AUGUST 2015, NO 16
Chair’s Moon Duchin visiting us from Tufts Corner University, Professor Michael Dam- ron, yours truly, Erica Isaacson, Jim Problem Corner ELIZABETH Hendrickson, several of our gradu- HOUSWORTH Problem: The king of Babylon ate students, as well as the orga- has three prisoners and ran- nizers themselves. Students in the domly places on their heads ei- Primary Circle learned about bi- ther a blue hat or a green hat. As I write this, I have not yet nary expansions (and expansions in None of them may see their been Chair for a year, but it is get- other bases) through dots and boxes, own hat, but they see the oth- ting close! My heartfelt thanks and the properties of random numbers, ers. They cannot communicate appreciation go out to all the faculty, dynamical systems, the mathemat- in any way. The king charges staff, students, parents, alumni, and ics of spirographs, and mathemati- them that one or more of them donors who make being Chair so re- cal games, among other things. Stu- must guess their own hat color, warding. In this newsletter, you will dents in the Secondary Circle ex- and all guesses (or the option read about their numerous accom- plored infinity, mathematical para- to pass on guessing) must oc- plishments. In this corner, I will fo- doxes, random walks, card tricks, cur simultaneously. If all the cus on events and accomplishments and topology through cutting and guesses that are made are cor- that may not appear elsewhere. taping strips of paper. While we rect, then they all go free. The first year of the department- have some issues to work through, However, if any of the guesses sponsored Bloomington Math Cir- the Circles were generally a success. are wrong, or no guesses are cle was a great success. We cre- This summer, Will Orrick and Shab- made, then they are all exe- ated two groups, the Primary Cir- nam Kavousian will participate in cuted. The prisoners were fore- cle for children who know multipli- Bob and Ellen Kaplan’s Math Cir- warned the night before of the cation, roughly grades 3-6, and the cle Summer Teacher Training Insti- challenge and therefore have Secondary Circle for children who tute, and the team of Bloomington had a chance to strategize. know algebra, roughly grades 7-10. Math Circle organizers will include Find the strategy that maxi- We met for nine Saturday afternoons Erica Isaacson next year. We also cre- mizes their chance of survival. during each of the Fall and Spring ated a linked 1-credit undergradu- What is that chance? Semesters. Tracy Whelan organized ate service learning course so the un- the Primary Circle in the Fall and dergraduate students can get course T-Shirts! Shabnam Kavousian organized it in credit for helping with the Math Cir- Where has your departmental the Spring. Andrew Dabrowski orga- cle, learning the mathematical type- T-Shirt been? Look for the new nized the Secondary Circle the en- setting program LaTeX, and typing T-Shirt and contest rules at: tire year. Guest speakers included up the Circle activities for posterity. m http://www.math.indiana. Professor Michael Larsen, Professor (continued on p. 2) edu/Outreach/TShirts2015
Indiana University Department of Mathematics Alumni Newsletter m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Page 1 One of the e-mails I sent out to and the department will try to bring my faculty had the subject line “101 the Mosaic Math and Art Exhibit Bureaucratic Efficiencies.” I must that the Mathematical Sciences Re- Student News have a bit of the parents in Cheaper search Institute sponsors to campus by the Dozen in me because this is that semester. On the purely mathe- one of the aspects of being Chair I matical side, we are still looking for- find most fun and rewarding. One ward to hosting a Sectional Meeting From DUGS Kevin Pilgrim: bureaucratic efficiency I made was for the American Mathematical Soci- to obtain a secure-print printer for ety April 1-2, 2017. the mailroom with the accompany- We are working on document- ing benefits including no worries ing the department’s history for the about printing an exam off where upcoming IU Bicentennial in 2020. a student might see it - the printer Former departmental chair John Ew- only prints when the document’s ing already documented the depart- owner is present and enters a pri- ment’s first 100 years for our move vate code; less paper and toner us- into Rawles Hall. Here are two facts age - if a document is misprinting, from Professor Ewing’s Indiana Uni- for instance, so that it is all black, versity Mathematics: The first 100 The past academic year has been the owner is there to cancel the job; years (1820-1920): very exciting and full of news. the old printer room, Rawles Hall More clubs, courses, majors, and stu- Fact: In 1930, more members of the dents... 368, is now an 18-student seminar American Mathematical Soci- room complete with tables, chairs, ety had received their under- More students than ever are tak- and a blackboard! A generous donor graduate training at Indiana ing math at IUB. For math majors, provided the department with some University than at any other this led to more course offerings. fancy erasers and eraser (vacuum) university, except Harvard. Resurrected are now Math-M 436 In- cleaners to cut down on the chalk Fact: During the twenty years from troduction to Geometries, taught for dust from our old-fashioned (and 1888 to 1908, out of 2084 the first time in 20+ years last Fall highly valued) use of blackboards. I students who received their 2015 by Matthias Weber, and Math- will mention one efficiency I made A.B. degree from Indiana, one M 420 Metric Space Topology, taught more before you fall asleep reading: eleventh had majored in math- by Dylan Thurston. Newly created the College Information Technology ematics. were Math-G 201 Service Learning Office provided the department