Continuum 2006.Indd

ContinuUM Newsletter of the Department of Mathematics at the Univer si ty of Michi gan 2006 Mathematical Modeling View from the in Sleep Gene Research Chair’s Offi ce The interdisciplinary research of As- Tony Bloch sistant Professor Daniel Forger is receiving The Department of Mathematics has wide recognition from the scientifi c com- had a busy and productive year. During munity. Forger, who joined the Department this time, many of our accomplished fac- of Mathematics this year in the Mathemati- ulty and excellent students received various cal Biology program, works in the area of honors, some of which are detailed else- circadian rhythms and the biological clock. where in this issue of ContinuUM. The core of his thesis involved the con- struction of a detailed biochemical model One should be cautious about taking of the mammalian intracellular circadian outside rankings too seriously. That said, clock. His model is now the most detailed we are pleased to report that our Depart- and realistic one available. mental ranking in the US News and World Report rose from 9th in 2002 to 7th in Forger used his model in recent re- 2006, tied with the California Institute of search with collaborators from the Univer- Technology, New York University and Yale sity of Utah’s Huntsman Cancer Institute. University. It is a pleasure to be associated The studies showed that the effect of a mu- with such a distinguished and exciting De- tation in a key gene involved in the regula- partment. tion of sleep and wake cycles in mammals works in the opposite way from what was The current size and quality of the De- previously thought. A paper on the topic partment is refl ected in the amazing range appears in the July 11 issue of the Proceed- and scope of our activities. During the ings of the National Academy of Science. 2005-2006 academic year we had more than 180 visitors. Special events for the The bodies of mammals know what Daniel Forger year included weekly colloquia by distin- time it is by constantly measuring the con- mutation is present. “I had this prediction guished mathematicians from around the centration of a protein called PER in the for a year or two,” Forger said. “Basically, world. Department members organized body. Drug companies continually investi- people said this is ridiculous, you’re a math- numerous conferences on varied subjects: gate ways to manipulate the level of PER in ematician, what do you know…” representation theory, future directions in the body to treat sleep disorders, and other 3-manifolds (honoring Peter Scott), recent disorders impacted by biological clocks. Forger's computer models solve a sys- tem of over 50 differential equations. This progress in birational geometry, math- The degradation of PER is regulated large number of equations comes from the ematical biology (see story on page 3), and by another protein, called CK1e, whose many states of PER and the fact that many geometric function theory. There was also production is controlled by the gene casein other proteins can bind to PER to regulate a lecture series in algebraic geometry, and kinase 1, or CK1. It was initially thought its behavior. Every time a new binding part- Mel Hochster’s Distinguished University that a mutation called “tau” in CK1 led to ner or state is included, the number of equa- Professorship lecture entitled “The Un- the production of defective CK1e proteins tions signifi cantly increases, perhaps even expected Usefulness of Prime Numbers.” that break down PER more slowly than is doubling. He also validated this prediction We have established a new web page to normal, causing the protein to accumulate with a simple linear model for which one document some of our events and lecture in the body. This buildup was thought to can derive a formula for the effect of tau on notes at http://www.math.lsa.umich.edu/ speed up a mammal’s internal clock, caus- the predicted period. lecturesmath/index.html. Please feel free ing it to have shorter days. to browse the information. Forger met David Virshup, M.D., while Forger’s computer models had always giving an invited talk at the University of As far as the faculty are concerned, we said that the opposite of the prevailing Utah. Virshup’s previous research was on currently have 68 regular tenured/tenure- thinking should be true—that the PER pro- track members, 7 other non-tenure-track tein should degrade more quickly when the Continued on page 2 Continued on page 2 Notes from the Chair Our development and fund raising ef- Mathematical Modeling (continued from page 1) forts have been successful thanks to the in Sleep Gene Research generosity of our loyal alumni. Our an- (continued from page 1) members, and 49 three-year post-doc fac- nual alumni fund raising letter consistently ulty positions. Faculty members of the raises a much needed $16,000 to $20,000. the gene involved in circadian rhythms and Department currently hold more than 153 This year these funds allowed us to provide its role in cancer development. Their ex- federal grants. scholarship support to 2 undergraduate periments had also suggested that genetic The student body comprises 140 gradu- students and summer support to 5 graduate mutation caused the protein to degrade ate students and approximately 285 math students (see story on page 16). Other fund more quickly. Virshup suggested they test concentrators. In the Fall 2005 term, 6596 raising allowed us to continue our affi lia- Forger’s simulation. students were enrolled in math courses. In tion with the Inquiry Based Learning pro- This new study proves their hypothesis: the winter term there were 4560 such stu- gram, a program which funds exciting new The tau mutation doesn’t slow down PER dents. There were 90 undergraduate math innovations in teaching. degradation—it speeds it up. Not enough majors who graduated this year, and 29 We are extremely grateful to all those PER leads to shorter days in animals af- new graduate students will be starting their who with their contributions help to make fected by the gene mutation. programs in the fall of 2006. our Department an excellent place for teaching, learning, and research. The researchers took cell cultures and observed that for those with the mutated UM Mathematics Department We are looking forward to a dynamic gene, the protein only took a couple of is now tied for 7th in U.S. new academic year with extremely exciting hours to degrade. For the normal gene, it News and World Report programs. There are several exceptional took 8-10 hours. events planned. One highlight will be our rankings among U.S. public colloquium which, this year, promises to be These fi ndings will have an impact Universities truly extraordinary: no fewer than 7 Fields on the development of new drugs for the Medal winners will be giving lectures! treatment of disorders such as insomnia, depression, and others that rely on the I have every confi dence that we will Another highlight will be the Ziwet and regulation of the inner body clock. continue from strength to strength even Rainich lecture series to be given in the though the Department continues to face fall by most distinguished mathematicians. Forger joined the Department of Math- the perennial challenges that have been Jerrold Marsden of Caltech will give the ematics in September 2005. He received mentioned here in previous years. In par- Ziwet Lectures in September. Philip Hol- his Ph.D. in Mathematics from the Courant ticular, unrelenting budget pressures con- mes of Princeton will present the Rainich Institute at New York University, and was tinue to be a problem in many areas, and lectures in November. Everyone is invited a Sloan Foundation Fellow at NYU in especially in the area of faculty retention. and encouraged to attend these memorable Computational Molecular Biology. From This results from the fact that the other best events, some of which are highlighted on his earliest contact in the Department, math departments in and out of the country page 17. Additional information on all Forger impressed his colleagues with his keep trying to lure away our many out- Department activities can be found on our knowledge, energy and enthusiasm. standing faculty members. website www.math.lsa.umich.edu. “Michigan is an ideal place to model We would like to remember here sever- circadian clocks,” says Forger. “Other al Department members who are no longer great modeling/experimental studies are with us: Professors Emeriti James Wen- being conducted by members of the Math- dell and Don Higman, and former faculty ematical Biology Research Group within members Raoul Bott, Hans Samelson and the Department targeting problems in areas Robert Thrall. Also, our much loved former Math Problem like infectious disease and cancer. Discus- secretary who was active in the Department Twenty-four delegates sit around sions about common modeling techniques until she died, Ethel Rathbun, passed away a round table. Two delegates can within the group are invaluable to model last fall (see story on pages 12-13). We speak to each other if at most four development as are discussions with other will miss them all. people sit between them. After Department faculty on how to accurately analyze and/or simulate models. It is also Peter Hinman and Pat Shure retired this a break each person sits down important to mention the large amount of year (see story on page 6). We wish them again, not necessarily in the same clock research being done on campus in- all the best for the future, and we thank seat as before. Show that there cluding circadian experiments here in East them for their many years of wonderful ser- exist two delegates who are able Hall, and a new center for Sleep Science.” vice to the Department. to speak to each other before and after the break. We welcome Erhan Bayraktar who will be a new Assistant Professor in the fall. Answer elsewhere in the newsletter See more news of the Uni ver si ty of Mich i gan Department of Mathematics on our website www.math.lsa.umich.edu

