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Home , Homework, Hyman Bass, Karen Uhlenbeck, Michael Artin, Oscar Zariski, Society of Actuaries

Department of ContinuUM NEWSLETTER • 2009

View from the Chair's Office - Fulton Named Distinguished Mel Hochster University Professor

This has been an exciting year Professor William Fulton has for the Department, and certainly been named the Dis- for me as Chair. We hired six new tinguished University Professor of faculty members: Assistant Profes- Mathematics. Appointment to a sor Dmitriy Boyarchenko (repre- Distinguished University Profes- sentation theory), and Associate sorship is one of the highest hon- Professors Thomas Lam (combi- ors conferred by the University natorics), Kartik Prasanna (number upon a faculty member. Math- theory), and Michael Zieve ( ematics faculty members Hyman and number theory) are already Bass, Mel Hochster and Professor here, while Associate Professor Da- Emeritus Fred Gehring previously vid Speyer (tropical ) and Professor Mark Rudelson received this recognition. (analysis) will arrive in 2010-11. New faculty are profiled on Fulton received a Ph.D. in mathematics from Princeton page 4. Daniel Forger was promoted to the rank of Associate University in 1966 and came to U-M in 1998 following a dis- Professor with tenure, and Stephen DeBacker, Harm Derksen, tinguished career at Brown University (1970-87) and the Uni- and Mattias Jonsson to the rank of Professor. See page 3 for versity of Chicago (1987-98). He was appointed as the first more faculty highlights. M.S. Keeler Professor of Mathematics. Fulton was elected to We mourn the loss of our longtime friend and colleague, the National Academy of Sciences in 1997, and to the Ameri- Professor Emeritus George Piranian (p. 16). He will be long can Academy of Arts and Sciences in 1998. In 2000 he was remembered. named a Foreign Member of the Royal Swedish Academy of Al Taylor retired this year after many years of service to Sciences. These the Department, including two three year terms as Chair. He are honors that go Inside will be greatly missed, but I am hoping and expecting that he only to the very top will still be around the Department a great deal. Dee Huddock tier of mathemati- View from the Chair's Office 1 and Rosemarie Aris retired from our staff this year, and I wish cians in the world. Fulton Professorship 1 them the best while at the same time wonder how we will sur- Although his External Review 2 vive without them. interests are very Faculty News 3 The Regents have awarded Bill Fulton the Oscar Zariski broad, most of New Faculty 4 Distinguished University Professorship in Mathematics, and Fulton’s work has Al Taylor Retires 5 Karen Smith became the new M. S. Keeler Chair in Math- been in the of Calculus Concept Inventory 6-7 algebraic geom- ematics, the position formerly held by Bill. Graduate Program News 8-10 etry (the study of An external review of the Mathematics Department was geometric proper- Undergraduate Program 11-12 conducted during the third week in March by a Committee ties of solutions Actuarial Program News 13 consisting of , Rob Calderbank, Herb Clemens, of polynomial Donors 14 George Papanicolaou and . Their assessment equations) and Alumni News 15 of the Department was very positive—here is the first para- neighboring areas. In Memoriam 16 graph of the report: Since a great many Development Highlights 17 “The quality of the Mathematics faculty is outstanding, of the most impor- Math T-shirts 18 and the Department is the center of a vibrant mathematical tant problems in Alumni Reply Form 19 community. The great variety of advanced courses makes mathematics and

continued on page 2 continued on page 5

UM-DEPARTMENT OF MATHEMATICS CONTINUUM – 2009 External Review View from the Chair’s Office (continued from page 1)

This year the Department was aged the Department to continue hiring Michigan attractive to graduate fortunate to have an external review in the applied mathematics programs, and potential faculty.” During the Fall done by several outside experts in the with particular emphasis on developing Semester there will be a dialogue be- field. Departments at major universities joint appointments with other disciplines tween the Department and the College regularly undergo review by peers to such as business, engineering, educa- concerning the results of the External provide feedback on current operations, tion, and statistics. The committee cited Review (see article on page 2). corroboration on successes, and advice that the large number of term assistant The Department’s interactive meth- for possible improvements. professors—or postdoctoral faculty— od of teaching calculus in Math 115 did The review committee consisted of contribute greatly to the dynamic atmo- impressively well in a multi-institution Chair Robert Calderbank (Princeton), sphere of the Department. These term assessment made using a new Calculus Michael Artin (M.I.T.), Herbert Cle- professors are an integral part of the Concept Inventory examination that mens ( State), George Papanico- instructional core, and contribute to the tests the students at the beginning and laou (Stanford), and Karen Uhlenbeck vibrant research environment. end of the course in order to factor out (). Their three day visit in March, Once again the Michigan Calculus the effect of prior background in the 2009, included meetings in the Depart- program was cited as a major strength subject (see pages 6-7). ment with all levels of faculty, as well of the Department (see page 6 for more The Department is still planning to as graduate and undergraduate students. information). The committee felt that make available on its website for The committee also met with deans and the program could be enhanced if more former and current students, faculty, associate deans in the College of Litera- senior faculty were involved in both visiting scholars, and staff, as well as ture, Science and the Arts and the Rack- the Introductory Calculus training pro- their families to provide contact and ham Graduate School. Their findings gram and the Inquiry Based Learning brief biographical information. If you were presented in an extensive report to initiative. The committee recognized return the form on page 19 we will be in College and Department administration. the striking increase in undergraduate touch with you about this. Once this is The committee referred to the math majors—from 125 in 2000 to 345 started, information about how to par- Department as the center of a vibrant currently. Approximately 50% of the ticipate will be available on our website. mathematical community. It praised the majors are in the Actuarial/Financial track. The committee was impressed by Everyone knows that economic active success of the applied mathemat- times are hard, and the State of Michi- ics research and interdisciplinary activi- the Actuarial program’s longevity and its established network of alumni, as well as gan has serious problems. The Univer- ties. The introductory Calculus program sity of Michigan has fared reasonably and the Inquiry Based Learning project connections with and companies. well under these circumstances, partly were recognized as being outstanding because, increasingly, much of the gen- components of the curriculum. The The graduate program was cited as eral fund comes from tuition rather than committee felt that U-M’s commitment having a high completion rate and a low from state appropriations, and partly to distinguished average time to degree. The committee because income from endowment is av- it among the top tier mathematics de- indicated that the number and variety of eraged over a seven year interval. None- partments. graduate courses and seminars offered theless, there will likely be tough times Upon examining the composition is “almost unparalleled” at other institu- ahead, and the Provost has a three year of the faculty, the committee encour- tions. The satisfaction of the graduate plan that will involve taking a close students with their education, as well as look at all activities and deciding which the instructional training they received, ones are the most important to continue ContinuUM Editorial Board: is high relative to other U-M depart- if resources are very limited. This will Mel Hochster, Chair ments. The committee encouraged the Suzanne H. Rogers, Editor undoubtedly be a challenging time for Doreen Fussman Department to continue recruiting under- the University and the Department. Curtis E. Huntington represented minorities, and to partner Agnes Soderbeck, design with other units in recruiting activities. The Department is pleased to have Photos by UM Photo Services, the Department of Mathematics, or had the opportunity to showcase our suc- personally submitted by the subjects. cesses to experts in the field. The useful feedback will be considered by the De- University of Michigan, Department of Mathematics, partment and College when developing 530 Church Street, 2074 East Hall, See more news on our website Ann Arbor, MI 48109-1043; future goals. [email protected]; fax 734-763-0937; www.math.lsa.umich.edu www.math.lsa.umich.edu/alumni/