with in Mathematics. This past year, seven There are many other important a secure file server for departmen- math majors received credit for as- accomplishments made by the fac- tal documents, helping my successor sisting in and developing materials ulty, staff, students, alumni, donors, find and modify departmental docu- for our new Math Circles 3rd-10th and friends of the department, some ments, like this newsletter! grade Outreach Program. that will fill the pages of this Gioia Di Cari’s monologue Truth Newsletter, but many that cannot be Also new is Math-M 298 Ca- Values: One Girl’s Romp through included. I thank you all for making reers in Mathematics, which brought M.I.T.’s Male Math Maze came to the department such a special place. IU math alums Lonnie Nicholson the Wells Metz Theatre on April ’86 (Kimball International), Robert 28. The monologue and the discus- About the Newsletter O’Connell ’09 (Epic), and Frances sion panel afterwards were both hits. Thanks go to Chris Connell, Richert ’12 (ACES Excellence in En- Continuing with this math/arts com- Michael Damron, Chris Judge, Dar- ergy) into our classroom to share bination, David Fisher has worked rell Haile, Michael Larsen, Russ their insights. If you would like to to bring Counting from Infinity: Yi- Lyons, Linda McKinley and Kevin Pil- be involvedâA˛eclickthe˘ “share your tang Zhang and the Twin Prime Con- grim for their contributions to this story” link!! We’d love to hear from jecture, a Zala Films documentary, newsletter. Special thanks go to Pe- you!! Spring ’15 also saw five teams to the IU Cinema on November 9, ter Sternberg, who has taken over of undergraduates working on ap- 2015. In Fall 2016, the College’s the bulk of the editing and format- plied projects in our Math-M 490 Themester program will be “Beauty” ing duties. (continued on p. 8)
Indiana University Department of Mathematics Alumni Newsletter Page 2 m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf formation (IET). These come up in a variety of places in mathematics Fields Medal nowadays, including in research of Faculty News Colloquia IUB faculty members Matthew Bain- bridge and Christopher Judge. A ma- jor result of Avila asserts: almost ev- Michael Mandell The 2014 Fields Medal was given ery IET is weakly mixing. That is, if out to four mathematicians, Artur one picks an IET “at random”, then Avila Cordeiro de Melo, Maryam iterates of f mix things up, in a cer- Mirzakhani, Manjul Bhargava and tain technical average sense. More Martin Hairer. As part of this year’s precisely: weak mixing means that Departmental Colloquium series, for any subintervals A, B ⊂ [0, 1], three faculty from within our De- n partment, Kevin Pilgrim, Chris Judge 1 X −n µ(f (A) ∩ B) − µ(A)µ(B) and Michael Larsen gave lectures n i=1 describing the remarkable achieve- ments of these mathematicians and approaches zero as n tends to in- Professor Michael Mandell has they provided the summaries you finity. Here µ(J) denotes the length been named a Fellow of the Amer- find below. (A former IU post-doc (Lebesgue measure) of a subset of ican Mathematical Society. Man- and now Assistant Professor at Vir- [0, 1]. The concept of weak mixing dell is an algebraic topologist, and gina Tech, Nathan Glatt-Holtz, gave appears in the branch of mathemat- he joins previously named fellows the lecture on the work of Martin ics known as ergodic theory. Ergodic from our Department Eric Bed- Hairer in the area of stochastic par- theory features in work of IUB fac- ford, Hari Bercovici, David Fisher, tial differential equations.) ulty members Ciprian Demeter, Mar- Robert Glassey, Michael Larsen, Rus- lies Gerber, and Russell Lyons. sell Lyons, Peter Sternberg, Roger Another milestone achievement Temam, Shouhong Wang and Kevin Artur Avila Cordeiro de Melo is his solution to the so-called Ten Zumbrun. Martini problem. The name comes Tracy Whelan Brazilian-French mathematician from mathematician Mark Kac, who Artur Avila Cordeiro de Melo re- offered 10 martinis to the person ceived one of the four Fields Medals who could solve this problem. The at the 2014 International Congress problem asks to show that the spec- of Mathematicians. He is the first trum of a certain specific operator is Latin American mathematician to re- a Cantor set. The spectrum of an op- ceive this prize. The medal recog- erator is kind of like a generalization nizes his outstanding contributions of the set of eigenvalues of a square to several areas of mathematics, in- matrix to an infinite-dimensional cluding dynamical systems and anal- setting. The spectral theory of oper- ysis. ators is studied by IUB faculty mem- Here is one (of many) dynam- ber Hari Bercovici. Dr. Tracy Whelan, a senior lec- ical systems that Arthur Avila an- The notion of renormalization turer in the Math Department, was alyzed. Start with the unit inter- appears in much of his work. Here is inducted into the Faculty Collo- val [0, 1]. Cut it into several non- an example of renormalization. Sup- quium on Excellence in Teaching overlapping pieces, and rearrange pose f : [0, 1] → [0, 1] is an IET (FACET) in Spring, 2014, joining them to form again the unit interval and J ⊂ [0, 1] is a sub-interval. Pick Professors Elizabeth Housworth and [0, 1]. The resulting transformation x ∈ J and apply f over and over Peter Sternberg as members from the f : [0, 1] → [0, 1], although discon- again until f(x) ∈ J. Since f pre- Department of Mathematics. FACET tinuous, is defined everywhere ex- serves µ, this happens with proba- is a community of Indiana University cept at a finite set of points, and bility 1. This gives a new function faculty members who are committed it preserves lengths. This is an ex- g : J → J. It often happens that to being – and helping others to be – ample of an interval exchange trans- (continued on p. 4) exceptional teachers.