2 Mathematical Biology Research Theme Semester

During the Winter 2006 semester, the The events of the theme semes- College of Literature Science and the Arts ter attracted faculty and student and the Department of Mathematics hosted participants from 15 different dis- a research theme semester in Mathematical ciplines across campus. The topics Biology. Mathematical Biology is a fast prompted discussion among all growing and exciting modern application levels of students, researchers and of mathematics that has gained worldwide faculty. This additional exposure recognition. Mathematical models can sug- should increase the visibility of gest possible mechanisms underlying spe- Mathematical Biology at UM, and cifi c biological processes, and through their promote the program as active and development and analysis one can gain innovative to prospective students insight into complex biological systems. and researchers. Proper development and analysis also can lead to predictions that may follow under The Mathematical Biology currently untested conditions. Involving Research Group, which will con- collaborations with scientists from many tinue the interdisciplinary research disciplines across campus, the Mathemati- presentations and collaboration, cal Biology Research Group encompasses is comprised of 30 faculty and 50 expertise in ordinary, delay and partial students from 15 different depart- differential equation modeling, analysis, ments. Nelson and Jackson are the Trachette Jackson and Patrick Nelson and simulation, as well as parameter inden- co-founders of the group, and other Math- tifi ability, estimation, and sensitivity. The ematics core faculty include Daniel Burns, who is Director of the new Bioinformatics current research also utilizes asymptotic Throughout the semester, other sym- Program, Daniel Forger, Philip Hanlon, analysis, dynamical systems, and scientifi c posia were held to highlight the various who continues in his appointment as As- computing. The discipline involves unique applications of Mathematical Biology. The sociate Provost, and Carl Simon, who also collaborations between experimentalists, Synthetic Biology Symposia featured a directs the Center for the Study of Complex modelers, and statisticians. The theme talk by Professor Ron Weiss from Princ- Systems. The group supports research in semester provided an opportunity for re- eton University. Synthetic biology is an mathematical modeling of infectious dis- searchers to develop new collaborations emerging discipline of engineering that eases, cancer, neurosciences, biological and for students to see the rich diversity investigates cells and cell behaviors as pro- oscillators, ecology, and cell biology. They that is mathematical biology. grammable matter. Synthetic biology will have developed numerous undergraduate improve our quantitative understanding of Mathematics faculty members Tra- and graduate courses on mathematical biol- natural biological processes and will also chette Jackson and Patrick Nelson ogy and now have a very successful under- have biotechnology applications in areas organized the semester and hosted many graduate program in math biology. such as bio-sensing, synthesis of pharma- special events to highlight current research ceutical products, molecular fabrication of in Mathematical Biology, both here at UM The Department of Mathematics, biomaterials and nanostructures, and tissue and at other universities. The fi rst sympo- jointly with the Molecular, Cellular and engineering. sium held in January featured Professor Developmental Biology, and Ecology and Evolutionary Biology, have devel- Michael Reed from Duke University, who The third symposium involved the oped a revolutionary new program titled spoke about the diffi culties of mathemati- modeling of infectious diseases. Dr. Alan SUBMERGE—Supplying Undergraduate cal biology. Mathematical models can be Perelson from Los Alamos National Labo- Biology and Mathematics Education and used to investigate causal mechanisms in ratory gave the keynote talk entitled “Mod- Research Group Experiences to Students. biological systems that are exceptionally eling the Kinetics of Hepatitis B and C Intended to train the next generation of diverse, complex, and special. The process, Viral Infections in Vivo.” His presentation interdisciplinary scientists, the program however, is fraught with complexity and showed how mathematical modeling has will allow undergraduate students to de- uncertainty. The event also included pre- provided basic insights into the pathogen- velop knowledge and acquire skills in sentations from UM faculty in Mathemat- esis of these viruses and provided a means research areas that are at the interface of ics and other disciplines on their current of quantitatively assessing the effects of Biology and Mathematics. The National research in the area. An informal luncheon therapy. He also highlighted a set of state- Science Foundation has pledged support for undergraduates interested in learning of-the-art models that in principle apply to help develop this cutting edge program. about a career in Mathematical Biology at- to these and other viruses of broad interest tracted an enthusiastic audience. such as HIV.

3 A conference honoring Professor Jef- Faculty Kudos frey Rauch was held at the University of Bordeaux, May 18-20, 2006. Associate Professor Jinho Baik was Assistant Professors Anna Gilbert and Professor Carl P. Simon (Professor promoted from Assistant to Associate Pro- Divakar Viswanath were invited speakers of Mathematics, Economics, and Public fessor. at the 2006 Abel Symposium in May. Policy) has been named the 2007 Distin- Professor Hyman Bass, the Roger Lyn- Professor Robert Lazarsfeld has been guished Senior Lecturer for the College of don Collegiate Professor of Mathematics, elected a member of the prestigious Ameri- Literature, Science and the Arts. received the 2005 Yueh-Gin Gung and Dr. can Academy of Arts and Sciences. The A conference honoring the 70th birth- Charles Y. Hu Award for Distinguished Ser- Academy honors distinguished scientists, day of Professor Joel Smoller was held at vice to Mathematics from the Mathematical scholars, and leaders in public affairs, Stanford University, April 29-May 6, 2006. Associtation of America. This is the most business and the arts. Fellows are selected Professor Kannan Soundararajan prestigious award made by the Association. through a highly competitive process that has been awarded the First SASTRA recognizes individuals who have made pre- Professor and Chair Anthony Bloch has Ramanujan Prize. The prize is given to eminent contributions to their disciplines. been awarded a Collegiate Professorship mathematicians not exceeding the age of from the College of Literature, Science and Assistant Professor Patrick Nelson has 32 for outstanding contributions in areas of the Art. He will hold the Alexander Ziwet been elected to the board of directors of the mathematics infl uenced by Ramanujan. The Collegiate Professorship in Mathematics for Society for Mathematical Biology effective prize was given during the International a fi ve-year term. July/August 2007. Conference on Number Theory and Math- Assistant Professor Anna Gilbert re- Professor Gopal Prasad has been ematical Physics in December 2005, at ceived a 2006 NSF CAREER award for her awarded a Humboldt Research Award for SASTRA University in Kumbakonam, the project “Modeling and Analysis of Data Senior U.S. Scientists. This award is given hometown of Ramanujan. from Massive Graphs.” The CAREER to researchers with internationally recog- Professor Sijue Wu has been appointed awards provide early career development nized academic qualifi cations, honoring the the Robert W. and Lynn H. Browne Profes- support for faculty with outstanding poten- academic achievements of the award win- sor in Science for a fi ve-year renewable tial. Anna previously received an Alfred P. ner’s lifetime. Winners are invited to un- term. The Browne Professorship recognizes Sloan Fellowship, an extraordinarily com- dertake research projects of their choice in the recipient’s outstanding contributions to petitive award involving nominations of the Germany in collarboration with colleagues. science and teaching. very best young scientists in the country. Gehring Recognized for Lifetime Achievements

Frederick Gehring, the T. H. Hildebrandt Distinguished Univer- Born in Ann Arbor, Gehring’s association with the Univer- sity Professor Emeritus of Mathematics, received one of the highest sity of Michigan goes back two generations to his grandfather, distinctions in his fi eld from the American Mathematical Society John Oren Reed, who was a member of the physics faculty and (AMS) in January at a joint meeting in San Antonio. Dean of the College of Literature, Science and the Arts. Gehring Gehring is a recipient of the 2006 joined the U.S. Navy in 1943, and subsequently earned two de- AMS Leroy P. Steele Prize for Life- grees from Michigan—Bachelor of Science in math and electri- time Achievement, an annual award cal engineering in 1946, and Master of Science in math in 1949. honoring those who have made out- He returned to teach mathematics at Michigan in 1955 after standing contributions to research in completing his Ph.D. at Cambridge, and spending three years as mathematics. a Benjamin Peirce Instructor at Harvard. He became a professor in 1962, was named to a collegiate chair in 1984, and became “For over fi fty years F. W. Geh- the T.H. Hildebrandt Distinguished University Professor in 1987, ring has been a leading fi gure in one of the University’s highest honors for faculty. Gehring’s the theory of quasiconformal map- long and distinguished history of service at Michigan includes pings,” the AMS prize citation states. three terms as chair of the Department. Gehring has received “Largely because of Gehring’s work, numerous awards, including the Distinguished Faculty Achieve- the theory of quasiconformal map- ment Award, the Sokol Faculty Award, Humbolt Award, Onsager pings has infl uenced many other Professorship, and he was the Henry Russel Lecturer for 1990. parts of mathematics, including com- In 1989 he was elected to the National Academy of Sciences. He plex dynamics, function theory, partial differential equations, and to- has also received honorary degrees from the University of Hel- pology ... Gehring’s mathematics is characterized by its elegance and sinki, University of Jyväskylä, and the Norwegian University of simplicity and by its emphasis on deceptively elementary questions Science and Technology. which later become surprisingly signifi cant.” Gehring retired in 1996. A year later the Frederick and Lois Gehring also is described as a person of incredible energy and Gehring Chair in Mathematics was endowed. Currently the enthusiasm, who generously shared his passion for mathematics and Chair is used to bring prominent young mathematicians to Ann research by mentoring over 70 successful Ph.D. students and postdoc- Arbor as visitors to collaborate with Department members. toral fellows during his career. 4 New Postdoc New Faculty Members Assistant Professors Selim Esedoglu - Assistant Professor Aaron King - Assistant Professor of of Mathematics Ecology & Evolutionary Biology and Assistant Professors who joined the Mathematics Department on term appointments dur- ing the past academic year are listed here King joins with their doctoral institutions and area of Michigan from speciality. the University of Petter Branden - Chalmers University Tennessee. He of Technology/Göteborg University, received his Ph.D. Combinatorics (Hildebrandt) in Applied Math- ematics from Robert Buckingham - Duke Univer- the University sity, Partial Differential Equations of Arizona. His Renzo Cavalieri - University of Utah, research inter- Algebraic Geometry ests lie in the interdisciplinary area of Masahiko Egami - Princeton Univer- Esedoglu joins the Department from theoretical population dynamics, and his sity, Mathematics of Finance the University of California, Los Angeles. primary appointment is with Ecology and He received a Ph.D. from the Courant In- Evolutionary Biology. King writes and Neil Epstein - University of Kansas, stitute at New York University, and then analyzes mathematical models of particular Commutative Algebra (Hildebrandt/NSF) was a Postdoctoral Fellow at the Institute biological systems in order to understand Grigor Grigorov - Harvard Univer- for Mathematics and its applications in observed patterns and make predictions. sity, Number Theory Minneapolis. His research involves the use He is deeply interested in the development Richard Kollar - University of Mary- of partial differential equations methods and analysis of new biological models for land, Differential Equations in image processing, involving rigorous concrete systems. mathematical analysis and application. Peijun Li - Michigan State University, Esedoglu is developing analytical tools Applied Mathematics and effi cient numerical algorithms for hard Yongbin Ruan - Professor of Michael Ludkovski - Princeton Uni- problems of nonconvex optimization. The Mathematics versity, Stochastic Control input in the problem is a “noisy image,” Tamar Ziegler - Hebrew University, while the solution to the optimization Dynamical Systems problem provides the “denoised” image.