2 CONTINUUM – 2009 Faculty Kudos Robert Megginson received the Yueh-Gin Gung and Dr. Charles Y. Hu was recently elected to Paul Erdös, who died in Award for Distinguished Service to the National Academy of Education. He 1996. Mathematics from the Mathematical is one of ten education leaders elected to Association of America. The award is Joel Smoller received the George intended to be the most prestigious for membership this year for their pioneer- David Birkhoff Prize. The prize is ing efforts in educational research and service offered by the Association, and awarded jointly honors distinguished contributions to policy development. The National Acad- by AMS and emy of Education is an honorary society mathematics and mathematical educa- SIAM once ev- tion. that currently has 174 members, who ery three years are elected on the basis of outstanding for an outstand- Actuarial Program Director, Curtis scholarship or contributions to educa- ing contribu- Huntington, is featured in an article in tion. tion to “applied the Fall 2008 issue of the LSA Maga- Jeffrey Lagarias gave the 2009 mathematics in zine. The full article is available on the Erdös Memorial Lecture at the March the highest and LSA website. Spring Central Section Meeting of the broadest sense.” Stephen DeBacker received a pro- American Mathematical Society. His The brief citation for the 2009 award motion to full professor. talk, “From Apollonian circle packings states “To Joel Smoller for his leader- Harm Derksen received a promo- to Fibonacci numbers,” described results ship, originality, depth, and breadth of tion to full professor. in number theory and theory that work in dynamical systems, differential arise from Apollonian circle packings, equations, mathematical biology, shock Daniel Forger received a promo- and contrasted some of the properties wave theory, and general relativity.” tion from assistant professor to associate relating to the circles’ curvatures with More detailed information is available professor with tenure. those of Fibonacci and Lucas numbers. at http://www.ams.org/prizes/birkhoff- Mattias Jonsson received a promo- The Erdös Memorial Lecture is an annu- prize.html tion to full professor. al invited address named for the prolific

Keeler Professorship

Karen Smith has been named the guished Dissertation Award, an Out- Postdoctoral Fellowship and CAREER M.S. Keeler Professor of Mathemat- standing Teaching Assistant Award, and Award, Sloan Research Award, Fulbright ics. The Keeler the Sumner Myers prize for best thesis. Award from Finland, and the Satter Re- Professorship Her dissertation solved two outstand- search Prize from the American Math- was established ing problems in ematical Society. in 1995 with a in what was then a relatively new area, In the Department, Smith’s mentor- gift from Mike tight closure theory, and she was imme- ing of young and teach- Keeler, and was diately recognized as one of the world’s ing record have both been stellar. She originally held by leading experts in the field. has supervised eight Ph.D. dissertations William Fulton. As her research career progressed, and has several current students. Her Smith joined the Smith connected tight closure to the presence in the Department and research U-M Department behavior of differential operators, to capabilities help to attract young alge- of Mathematics in 1996 as an associate certain special module structures on lo- braic geometers. She willingly takes professor, and was promoted to profes- cal , and to the cohomology on courses that other faculty may be sor in 2001. of bundles on algebraic varieties. All of reluctant to teach. In recognition of her Smith received her undergraduate her research is characterized by amazing success, Smith has received the Neary degree from Princeton and her Ph.D. originality, imagination and perception. Award for Faculty Excellence and a Fac- from U-M in 1993. While a graduate Smith’s recognition for her research ulty Recognition Award, both of which she won a Rackham Distin- includes a National Science Foundation are significant honors from U-M.

U-M DEPARTMENT OF MATHEMATICS 3 New Faculty Zieve was a researcher at the Center for Communications Research at Princeton. He has also Dmitriy Boyarchenko at , and postdoctoral held teaching Dmitriy Boyarchenko joined the fellow at the American Institute of and research Department in September 2009 as an Mathematics. appointments assistant professor. He received his Lam’s research is in algebraic com- at the Univer- bachelor’s degree from the University binatorics, particularly with problems sity of Southern of Pennsyl- arising in geometry and representation , the vania, and his theory. He has published over 20 pa- Mathematical Ph.D. from pers, several in high-ranking journals, Sciences Re- the University and has some impressive and truly im- search Institute, Leiden University, and of Chicago in portant results. He has been awarded the Institute for Advanced Study. 2007. Since a Clay Liftoff Fellowship, and recently Zieve’s research touches many areas that time he received a Sloan Fellowship. Lam has including algebra, number theory, alge- has been an proven to be an effective instructor, braic geometry, dynamical systems, dis- L.E. Dickson which was recognized at Harvard Uni- crete mathematics, theoretical computer Instructor at versity with a teaching award in 2008. science, and cryptography. He has done the , and was a Kartik Prasanna extensive study of polynomial functions member of the Institute for Advanced over various sorts of fields, and has also Study in 2008. Kartik Prassana joined the Depart- worked on algorithmic aspects of alge- Boyarchenko’s research has been ment in September 2009 as an associate bra. Zieve has written 36 papers with in the area of geometric representation professor. He 37 coauthors. His gregarious nature and theory. He produced results in areas as received his mas- enthusiasm for the subject contribute to diverse as , partial ter’s degree from his success as a . He was named differential equations, non-commutative the Indian Institute an Outstanding Graduate Student In- algebra, symplectic geometry, and repre- of Technology, structor at Berkeley. Even when he was sentation theory. and his Ph.D. from out of academia, Zieve sought out op- Princeton Univer- portunities to teach at all levels, working While at the University of Chicago, sity in 2003. He with undergraduates and middle school Boyarchenko had the opportunity to was an assistant students through a National Science establish a very solid teaching record professor at the University of California, Foundation Summer Program. and gained experience mentoring at the Los Angeles, and in 2006 was appointed graduate and undergraduate level. He as an assistant professor at the Univer- guided students in the Directed sity of Maryland. Program through topics such as alge- braic number theory, complex analysis, Prasanna is viewed as a leader in his and , and directed generation of number theorists with re- projects in the Research Experiences for search that has had significant impact on Undergraduates Program. several of the many subspecialties in the area. His research represents outstand- Thomas Lam ing work, and has appeared in top math- ematics journals. In his teaching career, Thomas Lam joined the Depart- Math Problem ment in September 2009 as an associ- Prasanna has taught a variety of courses ate professor. for a wide spectrum of students. His ef- forts were recognized by the University Lam received Does there exist a polynomial of California with the Robert Sorgenfrey his bachelor’s with integral coefficients, such Distinguished Teaching Award. degree from that P(0) = 1, P(2) = 3, and P(4) the University Michael Zieve = 9? of New South Michael Zieve joined the Depart- Wales and Ph.D. Answer elsewhere in the newsletter from the Massa- ment in September 2009 as an associate chusetts Institute professor. He received his bachelor’s of Technology degree from Harvard University, and his in 2005. Since graduating he has been Ph.D. from the University of California, a Benjamin Pierce Assistant Professor Berkeley, in 1996. From 2000-2007,

4 CONTINUUM – 2009 Al Taylor Retires William Fulton (continued from page 1)

B. Alan Taylor, Pro- ing Mathematics whose au- science lead to such equations, the field fessor of Mathematics in dience included faulty from has long stood at the center of math- the College of Literature, the School of Education ematics. Fulton’s presence in the De- Science, and the Arts, and Mathematics that has partment helped to transform an already retired from active faculty helped advance the peda- strong, important and vital research status on May 31, 2009. gogy of the Department. group into a leading center of algebraic He worked tirelessly during geometry in the , and argu- Taylor attended the his tenure in the promotion ably the world. University of Kansas and support of the Depart- where he received his Through his research, writing and ment’s introductory calculus B.A. in 1961 and M.A. teaching, Fulton has set the shape of program. in 1962. He earned his large parts of the landscape of contem- Ph.D. in mathematics in Taylor was active in porary algebraic geometry. His famous 1965 from the University Departmental governance book, Intersection Theory, was awarded of Illinois (Urbana). He joined the Uni- and administration, serving as Chair of the Leroy P. Steele Prize for mathemat- versity of Michigan faculty in 1965 as the Honors and Doctoral Committees, ics exposition by the American Math- a T.H. Hildebrandt Research Instructor Associate Chair for Graduate Affairs, ematical Society. His major research and was promoted through the ranks to and six years as Department Chair thrust currently is the writing, with sev- professor in 1974. (1994-97, 1998-01). During his tenure eral coauthors, of three books, on toric as Chair, the Department saw a surge varieties, equivariant cohomology, and Taylor’s research is in complex in the hiring of faculty in pure and ap- stacks. analysis. His early work studied the plied mathematics. He was instrumental zeros of analytic functions and their Fulton’s devotion to the cause of ed- in bringing very strong tenured faculty connection with the classification of ucation is evidenced through his success members to the Department, as well as closed ideals in of such func- as a mentor of students and young fac- outstanding young mathematicians. His tions. The connection of this work ulty. He has been instrumental in shap- leadership helped to establish the Ap- with classical potential theory and the ing several generations of students and plied and Interdisciplinary Mathematics problem of extending it to functions of young researchers. His presence in the Graduate Program. Taylor was instru- several complex variables led him to Department has attracted many strong mental in establishing the Mathematics the study of pluripotential theory, a new postdoctoral researchers, and helped to Career Day, bringing alumni to campus area of study in the theory of functions secure permanent faculty members who to talk to students about career options of several complex variables. Much of also had offers elsewhere. for mathematics majors, as well as the his research throughout the 1970s and Mathematics Awards Ceremony that Fulton honors Oscar Zariski (1899- 1980s was fundamental in establishing recognizes outstanding students. 1986) with the naming of this Profes- the tools and principles of this field. His sorship. Zariski was one of the most latest research has focused on how geo- Besides his outstanding service to influential algebraic geometers of the metric properties of analytic varieties the U-M, Taylor’s service to the math- 20th century. He completed his doctor- influence the growth rates possible for ematics community included six years ate in mathematics at the University of plurisubharmonic and analytic functions as Chair of the Mathematical Reviews Rome in 1924, and immigrated to the and the connection of these properties Editorial Committee and ten years as United States in 1927. Zariski served on with properties of linear partial differ- Associate Treasurer and Member of the faculty of ential operators. Considered a generous the Board of Trustees of the American until 1947, and then moved to Harvard, and prolific writer, Taylor authored or Mathematical Society. In 1995 Taylor where he remained until his retire- co-authored over 120 research papers. was named an Alexander von Humbolt ment in 1969. His work reformulated Senior Fellow. He received the Excel- A well liked and effective lecturer, algebraic geometry in terms of modern lence in Education Award from the Col- Taylor taught mathematics courses at all algebra and provided the basis for its lege of Literature, Science, and the Arts th levels, from freshman through graduate. 20 century development. Their paths in 1992 and 1996. He was the dissertation advisor for ten crossed in 1980 when Fulton solved doctoral students and served on many a famous conjecture of Zariski about doctoral committees, both inside and plane curves. outside the Mathematics Department. Taylor established a seminar on Teach-