Indiana University Department of Mathematics Alumni Newsletter m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Page 3 Russell Lyons mathematics, with a strong empha- Professor Kevin Zumbrun has sis on underrepresented groups, as been promoted to distinguished pro- well as support undergraduate re- fessor, the highest academic rank search and the establishment of a the university can bestow upon its math club for mathematics educa- faculty. He joins Professors Michael tion majors at IU Bloomington. Larsen and Roger Temam in this Roger Temam distinction. Zumbrun works in the area of nonlinear partial differential equations, having made deep contri- butions to the understanding of sta- Professor Russell Lyons gave an bility of shocks. He has published invited address at the annual joint over 150 articles in his career. meeting of the American Mathemati- cal Society and the Mathematical As- sociation of America in San Antonio. His talk was titled “Random order- Fields Medalists ings and unique ergodicity of auto- continued from page 3 morphism groups.” g : J → J is again an IET, and then Noah Snyder Professor Roger Temam has been g is called a renormalization of f. selected for membership in the Noteworthy is that most pub- American Academy of Arts and Sci- lished work of Arthur Avila has been ences, one of the nation’s oldest and co-authored, and that he proved his most prestigious honorary societies. first major result on renormalization Temam has made fundamental con- at the age of just 19! tributions to several large areas of applied mathematics, including nu- merical computation of fluid flows, Maryam Mirzakhani slow dynamics and inertial mani- folds, turbulence theory, and climate Maryam Mirzakhani of Stanford modeling. He is one of the top ex- University became the first woman Professor Noah Snyder was the perts in mathematical models for and the first Iranian to win the Fields recipient of a prestigious NSF Ca- climatology and a leading expert Medal. reer Award, and will begin receiving worldwide in nonlinear partial dif- Periodic phenomena is often the more than $455,000 over five years ferential equations and their applica- most striking and the most use- to advance the study of quantum tions. He has received numerous in- ful. The ancients discovered the pe- groups and subfactors, a form of the- ternational honors and awards and riods of the moon, the sun, and oretical mathematics with potential is a fellow of the Society for In- the stars. In a chaotic universe, the applications in areas such as physics dustrial and Applied Mathematics, rare examples of periodicity pro- and quantum computing. In addition the American Association for the Ad- vide us with frames of reference in to advancing knowledge in the field, vancement of Science and the Amer- time and space. Most of the work Snyder’s grant will support the de- ican Mathematical Society. of Mirzakhani concerns estimating velopment of new curriculum based the time—the period—it takes for on his work – which employs a tech- Kevin Zumbrun some object to return to a previous nique known as higher dimensional state. For example, the Earth takes algebra – for high school students one (Earth) year to revolve around at Canada/USA Mathcamp, an elite sun. Saturn takes about thirty years. mathematics summer program. The Uranus takes eighty-four years. If grant will also fund dissertation fel- the Sun were the only star, one lowships for graduate students with might imagine an infinite sequence an established record of extraor- of planets at farther and farther dis- dinary education and outreach in tances all orbiting the sun. Mirza-
Indiana University Department of Mathematics Alumni Newsletter Page 4 m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf khani would be interested in the triangles, pentagons, hexagons...For asymptotics of the associated se- these exotic tables, much less is quence of periods. known. In fact, we don’t even know New Faculty An example closer to home is whether for each trianglular table found in playing billiards. Imagine there exists a periodic billiard trajec- the motion of a billiard ball on a fric- tory! Nam Le tionless square pool table, the ball For polygonal tables for which bouncing off the sides but other- each angle is a rational multiple of wise following straight paths. One π, Howard Masur showed that in- can create a periodic orbit by shoot- finitely many periods do exist and ing the ball in a direction perpendic- that there exists a constant c so that ular to one of the sides. Indeed, since c · x2 ≤ N(x) ≤ c−1 · x2 for x large. the table is rectangular, the ball will On the other hand, an asymptotic bounce off this side, retrace its path formula like (∗) is unknown for so- in the opposite direction, bounce off called ‘rational’ tables. the opposite side, and finally return Professor Nam Le (Ph.D. Courant With her collaborator, Alex Es- to its original state in both position Institute, NYU, 2008) joined the fac- kin, Mirzakhani proved that for any and velocity. Since the table is fric- ulty of the Math Department during rational table T there exists an ex- tionless, the period depends only on the academic year 2014-15. Le re- plicitly computable constant c(T ) the initial velocity. ceived his Ph.D. from the Courant such that One could do fancier shots that Institute at NYU and previously yield periodic orbits. For example, held a post-doctoral appointment at one can shoot the ball at angle that 1 Z x N(es) Columbia University. He received the lim s 2 ds = c(T ).