Daniel Forger - Assistant Professor of Mathematics Forger joins the Department from the Computational Molecular Biology Depart- ment at New York University. He received a Ph.D. from the Courant Institute at New York University. His research in Mathe- Solution to Math Problem matical Biology on mammalian intracellu- lar circadian clocks included construction In fact, there are two delegates of a biochemical model of the clock. His such that there are at most three recent discoveries have received much at- people between them, before and tention from his colleagues and the press Ruan joins Michigan from the Univer- after the break. Consider fi ve del- (see article on page 1). sity of Wisconsin. He received his Ph.D. egates who sit next to each other from the University of California, Berke- before the break. Each pair of ley. He is a widely recognized researcher these fi ve can talk to each other. in the area of symplectic geometry, in par- If there are at least 4 delegates ticular the development of Gromov-Witten between each two of them after the break, then there will be at invariants. These invariants have become a . mainstay in symplectic topology and gauge least 5 4 + 5 = 25 delegates. theory. Ruan has also worked on signifi - Contradiction. One can fi nd two cant discoveries in the area of quantum of these fi ve delegates with at cohomology. His infl uential joint work on most three people in between the cohomology of orbifolds has become them after the break. known as the “Ruan Cohomology.” 5 Two Faculty Members Retire recursion theory editor for the “Omega of Arts in Anthropology, Masters of Arts Bibliography of Mathematical Logic,” a in Mathematics, and achieved candidacy project that involved classifying by topic status toward a Ph.D. in Mathematics. She the entire literature of recursion theory from taught mathematics in private secondary its beginnings until 1985. Most recently, he schools from 1963 to 1981 and came to published a graduate-level comprehensive the University as Mathematics and Science textbook, “Fundamentals of Mathematical Coordinator for the Comprehensive Studies Logic.” Program. Shure was appointed as a Lectur- During his tenure Hinman held numer- er III in the Department of Mathematics in ous administrative positions at the Depart- 1983, and was named a Senior Lecturer in ment, College and University levels. Most 2002. She served as the Associate Director notably in Mathematics, he served as As- and then the Director of the Department’s sociate Chair for Graduate Studies (1980- freshman-sophomore program from 1993 Peter G. Hinman, Professor of Mathe- to 2006. matics in the College of Literature, Science 83, 1986-87), Mathematics Undergraduate and the Arts, retired from active faculty sta- Program Director (1989-92, 1994-2000), In 1992, Shure became co-principal tus on May 31, 2006. Associate Chair for Education (1997-2000), investigator of an NSF-funded project and the inaugural Associate Chair for Fac- to develop and implement a reformed Hinman received his Bachelor’s degree ulty Appointments (2002-03). He served on calculus program at UM. The resulting in mathematics from Harvard College, and the Department’s Executive Committee in program, known nationwide as “Michigan his Ph.D. from the University of California, fi ve consecutive decades. In 1980 Hinman Calculus”, has become a model of how to Berkeley. He came to Michigan in 1966 as established the Math Lab, giving mathemat- integrate real-life problems, technology, a T.H. Hildebrandt Research Instructor, and ics students a venue for learning, tutoring, and cooperative learning into a calculus was promoted through the ranks to Profes- and working together. He was Chair of the course. For many years Shure supervised sor in 1983. He held visiting positions in Quantitative Reasoning Task Force that the large multi-section introductory courses Norway, Germany, Switzerland, Australia established an undergraduate requirement that serve roughly 3000 students each and the U.K. He has received internal and for quantitative reasoning, and identifi ed a fall. To strengthen the instruction in these external recognition for his work, includ- diverse array of courses around LS&A that courses, she developed and directed the ing a Fulbright-Hays grant, NSF research would contain components to fulfi ll that re- Department’s intensive training program for grants, the AMOCO Good Teaching Award, quirement. Hinman directed seven doctoral incoming junior faculty and Graduate Stu- and four LS&A Excellence in Education dissertations. dent Instructors. awards. He was always considered an ex- ceptional teacher at all levels. Shure was a leader in the development of pedagogy and pedagogical tools. She is The main area of Hinman’s research the co-author of a widely used pre-calculus concerns the subarea of Mathematical textbook, and recently was co-principal Logic known as Recursion Theory or Com- investigator of an NSF-funded project to putability Theory, which deals with theo- create web-based skills enhancement tools retical questions about the computability of for college and high school students. She functions. It involves the precise relation- worked in the area of high school math- ship between sets of natural numbers which ematics curriculum design at the state and formalizes the intuitive notion of relative national level. effective computability. This area has con- nections with theoretical computer science Recognition of her achievements in- and other areas of mathematical logic, es- cludes the LS&A Excellence in Education pecially descriptive set theory. Hinman’s Award (each year 1991-1997), the Mat- early work was primarily about extensions thews Undergraduate Teaching Award in of recursion theory beyond the traditional 1986, the Sarah Goddard Power Award domain of natural numbers and other fi - from UM in 2000, and the Louise Hay nitely described objects. His publications Award for Contributions to Mathematics in this area include numerous papers, the Education from the Association for Women research-level monograph “Recursion- Patricia D. Shure, Senior Lecturer in in Mathematics in 2001. Her presentation Theoretic Hierarchies,” and a chapter in the Department of Mathematics in the Col- “The Scholarship of Learning and Teach- the “Handbook of Computability Theory.” lege of Literature, Science and the Arts, ing,” given as the 2001 Falconer Lecure, More recently, he has worked in more clas- retired from active faculty status on May was a highlight of the summer meeting of sical areas of recursion theory, in particular 31, 2006. the study of relative recursive enumerability Shure is an alumna of the University of and of the Medvedev lattice. He was the Michigan, where she received her Bachelor