U-M DEPARTMENT OF MATHEMATICS 5 Calculus Concept Inventory

The U-M Mathematics Department has for many years had U-M Calculus Training a unique focus on Calculus teaching. The instructional meth- It is clear that the IE style of teaching can be fostered and ods and teacher training have been recognized over the years developed; over one third of the Calculus I sections at U-M in as innovative and effective among its peer institutions. This the Fall 2008 semester were taught by instructors new to the year the U-M participated in a of conceptual gain in under- course. All new instructors within the Mathematics Depart- standing using the Calculus Concept Inventory (CCI). ment, including graduate students, post-doctoral faculty and tenure-track faculty, participate in a week-long training pro- Background gram that introduces the concepts of the IE classroom. This The CCI was developed under an NSF grant by a panel of hands-on training includes activities for the classroom, actual experts led by mathematician Jerome Epstein of Polytechnic role playing and practice, and handling challenges that may arise. University. The instrument is designed to test the concepts of Karen Rhea, a senior lecturer with the Department, is the differential Calculus with 22 multiple choice questions in the director of the Freshman-Sophomore program and manages form of a pre-test and post-test. The normalized gain of the the training program as well as the Calculus I course. “The class is determined by the percent of correct answers using the instructor training is one of the significant factors in the suc- following formula: cess of our Calculus program,” Rhea says. “I believe that Gain = (mean post-test score of class – mean pre-test score this type of training is unique on campus.” In addition, there of class) ÷ (100 – mean pre-test score of class) are weekly meetings for the Calculus I instructors to discuss activities and provide feedback and support. While each in- Studies on similar inventories used in other academic sub- structor independently manages their sections of the course, jects, particularly Physics, show that the normalized gain is there is a great deal of collaboration. From the initial training, independent of students’ prior knowledge, but highly related the instructors bond both professionally and socially, helping to teaching methodology. The Physics research has indicated them to acclimate to the Department. that classrooms that are “interactively engaged” (i.e., students are continually engaged in developing concepts and strategies The conceptual to solve problems, testing solutions, and receiving immedi- understanding of the ate feedback), show more significant normalized gains than students in all of the traditional lecture classrooms. Prior to the fall of 2008, the introductory courses CCI had been administered to approximately 2000 students in is continually as- 25 universities and colleges. The normalized gains from all sessed through schools were very low, ranging from 0.08 to 0.20. Exceptions regular quizzes as to these results were from three specific instructors striving to well as standard- teach in an interactively engaged (IE) style. ized exams. “I am pleased that our U-M Testing and Results students have shown Calculus students working on group projects In the fall 2008 semester the CCI was administered to all significant conceptual sections of Calculus I at U-M. There were 51 sections, each gains as measured by the CCI” says Rhea. U-M Mathematics with 32 or fewer students. Instructors in the course have full will continue to encourage the IE teaching style in Calculus responsibility for teaching their individual sections. All new I and other courses, in particular the Inquiry Based Learn- math instructors at U-M (faculty and graduate students) attend ing courses. In all of these courses, there is an emphasis on a week-long training workshop designed to help them teach in the underlying ideas of the course as well as development of the IE style. For the semester, 96% of the students in Calculus skills. In the related articles, two instructors share their expe- I took both the pre- and post- CCI tests. On the post-test, stu- riences with learning and teaching Michigan Calculus. dents were asked to rate the perceived interactivity level of the classroom, and the percentage of time spent on interactively engaged activities. Join us for the Michigan Reception at the The U-M Calculus program achieved outstanding results on the CCI. The average gain over all 51 sections was 0.35, Joint AMS Meetings in San Francisco, CA, and 10 sections had a gain of 0.40 to 0.44. These 10 high- Friday, January 15, 2010 est scoring sections also had the highest scores for perceived 5:30–7:00 PM interactivity, and were reported as spending the most time on Pacific Room J. San Francisco Marriott interactively engaged activities. www.math.lsa.umich.edu/alumni

6 CONTINUUM – 2009 Interactively Engaged (IE) Classrooms from the Instructor’s View

Here a postdoc and graduate student share their experi- students use and experiment with new ideas immediately upon ences teaching Michigan Calculus in an IE classroom for the being introduced to them. first time. None of this is possible without the effective training that Christopher Mooney we received. I was definitely on board with the conceptual emphasis, but the movement towards group work and away Christopher Mooney joined the from lecture I found quite uncomfortable. The trainers empha- Mathematics Department in September sized the importance of it and modeled it for us, which helped 2008 as a postdoc assistant professor. immensely in implementation. I discovered that the students He received his Ph.D. from UW-Mil- were much more engaged with the concepts than when they waukee. His research is in the area of simply watched me do it on the board. I now find this teaching geometric . style to be more effective and enjoyable for both parties. Coming into the calculus program at Michigan was a novel experience for me. Having taught for the previ- ous six years using the traditional lecture style with its tradi- Geoffrey Scott tional focus on computations and proofs, the movement to this new paradigm was certainly challenging. I quickly became Geoffrey Scott joined the Mathematics Department as a a convert, however, when I discovered the amazing fact that graduate student in 2008. He received his undergraduate students really can learn underlying ideas. Students who are degree from Dartmouth College and is interested in studying taught under the traditional lecture style may learn to compute . the derivative or integral of a function, but more often than Throughout the week of teacher training, the program not they do not understand the reasoning. For the engineers directors make it clear that calculus is taught differently at and accountants going into the field, it is much more important Michigan. Through role-playing sessions, we learn not only that they understand the meaning of the derivative rather than the basics of lecturing, but also techniques to make class simply how to compute it. But if they forget how to take the engaging and interactive, and ways to emphasize conceptual derivative and remember why they need to, they are much bet- understanding above mere symbol manipulation. ter off than if they simply remember the computation, which is Like all instructors in the calculus sequence, I lecture for something any computer can do. only about half of the allotted class time. During the other For me there are two key new ideas in this nontraditional half, the class works on problems while I visit with small way of teaching calculus. The first is an increased emphasis on groups of students at a time. This practice helps students in- understanding and interpretation rather than simply on com- ternalize the lesson before class ends. At most schools, a stu- putation. The book we use is especially helpful in facilitating dent could attend a lecture on Monday and be unaware they this. It has more narrative than books I have used in the past, need help until they attempt their homework several days and the thought-provoking problems usually had some real- later. At Michigan, since students work on problems during world context. One of the problems which will remain etched class, we can immediately resolve any confusions that may in my memory as the “Classic Michigan Calculus Problem” arise. is that of interpreting the derivative in the simplest possible Towards the goal of emphasizing conceptual understand- terms. Of course the students find this exercise particularly ing, Michigan has adopted non-traditional syllabi and assign- challenging, but it was a very useful application of using de- ments for the calculus sequence. To be sure that students are rivatives to solve word problems. absorbing the concepts, we require them to work weekly with The second new idea is the practical side of the first. a group of peers on difficult problems, and to hand in not just Through a movement away from lecture and towards group their solutions but also a detailed account of the reasoning work and open discussion in the classroom, students develop a behind their work. Since most groups arrive at the correct deeper understanding of the subject. Students would work in numerical solution to each problem, their homework grade groups, with me moving from group to group watching them is based mostly on the soundness and completeness of their struggle and discuss. I would find a student who had the cor- reasoning. rect answer and have them do it on the board. The students’ Many incoming students expect their intro calculus class natural nervousness abated when they discovered that they to be lifeless. By making class a cooperative and interactive didn’t have to get their answer perfect. As a class we would experience, we ensure that they’re engaged. I feel that most help them fix their mistakes and everyone would learn. The students leave the class understanding the material on a quite conceptual understanding of the subject is strengthened when deep level. It makes the class very satisfying to teach.