(∗∗) is forty-five degrees from a side. In x→∞ x 0 (e ) prestigious Scientific Prize of the In- fact, one choose any direction that stitute of Mathematics at the Viet- has rational slope where we imagine nam Academy of Science and Tech- The constant c(T ), introduced ear- the sides of our table parallel to stan- nology in 2013. Professor Le works lier by William Veech, involves the dard coordinate axes. Because there in the area of nonlinear partial dif- volumes of moduli spaces and ele- are infinitely many rational num- ferential equations and the calculus mentary combinatorial invariants as- bers, there are infinitely many pos- of variations. sociated to the polygon T and is sible periods. Three new lecturers joined the known to be a rational multiple Even if Gauss were not a pool Math Department faculty in the fall of some power of π. Formula (∗∗) player, he would have understood of 2014. All three earned either should be regarded as an averaged that if N(x) is the number of periods graduate or undergraduate degrees version of (∗). The proof is a tour of size less than x, then in mathematics at IU Bloomington. de force involving techniques from dynamical systems, geometry, and N(x) π Zhixu Su lim = . (∗) probability. x→∞ x2 23 · s2 The elusive analogue of Gauss’ Indeed, it’s not hard to see that asymptotic (∗) for exotic tables the set of periods is essentially the awaits a future Fields Medalist. set of lengths of vectors of the form (2s · n1, 2s · n2) where m1 and m2 are integers s is the sidelength of the Manjul Bhargava table. The number of such vectors inside the disc of radius x was first Manjul Bhargava of Princeton re- estimated by Gauss, and the search ceived the Fields Medal for his work Zhixu Su did her graduate work for better estimates is known as the in number theory. He is the first per- in the Mathematics Department Gauss circle problem. son of Indian descent to win this studying under Jim Davis. She com- One can also play billiards on ta- most coveted prize in mathematics. pleted her Ph.D. in geometric topol- bles made from exotic shapes such as (continued on p. 6) ogy in the fall of 2009, and was
Indiana University Department of Mathematics Alumni Newsletter m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Page 5 a member of the mathematics fac- an M.A. in mathematics in 2002. completely analogous criterion for ulty at Rose Hulman University from After that, Jim was the Director of integers of the form x2 + xy + y2. 2009 until 2012. Just prior to return- the Math Learning Center for three However, the argument breaks down ing to Bloomington, she held a lec- years. Since then, Jim has been a fre- in most cases. For instance, 2 and turer position in mathematics at the quent visiting instructor in the Math 3 are relatively prime integers and University of California, Irvine. Department and brings a wealth of 2 · 3 is of the form x2 + 5y2 while 2 experience with large sections of fi- and 3 are not. Gauss devoted much Erica Isaacson nite math and calculus to his new of his classic number theory treatise position. The appointment of Erica, Disquisitiones Arithmeticae to explor- Jim and Su brings the number of ing this phenomenon. He developed lecturers in the Department up to a theory of composition of binary eleven. A primary responsibility of quadratic forms of the same discrim- the lecturers is to teach most of the inant. For instance, 2x2 + 2xy + 3y2 Department’s large (270-student) and x2 +5y2 are both of discriminant sections of our service courses. As a −20, and the formula
group, lecturers touch the academic 2 2 2 2 lives of the majority of IU undergrad- (2x +2xy+3y )(2u +2uv+3v ) = Erica Isaacson, a Bloomington uates as they seek to meet their gen- (2xu+xv+yu−2yv)2+5(xv+yu+yv)2 native, studied as an undergradu- eral education requirements. During fall semester of 2014, for example, explains why 6 factors into two in- ate at IUB and earned a B.S. in 2 the total number of students en- tegers of the form 2x + 2xy + mathematics and a B.S. in Physics in 2 rolled in our lecturer-taught classes 3y . Later, it was understood that the spring of 2006. She studied un- this phenomenon occurs for num- der Jon Wilkening at University of was nearly 3500. Lecturers may also be asked to do course coordination, ber rings where unique factorization California, Berkeley and completed into irreducible factors breaks down: her Ph.D. in applied mathematics participate in curriculum develop- √ in the ring Z[ −5], 6 has two dis- in 2012. After returning to Bloom- ment, and take on a variety of ser- vice activities. √tinct factorizations:√ 2 · 3 and (1 + ington, Erica taught as a visitor in −5)(1 − −5). The group of forms the IUB Math Department for several of a given discriminant is a special semesters before she was appointed case of an ideal case group. It was as a lecturer last fall. understood that this was the end of Fields Medalists the story. Jim Hendrickson However, Bhargava discovered a continued from page 5 new and unexpected continuation, Fermat’s “Two Squares” theorem a completely different direction in says that a positive integer can be which the theory of composition of written as x2 +y2, where x and y are binary quadratic forms can be ex- integers, if and only if it is a product tended. There are a number of kinds of primes p 6≡ 3 (mod 4) and expres- of forms of higher degree which sions p2, p ≡ 3 (mod 4). A key part have a composition law analogous to of the argument is the identity the one developed by Gauss. Bhar- gava classified them, using ideas 2 2 2 2 Jim Hendrickson graduated (x + y )(u + v ) = from the theory of Lie groups. Just as from the University of Wisconsin- it is hard to count the forms of a sin- (xu − yv)2 + (xv + yu)2. Parkside, where he majored in psy- gle discriminant but easy to estimate chology and history. He rediscovered Conversely, if m and n are relatively the number of forms of discriminant a love for math late in his under- prime and mn can be written as a less than some given bound, so it is graduate career and took an extra sum of squares, one can run this possible to use Bhargava’s theory to year to complete a B.S. in mathe- backward to write m and n as sums count various objects of interest to matics. From there, he entered our of squares. This generalizes to some number theorists, for instance quin- graduate program, graduating with other cases; for instance, there is a tic fields of bounded discriminant.