6 Recent Ph.D. Recipients Graduate

Ilesanmi Adeboye completed his thesis Milena Hering completed her thesis Recruiting “Volumes of Hyperbolic Orbifolds” under “Syzygies of Toric Varieties” under the the direction of Dick Canary. He will be an direction of William Fulton. She will be The Michigan Mathematics Graduate Assistant Professor at UCLA. a Postdoctoral Fellow at the Insitute for Offi ce had another busy admissions season. There were a total of 417 applicants for Alina Andrei completed her thesis Mathematics and its Applications in Min- the Ph.D. program, of which 75 applied “The Parameter Space of a Family of Qua- nesota. to the AIM (Applied and Interdisciplinary dratic Polynomial Maps of C2” under the Thiradet Jiarasuksakun completed Mathematics) program. For the 2006-07 direction of John Erik Fornæss. She will his thesis “On Expander Graphs and Hy- academic year, the Department admitted 93 be a Postdoctoral Fellow at the University pergraphs” under the direction of Andreas students and received 29 acceptances, with of Wisconsin. Blass. He will be a Lecturer at King Mong- 18 in the pure program and 11 in the AIM kut's University of Technology in Bangkok. Trevor Arnold completed his the- program. Among those who accepted are sis “Anticyclotomic Iwasawa Theory for Leon Kaganovskiy completed his 12 women (7 Pure, 4 AIM). Modular Forms” under the direction of thesis “Adaptive Hierarchical Tree-Based Five Research Science Award offers Chris Skinner. He will be an Assistant Panel Method for 3-D Vortex Sheet” under were made to students, with 2 acceptances. Professor/VIGRE Fellow at University of the direction of Robert Krasny. He will be The total number of applicants from his- Washington. an Assistant Professor at the New College torically underrepresented groups was 14. of Florida. Yann Bernard completed his thesis When taking deferrals into account, the “The Coupling of Gravity to Yang-Mills Bart Kastermans completed his thesis incoming class will have 30 students (19 Fields and Fermions in Static Spherically “Cofi nitary Groups and Other Almost Dis- Pure, 11 AIM). Of these there are 18 U.S. Symmetric Spacetime” under the direction joint Families of Reals” under the direction citizens (12 Pure, 6 AIM) and 12 women (8 of Joel Smoller. He will be an Assistant of Andreas Blass. He will be an Assistant Pure, 4 AIM). Professor at ETH Zurich. Professor at the University of Wisconsin. In March the Department hosted a Re- Sebastien Chivoret completed his the- Krzysztof Klosin completed his thesis cruiting Weekend, bringing 24 potential sis “Properties of Multiple Stochastic Inte- “Congruences Among Automorphic Forms graduate students to campus. Of those who grals with Respect to Fractional Brownian of the Unitary Group U(2,2)” under the di- visited, 16 students accepted our offer. This Motion and Applications to Nonlinear rection of Chris Skinner. He will be an As- is an encouraging statistic. Filtering” under the direction of Charles sistant Professor at the University of Utah.

Doering. He will be an Associate with Nam-Hoon Lee completed his thesis Goldman Sachs. “Constructive Calabi-Yau Manifolds” under Jungmin Choi completed her thesis the direction of Igor Dolgachev. “Partial Hedging in Financial Markets William Andrew Lorenz completed his with a Large Agent” under the direction of thesis “A Self-Adaptive Random Walk Algo- Mattias Jonsson. rithm to Identify Genetic Epistatic Effects” Serban Costea completed his thesis under the direction of Philip Hanlon. ∞ “Strong A -Weights and Scaling Invariant Lu Lu completed his thesis “Bounds on Besov and Sobolev-Lorentz Capacities” the Enstrophy Growth Rate for Solutions of under the direction of Juha Heinonen. He the 3D Navier-Stokes Equations” under the will be a Postdoctoral Fellow at the Uni- direction of Charles Doering. He has a po- versity of Helsinki. sition with Wachovia Capital Markets. Hailong Dao completed his thesis Afsaneh Mehran completed the thesis “Homological Properties of Modules Over “Even Eight on a Kummer Surface” under Complete Intersections” under the direction the direction of Igor Dolgachev. Afsaneh Sreekar Shastry completed his thesis “The Drinfeld Modular Jacobian J (N) of Mel Hochster. He will be an Assistant will be a Postdoctoral Fellow at the Univer- 1 Professor at the University of Utah. sity of Geneva. Has Connected Fibers” under the direc- tion of Brian Conrad. Sreekar will be a Peng Gao completed his thesis “N-Lev- Samuel Payne completed his thesis el Density of the Low-Lying Zeros of Qua- Postdoctoral Fellow at the Tata Insitute for “Toric Vector Bundles” under the direction Fundamental Research in India. dratic Dirichlet L-Functions” under the of William Fulton. Sam will be a Research direction of Hugh Montgomery. He will be Fellow at the Clay Mathematics Institute. Cornelia Yuen completed her the- a Postdoctoral Fellow at the University of sis “Jet Schemes and Truncated Wedge Montreal. Benjamin Schmidt completed his Schemes of Monomial Schemes and Deter- thesis “Weakly Hyperbolic Group Actions” minantal Varieties” under the direction of under the direction of Ralf Spatzier. Ben Karen Smith. She will be a Postdoctoral will be an NSF Postdoctoral Fellow at the Fellow at the University of Kentucky. University of Chicago.

7 Graduate Program Fellowships & Awards

Allen L. Shields Memorial Scholarship Lucent Fellowship Samsung Fellowship Serban Costea Ellen Eischen Jungwoon Park

Alice Webber Glover Math Fellowships Luther Claborn Mathematics Fellow Dennis Clark Ray Maleh David Constantine Leo Goldmakher Mathematics Alumni Scholarship Hester Graves Kelli Carlson Geri Izbicki Sarah Crown Brian Jennings Russell Golman Jason Kutch Christopher Hammond Aaron Magid Kyle Hofmann Johanna Mangahas Kevin Tucker Mathematics Department Graduate Marshall Williams Fellowship Catherine Dupuis Arthur Herbert Copeland, Sr. Kristin Shaw Memorial Scholars Benjamin Weiss Jose Gomez-Guerra Johnson Jia National Physical Science Consortium 2005 Sumner B. Myers Memorial Prize Marc Krawitz Fellowship for the Best Thesis Hyekyung Min Marie Snipes Calin Chindris (pictured above) Tomoki Ohsawa National Defense Science and Graduate Departmental Scholarship A.V. Flint Memorial Scholarship Engineering Graduate Fellowship Spring 2006 Tigran Ananyan Brian Wyman Henry Boateng Jasun Gong Cameron & John Courtney Scholarship National Science Foundation Fellows Mark Iwen Fidel Jimenez Jose Gonzalez Ryan Kinser Shin-Yao Jow John Mackay Ellen Veomett Brian Jurgelewicz Nicholas Rupprecht Hyosang Kang Natural Science & Engineering Research Rizwanur Khan Carroll V. Newsom Scholars Council of Canada Scholarship Wansu Kim Jonathan Bober Luis Serrano Cagatay Kutluhan Aubrey da Cunha Xinyun Sun Kyungyong Lee Oscar Fernandez Victor Lozovanu Daniel Hernandez Rackham International Fellowship Gregory McNulty Felipe Ramirez Alan Stapledon Yogesh More Chelsea Walton Alvaro Pelayo Rackham One-Term Dissertation Jordan Sahattchieve CONACYT Fellowship Fellows Matthew Smith Giancarlo Urzua Gerardo Hernandez Mark Conger Diane Vavrichek Nam-Hoon Lee Liz Vivas Edwin Wilkinson Miller Scholarship Alvaro Pelayo Lei Wang Michael Lieberman Emily Witt Rackham Predoctoral Fellow Hao Xing Fulbright Scholarship Ivan Middleton Zhengjie Xu Richard Vasques Bo Yang Mario Boudalha-Ghossoub Research Training Grant (RTG) Algebra Hsu-Wen Young David Anderson Gabrielle & Sophie Rainich Fellows Bryden Cais Rackham Outstanding Graduate Student Instructor Award Harsh Jain Susan Sierra Craig Spencer Yann Bernard

8 Congratulations to our 2005-06 Mathematics Bachelor of Arts/Science Degree Recipients

Bryan Abbe Sarah Haberman Bradley Polizzano Ruchir Agarwal Peter Hach Steven Privasky Shailesh Agarwal Daniel Hidlay Michael Radakovich Murat Ahmed Robert Hines Mustafa Rangwala Hye-Youn Baek Daniel Hirschman Amy Rice Amy Baker Rebecca Jackson Robert Rizzo Brett Barna Nathan Jhaveri Benjamin Ruskin Karen Barr Rishabh Jhunjhunwala Benjamin Salvette Brian Berends Marit Johnson Rajeev Shahani Joseph Bertram Michael Kagan Rajiv Shende Kenneth Beyerlein Jodi Keller David Smith Timothy Bodiya Sun Kim Paul Son Andrea Busch Michael Koss Benjamin Sonday Stephanie Calandro Keith Kwiatkowski Molly Spalding Kenneth Charette Christina Kyrtsos Stephen Sullivan Omer Chowdhry Tomislav Ladika Andrew Taylor Charles Crissman Chun Lam Joshua Tebeau Christopher Cunningham Alan Law Gillian Todd Michael Dombrowski Heather Lewis Breanna Turcsanyi Spencer Dowdall Christopher Li Michael Turner Julia Driessen Chi-Wen Liang Asad Usman Andre Edwards Chin-Swan Liew Anish Vora Matthew Elsey Rebecca Lynch Karl Weintraub Jonathan Falk Keith Maciejewski Amanda Wilke Mildred Fernandez Stephen Marin Christopher Wing Chi Wang Fong Jason Miller Pak Hin Wong Ashley Frazier Michael Morgan Richard Yarger Catherine Free Maggie Mulcrone Mark Yeo Robert Gaunt Alexander Nagle Jeffrey Zheng Teow Lim Goh Randolph Pistor Jonathan Zimbler Edward Grant Rachel Platte

The Mathematics Graduate Student Soccer Team was victorious over the team from Physics in 2006 to win the Intramural Sports Indoor Mini Soccer tournament. Team members were: front row, l-r: Jose Gonzalez, Jose Gomez-Guerra, Henry Boateng, Fidel Jimenez back row, l-r: Aubrey da Cunha, Brian Wyman, Alan Stapledon