U-M DEPARTMENT OF MATHEMATICS 7 2008-09 Graduate Program Chelsea Walton Emily Witt Fellowships & Awards Research Training Grant The Wirt and Mary Cornwell Prize Zachary Scherr (RTG)- Geometry in Mathematics Austin Shapiro Christopher Hammond Paul Shearer Paul Johnson Paul D. Johnson Brian Wyman Aaron Magid Alan M. Stapledon Johanna Mangahas Mathematics Scholarship Fund Mathematics Research Kyle Ormsby Assistantship Fellowship Mark Shoemaker Felipe Ramirez Benjamin Weiss Jordan Sahattchieve Arthur Herbert Copeland, Sr. Crystal Zeager Memorial Scholar National Physical Science Consortium Fellowship Sumner B. Myers Memorial Prize Samuel Altschul Jordan Watkins Marie Snipes Susan Sierra Cameron & John Courtney National Defense Science and Departmental Spring Scholarship Scholarship Engineering Graduate Fellowship Sohhyun Chung William Gignac Sarah Mayes Michael Chmutov Huaiying Gu Geoffrey Scott Ross Kravitz Shawn Henry Carroll V. Newsom Scholarship National Science Foundation Xueying Hu Aubrey daCunha Fellow Yu-Jui Huang David Constantine Hyosang Kang CONACYT Jae Kyoung Kim Natural Science & Engineering Gerardo Hernandez Marc Krawitz Luis Nunez Betancourt Research Council of Canada Kin Kwan Leung Scholarship Sijun Liu Fulbright Scholar Eugene Eisenstein Zhipeng Liu Richard Vasques Linquan Ma President’s Challenge for Joseph Marincel E.S. & A.C. Everett Memorial Graduate Support Scholarship Ajinkya More Peter Bosler Hieu Ngo Darragh Rooney Max Glick Tomoki Ohsawa G. Cleaves Byers Endowment Robin Lassonde Kristofer-Roy Reyes Jeffrey Meyer Sara Lapan Julian Rosen Ashley Selegue Lindsey Selegue Gabrielle & Sophie Rainich Rackham One-Term Dissertation Luis Serrano Fellowship Fellows Nathan Totz Fidel Jimenez Aditi Vashist Marc Krawitz Michael Von Korff Luther Claborn Mathematics Nicolas Rupprecht Ting Wang Fellows Hao Xing Benjamin Weiss Florian Block Rackham Predoctoral Fellow Nina White Jinchen Wu Juha Heinonen Memorial Graduate Cagatay Kutluhan Kevin Tucker Yilun Wu Student Fellowship Zhengjie Xu Qian Yin Rackham Science Award (RSA) Zhixian Zhu Mathematics Alumni/Alumnae Ricardo Portilla Scholarship Ashley Wheeler Andrey Mishchenko Research Training Grant Nicholas Rupprecht (RTG)- Algebra Mathematics Department David Anderson Graduate Fellowship Jonathan Bober Daniel Hernandez Timothy Ferguson Brian Jurgelewicz Aurel Fulger Kelli Talaska Seung Jin Lee Recent P.h.D. recipient Liz Vivas

8 CONTINUUM – 2009 Recent Doctorate Degrees rad. Wansu will be a Chapman Fellow at the Imperial College in London. Ryan Kinser Tigran Ananyan completed his dis- al fellow at the University of Toronto. completed his disserta- tion “Rank Functors and Representation sertation “Topics in Tight Closure Theo- Russell Golman completed his dis- ry” under the direction of Mel Hochster. Rings of Quivers” under the direction of sertation “Essays on Population Learn- Harm Derksen. He will be a postdoc- Tigran will be an assistant professor at ing Dynamics and Boundedly Rational Adrian College. toral fellow at the University of Con- Behavior” under the direction of An- necticut. David Anderson completed his dis- dreas Blass. He will be a postdoctoral Cagatay Kutluhan completed the sertation “Degeneracy and G2 Flags” associate at Carnegie Mellon University. under the direction of William Fulton. dissertation “Floer Homology and Sym- Hester Graves completed the dis- plectic Forms on S1 X M3” under the di- He will be a postdoctoral fellow at the sertation “On Euclidean Ideal Classes” University of Washington. rection of Dan Burns. Cagatay will be a under the direction of Nicholas Ramsey. postdoctoral fellow at the Mathematical Arvind Baskaran completed the She will be a Coleman Postdoctoral Fel- Science Research Institute at Berkeley. dissertation “Modeling and Simulation low at Queen’s University in Canada. Michael Lieberman completed his of Hetero-epitaxial Growth” under the Christopher Hammond completed direction of Peter Smereka. Arvind will dissertation “Topological and Category- his dissertation “Invariants of Transfor- Theoretic Aspects of Abstract Elemen- be a postdoctoral fellow at the Institute mation Groups Acting on Real Hyper- for Pure and Applied Math at UCLA. tary Classes” under the direction of surfaces in Complex Spaces” under the Andreas Blass. He will be a lecturer at Jonathan Bober completed his dis- direction of David Barrett. He will be the University of Pennsylvania. sertation “Integer Ratios of Factorials, an assistant professor at Texas A & M Aaron Magid Hypergeometric Series, and Related Step University. completed his dis- Functions” under the direction of Jeffrey sertation “Deformation Spaces of Klein- Lagarias. He will be a postdoctoral fel- ian Surface Groups are not Locally low at the Institute for Advanced Study. Connected” under the direction of Dick Canary. He will be a NSF Postdoctoral Katarina Bodova completed her Associate at the University of Maryland. dissertation “Topics in Applied Stochas- tic Dynamics” under the direction of Ray Maleh completed his disserta- Charlie Doering. She will be a postdoc- tion “Fast Sparse Approximation Algo- toral fellow at Comenius University in rithms for Medical Imaging” under the Slovakia. direction of Anna Gilbert. David Constantine completed his Associate Chair Sergey Fomin & Kyle Hoffman Jessica Metcalf-Burton completed dissertation “Hyperbolic Rank-Rigidity her dissertation “Information Rates for Kyle Hofmann completed his dis- Secret Sharing Over Various Access and Compact Forms of Homogeneous sertation “Triangulation of Locally Spaces” under the direction of Ralf Structures” under the direction of An- Semi-Algebraic Spaces” under the di- dreas Blass. Spatzier. He will be a L.E. Dickson In- rection of Mircea Mustata. He will be structor at the University of Chicago. an applied research mathematician at Sourya Shrestha completed the dis- Ellen Eischen completed her disser- the National Security Agency. sertation “Modeling Transmission and Evolutionary Dynamics of Infectious tation “P-adic Differential Operators on Paul Johnson completed his disser- Automorphic Forms and Applications” Diseases” under the direction of Patrick tation “Equivariant Gromov-Witten The- Nelson. under the direction of Chris Skinner. ory of One Dimensional Toric Stacks” She will be a Boas Assistant Professor at under the direction of Yongbin Ruan. Marie Snipes completed her disser- Northwestern University. He will be a postdoctoral research fel- tation “Flat Forms in Banach Spaces” Oscar Fernandez completed his dis- low at Imperial College in London. under the direction of Juha Heinonen sertation “The Hamiltonization of Non- and Mario Bonk. She will be a visiting Shin-Yao Jow completed the disser- assistant professor at Kenyon College. holonomic Systems and its Applications” tation “Mori Dream Spaces and Okounk- under the direction of Tony Bloch. He is ov Bodies” under the direction of Robert Alan Stapledon completed his dis- an AGEP research fellow at U-M. Lazarsfeld. Shin-Yao will be a lecturer at sertation “The Geometry and Combina- Leo Goldmakher completed his dis- the University of Pennsylvania. torics of Ehrhart Δ-Vectors” under the sertation “Multiplicative Mimicry and direction of Mircea Mustata. He will Wansu Kim completed the disserta- be a postdoctoral fellow at the Math- Improvements of the Polya-Vinogradov tion “Galois Deformation Theory for Theorem” under the direction of Kannan ematical Science Research Institute at Norm Fields and its Arithmetic Applica- Berkeley. Soundararajan. He will be a postdoctor- tions” under the direction of Brian Con-