Indiana University Department of Mathematics Alumni Newsletter Page 6 m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf tics department of Columbia Univer- many, and Romania, he climbed to sity. However, New York felt unsafe, the top of the Matterhorn. A few Retirements and getting mugged did not help. He years later, in 1986, he was invited moved to IU in 1980; driving out of to the First World Congress of the New York for the last time, he said, Bernoulli Society, in Tashkent, USSR. felt like getting out of prison. This Congress was especially mem- Rick Bradley What is his chosen field of strong orable because 50 of its 1000 par- mixing about? Suppose one throws ticipants had to be hospitalized due dice or tosses coins repeatedly, shak- to poor local sanitation. Rick felt ing them very well each time. Then lucky that his assigned roommate each outcome is independent of the gave him good advice on how to others, and there is a well-developed cope with the conditions. theory to describe what happens. Along with all of Rick’s success at For example, if one tosses a coin IU over the years, he has contributed 2000 times, then one expects to get in so many ways to the Mathemat- around 1000 heads, but not exactly ics Department. He won departmen- 1000; the distribution of the number tal awards for teaching and has been Born in Berkeley, CA in 1950, of heads is given approximately by a favorite among graduate students Richard C. Bradley, Jr., comes from the famous bell curve. However, sup- to serve on doctoral exams. He is a long and distinguished line of pro- pose that one shakes the dice only a known as a conscientious colleague fessors. He grew up in Ithaca, New little each time. Then the outcomes and one who always carries out his York and Colorado Springs, Col- are dependent, but outcomes that work with efficiency and thorough- orado and his interest in mathemat- are far separated in time should be ness. For example, while serving as ics dates back to elementary school. almost independent. How does this Director of Graduate Studies, he dis- By 8th grade, playing Parcheesi and affect the bell curve for the dice aver- covered that it was very hard to other games of chance, Rick al- age? This sort of question about limit know all the rules and regulations ready became fascinated by proba- behavior (laws of averages) is the that students needed to follow. Con- bility. Later, when he entered MIT as basis of the theory of strong mixing, sequently, he prepared a 50-page an undergraduate in 1968, he had a which is of interest not only mathe- document so that all future Direc- course on probability from the leg- matically, but also in a wide area of tors would not have to learn on their endary teacher Gian-Carlo Rota and applications. own like he did. Rick has also been this course solidified his interest in a very patient and effective advisor, Rick is recognized as one of the the field. directing seven doctoral theses and top people worldwide in this field. After graduating from MIT, Rick successfully mentoring three under- He is especially noted for construct- was looking for adventure and took graduates in summer research. Be- ing ingenious examples or counter- a break from school. He worked for yond service to IU, he also served examples and for proving structural a year as a cowboy after college, the profession as Probability Editor properties, all of which elucidate the herding cows on horseback and even of the “Proceedings of the Ameri- relationships among various kinds of helping cows give birth. Ready to can Mathematical Society” for 8 1/2 mixing conditions. He also wrote a resume school in 1974, he entered years. His name is well known and masterful 3-volume “Introduction to UCSD and left with a Ph.D. in prob- his work is admired by both theoret- Strong Mixing Conditions” totaling ability in 1978. During that time, ical and applied researchers. 1681 pages. For his work, he was his advisor, Murray Rosenblatt, gave Rick has been a wonderful col- honored with election as a Fellow of him a paper to read by Ibragimov on league in every respect. His fellow the Institute of Mathematical Statis- strong mixing conditions, and posed faculty and students will miss him tics. several questions for Rick to work for his remarkable energy, conscien- on. This field grabbed Rick’s interest, Rick regularly gives invited talks tiousness, devotion, and selfless in- and it remained his principal area of in the US and Europe. Ever retain- tegrity. research for the rest of his career. ing his adventurous spirit, in the by RUSS LYONS Before coming to IU, Rick spent summer of 1982, between meet- two postdoctoral years in the statis- ings in Hungary, France, West Ger-
Indiana University Department of Mathematics Alumni Newsletter m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Page 7 Jiri Dadok decades. ous family events surrounding his In 1980 he arrived in Blooming- sons, daughters and grandchildren, ton, serving the last twenty years in whose lives he plays a central role. at the rank of Full Professor. Jiri’s He is equally content to hike a trail mathematical interests have always or listen to classical music and he been very broad. His influential con- plays some classical guitar himself tributions include work on harmonic when seeking a moment of tranquil- analysis of Lie groups and homoge- ity. neous spaces, several complex vari- So many of us in the Mathemat- ables, differential geometry, calibra- ics Department who value his friend- tion theory and partial differential ship and the always lively conver- equations. sation that accompanies any walk with Jiri to the coffee shop hope that As a mathematician, he is known he will still spend plenty of time in for his ability to cut through com- Rawles Hall in the coming years. Jiri Dadok is retiring this plex problems to see the essence of by PETER STERNBERG semester after spending the last the difficulty and most especially for thirty-five years as a vital member his ability to arrive at elegant so- of the Department of Mathemat- lutions to seemingly messy or even ics. Jiri has been a wonderful col- intractable mathematical situations. Student News