9 2006 Undergraduate Award Recipients

The Department’s team for the Wil l iam Lowell Putnam Mathematics Com pe ti tion placed 29th out of 395 teams in the event. This year’s team was com prised of Chris- to pher Cunningham, Fernando Delgado Salas and Spencer Dowdall. The in di - vid u al com pe ti tion in clud ed 3545 stu dents from across North Amer i ca. Fernando Delgado Salas re ceived an hon or able men- tion, plac ing the high est of UM stu dents at 57. Jeffrey Madsen and Chris to pher Cunningham also fi nished in the top 300. The winner of the 23rd Annual Uni- ver si ty of Mich i gan Un der grad u ate Math e - Professor Ralf Spatzier (left) with some recipients of the Outstanding Achievement in mat ics Com pe ti tion was Jeffrey Madsen. Mathematics Award. l-r: Breanna Turcsanyi, Teow Lim Goh, Chi Wang Fong, Murat Tied for second place were Timothy Heath Ahmed, and Jeffrey Zheng. and Nathan Stiennon. The William LeVeque Award in Num- The following students received Math- ber The o ry was pre sent ed to Paul Siegel. ematics Alumni/Alumnae Scholarships The award rec og niz es a stu dent who is at for the 2005-06 ac a dem ic year: most a junior and ex cels in the study of Ruchir Agarwal num ber theory. Kevin Wilson Outstanding Achieve ment in Math- e mat ics Awards went to the fol low ing The fol low ing stu dents re ceived Evelyn se niors: O. Bychinsky Awards, which rec og nize Murat Ahmed underclass stu dents who show ex cep tion al Matthen Elsey prom ise in math e mat ics: Chi Wang Fong Joseph Golden Teow Lim Goh Zachary Maddock Daniel Hirschman Department Chair Tony Bloch Timothy McQuade Breanna Turcsanyi with Outstanding Graduating Richard Turner Michael Turner Senior Benjamin Sonday. Erin Wood Pak Hin Wong Jeffrey Zheng The Irving Wolfson Award in The fol low ing stu dents re ceived Ac tu ar i al Sci ence was presented to Mar g a ret S. Hun ting ton Awards in The Otto Richter Me mo ri al Prize in Rebecca McQuillan. Actuarial Out reach: Ac tu ar i al Sci ence was pre sent ed to Keith The Lois Zook Levy Me mo ri al Award Kwiatkowski. Karen Boore was pre sent ed to Peter Hach. The award Andrew Danielsky The CIGNA Award in Ac tu ar i al rec og niz es an out stand ing Mathematics Scott De Orio Sci ence was pre sent ed to Wei Heong Koh. stu dent who plans to pur sue a ca reer in K- Christopher Kurdelski 12 Mathematics ed u ca tion. John Shepard Charles Crissman and Benjamin Son- Seth Siegel day were named the Out stand ing Grad u - Malorie Spunger at ing Seniors. Laura Ventimiglia William Wilcox Jason Miller received the Wirt and Suellen Yin Mary Cornwell Prize, rec og niz ing a stu- dent who has dem on strat ed the greatest Randolph Pistor re ceived the in tel lec tu al curiosity, given the most prom- Leon P. Zukowski Prize for out- ise of orig i nal study and creative work in stand ing ser vice in the Mathemat- math, and also shows an interest in music. ics Learning Center (formerly known as the Math Lab). Professors Curtis Huntington and Stephen DeBacker with Bychinsky Award recipients Joseph Golden and Zachary Maddock.

10 Math Undergrad Awarded Prestigious Churchill Scholarship

Mathematics Major Charles Crissman real interest is doing research in something was one of 11 American students awarded related to modern algebra,” he said. Upon the elite Winston Churchill Foundation completion of his year at Cambridge, Criss- Scholarship this year. The extremely com- man intends to pursue a Ph.D. in mathemat- petitive scholarships are awarded based on ics working toward a career in academia. an applicant’s academic record, score on In addition to his interest in modern al- the Graduate Record Examination and let- gebra, Crissman's studies are well rounded, ters of recommendation. as evidenced by his triple major. He is a Crissman graduated in May with a member of a snowboarding club at the Uni- Bachelor’s degree, majoring in math, lin- versity, and an editor at the student publica- guistics and Italian. The scholarship will tion the Every Three Weekly. He is an avid send Crissman to the University of Cam- scholar of fi ve foreign languages: Russian, bridge, where he will spend the next year Finnish, Italian, French and ancient Greek. studying mathematics. The Churchill Scholarship, established After graduating from high school in in honor of the former British prime minis- Midland, MI, Crissman initially considered ter, annually offers 75 colleges nationwide studying biochemistry at Michigan, leading the opportunity to nominate two students to medical school. In his sophomore year for consideration by the foundation. Other he realized that he was truly inspired by participating institutions include Boston math. College, the University of Chicago and Crissman said he is looking forward Michigan State University. Selected stu- to learning about another culture and tak- dents pursue graduate study in the fi elds of ing more specialized math classes. “My engineering, science and mathematics.

Undergraduate and Actuarial Program News

The Student Actuaries at Michigan for fi rst year students that was presented 2005-06 academic year which incorporated (SAM) group had an active year. More this year. This act of generosity by an un- the inquiry-based concept in which students than 250 members regularly received infor- dergraduate student group was somewhat are encouraged to learn mathematics by mation and about half that number partici- unusual and greatly appreciated. actively "doing" mathematics under the pated in activities. The group’s activities The Undergraduate Math Club con- guidance of an experienced and dedicated included a balance of athletic, social, aca- tinued their weekly meetings this year mentor, while testing their understanding of demic, and professional agendas. with presentations on a variety of pure and concepts using their own capacity for clear, Highlights of their year included visit- applied mathematics topics. One of the logical reasoning. The program is fund- ing two local actuarial consulting fi rms, speakers this year was an undergraduate, ing a postdoc position in the Department organizing 10 information sessions spon- and in the second semester the majority of for 2006-07 who will help to develop more sored by national fi rms, and hosting a well- talks were by graduate students and junior courses and teaching methods. attended meeting of the Michigan Actuarial faculty, as opposed to faculty in the fi rst The Mathematics Learning Center Society involving participation in the semester. A well-attended movie night was (MLC-formerly MathLab) in the basement current industry-wide CRUSAP (Critical held to view “The Proof.” The undergradu- of East Hall continues to offer free tutoring Review of the United States Actuarial Pro- ates all seem to appreciate the informative to math students, and administer computer- fession) research project. In Winter 2006, talks, discussion, camaraderie, and pizza. ized gateway exams which are required 31 actuarial related companies conducted The Undergraduate Scholarship Com- to ensure the acquisition of algebraic and on-campus recruiting visits. SAM contin- mittee was fortunate to be able to award computational skills in the various levels of ued to hold semester-long study groups for scholarships to 42 students for the 2005-06 calculus courses. Students made more than the May professional actuarial examina- academic year, totalling $107,194. Indi- 25,000 visits to the MLC during the 2005- tion, led by experienced students. vidual scholarship amounts ranged from 06 academic year. During this time more SAM decided to take $1,000 of ac- $3000 to $6000. that 23,000 gateway exams were given for cumulated surplus and return it to the Uni- students in four levels of calculus courses The Inquiry Based Learning (IBL) (Math 105, 115, 116, 215). The MLC also versity in appreciation for past services by initiative continues to develop and grow. funding one of the Huntington Scholarships maintained an outpost at the Ross Academ- Several courses were taught during the ic Center in the Athletic Department.

