volume. Mumford suggested that Vedic Indians even pondered problems of limit in integral calculus.

Contrary to Western historical belief, Mumford showed, the West did not always lead in mathematical discovery. Apparently, the origins of calculus sprang up totally independently in Greece, India, and China. Original concepts included area and volume, trigonom-etry, and astronomy. Mumford considers the year 1650 a turning point, after which mathematical activity shifted 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.


special Workshop

IMA Holds Workshop on Career Options for Women in Mathematical Sciences

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...”

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 mathemati-cians 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 prin-ciples of negotiation. Workshop participants included graduate students and Ph.D.s in the early stages of their post-graduate careers. On 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).

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.


John Burns (Department of Mathematics, Virginia Polytechnic and State University), Satish Narayanan (United Technologies Corporation), and Chai Wah Wu (IBM) served as organizers. Participants from both industry and academia came together around this topic because both sides are highly interested in developing solutions to designing and operating more energy-effi-cient buildings. The workshop connected attendees from across a spectrum of disci-plines, including mathematicians, engineers, scientists, and students in different stages of their careers all working on the same problems.

According to organizer Burns, “The work-shop was timely because of the emphasis on energy consumption and efficiency. Over the last 10 years, a lot of fairly modern, sophisticated tools have gone into some fairly simple buildings and really reduced energy consumption. Simple tools that deal with more complex buildings are the state of the art. You need to be able to take these modern mathematical tools and scale them to larger buildings.”

“The IMA was a good place to do this because people come from all over the world—hard core engineers, electrical engi-neers, civil engineers, mechanical engineers,

in June 2013, the ima held a well-attended Hot Topics Workshop on the mathematical and computational challenges in the control, optimization, and Design of energy-efficient Buildings.

aerospace engineers, and mathematicians all sitting in a room learning the language, gathered together looking at the same types of problems,” Burns said.

There are incentives to greener building practices. First, it saves money. According to workshop organizers, buildings consume 40% of the energy in the United States and they produce 40% of the greenhouse gases.

“If you can make the buildings 50% more efficient, that’s equivalent to taking all the cars and trucks off the highway. The scope of this is so huge for both energy independence and greenhouse gas emissions. In terms of the impact, it’s huge,” explained Burns.

There is still a lot of opportunity for more sophisticated mathematical control tech-niques. However, according to organizers, this industry is still pretty low-tech.

“In a building like this [Lind Hall, Univer-sity of Minnesota], 84% of all the energy used is due to how you use the building. It’s like a control problem. The dynamics change from day to day, hour to hour,” Burns explained, adding another level of complexity to this layered and challenging issue of creating and maintaining greener buildings.

hot topics Workshop

Green by Design


The majority of the research being conducted in this field has taken place in Europe, thus the IMA was pleased to offer this intense program with the experts in the field as a means of sparking interest in this burgeoning field here in the United States.

Like all game theory, it is a set of concepts, mathematical tools, theorems, simulation methods, and algorithms intended to help specialists (economists [micro or macro], sociologists, engineers, architects, urban planners) model situations where agents make decisions strategically. Mean field games are extremely useful for applications in many domains of the human sciences. Lasry said that, at a very general level, mean field games use a variety of mathematical tools for contexts in which there are so many players that individual strategies depend only on the statistical average of other agents strategies.

Moreover, mean field games are modeled by a class of systems of partial differential equations (PDEs), whose solutions provide an understanding of the behavior of infi-nitely many agents in a world where each agent is individually optimizing his own

Short course

Evolving Mean Field Game Theory Comes to the United Statesmean 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.

criteria and where this criteria is partly determined by the choices of all the other agents, according to Cardaliaguet.

For example, he said, one can think about traffic congestion—each agent wants to go as fast as possible from one position to another, but his velocity depends on the other agent’s behavior.

“More specifically, mean field game theory is the study of limits (when they exist) of stochastic differential games when the number of players goes to infinity,” Lasry explained.

Although, mean field game theory has long been studied and developed for use in practical applications, from economics and finance to the dynamics of crowds, according to Cardaliaguet, this is just a starting point, and many applications remain to be discovered.