league who is known for his quick The breadth of Jiri’s mathematical continued from page 2 and powerful mathematical insights interests are also reflected in the im- and his equally quick wit and gener- pressive array of high level courses Problem Seminar course. One team, ous laugh. he has volunteered to teach, includ- led by graduate student Ozan Jiri was born in Brno, Czechoslo- ing 400-level classes in geometry, Yolasigmaz, worked with IU Phys- vakia in 1950. He and his fam- complex analysis, algebra, real anal- ical Plant. The problem: to design a ily traveled to the United States in ysis, number theory, partial differen- model that determines the optimal 1968 during the Prague Spring, a tial equations, probability and statis- dorm assignments for students in period when his father Josef was tics. For over three decades, Jiri has summer programs and classes at IU conducting research at Carnegie- remained one of the Mathematics so as to save money on electricity. Mellon. With the subsequent Soviet Department’s most popular teachers. Ozan’s work this summer is sup- invasion of Czechoslovakia, the fam- Students delight in his ability to con- ported by a $2,000 grant from the ily decided to remain in the United vey complicated and often abstract IU Office of Sustainability. States. Jiri’s father joined the faculty notions through a few key pictures For non-majors, in order to meet of Carnegie-Mellon and Jiri enrolled and short calculations, without the anticipated demand for interest- there as an undergraduate, finishing clutter of messy details. In recogni- ing General Education mathematics his bachelor’s degree in mathematics tion of his talents in the classroom, courses in Fall 2016, faculty mem- in 1972. Jiri received the Mathematics De- bers Andrew Dabrowski, Jim Hen- Jiri went to MIT for graduate partment’s Rothrock Teaching Award drickson, Shabnam Kavousian, Will work, completing a PhD under Sig- in 2011. Orrick, and Bruce Solomon are de- urdur Helgason in 1977 with a While retirement for some may veloping topics in areas like art, dissertation titled, “Fourier Trans- seem a daunting transition, for a game theory, groups and symmetry, forms of Distributions on Symmet- person of Jiri’s wide interests, there music, and voting. This will be a ric Spaces.” After holding a one-year can be no such qualms. Jiri and unique and valuable addition to our visiting position at the University of his wife Carolyn Begley are enthu- already diverse offerings. Connecticut, Jiri went on to take siastic bird watchers, participating New also was the founding of our a post-doctoral position as a G.C. frequently in bird counts through- first student chapter of the Associa- Evans Instructor at Rice University out the surrounding forests. He is tion for Women in Mathematics, led from 1977-1980. There he began an accomplished photographer, al- by senior Lea Beneish, now bound a fruitful collaboration with Reese ways volunteering for the role of for the PhD program at Emory Uni- Harvey that eventually spanned two family photographer at the numer- versity. (continued on p. 10)
Indiana University Department of Mathematics Alumni Newsletter Page 8 m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf set of notes based on lectures by nected with the development of the Robert Steinberg. In 1978 he was Kazhdan-Lusztig polynomial, which Obituary awarded the Young Scientist Award plays a central role in modern rep- from the Indian National Academy. resentation theory. Vinay is also one of the developers Vinay was also a very popular Vinay Deodhar of Kazhdan-Lusztig theory (and in teacher, highly organized and known fact, he coined the term) and has for his clear exposition. In 1998 he done important work on the geom- earned our highest teaching award, etry of flag varieties. In 1992 he the Rothrock Teaching Award. He edited a volume of the AMS series stamped his personality on two of Contemporary Mathematics on the our courses, Lie Groups and Lie Alge- subject. He also has made impor- bras. He also supervised three Ph.D. tant contributions to the theory of students, all of whom remain aca- Bruhat orderings on Coxeter groups. demic mathematicians: Dijana Jake- During his last sabbatical at Indiana lic, at UNC Wilmington; Wansoon University he started on an entirely Kim, at Hoseo University, in South new project with Israel Gelfand, one Korea; and Yi Ming Zou, at UW Mil- This year marked the passing of of the greatest Russian mathema- waukee, who has given Vinay the long-time colleague Vinay Deodhar. tians, who was by then in the United distinction of having mathematical Vinay Deodhar was born in Bom- States. Vinay was quite enthusiastic grandchildren. bay, India, on December 3, 1948. He about the project but Gelfand died Vinay served a term as director attended Bombay University, where before it reached fruition. of graduate studies, a job he took he received his doctoral degree in Vinay wrote several highly influ- very seriously, especially in the se- 1974 studying under M. S. Raghu- ential papers on the (weak) Bruhat lection of new graduate students. He nathan. He came to Indiana Univer- order on Coxeter groups. In the mo- also played a major role in running sity in 1981 from a faculty position tivating case of symmetric groups the teaching mentor program for the at the Tata Institute of Fundamental this can be understood as follows. Math Department. Research, one of the great centers of The length of a permutation A is mathematics in the world, which re- the minimal number of times a con- Vinay was greatly devoted to his mained for him the standard of ex- secutive pair of elements must be family, his wife, Vineeta, and his two cellence. Prior to his position at the exchanged in order to achieve A. children, Abhijit and Aditi, both of Tata Institute, he spent three years at There may be several different ways whom have been students here at IU. the Institute for Advanced Study and to realize A by consecutive transpo- In the last several years of his life, he one at the Australian National Uni- sitions in this smallest possible num- exhibited exceptional courage deal- versity in Canberra. ber of steps. All the permutations ob- ing with illness while still continuing Vinay has made fundamental tained as intermediate steps along his distinguished teaching and men- contributions to mathematics, par- any of these sequences are consid- toring. We all indeed count it as a ticularly Lie theory. While still a stu- ered to be less than A. His work on privilege to have been his colleague. dent, he wrote a highly influential the Bruhat order is inextricably con- by DARRELL HAILE Around the Department