11 In Memorium Professor Emeritus of Mathematics Besides these, Higman made numerous Donald G. Higman passed away in Febru- contributions to groups and combinatorics, ary, 2006. Higman was born in Vancouver, including studies of intersection matrices, in 1928. He attended college at the Univer- calculations of degrees of irreducible con- sity of British Columbia, then did graduate stituents of permutation representations, work at the University of Illinois, where he work on the Krein condition, bounds for studied with Reinhold Baer, an important parameters of generalized polygons and a fi gure in modern algebra in the mid twen- monomial version of Scott’s modular theory tieth century. After his doctorate in 1952, for permutation representations. he spent two years as a National Research His 1970s philosophy of “geometry Council Fellow at McGill University, then without groups” stressed the essential com- Ethel M. Rathbun, former assistant to two years on the faculty of Montana State binatorial ideas which recurred in studies several Associate Chairs and Chairs in the University. Thereafter, he accepted an as- of groups and geometries. It led to the sig- Department of Mathematics, died in No- sistant professorship at the University of nifi cant theory of coherent confi gurations. vember 2005 after returning home from a Michigan and became professor in 1960. These are essentially association schemes, vacation in Germany. She was 73. Higman made basic contributions in and Higman was one of the fi rst to em- Rathbun joined the mathematics staff in several areas of algebra, starting in the the- phasize the value and interest outside their 1967 and quickly became a major support- ory of fi nite groups, then moving through statistical and graphical origins, particularly ing pillar of its activities. She represented group-inspired geometries to work in ab- in group theory. Thus he was one of the the Department to faculty, visitors and stu- stract combinatorics. He was recognized as founders of the area now referred to as “al- dents for 27 years before retiring in 1994. a worldwide expert in this latter area during gebraic combinatorics.” Her skills and warm spirit rapidly the last three decades. Higman served extensively on Depart- endeared her to all who came through In early work on homological aspects ment committees, notably the executive, the the department. Rathbun became known of group representation theory, Higman doctoral, and master’s committees, and on throughout the world’s mathematical com- established the important concept of a the University’s grievance committee. He munity because of her concern for all relatively projective module and gave a supervised 15 doctoral theses. members of the Department and the many criterion, which bears his name, for relative Professor Higman’s academic honors students and international faculty constantly projectivity. His result that boundedness of include giving an invited lecture to the 1970 fl owing through Ann Arbor. degrees of indecomposables in characteris- International Congress of Mathematicians One current faculty member reports tic p is equivalent to cyclicity of the Sylow in Nice, where he presented his theory of that, when he saw former students, visi- p-group is a basic result in the theory of rank three groups, and the 1975 receipt of tors or faculty, their fi rst query was “How’s modules for group algebras. He did some the Alexander von Humboldt Stiftung Prize. Ethel?” Her friendships ranged from mem- of the earliest computations of degree 1 co- He spent sabbatical and academic leaves bers of the National Academy of Sciences homology of classical groups as part of his in Eindhoven and Giessen, was a visiting to beginning graduate students. Indeed, one study of fl ag-transitive groups. His theory professor at Frankfurt, a visiting senior department chair referred to her as die Herr of the focal subgroup of a Sylow subgroup scientist at Birmingham and Oxford and a of Mathematics. She retired after a distin- was a basic tool in local analysis in fi nite visiting fellow at the Institute for Advanced guished career during which she gave her group theory. Works with UM colleague Study in Canberra, Australia. behind-the-scenes competence and compas- Jack McLaughlin on low rank classical sion to all with whom she made contact. groups were models for later theories on Donald Higman, wife Betty and their characterizing fi nite simple groups and their fi ve children were generous hosts to mem- Rathbun was born in 1932, in Fairfi eld geometries. bers of the mathematical community on Township, MI, the daughter of Leland and many social occasions. Don was for many Florence Davenport Rathbun. After an early Higman‘s theory of rank 3 permutation years an active member of the Flounders education in a one-room school, she gradu- groups gave a simple and elegant theory and the Ann Arbor Track Club. After retir- ated in 1950 from Sand Creek High School, which assisted in the discovery of several ing, the Higmans designed and built a home and from Cleary College in Ypsilanti in of the sporadic simple groups, the most on the shore of Grand Traverse Bay in the 1951. From 1960-67 she lived and worked elusive and provocative of the fi nite simple northwest corner of Michigan’s lower pen- in Germany. groups sought so intensely in the 1960s and insula, where they enjoyed spending sum- 1970s. An initial application of his theory She enjoyed travel and was fortunate mers. Higman had cancer and volunteered enough to have visited all provinces in was the Higman-Sims simple group, of or- to be part of an experimental research study der 44,352,000, and a rank three graph on Canada, except Prince Edward Island, and at the UM Comprehensive Cancer Center, countries on all continents but Antarctica. 100 vertices using the combinatorics of the contributing in whatever way he could to Mathieu group on 22 letters. It is a testimo- fi nd a cure for the disease. It was impor- Memorial contributions may be made to ny to the elegance of his theory and the wit tant to him to be a contributing member to the Scholarship Fund at Cleary University, of Higman and collaborator Charles Sims society even as he went through his own 3750 Cleary Dr., Howell, MI, 48843, the that this sporadic group was envisoned and personal struggle with the disease. American Heart Association, or the Ameri- elegantly constructed in a single day! can Cancer Society. 12 Robert M. Thrall, former University ects, including a stint in Linus Pauling’s teaching has been described as inspirational of Michigan Department of Mathematics laboratory. Following completion of his and awe-inspiring, and he was considered faculty member for 32 years, died at his Ph.D. in mathematics at California Techni- one of the most erudite of faculty members home in Philadelphia, PA in April, 2006, cal University in 1948, Wendel had aca- at the time. Samelson left the Department in at age 91. Professor Thrall joined the fac- demic appointments at Yale and Louisiana 1960 for a position at Stanford University. ulty in Ann Arbor in 1937 and served until State University, prior to moving to Ann Samelson was one of the world’s lead- 1969. In 1947, he received the Henry Rus- Arbor in 1955 to join the faculty of the UM ing fi gures in the mathematics research sell Award from the University of Michigan Department of Mathematics. He was named areas of differential geometry, topology and and in 1965 received the Distinguished Professor in 1961, and retired in 1987. the theory of Lie groups and Lie algebras— Faculty Award. He received an honorary During his tenure at Michigan, Wendel important in describing the symmetry of Doctor of Sciences degree from his alma served as Associate Chairman for a total of analytical structures. He was the author of mater, Illinois College, in 1960. eleven years, was a member of SACUA and many research articles and two widely used Professor Thrall left UM in 1969 to was its Vice-Chairman in 1966-67. His re- textbooks—an undergraduate book about become the founding Chairman of the De- search was in the area of probability, and he linear algebra and a graduate text on the partment of Mathematical Sciences at Rice was well known as a brilliant teacher and theory of Lie algebras. University in Houston, TX where he was for his great breadth of knowledge. Wen- On the occasion of his 70th and 85th appointed the Distinguished Noah Harding del was an inveterate problem solver, who birthdays, conferences were held in his Professor of Mathematical Sciences. Early loved the challenge and was often called to honor at Stanford, attended by the world’s in his career Professor Thrall became inter- set problems for collegiate competitions. leading fi gures in mathematics research, ested in applying mathematics to problems A popular lecturer, he received many in- including many of his former students and of the real world. His book “Decision Pro- vitations from abroad, and was a visiting colleagues. This was a small measure of the cesses” (John Wiley and Sons, 1954, New professor in Denmark , England , Austra- great esteem in which he was held by his York), co-edited with UM colleagues Clyde lia, and Israel. Following his retirement, students, colleagues, and the entire math- C. Combs and Robert L. Davis, chronicled Wendel moved to Palo Alto , CA , where ematics community. a unique initiative that brought mathemati- he stayed until 2000, at which point he re- Samelson was married twice, to the late cians, statisticians, psychologists, econo- turned to his original home of Portland. Renate Reiner in 1940 and to Nancy Morse mists and philosophers together to both Jim Wendel was a man of great intel- in 1956. He is survived by his wife, Nancy, create and test mathematical formulations lect, possessing not only a life-long love of a brother, Franz, three children and two in behavioral science theory, including the mathematics, but an impressive depth and grandchildren. Donations in Samelson’s theory of games. Early, seminal contribu- breadth of understanding of history, sci- memory can be made to the Samelson Me- tions by two Nobel laureates in Econom- ence, art, literature, culture, language, and morial Fund, Department of Mathematics, ics, Gerard Debreu (1983) and John Nash music. He had an insatiable curiosity, and Stanford University, Bldg. 380, 450 Serra (1994), appeared in the book. his many interests seemed to be matched by Mall, Stanford, CA 94305-2125 Professor Thrall remained active in an equal diversity of talents. Wendel loved research well into his eighties and looked to travel and was moved deeply by music, at his latter years as the most interesting the former refl ected in his interest in lin- Former Department of Mathematics and productive period of his career. He guistics and in learning foreign languages Professor Raoul Bott passed away in De- focused on the emerging discipline of data and the latter expressed most fully through cember, 2005. A native of Hungary, Bott envelopment analysis and contributed over his playing of the accordion and piano. He studied engineering at McGill University in 35 publications on the topic after his formal also was fond of his after-work martini. Montreal, then received his Ph.D. in science from the Carnegie Institute of Technology retirement. Wendel was preceded in death by his in Pittsburgh. He joined UM in 1951, and Professor Thrall's wife of 68 years, younger brother Thomas in 2004 and his was promoted through Professor before ac- Natalie, preceded him in death in 2004. He wife of 56 years, June (nee Herzog), in cepting a position at Harvard in 1959. He is survived by three children, three grand- 2000. He is survived by his sister, and by formally retired in 1999. children and three great-grandchildren. In six children and 12 grandchildren Bott had a tremendous infl uence in the lieu of fl owers contributions may be made Donations to honor his memory may be development of topology and differen- to Illinois College, 1101 W. College Ave, sent to Reed College, 3203 SE Woodstock tial geometry and their application to Lie Jacksonville, IL 62650 Blvd., Portland , OR 97202-8199 . groups, differential operators and math- ematical physics. His contributions to this Professor Emeritus of Mathematics Former Department of Mathematics area were considered as great as any one James G. Wendel, 83, died of compli- Professor Hans Samelson passed away in person. cations from cancer in January, 2006 in September 2005. He was 89 years old. A Among the mathematics awards Dr. Portland , OR. He was born in Portland native of Germany, Samelson left in 1936 Bott received were the National Medal of on April 18, 1922, where he lived until for Zurich, where he studied at the Swiss Science in 1987, the Wolf Prize in 2000, graduating from Reed College in 1943. His Federal Institute of Technology, receiving and two from the American Mathematical collegiate years were interrupted by World his doctorate in 1940. Society—the Oswald Veblen Prize in 1964 War II, an effort to which he contributed Samelson joined UM in 1946 and was and the Steele Prize for lifetime achieve- through his work on defense-related proj- promoted through Professor in 1955. His ment in 1990.