U-M DEPARTMENT OF MATHEMATICS 9 Richard Vasques completed his Liz Vivas completed her disserta- Marshall Williams completed his dissertation “Anisotropic Diffusion of tion “Fatou Bieberbach Domains and dissertation “Metric Currents and Dif- Neutral Particles Automorphisms Tangent to the Identity” ferentiable Structures” under the direc- in Stochastic under the direction of Berit Stensones. tion of Juha Heinonen and Mario Bonk. Media” under the She will be an assistant professor at He will be a postdoctoral research direction of Peter Purdue University. fellow at the University of Illinois at Smereka. He Michael Weiss completed his dis- Chicago. will be an associ- sertation “Mathematical Sense, Math- Hao Xing completed the dissertation ate consultant at ematical Sensibility: The Role of the “Analysis of the Option Prices in Jump McKinsey and secondary Geometry Course in Teach- Diffusion Models” under the direction Company in Bra- ing Students to be like Mathematicians” of Erhan Bayraktar. Hao will be a post- zil. under the direction of Hyman Bass. He doctoral research associate at Boston Richard Vasques will be an assistant professor at Oak- University. land University (Michigan).

Graduate Student Team Wins Bridge Tournament Graduate Research Highlight: A Tetraheda A team of five U-M stu- Packing Breakthrough dents, four of whom are pursu- ing their Ph.D. in mathematics, won the Flight C division of Graduate student Elizabeth Chen the Grand National Teams formulated a system of densely packing national bridge championship tetrahedra the results of which achieved in July 2009. Teams qualify the highest know packing density at that for the championship by win- time. In her 2008 article “A dense pack- ning their district title, and ing of regular tetrahedra” (Discrete the event included teams from Comput. Geom. 40, 214–240), Chen across the country. The divi- used a computer algebra system to opti- sions, or flights, are classified mize placement of the tetrahedra—solid on the number of masterpoints Zach Scherr, Bryan Wyman, Benjamin Weiss, Zachary figures with four triangular faces—in accumulated by the players. Wasserman, and Max Glick a “wagon wheel” type formation, and Flight C is the lowest bracket, ate school. Wyman has been playing achieved a density of 77.86%. This reserved for players with under 500 bridge for about six years. “Bridge is was a vast improvement over the previ- masterpoints (only about 30% of all a great game that somehow has missed ous record of 71.75%. This research American Contract Bridge League play- our generation,” he says. “When there showed that tetrahedra can be packed ers have more than 500 master points). are a bunch of younger people in an more densely than spheres. Understand- The team, consisting of Mathematics area that all play the game, they’ll tend ing the efficient packing of solids is key graduate students Brian Wyman, Benja- to come together.” The team is grateful in the development of error-detecting min Weiss, Max Glick, and Zach Scherr, for the help of unofficial coach Mark and error-correcting codes used in the and U-M music major Zach Wasserman, Leonard of Ypsilanti. “Mark is a great storage and compression of informa- represented District 12 (there are 25 dis- mentor and mediator. Without his help, tion for electronic transmission, as well tricts in North America). A sixth mem- I don’t think we’d have come nearly this as material science and engineering. ber of the team, Jonathan Fleischmann, far.” A variant of Chen’s ingenious con- who did not make the trip, is a 2009 The atmosphere in the Department struction has since been developed by U-M graduate who has been playing is conducive to their pastime. There is other scholars to achieve slightly more with Wasserman since they were kids. always a lunchtime bridge game hosted densely packed tetrahedra in a lattice formation. Weiss learned to play bridge at age by the Chair in the common room, and nine with his grandfather, and started there are usually games on Friday in the playing seriously with Wyman in gradu- afternoon.

10 CONTINUUM – 2009 Undergraduate Degree Recipients

Syazrah Abd Salam Sarah Dee Khizar Jahangir Max Mikulec Eric Sorenson Valerie Albers Kevin Dilks Nikhil Joseph Amrit Misra Avinash Sridharan Elizabeth Allen Shiv Dixit Steve Kang Galin Mitchener Rohitkumar Srinivasa Luay Almassalha Fei Dong Katen Kapadia Emily Mohon Kevin Steinhelper Emily Altman James Dulin Jenna Keefe Koki Momose Myung Ki Suh Leandro Ao Sahar Emambakhsh Kimberli Keller Derek Moree Cher Yang Tan Brian Ball Sam Espahbodi Joo Lee Khoo Matthew Morlock Jonathan Tang Jeffrey Barry Fan Fei Bum June Kim Joseph Most Minyi Tang Benjamin Berman Michael Fenchel Megan King Jessica Moton Sharon Traiberman Rebecca Bernard Aaron Fenyes Andrew Klein Ania Musial Alexandru Trambitas Andrew Bollinger Christine Ferrini Corey Kosch Zhengping Ng Tsang Tsang Todd Boynton Michael Filicicchia Zachary Kramer Rose O’Hara Arthur Urban Anthony Brune III Sarah Forney Anthony Kuehne William Patterson III Douglas Vandevusse Sam Capone Stephen Gao Christopher Kurdelski Geoffrey Purvis Narendra Vempati Jose Carlo Andrew Giffin Michele Lagrasso He Wei Quah Bettie Wade Kwan Chan Lauren Gillette Alexander Larson Whitney Rutherford Matthew Wadel Hasan Cheema Pei Ying Goh Elizabeth Lee Erica Rutter John Wanielista Daniel Cheong Blumie Gourarie Sungjun Lee Bana Sakr Alfredo Wetzel Cheuk Man Chiu Mansi Goyal Edman Leung Emily Samra Katherine Williams Young Noh Choe Timothy Heath Xuan Liang Jonathan Schlossberg Sean Williamson Bongseog Choi Evan Herring Siew Gee Lim Michael Schultz Yan Yee Ann Wong Min Li Chong Bruce Hicks Stephanie Lin Christina Seeber Scott Woods Penn Chou Nancy Ho Larry Liou Rahul Shah Gretchen Wrolstad Sarah Chow Douglas Hom Haoshun Liu Laura Shefner Britta Wunderlich Jaewon Chung Ju Hong Hans Shu Lo John Shepard Yang Yang Thomas Church Varsha Hotchandani Wai Tak Louie Seth Siegel Andrew Yeow Bridget Conlon Ping Hsieh Sohini Mahapatra Giffin Slick Suellen Yin Ryan Cotton Alex Jacobson Andrew Meier James Somers

Charles Mather, Professor Curtis Professor Stephen Huntington presents a DeBacker, Paul Huntington Award to Lewis, David Julia Kong. Montague, Bychinsky Awards.

Adam Dearing receives an Outstanding Achievement in Math Award from Professor Curtis Huntington.

Professor Curtis Huntington presents a Huntington Award to Caroline Morel. Recipients of Outstanding Achievement in Math awards.