Undergraduate Awards These second-year students won Scholarship); and Ben Briggs (Marie awards and scholarships: Jennifer S. Wilcox Scholarship). Huang and Samuel Pilgrim (Thelma These first-year students won These third-year students won Abell Prize); Sarah Butchko (Ruth E. awards and scholarships: Andrew awards and scholarships: William Gilliatt Memorial Scholarship); Tay- Henderson and Jordan Lenchitz Bowman, Christopher Farris and lor Ball (Cora B. Hennel Memorial (Thelma Abell Prize). Jared Wentz (Cora B. Hennel Memo-
Indiana University Department of Mathematics Alumni Newsletter m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Page 9 rial Scholarship); and Max Zhou Graduate Awards Woo, Shizhuo Zhang, and Yining (Ciprian Foias Prize). Zhang (Glenn Schober Memorial Travel Award); Rafael Monteiro da These fourth-year students The following graduate students Silva (College of Arts and Sciences won awards and scholarships: won awards and scholarships: Tim Dissertation Year Award); Rafael Kevin Miloshoff and Mary Pasquale Lai and Brady Thompson (Hazel Monteiro da Silva (Outstanding The- (Thelma Abell Prize); Jennie Lipson King Thompson Fellowship); Patrick sis Award); Samantha Allen, Nikhil (Ruth E. Gilliatt Memorial Schol- Chu, Gregory Cook, Derek Donner, Gupta, Matthew Heimerdinger, arship); Luke Andrejek (Trula Sid- Sailaja Gajula, Dong Han, Jordyn Zachery Lindsey, Thang Nguyen, well Hardy Scholarship); Eva Love- Harriger, Jacob Herlin, Sarah Hoban Michael Novack, Eunhee Park, and land, Sarah Reifeis, Chloe Urbanski, Halvorsen, Jandos Jayikbaev, Luke Ranjan Rohatgi (David A. Rothrock Zachary Wampler, and Zhengang Kwiakowski, Aranya Lahiri, Geunho Associate Instructor Award). Zhang (Marie S. Wilcox Scholar- Lim, Didac Martinez-Granado, Jihye ship); and Lea Beneish (Rainard Park, Min Woo Park, Kaluthanthrige Faculty Awards Benton Robbins Prize). Perera, Kursat Sozer, Kevin Switzer, Pengfei Tang, and Cong Zhou (Col- Ayelet Lindenstrauss received Shelby Kruse won the M118 Un- lege of Arts and Sciences Fellow- the Rothrock Mathematics Faculty dergraduate Intern Award. ship); Pengfei Tang (Robert E. We- Teaching Award. Marlies Gerber, ber Memorial Award); Kelvin Guil- Kevin Pilgrim and Tracy Whelan won bault and Pengfei Tang (James P. the IU Trustees Teaching Award. Williams Memorial Award); Ruiyu Yang (Muriel Adams Stahl Gradu- ate Fellowship); Marco Hernandez and Wai Kit Lam (William B. Wilcox Mathematics Award); Ashley Light- foot (College of Arts and Sciences Travel Award); Eduardo Fischer, Fourth-year scholarship winners Deniz Kutluay, Rafael Monteiro da Sarah Reifeis, Chloe Urbanski and Silva, Pawan Patel, Xuqiang Qin, Eva Loveland. Andrew Tapay, Shida Wang, Calvin Ayelet Lindenstrauss
Student News continued from page 8
Goldwater Scholars team. Yale University. Eighteen of our ma- Mathematics majors took two of Accolades and Awards jors were elected to Phi Beta Kappa this year’s three Goldwater Schol- Outgoing Math Club president honor society. arships awarded to IUB students. Timothy Zakian received a pres- Putnam Team Thomas Dauer is a junior from New- tigious Clarendon Scholarship to Our Putnam Team this year, with burgh, Indiana. He plans to pur- study at Oxford University. Rising ju- members Thomas Dauer, Joshua Fos- sue a Ph.D. in physics, conduct re- nior Taylor Ball attended the pres- ter, and Max Zhou, placed 35th in search in theoretical condensed mat- tigious Director’s Summer Program the nation. This is an exam where ter physics and quantum informa- at the National Security Agency. the median score is often 0! These tion, and teach at the university Math majors won numerous campus students trained for the exam under level. Joshua Foster is a junior from awards too, including Wells Scholar Professor Hari Bercovici. Carmel, Indiana. He also plans to Jonathan Hawkins ’15, recipient of REU pursue a Ph.D. in physics. Both a Kate Hevner Mueller Outstanding Expanding the frontiers of Thomas and Joshua were members Senior Award, who is now headed knowledge since 1966, our Re- of our 2014 Putnam Competition to the PhD program in Economics at search Experience for Undergrad-
Indiana University Department of Mathematics Alumni Newsletter Page 10 m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf uates (REU) program has been reg- we hope to see him on campus some- ative types.” “We’re looking for solid ularly funded by grants from the day soon! Incoming president Cheng performance in analytical courses.” National Science Foundation for the Shi and I are already corresponding “The algorithmic thinking of math last few decades. Thanks to the lead- about logistics for Fall ’15. majors is valuable to us.” “We have ership of faculty member Chris Con- Did you know Disney has a math no quota for IUB math majors.” I’ve nell, we’re pleased to report we have research group? They do–and the heard this from several recruiters NSF funding for summers ’16-’18, math behind the snow in the hit over the past two years. This would inclusive. A “gap year” this summer movie Frozen was discussed during a seem to refute the myth that a Lib- led to a temporary downsizing of Math Club presentation by Michael eral Arts degree is less valuable than our program and to a cohort com- Dorff from Brigham Young Univer- a professional degree. To help get ing exclusively from IUB students. sity. In addition to numerous cool this word out, I’ve been drawing on I thank faculty mentors Matthew talks by IU Mathematics faculty, the the wisdom shared by 38 of you Bainbridge, Chris Connell, Dylan Club also had panel discussions on IU math alums in our “Share your Thurston, and Zorn postdoctoral REU programs, problem solving