13 Many Thanks to our Generous Supporters

The following individuals, foundations and companies made contributions to the Mathematics De part ment be tween June 1, 2005 and June 1, 2006

Financial/Actuarial Mathematics Mathematics Department Special Fund Ms. JJ Lane Carroll Development Fund Mr. Richard L. Astrom James and Patricia Case The ACE INA Foundation Sanford A. Bell Miss Lorraine A. Chorkey Marc N. Altschull, F.S.A., M.A.A.A. R. James Bennett Craig and Susan Colby Jean S. and Jeffrey T. Dukes Alan Cline and Elaine Rich Mrs. Rhonda M. Cooke Ernst & Young Foundation Deloitte Foundation Mrs. Lee S. Cooper Alan W. Finkelstein Ms. Diane M. De Santis Dr. Bruce Nathan Cooperstein Mr. and Mrs. David G. Hartman Mr. Robert V. DeVore David G. Crandall ING Community & Volunteer Program Mr. Trevor J. Fast Dr. Helen F. Cullen Walter and Barbara MacGinnitie Dr. Barbara B. Flinn DaimlerChrysler Corporation Fund John L. Marakas Thomas J. Hansen Dan and Gail Dall’Olmo Edward B. Martin Charles and Susan Holmes Mr. Bruce Campbell Dane Nationwide Foundation Dr. William E. Lakey Dr. Carl-Wilhelm R. de Boor Gregg A. Schwab John F. Langhans Dr. Sandra J. DeLoatch Jim and Laurel Lannen Deloitte Foundation Margaret S. Huntington First Year Lorraine D. Lavallee, Ph.D. Henry Albert Dihm, Jr. Actuarial Scholarships Dr. Earl Edwin Lazerson Ronald J. Dolan Class of 2006 Student Actuaries at Michigan William and Carolyn J. Lucas Ms. Nancy J. Dynes Mr. and Mrs. Herald Hughes, Jr. Charles D. and Sharon J. Wall McLaughlin Paul Eitner and Denise Roy Dr. and Mrs. Rogers J. Newman Larry D. and Peggy Elliott Inquiry Based Learning Dr. Eric Albert Nordgren Frederick W. Erdmann Mr. Harry Lucas, Jr. Mr. Matthew A. Posthuma Elsbeth T. Falk Dr. G. Robina Quale-Leach Dr. Vincent J. Ferlini Mathematics Department Strategic Fund Mrs. Gretchen S. Ryan Mr. James R. Feutz Joel and Kelley Adams David and Joan Sanchez Alan W. Finkelstein Mr. and Mrs. C. Philip Bartlett Michael Sattinger and Ulla Jensen David and Susan Flesner Alfred and Elizabeth Bown Ms. Mary A. Savas Dr. Robert Samuel Fortus Timothy and Teri Buchowski Mr. David A. Scott Dr. C. Allan Foy, Jr. Craig and Susan Colby Charles and Marianne Snygg Michael L. Frank Dan and Gail Dall’Olmo Mr. Thomas E. Stolper Mrs. Jennifer L. Furst Hittinger Harvey Epstein and Rita Klein Drs. Emil and Judith Sunley Richard L. Gibbs Denise Yee Friedrich B. Alan and Lynn Taylor Catherine Giebel and James Maslanka Dr. and Mrs. David M. Gay Dr. Mavina K. Vamanamurthy Marcia and John Gilroy Mr. and Mrs. Herald Hughes, Jr. John C. and Sally Wenger Roberta and Thomas Glassman Dr. George A. Kozlowski, Jr. Karen and Lewis Gold Melanie and Phillip Kraft Michigan Math & Science Scholars Mrs. Suzanne D. Goodrich Mr. and Mrs. Thomas E. Kruger Sheila and Harold Cumberworth Mr. Dennis P. Graham Lockheed Martin Corporation Martha and Robert Hanna Pedro and Lydia Marrone Mathematics Alumni/Alumnae Thomas J. Hansen Donald and Doris Mela Scholarship Fund William Albert Harper New York Life Foundation Dr. Ian M. Aberbach Drs. Thomas and Carol Herbig Dr. Cris T. and Susan S. Roosenraad The ACE INA Foundation Dr. Jeffrey A. Furst Hittinger Bette Ross Dr. Hassoon S. Al-Amiri Mr. and Mrs. Brian J. Howard Dr. Donald E. Sarason Marc N. Altschull, F.S.A., M.A.A.A. Susan Howard and Don Swartwout Norman and Dianne Scherr Mr. Arnold H. Anderson Mr. and Mrs. Brian J. Howard Gary and Kathleen Trock Aon Foundation Merrill Hudson Mr. Charles A. Weibel Mr. and Mrs. William R. Averill Mr. and Mrs. Herald Hughes, Jr. Ms. Elizabeth C. Wurster Matthew Ryan and Dorothy Bambach Dr. and Mrs. Fredrick W. Humburg Felice D. and Paul T. Bateman Gudmund R. and Roberta R. Iversen Michigan Pension Education Training Mr. Jacob Bernstein Derek and Jessica Kane Program Mr. and Mrs. James Besancon Charles and Geraldine Keene ASPA Pension Education Research Foundation Pat and Sarah Bidigare Dr. and Mrs. Soon-Kyu Kim Bradley J. Biggerstaff Dr. Eduard-Wilhelm Kirr Mathematics Scholarship Fund The Boeing Company Phillip and Melanie Kraft Alta M. West Trust Dr. and Mrs. Denis L. Bourke Mr. and Mrs. Thomas E. Kruger Alfred and Elizabeth Bown Michael M. and Linda Kurpinski The Dave & Kitty Hartman Fund Thomas L. Boynton Dr. Harris Kwong Mr. and Mrs. David G. Hartman Dr. and Mrs. Robert F. Brammer Todd and Melinda Lanski Ruth and Stanley Briggs Victoria Lee Mr. and Mrs. Richard A. Cabot Lockheed Martin Corporation