“At the level of theoretical aspects, mean field games have reached a point where many interesting issues are identified, but not yet solved. If some points are well understood (e.g., existence/uniqueness for

the reduced system), others remain obscure and challenging. All of this makes mean field games a very exiting topic,” he said.

Mean field game theory is an important and evolving area of mathematics. It’s useful for applications in many domains of human sciences and also serves to trigger many new classes of mathematical problems.

Organizers noted that the time was right for a workshop on this area in light of the extremely high speed of development of mean field game mathematical tools and applications. Mean field games has triggered many new classes of mathematical prob-lems. Examples to date, according to Lasry, are the study of forward/backward coupled Hamilton-Jacobi-Bellman (HJB) equation/Fokker-Planck (FP) PDEs (an extension of the HJB and FP theories); the theory of a new subclass of hyperbolic PDE systems, called “monotone systems”; stochastic PDE approach of mean field game equilibrium; new algorithmic ideas in statistics; and engineering theory.

organizers Pierre-louis lions, Panagiotis souganidis, and Pierre cardaliaguet


science Buzz Kiosk at science museum of minnesotaThe 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 really interesting things from computer design to weather prediction. By allowing them to interact with this hands-on exhibit, we hope to demonstrate the value of math in a fun and engaging way,” explained IMA Director Fadil Santosa.

The IMA’s Science Buzz kiosk was housed at the Science Museum through the fall. A grand total of 15,241 TSP images were generated on the kiosk camera. Overall, the collaboration was a huge success!

support for K-12 math modeling ProgramSince 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.

We rarely get to reach this audience, and it’s fundamental that we show the next generation that math is behind a lot of really interesting things from computer design to weather prediction.”

—Fadil sanTosa

outreach

students from the ima’s week-long session at the University of minnesota’s ecePs program.

The University of iowa

University of central Florida

University of chicago

University of Delaware

University of Houston

University of illinois at Urbana-champaign

University of Kansas

University of Kentucky

University of maryland

University of michigan

University of minnesota, Twin cities

University of North carolina, greensboro

University of Notre Dame

University of Pennsylvania

University of Pittsburgh

University of Tennessee

University of Wisconsin, madison

University of Wyoming

Wayne state University

Worcester Polytechnic institute

Zhejiang University

coRpoRaTions

corning incorporated

Boeing company, The

eaton corporation

exxonmobil

Ford motor company

general motors

Honeywell

iBm

lawrence livermore National laboratory

los alamos National laboratory

medtronic

sandia National laboratories

schlumberger-Doll

siemens

insTiTUTions

arizona state University

colorado state University

georgia institute of Technology

indiana University

iowa state University

Korea advanced institute of science and Technology (KaisT)

michigan state University

michigan Technological University

mississippi state University

Northern illinois University

Pohang University of science and Technology (PosTecH)