ses- story” survey. This has helped a lot professor Jeffrey Meier for keep- sions, and the occasional game of when discussing the value of math ing the program running this year. Mathematics Pictionary. degrees with potential recruits and Five students will work very hard Field Trip their families and potential majors. in this eight-week program; the ex- In a first-ever formal collabora- Thanks to all who have responded!! perience is invaluable preparation tion, the Departments of Economics by KEVIN PILGRIM for the rigors of graduate studies. and Mathematics supported a group Other current students are at REU of 24 mathematics and economics programs around the country. majors on a trip to St. Louis, MO Actuary Club, AWM Chapter, and February 19-21, 2015, led by Ger- Groups Program Math Club hard Glomm (Econ) and myself, Founded just this past Fall 2014, Kevin Pilgrim ’89 (Math). Our first our new chapter of the Association event was a stop at the Federal Re- for Women in Mathematics has had serve Bank of St. Louis for an alumni a busy year. An outstanding lineup of mixer event and a speech by Presi- visitors, including Cornelia van Cott dent James Bullard (PhD ’90, Eco- ’08, (U. of San Francisco) and Moon nomics). The next day saw panel Duchin (Tufts), gave inspiring pre- discussions with several varied busi- sentations. Events included network- ness leaders in two locations: Brown ing with alumna Frances Richert Shoe Company and Buckingham Fi- Groups 2015 problem-solving stu- during her Careers class campus nancial. At the latter event, we met dents with Associate Instructor Emily visit, viewing the one-woman hit Sharol Brickman ’86. Now an as- Walther play Truth Values, and outreach to sociate partner at Aon Hewitt, she The summer of 2015 will mark the local chapter of Girls Inc. I look shared valuable perspectives about nearly 50 years of Mathematics De- forward to working with new presi- the business world, work ethic, and partment participation in the Groups dent LeeAnn Sager this coming year! the power of mathematics. The trip Scholars Summer Experience Pro- Under the leadership of senior also included a theatrical play, a trip gram. The Groups Program is ex- Neelan Scheumann (now headed to to the St. Louis Art museum, and a pecting at least 384 students (its OneAmerica in Indianapolis), our stop at the Cahokia Mounds State largest class ever) to come to cam- Actuary Club continues to thrive. Historic Site. pus in June for six weeks of in- The year was busy, with Club mem- We thank Anne Koehler, whose tensive academic preparation. The bers holding study sessions, techni- generosity supported this trip for Program’s participants are Indiana cal training sessions, and attending several Mathematics majors from residents who are “first generation networking events to help members our new Careers in Mathematics college” or from low-income fami- gain valuable industry contacts. Past course. lies. They will all enroll in composi- Club president Bradley Hipsher ’14 Perspectives on careers tion, critical reading and mathemat- is now a recruiter for AllState and “We’re looking for smart and cre- ics courses, and many will also elect
Indiana University Department of Mathematics Alumni Newsletter m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Page 11 to study business, chemistry or par- students who were born in more an honors version of the problem- ticipate in a musical theater produc- than 30 different countries includ- solving course. This summer we are tion. There is no cost to the students ing Afghanistan, Bosnia, Yemen, hoping to hire 21 associate instruc- for the summer program. Nearly all Bangladesh, Iran, Pakistan, Mexico, tors and 7 undergraduate tutors to will return to IUB fall semester to Ecuador, Ghana, Zimbabwe, Fiji and staff the summer classes. formally begin their academic ca- Thailand. Mathematics is the only aca- reers. The Mathematics Department demic area that also offers classes The Groups Program was has been a major participant in the specifically for Groups students dur- founded in 1968 as a means of in- Groups Summer Program since its ing the academic year. Our J113 creasing diversity at IUB. A large inception. Dan Maki and Maynard (brief calculus) class, for example, network of recommenders in high Thompson were involved in design- meets daily in very small sections schools and community groups ing the original summer math cur- to maximize student-teacher con- throughout the state was put in riculum, which targeted preparation tact hours and provide students place to seek out well-qualified stu- for entering the School of Business. with a more structured and support- dents and help them apply to the In the early years, the Mathemat- ive learning environment than they program. The recommender system ics Department hired faculty specif- might have in a large lecture class. is still used today and ensures access ically to teach algebra and computer The close relationship between en- to the program for students in ru- science classes for the Groups stu- tering Groups students and instruc- ral areas and small towns as well as dents. As the number of program tors is an important factor in the stu- the large urban high schools in In- participants has grown, the teach- dents’ ultimate success in the Uni- dianapolis, Fort Wayne, Evansville, ing responsibilities have shifted to versity. We can be very proud of the South Bend and Gary. Each enter- graduate students, and the curricu- hundreds of mathematics graduate ing Groups class includes students of lum has also evolved to meet the students who have so positively af- African American, Hispanic, White, needs of the students. We currently fected the lives of first generation Asian and mixed ethnicities. In ad- offer four courses during the sum- students over the last five decades. dition, in the last two years alone, mer program: pre-algebra, algebra, the Groups Program has welcomed introduction to problem solving and by LINDA MCKINLEY
Indiana University Department of Mathematics Alumni Newsletter Page 12 m http://www.math.indiana.edu/mathnews/AlumiNewsletter2015.pdf Giving
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