U-M DEPARTMENT OF MATHEMATICS 11 Undergraduate Awards

Putnam Competition Evelyn O. Bychinsky Awards Adam E. Dearing The Department’s team for the 68th recognizing underclass students who Kevin Dilks Annual William Lowell Putnam Com- show exceptional promise in mathemat- Aaron J. Fenyes Amrit Misra petition placed 9th out of 405 teams in ics: Sohini Mahapatra the competition. This is an outstanding David C. Clyde Zhengping M. Ng result! The members of the team were Mendel A. Feygelson Samuel L. Rosenbaum Daniel Hermes, Jeffrey Madsen and Ruthi Hortsch Laura E. Shefner Timothy Heath. The individual com- Paul D. Lewis petition included 3627 students from Charles T. Mather Otto Richter Memorial Prize in across North America. Daniel Hermes David W. Montague placed highest of the UM students, tied Leon P. Zukowski Prize Siew Gee Lim at 65th. The placement of other UM CIGNA Award in Actuarial Science students in the competition included recognizing outstanding service in the Jeffrey Madsen (115), Zili Huang (189), Mathematics Learning Center: Su Jane Ling Syed Nabil Shahabudin Timothy Heath (225), Ruthi Hortsch and Benjamin P. Berman Paul Lewis (tied at 242), and Alex Car- Sumner B. Myers Award in Irving Wolfson Award in Actuarial ney (tied at 252). Analysis Science The 25th Annual University of Daniel J. Hermes Joshua Z. Lim Michigan Undergraduate Mathematics Lois Zook Levy Award Competition ended in a tie between Zili William LeVeque Award in Number recognizing an outstanding Mathematics Huang and Jeffrey Madsen. Garrett Theory student who plans to pursue a career in Lyon placed third. David W. Montague K-12 Mathematics education: Jack McLaughlin Award in Algebra Margaret S. Huntington Awards in Emily L. Mohon Actuarial Outreach Wade M. Hindes Michigan Mathematics Merit Alex T. Albaugh Mathematics Alumni/Alumnae Scholar Andrew D. Brown Scholarship Sam Espahbodi Colin E. Fitzner Yun Choi Mohammad K. Jawed Outstanding Graduating Senior Outstanding Achievement in Julia Kong Timothy C. Heath Darin J. McLeskey Mathematics Awards Kunal S. Mehta Cheuk Man Chiu Caroline E. Morel Daniel T. Cook Muneet K. Parhar Silu Zuo

Emily Mohon receives the Lois Zook Levy Award from Chip Levy.

Putnam Competition participants Jeffrey Madsen, Zili Chair Mel Hochester and Timothy Heath, the Outstanding Huang and Dan Hermes. Graduating Senior.

12 CONTINUUM – 2009 Actuarial Program News Director, Professor Curtis Huntington, for his tremendous contributions to the profession by presenting him with a Presi- dential Award. Our programs in Actuarial and Financial Mathematics We here at University of Michigan also want to recognize are extremely popular and continue to thrive. At last count, and celebrate Professor Huntington’s incredible contributions just over half of our undergraduate concentrators are enrolled and dedication to our Department, College, University, and the in the Actuarial and Financial Mathematics concentration. profession at large. In his 16-year career at the U-M, Profes- Moreover, we have 10 Masters students focusing on Actuarial sor Huntington has worked tirelessly to prosper the actuarial Mathematics. We currently have 7 Ph.D. students working program and the broader undergraduate mathematics program. on problems in insurance and finance, and two others finished In fact, one can argue convincingly that he single-handedly their Ph.D.s last year. rescued the actuarial program at a time that it would have fal- Our students are well-recruited by employers. In 2008- tered. He has always been generous with his time, energy, and 2009, representatives from 15 companies visited campus to money. It’s no secret that giving to the University is a cause recruit our students for full-time positions and summer intern- that is near and dear to Professor Huntington’s heart, and he ships. Thus far, for the 2009-10 school year 12 company visits leads by example. are confirmed, with more to come. Our Department is establishing a fund in Curtis Hunting- Our student-run actuarial club, Student @ Michi- ton’s name that will be used to support the actuarial program. gan, or SAM, had a busy year. With more than 100 members, Information on contributing to the fund can be found on our this group is one of the more active academically-focused webpage at http://www.math.lsa.umich.edu/alumni/index.html groups on campus. Some of their activities include a field trip The faculty and students look forward to hearing from you to Chicago to visit three actuarial companies and outreach to a with any comments, questions or suggestions you might have. local high school to promote the actuarial profession. And, if your travels bring you though Ann Arbor, please let us Students who are members of SAM and have completed know so that we can host a visit in our East Hall home. courses related to the professional examinations (for example, Kristen Moore, Associate Professor of Mathematics Mathematics 425 – Probability for the first examination – Exam P/1) become eligible for a subsidization of their exami- nation fees. These fees, particularly for college students are not trivial. The first two examinations cost $200 each; the next ones are in the $300-360 range. With increased enrollments and increased examination fees, the subsidization program has become a significant recurring expense. Our April 2009 Cecil J. Nesbitt Commencement Lecturer was Thomas Terry (MA 1975), CEO of JP Morgan Compensa- tion and Benefit Strategies. This was the seventh event in this series. It was attended by about 80 people, including graduat- ing seniors, their families, and the faculty. This event is a high point of the actuarial academic year. In October 2009, students, faculty, and alumni attended the Actuarial Alumni/ae Leadership Council to discuss future directions for the Michigan program. At right is a photo from the meeting. Actuarial Alumni/ae Leadership Council meeting: Kristen Moore, Susan Smith, Dave Hartman, Jason Flynn, Virginia Young, Cutis Huntington, Gabe At their annual meeting in Boston, the Shaheen, Alexa Nerdrum, Alexander Xie (Pres., SAM’09), Tom Levy, Joe recognized our Actuarial and Financial Mathematics Program Marker, and Richard Ireland (VP, SAM’09). Missing from photo: Dan Arnold (photographer)

Solution to Math Problem Suppose that P(x) is such a polynomial. Write P(x) = xQ(x) + 1. Then Q(x) has integral coefficients andQ (2) = (3 − 1)/2 = 1 and Q(4) = (9 − 1)/4 = 2. Write Q(x) = 1 + (x − 2)R(x). Then R(x) is a polynomial with integral coefficients and R(4) = (2 − 1)/2 = 1/2. Contradiction! Hence, no such polynomial P(x) exists.

U-M DEPARTMENT OF MATHEMATICS 13 Many Thanks to our Generous Supporters The following individuals, foundations and companies made contributions to the Mathematics Department between September 1, 2008 and August 31, 2009

CIGNA Life Actuarial Sciences Dr. Daniel Levine Mr. Elliott M. Steiner Gary M. Fotiu Mr. & Mrs. Charles D. McLaughlin Dr. & Mrs. Melbourne G. Stewart, Jr. Financial Mathematics Development Fund Professor & Mrs. Robert E. Megginson Dr. Craig J. Sutton Marc N. Altschull, CFA, FSA, MAAA Mr. Matthew A. Posthuma John R. Tomlinson, Jr. Sam Gutterman Professor Emeritus & Mrs. Maxwell O. Mrs. Ching-Shung Tu Mr. & Mrs. David G. Hartman Reade Drs. Anthony & Dana Vazzana John L. Marakas Dr. & Mrs. Raymond C. Roan Dr. Nianqing Wang Edward B. Martin Cris & Susan Roosenraad Dr. Hugh Eugene Warren Gregg A. Schwab Dr. David A. Sanchez Susan Meredith Smith Professorship Professor G. Peter Scott Margaret S. Huntington First Year Actu- in Actuarial Science Mr. Thomas E. Stolper Ms. Susan M. Smith arial Scholarships Robert David Thompson Marc N. Altschull, CFA, FSA, MAAA Leon P. Zukowski Prize Herald H. Hughes, Jr. Mathematics Department Special Fund Dr. Daniel M. Burns, Jr. Professor Curtis E. Huntington R. James Bennett Dr. Smilka Zdravkovska Miss Linda Marie Clark Inquiry Based Learning Mrs. Anjela Y. Govan Lois Zook Levy Memorial Prize Mr. Harry Lucas, Jr. Mr. Dennis P. Graham Mr. Emanuel Epstein Mathematics Strategic Fund Mr. Peteris Eriks Graube Emeritus Professor Thomas Storer Fund Thomas and Sallee Anderson Douglas G. Hakala Lorraine Lamey Dr. Dean N. Arden Dr. Charles S. Holmes Thomas J. Hansen Dr. & Mrs. Denis L. Bourke Mr. Charles R. Keene Professor B. Alan Taylor Dr. & Mrs. Alfred J. Bown Professor Robert Krasny Mr. Leon P. Zukowski Dr. & Mrs. Daniel P. Dall’Olmo Dr. William E. Lakey Emeritus Professor Maxwell Reade Fund Dr. Barbara B. Flinn James R. Lannen Dr. Daniel M. Burns, Jr. Dr. Robert Samuel Fortus Lorraine D. Lavallee, Ph.D. Dr. Stephen M. DeBacker Dr. C. Allan Foy, Jr. Dr. Earl Edwin Lazerson Mr. Eugene W. Nissen David M. Gay Dr. William F. Lucas Prof. Gopal Prasad David C. Jones Dr. G. Robina Quale-Leach Mrs. Indu D. Prasad Dr. George A. Kozlowski, Jr. Mr. Michael L. Quinn Dr. Smilka Zdravkovska Ms. Carol S. Martin Mr. David A. Scott Mr. Leon P. Zukowski John D. McKenzie, Jr., Ph.D. Charles E. Snygg, Ph.D. Michael J. Merscher Drs. Emil M. & Judith S. Sunley, Jr. The Allotta Family Scholarship Fund Joseph L. Miessner Mrs. Nancy Lindow Wolf Mr. Joseph J. Allotta Mr. James A. Nunez Mr. Philip M. Wolf Juha Heinonen Memorial Graduate Paul Renard Michigan Math & Science Scholars Student Fellowship Thomas G. Ruehle Sheila & Harold M. Cumberworth Marc N. Altschull, CFA, FSA, MAAA Dr. Clarence F. Stephens Professor Jinho Baik Robert F. Thornthwaite Mathematics Alumni/ae Scholarship Fund Professor & Mrs. Anthony M. Bloch Harvey Alan Wartosky Sanford A. Bell Professor Joseph G. Conlon Mrs. Janet E. Weaver Mr. John M. Bisaro Ms. Atreyee R. Datta Mr. Timothy A. Wendt Mr. Allan K. Compton Professor Stephen M. DeBacker Joyce Marie White Mr. Fazli M. Datoo Professor & Mrs. Peter L. Duren William P. & Suzanne R. White Mr. Robert V. DeVore Professor Sergey Fomin Lee Lynn Zia Mr. & Mrs. James R. Feutz Dr. David A. Herron Alan W. Finkelstein Professor Mattias Jonsson David & Kitty Hartman Fund Dr. & Mrs. David E. Flesner Mr. & Mrs. David G. Hartman Professor Smadar Karni Dr. Jeffrey A. Furst Hittinger Professor Jeffrey C. Lagarias Mathematics Graduate Student Support Mr. & Mrs. Edward M. Kimball Professor & Mrs. Gopal Prasad Fund John L. Marakas Professor Emeritus & Mrs. M.S. Ms. Dorothy E. Bambach Mr. David C. Marty Ramanujan Professor Anthony M. Bloch Jennie E. Master Professor Karen E. Smith Dr. Ward D. Bouwsma Edmund B. McCue Professor Ralf Spatzier Mr. & Mrs. Ronald B. Colby Virginia D. McCulloh Professor B. Alan Taylor Robert B. Doorenbos Dr. Howard Earl Reinhardt Dr. Jeremy T. Tyson Ronald Craig Jantz Mark and Lois Shaevsky Howard B. Weinblatt, M.D. Dr. Leon Kaganovskiy Professor Alan Shuchat Mrs. Judith D. Weinblatt Richard Paul Kosinski Ms. Ellen R. Simich Mr. Leon P. Zukowski