Portland state University

Purdue University

rice University

seoul National University

Texas a&m University

The ohio state University

The Pennsylvania state University

Board of Governors

PeTer W. BaTes michigan state University, 2009–2013

reNe carmoNa Princeton University, 2011–2015

DaViD cHocK University of michigan, 2009–2013

amir DemBo stanford University, 2012-2016

BJorN eNgqUisT University of Texas, austin, 2013–2017

roBerT gHrisT University of Pennsylvania, 2009–2013

THomas graNDiNe The Boeing company, 2012–2016

alice gUioNNeT massachusetts institute of Technology, 2013–2017

THomas yiZHao HoU california institute of Technology, 2010–2014

TracHeTTe l. JacKsoN University of michigan, 2012–2016

erica Zimmer KlamPFl Ford motor company, 2013–2017

ricHarD m. mUrray california institute of Technology, 2011–2015

DoUglas W. NycHKa National center for atmospheric research,

2011–2015

DaNa raNDall georgia institute of Technology, 2010–2014

PaNagioTis e. soUgaNiDis University of chicago, 2010–2014

community Relations committeelocKWooD carlsoN

carlson consulting group

HeNry coHN microsoft research

KaTHeriNe cramer ima

aNasTacia qUiNN DaVis University of minnesota

JoHN DeXHeimer First analysis

raNDy JacoBUs asa

DoNalD KaHN University of minnesota

roger lUi, cHair Worcester Polytechnic institute

WillarD miller University of minnesota

William PUlleyBlaNK United states military academy

sUsaN ryDell metropolitan state University

FaDil saNTosa ima

riDgWay scoTT University of chicago

carlos TolmasKy cargill

iMa directors and staff

Fadil santosa, Director

Jiaping Wang, Deputy Director

luca capogna, associate Director

chehrzad shakiban, associate Director

Katherine cramer, chief of staff

eve raymond, office supervisor

georgia Kroll, Workshop coordinator

Holly Pinkerton, Housing/Visa coordinator

ines Foss, accounting supervisor

sam richter, accountant

amanda Baumann, communications coordinator

Kumsup lee, systems manager

Brian Hayden, Database applications Programmer

chad sullivan, assistant systems manager

2012-2013 postdoctoral Fellowsanna Barry, 2012 Ph.D., Boston University Nitsan Ben-gal, 2010 Ph.D., The Weizmann institute of science renato calleja, 2009 Ph.D., mcgill University Juraj Foldes, 2009 Ph.D., Vanderbilt University Nathan glatt-Holtz, 2008 Ph.D., indiana UniversityXingye Kan, 2012 Ph.D., illinois institute of Technology Ji li, 2012 Ph.D., Brigham young University rui Peng, 2012 Ph.D., memorial University of Newfoundland geordie richards, 2012 Ph.D., University of Torontoyannan shen, 2012 Ph.D., University of massachusetts

industrial postdoctoral FellowsKrystal Taylor, 2012 Ph.D., University of rochesterZhu Wang, 2012 Ph.D., Virginia Polytechnic institute and state University

postdoctoral employment, 2013Brendan ames, california institute of Technologyrenato calleja, georgia institute of TechnologyPaolo codenotti, google, inc.Nathan glatt-Holtz, Virginia Polytechnic institute and state UniversityXin liu, clemson Universityshiqian ma, chinese University of Hong Konggeordie richards, University of rochesteryannan shen, University of Texas, DallasDivyanshu Vats, rice UniversityTeng Zhang, Princeton University

iMa partners

The ima is a partnership of the National science Foundation, the University of minnesota, and a broad consortium of affiliated universities, government laboratories, and corporations. affiliation brings many benefits to members, including access to research, influence over the ima’s agenda, collaboration within the ima’s network, and opportunities to participate in workshops, short courses, and tutorials.

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-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 University of minnesota.

The University of minnesota is an equal opportunity educator and employer. The University’s mission, 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].

© 2013 regents of the University of minnesota. all rights reserved.

credits Writer/editor: amanda BaumannDesigner: Dawn mathersPhotography: istock, amanda Baumann, Ken golden, science museum of minnesota



400 lind Hall207 church street, seminneapolis, mN 55455

Nonprofit org.U.s. Postage

paidTwin cities, mN

Permit No. 90155

institute for mathematicsand its applications

www.ima.umn.edu

Discrete Structures: Analysis and Applications

Workshops Probabilistic and Extremal Combinatoricsseptember 8–12, 2014

Additive and Analytic Combinatoricsseptember 29–october 3, 2014

Geometric and Enumerative Combinatoricsnovember 10–14, 2014

Convexity and Optimization: Theory and ApplicationsFebruary 23–27, 2015

Determinism versus Randomization in ComputationMarch 16–20, 2015 (at georgia institute for Technology)

Information Theory and Concentration Phenomenaapril 13–17, 2015

Graphical Models, Statistical Inference, and Algorithms (GRAMSIA)May 18–22, 2015

Analytical Tools in Probability and ApplicationsJune 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

September 2014–June 2015

Documents

IMA Institute for Mathematics and its Applications 2012 · IMAInstitute for Mathematics and its Applications 12012-2013 annual Program: infinite Dimensional and stochastic Dynamical