14 CONTINUUM – 2009 Cecil J. Nesbitt Commencement Lecture Mathematics Department Special Corporate & Foundation Gifts Fund Endowment Aetna Foundation, Inc. Mr. & Mrs. John B. Kleiman Dr. & Mrs. James O. Friel Babson Capital Management LLC Cecil J. & Ethel M. Nesbitt Professorship Mrs. Gloria M. LaPontney Cigna Foundation Mr. & Mrs. Michael J. Cowell Sumner B. Myers Prize CNA Foundation Ralph E. Edwards Estate Professor Stephen M. DeBacker Deloitte Foundation Mr. & Mrs. Jerome M. Powell FBL Financial Group. Inc. Allen L. Shields Memorial Fellowship Mr. & Mrs. Clifford R. Simms ING Community & Volunteer Program Professor Daniel M. Burns, Jr. Mrs. & Mrs. Donald R. Sondergeld Kellogg’s Corporate Citizenship Fund Professor & Mrs. Gerald T. Cargo Wendell C. True Lockheed Martin Corporation Mr. & Mrs. Clay R. Cprek William D. Ward MetLife Foundation Professor & Mrs. Peter L. Duren Louis M. Weisz New York Life Foundation Alan L. Kaufman Owens-Illinois Charities Foundation Irving S. Wolfson Fund Professor Emeritus Wilfred M. Kincaid PricewaterhouseCoopers Michael & Susan Bowden Dr. Yuk J. Leung Qualcomm Incorporated Mr.& Mrs. James S. Wolfson Professor & Mrs. Frank A. Raymond Towers Perrin Dr. Lester M. Wolfson Dr. Donald E. Sarason Carl H. Fischer Fund Professor John R. Stembridge Jane & Daniel Arnold Dr. Smilka Zdravkovska Dr. Patrick C. Fischer

Alumni News

Harold Randolph Dukes (BS 1946) sultant. During his career he wrote 13 of Massachusetts. In 2008 he started a completed the Industrial College of reports and position papers on Philip- 3-year term as Head of the Department Armed Forces in 1971. He retired from pine companies’ insurance experiences of Mathematics and Statistics at UMass. the U.S. Air Force as a pilot and Lieu- and actuarial practices, and co-authored His research has shifted almost com- tenant Colonel. the 15th and 16th reports of the Retire- pletely to computer science, and he was named a Distinguished Scientist by the William G. Sutcliffe (BS 1960, PhD ment and Separation Benefit System of Association for Computing Machinery Physics U. Delaware 1969) spent four the Armed Forces of the Philippines. in 2006. He is an adjunct professor in years in the Navy after his undergradu- He also taught mathematics and struc- the computer science department, but ate career. After receiving his Ph.D., he tural design from 1956 to 1974 at the his primary appointment, classroom joined the Lawrence Livermore National Manuel L. Quezon University. teaching, and administrative duties have Lab, and stayed until his retirement in Douglas Leonard (BS 1970, PhD remained in the math department. 1999. During his tenure he worked on Ohio State 1980) is a Professor in the numerous projects including develop- Department of Mathematics and Sta- Martin Erickson (PhD 1987), ing large hydrodynamic and radiation tistics at Auburn University. He came Professor of Mathematics at Truman transport computer codes; nuclear waste back to U-M in August 2008 for the State University, has recently written management and analysis of nuclear first day of the Hochster conference. the mathematical problem-solving book “Aha! Solutions” (MAA 2008) and the weapons systems; nonproliferation of Barry Garelick (BA 1971) is an book “Pearls of Discrete Mathematics” nuclear weapon technology and materi- environmental protection specialist (CRC Press, 2009). als disposition. Since retiring, he con- with the U.S. EPA. He maintains a tinues to serve as a part time consultant keen interest in mathematics and math- E. Deronn Bowen – a.k.a. “Teach” for the Lab. He also enjoys flying and ematics education. He has published (BS 1997, MA Eastern Michigan 2001, providing flight instruction, and spend- several web articles and blogs on the JD Univ. Miami expected 2010) is a As- ing time with his wife, four children and subject that have garnered extensive sistant Professor of Mathematics at Bro- ten grandchildren. interest on the internet. ward College and a Lecturer at the Univ. of Miami. Mariano M. Mercado, Jr. (MS Christine Schaffran (BS 1971, MA 1962) is a consulting in the Phil- Computer Science Columbia U. 1980) Jennifer (Hohmann) Walsh (BS ippines. He worked with the Philippine is a research assistant at the New York 2000, MA Education Harvard 2003, MS Government Service Insurance System State Psychiatric Institute. School Administration Touro College from 1960 –1968 and later with the 2006) is the Mathematics Department George Avrunin (BS 1972, PhD Insular Life Assurance Company until Chair for Sleepy Hollow Middle School 1976) is a Professor at the University 2000 as the company actuary and con- and High School in New York.

U-M DEPARTMENT OF MATHEMATICS 15 In Memoriam - George Piranian

George Piranian, 95, died peacefully on August 31, raced, and helped with general service. He was a long time 2009 at his home of 37 years on Englave Drive, Ann Arbor. violist with fellow mathematicians in the Sub-Harmonic George was born to Bertha String Quartet. Piranian (née Walser) and Just as his mind was not limited to mathematics, his life Badwagan Piranian on May was not constrained to intellectual pursuits. By the mid 1950s 2, 1914 in Thalwil, Swit- George was known as the man with a beard who rode his bike zerland. In 1929 he moved to work year around, until his doctor forbade it around 2001. with his family to Utah. Into his late 80s, he chopped and split all the wood for his When his family returned and Louise’s supplemental wood stove. Throughout his life to Switzerland 2 years later, he and his family spent many summers camping, hiking, and George remained in the U.S. backpacking. and was informally adopted by a friend’s family so he George is preceded in death by his brother, David, and could continue his passion his sister, Ausdrig. He is survived by his wife, Louise; his for education. He attended 5 daughters, Libby, Maggy, Inga, Barbara, and Deb; three Utah State Agricultural grandchildren; great-grand children; and a great-great-grand- College, where he earned a son. B.A. and M.S. in botany. A Rhodes Scholarship allowed him to study for 2 years at Oxford University, where he redirected his studies to mathematics. After spending a summer cycling around Europe, he returned to the U.S. to pursue a Ph.D. in mathematics at Rice Institute in , Texas. As a gradu- We Need You! ate teaching assistant, George met a student, Joe Louise Mills, whom he married in 1941. In 1943 he completed his Ph.D. Want to get involved with the UM Department of Math- dissertation: A Study of the Position and Nature of the Singu- ematics? Here are some areas where alumni participa- larities of Functions Given by Their Taylor Series. tion is vital. Contact us if you are interested in working George joined the University of Michigan Department of with us on these initiatives. Mathematics in 1945 where he remained until his retirement • Recommend the UM mathematics program to in 1983 and afterwards as Professor Emeritus. In 1954 he students interested in undergraduate or graduate became managing editor of the then floundering Michigan studies. Mathematical Journal (MMJ), which, under his leadership, • Participate in our annual Career Day, held each gained international recognition. He had strong ideas about year in late October/early November. how to run a journal and how to write mathematics. During his 20-year editorship of MMJ, he did not hesitate to make • Visit the Department for afternoon tea (weekdays extensive stylistic revisions in manuscripts, sometimes to ob- at 3:45 sharp) if you are in town for the weekend, jections of the authors. His high standards for both the math- including Homecoming, Parent’s weekend, or the ematics and exposition of the papers published established Presidential Society weekend. the MMJ as a respected publication and viable enterprise for • Be a mentor (in person or via email) to a current the Michigan Department of Mathematics. George was an student. extremely active researcher and author himself, and published • Set up a recruiting program with your company over 80 papers in complex function theory and related areas. for graduating students. In later years he was especially known for ingenious con- • Offer internships in your company to mathematics structions of counterexamples, which became a specialty of students. sorts. He has an Erdös number of 1/14. Throughout his ca- • Allow groups of mathematics students to visit reer George was very active in the honors program, serving as your company. chair and member of the mathematics honors committee, and counseling honors students at the Department and University • Give an informal talk to mathematics students level. about how you have used your math knowledge. His passion for life found many forms. George shared his love for literature by teaching a freshman literature seminar. Email: [email protected] For over two decades he and his wife, Louise, were active in or call 734-647-4462 the University of Michigan Sailing Club, where they taught,

16 CONTINUUM – 2009 Development arial profession. Additional information regarding the fund and how to donate Events Highlights can be found on our website at www. math.lsa.umich.edu/alumni. An alumnus Department Colloquium First we would like to extend our and his father are in the process of estab- Every Tuesday at 4:00 sincere thanks to all of our supporters lishing an endowed scholarship fund for this year. It is not said enough how the actuarial program. In addition, some monies earned by the Michigan Math- American Mathematical much we appreciate, need, and use all Society of the donations we received from our ematical Journal have been endowed alumni and friends. All gifts—large or for the purpose of supporting prizes 2010 Joint Mathematics small, endowed or expendable, student in undergraduate mathematics. The Meetings support or general fund—are extremely awards will be specific to various areas Michigan Reception important and helpful to achieving de- of mathematics, and include the Jack Friday, January 15, 2010 partmental goals. As indicated in this E. McLaughlin Award in Algebra and 5:30 p.m. to 7:00 p.m. newsletter, your gifts extend to help the William LeVeque Award in Number Pacific J Room, many causes in the Department. Theory, among others to be determined. San Francisco Marriott This year we received significant The Alumni Scholarship this year support to our Actuarial program in the supported both undergraduate and gradu- ate students. Here is some information Marjorie Lee Browne form of a bequest. Ralph Edwards (MA Colloquium 1935) passed away in April 2008, three on two recipients: Professor Rodrigo Bañuelos years after his wife Norma (MS 1934). Undergraduate Student Yun Choi: January 18, 2010 They left a portion of their estate to Yun hails from Montville, NJ. He first the Department. This gift will help to attended U-M in 2003, and joined the continue the excellence of the Actuarial/ U.S. Navy the following year. After Financial mathematics program and serving three and a half years aboard the Alexander Ziwet Lectures assure the students have significant USS Hawes, including two deployments Professor Chris Skinner, professional opportunities for years to to the Persian Gulf as a combat systems January 26, 2010 come. operator, he was honorably discharged In May 2009, Mathematics alumnus in 2007 and returned to U-M. Yun is Josef Blass (Ph.D 1971) and his wife entering his senior year in the Honors G.Y. Rainich Lectures Ewa Schlaff Blass (MD 1973) estab- Program, concentrating in mathematics Professor Terence Tao, lished the Maxwell and Marjorie Reade and . He has always enjoyed March 16, 2010 Graduate Fellowship in the Weiser mathematics, and says after experiencing Center for Russian and Eastern Euro- the excitement of research through the pean Studies. Maxwell Reade worked Research Experience for Undergraduates 2010 Michigan Math and tirelessly in his support of graduate program, he decided to pursue a career Science Scholars Summer in math. Yun feels that math’s smaller students, and his efforts particularly Program impacted Josef and Ewa Blass. While classes allow for a closer interaction be- tween the students and faculty. Two sessions for qualified high this fund will support graduate students school students: in Russian and Eastern European Stud- Graduate Student Andrey Kurt ies, the Department of Mathematics also Mishchenko: Kurt is a third year gradu- June 27–July 9, 2010 has an endowment honoring Maxwell ate student born in Kiev, Ukraine. He July 11–July 23, 2010 Reade. The Emeritus Professor Max- moved to New York at the age of four, well Reade fund supports diversity and and eventually attended the City College recruiting efforts at all levels within of New York. Kurt skipped some grades the Department of Mathematics. It is in his educational career, so he started highly indicative of Maxwell Reade’s college at age 16 and entered grad school Please visit our website for impact on students that two separate at 19. He is currently studying circle additional information on these funds at the U-M have been established packing under Professor Jeff Lagarias. and other events in the in his honor. He chose math as a career because he en- Department. As mentioned in the Actuarial High- joys and excels at problem solving. He www.math.lsa.umich.edu lights column, there is a new fund being enjoys the social atmosphere of the De- established to honor Curtis Huntington partment and the many diverse seminars and his dedication to U-M and the actu- available each week.

U-M DEPARTMENT OF MATHEMATICS 17 Where’s Your Math T-shirt Been?

Last year we asked for photos of you in your Math T-shirts to post on our website. http://www.math.lsa.umich.edu/tshirts/ The Math T-shirt was designed several years ago by math alumna Huey Fang (BS 2007) and has been worn proudly around the world! Here we include a few photos we have received. Keep the pictures coming! To order a shirt, contact [email protected]

Undergrad Zili Huang in Budapest.

Undergrad Sam Faught at the Vatican.

Undergrad So-Young Nam at the University of Chicago Oriental Institute.

Undergrad student Karl Lundquist at the Tetihuacan Pyramids, Mexico. The Hindes family of Port Huron, MI, with Math undergrad Wade (second from right).

Alum Zach Maddock (BS 2008) proposes to Lauren at the 2009 gathering of current and recent Honors Math Students. She accepted!

Undergrad Justin Campbell in Manhattan. Undergrad David Montague fishing in Newago, MI.

18 CONTINUUM – 2009 What Are You Doing? We’d like to hear from you! Please complete and return this form for our alumni/ae files. You may mail it to the address below, fax it to 734-763-0937, or email the information to [email protected]. See www.math.lsa.umich.edu/alumni/

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Please mail to Alumni Updates, University of Michigan, Department of Mathematics, 530 Church Street, 2074 East Hall, Ann Arbor, MI 48109-1043; [email protected]; fax 734-763-0937; www.math.lsa.umich.edu/alumni/

U-M DEPARTMENT OF MATHEMATICS 19 Department of Mathematics NONPROFIT University of Michigan ORGANIZATION 530 Church Street, 2074 East Hall U.S. POSTAGE Ann Arbor, MI 48109-1043 PAID Ann Arbor, Mich Permit No. 144

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