14 Dr. Charles R. MacCluer The Susan Meredith Smith Fund Cecil J. and Ethel M. Nesbitt Gordon Pier MacDougall Susan Smith Gray and Robert Gray Pro fes sor ship John L. Marakas Aetna Foundation, Inc. David and Marcy J. Marcus The Leon P. Zukowski Award Fund Mrs. Marjorie Van Eenam Butcher Mark A. Schwab & Associates, Inc. Dr. Smilka Zdravkovska and Mr. and Mrs. Clay Richard Cprek George E. Martin, Ph.D. Professor Daniel Burns Ernst & Young Foundation Mr. David C. Marty Howard and Marjorie Fosler Donald E. Masters Lois Zook Levy Memorial Award H. and M. Fosler Fund of the Ms. BeLinda I. Mathie Hiram Levy II Sam and Peggy Gutterman Edmund B. McCue The Hartford . Professor Thomas Storer Fund Virginia D. McCulloh Mr. and Mrs. John B. Kleiman Thomas J. Hansen John D. McKenzie, Jr., Ph.D. Lincoln Financial Group Foundation Inc. Mr. Anand C. Parekh Jo and Richard N. Miller Karen Olsen MacDonald Mr. David J. Venzon Mr. Kelly K. Miller Walter and Barbara MacGinnitie Mr. Leon P. Zukowski Mr. Kurt M. Miller MetLife Foundation Richard N. and JoAnne Miller Professor Maxwell Reade Fund Jeffrey S. Paciero W. Reynolds and Diane Monach Professor Hyman Bass Mr. and Mrs. Jerome M. Powell Prof. M. Susan Montgomery Professor Anthony M. Bloch PricewaterhouseCoopers Foundation Charles and Sonya Moore Bill and Dee Brehm Doris Krueger Roeder Nationwide Foundation Mrs. Joanna Brumfi el Mr. Richard G. Roeder, F.C.A. New York Life Foundation Professor Joseph G. Conlon Mr. Jeffrey Carroll Rose Thomas N. Nock Professor Brian D. Conrad Jack and Marguerite E. Seigel Jeffrey S. Paciero Professor Stephen M. DeBacker Mr. and Mrs. Clifford R. Simms Dr. and Mrs. Maurice S. Pelto Professor Emeritus Douglas G. and Mr. and Mrs. Donald R. Sondergeld Paula Rabinowitz and David Bernstein Marilyn Dickson John and Earlene Taylor Ellen R. and Richard G. Racusin Professor Igor V. Dolgachev Wendell C. True John G. and Susan K. Ratcliffe Professor Peter L. Duren William D. Ward Dr. James T. Renfrow Professor Selim Esedoglu Mr. and Mrs. Louis M. Weisz Robert B. Rosalsky Professor William E. Fulton Mr. and Mrs. Peter Rothmaler Irving S. Wolfson Fund Professor Emeritus Frederick W. and Denise Roy and Paul Eitner Michael P. and Susan W. Bowden Lois Gehring Thomas and Carrie Ruehle James and Edith Wolfson Professor Emeritus Donald G. Higman Miss Lynn J. Sapoff Dr. Lester M. Wolfson Professor Peter G. Hinman and The Sapoff Foundation Dr. Elizabeth A. Young Mark and Anelly Schwab CIGNA Life Acutarial Sciences Fund Professor Curtis E. Huntington Thomas and Maryellen Scott CIGNA Foundation Professor Mattias Jonsson Prof. Alan Shuchat Professor Emeritus Wilfred Kaplan Carl Hahn Fischer Fund Mr. Lawrence C. Silton Professor Emeritus Wilfred M. Kincaid Jane and Dan Arnold Frederick W. Silverman, M.D., J.D. Professor Robert Krasny David Lawrence Hoffman Mr. Jason B. Sindler Mrs. Ethel M. Nesbitt St. Paul Travelers Foundation Professor Gopal Prasad Mathematics Special En dow ment Dr. Stan Stahl Professor Emeritus and Mrs. M.S. James H. Ellis, M.D. James and Ann H. Stasheff Ramanujan Mrs. Gloria M. LaPontney Mr. Elliott M. Steiner Professor Peter Scott Jean A. Lawton, M.D. Dr. Clarence F. Stephens Mrs. Pat Shure Melbourne and Nancy Stewart Sumner B. Myers Memorial Prize Fund Professor Kannan Soundararajan Robert and Amy Stewart Dr. Todd E. Cochrane Professor J. Tobias Stafford & Dr. E. Ramnath Suryanarayan Professor Stephen M. DeBacker Dr. Carolyn Dean William and Sally Sutcliffe Dr. Eduard-Wilhelm Kirr Professor John Stembridge Don Swartwout and Susan Howard Professor William J. LeVeque Professor Divakar Viswanath Swiss Re Life & Health America Inc. Eva and Raymond Shapiro Professor Arthur G. Wasserman Dr. Khyson Swong Chung-Tuo and Ann Shih Professor David J. Winter Gerald and Antoinette Szilagyi Professors Joel and Margaret Smoller Professor Trevor Wooley Jean and Ronald Tidball Professor Ralf Spatzier Dr. Smilka Zdravkovska Mrs. Ching-Shung Tu Mr. Leon P. Zukowski Ms. Angela M. Valdick Allen L. Shields Memorial Fellowship Mr. and Ms. Edward T. Veach Donald J. Lewis Fund Dr. Ward D. Bouwsma Gerald and Barbara Cargo Dr. Nianqing Wang Robert and Ann Fulmer Professor and Mrs. Peter L. Duren Dr. Hugh Eugene Warren Mrs. Carolyn Dana Lewis James and Bonnie L. Watson Alan Kaufman and Iris Lopez Thomas Wilkerson and Mary Palmer Allotta Family Scholarship Fund Dr. Donald E. Sarason Joel and Katherine Wisdom Allotta Family Foundation Mr. and Mrs. Clayton Timmons Ms. Joan Mae Wolchok Ward D. Bouwsma Trust Dr. Ruth E. M. Wong Dr. Smilka Zdravkovska and Valerie F. and Edward Zablocki Professor Daniel Burns Mr. Stuart L. Zussman

15 Huntington Endows Actuarial Scholarships

Curtis E. Huntington (AB 1964, MAS 1965), Associate Chair of the Depart- ment of Mathematics and director of its actuarial studies program, has made a gift of $500,000 to the Department through a charitable remainder unitrust to endow the Margaret S. Huntington Actuarial Scholarship. The contribution, made in memory of his mother, strengthens the scholarship he previously created and will provide 10 promising fi rst-year students with $1,000 awards. Recipients are evaluated based on their strong performance in introductory cal- culus and their appreciation for the actuarial fi eld as demonstrated in their answers to questions in the scholarship application. Between 40 and 80 students a year have applied for the scholarships since they were fi rst offered in 1999. “The goal is to get good young mathematicians to consider the actuarial fi eld as a career option,” said Huntington, a Boston native and still a part-time resident, who worked as an actuary for New England Mutual Life for nearly three decades before joining the Department in 1993. Huntington’s father was an actuary, and his mother, also a mathematician, took actuarial course work. Actuaries use fi nancial mathemat- ics to evaluate the probability of future events for businesses and organizations and develop programs to avoid projected risks or reduce their impact. “We are so honored that Curtis has decided to permanently endow this scholar- ship fund” says Tony Bloch, Department Chair. “His tireless efforts on behalf of the actuarial program and the Department of Mathematics are paramount to a successful program. In his recent role of Associate Chair of Education, Curtis has truly shown his genuine concern for the students and the educational process.” Alumni/ae Scholarship Recipients Ruchir Agarwal is from Calcutta, In- Kellie Carlson is from Romeo, MI, and ests, from physics to economics, that share dia, and is a double major in mathematics will be in her third year of graduate studies a common grounding in the precision of and economics. He chose math for its beau- this fall. She is studying combinatorics and mathematics.” ty and the rigorous thinking and discipline hopes to work with Sergey Fomin or John Christopher Hammond is a second required. His fi nancial need was desper- Stembridge. Kellie has been interested in year graduate student from Ohio. He re- ate, and with the help of this scholarship, math since she was very young, and is par- ceived his BS from Ohio State University, Ruchir was able to graduate as scheduled in ticularly drawn to its artistic aspects. This but emphasizes that he much prefers at- May. “There are far fewer funding oppor- summer she will fi nish her QR require- tending UM! Chris is currently working tunities available for foreign students,” he ments and begin to study preliminary exam with Berit Stensones in several complex says, “and I am extremely grateful for this material. variables. The scholarship will allow him support.” Ruchir will be attending Harvard Sarah Crown is from Needham, MA, to continue his research toward his thesis for graduate studies. and just fi nished her fourth year of graduate and prepare for his oral exams. Kevin Wilson just fi nished his second study in algebraic combinatorics with Phil Kyle Hofmann is from San Francisco, year at UM. He grew up on a dairy farm in Hanlon. Sarah credits her interest in math CA, and received his undergraduate degree rural Simpsonville, KY. Kevin challenged to a wonderful high school pre-calculus from the University of California, San himself in high school, fi nished Calculus II teacher. “It was then that I decided that I’d Diego. He is in his third year, studying in his sophomore year, and did much self- like to teach math, and after taking a com- singularities using jet schemes with Mircea directed study thereafter. The excitement binatorics class in college, I decided to go Mustata. Kyle became interested in math of working out proofs to problems solidi- to graduate school.” in high school when a mathematically- fi ed his interest in mathematics. Besides Russell Golman is from Orangeburg, minded friend suggested Walter Rudin’s helping to alleviate the fi nancial burden on NY and received a BS in math from Stan- “Principles of Mathematical Analysis.” Kevin’s family, he says the scholarship is ford. Russell completed his second year Kyle says “I love the precision and struc- an “immense honor that the Department has in the Applied and Interdisciplinary Math ture of mathematics. Trying to understand given me…and shows their faith in me by PhD program, studying game theory un- the structures of mathematical objects entrusting me with an award that represents der Scott Page in the Complex Systems forces me to make precise statements, and the collective weight of all alumni.” Department. He chose the AIM program trying to make my intuition precise leads “because it lets me explore various inter- me to a thorough understanding of the structures involved.”

16 Upcoming Maxwell Reade at 90 Events In April 2006, Professor Emeritus of ate Chair and LSA Scholarship Committee Mathematics Maxwell Reade celebrated Chair,” says Lee. “He would make visits Department Colloquium his 90th birthday. His to high school students, children organized a help people with entry Every Tuesday at 4:00 gala party for him which into the country and included friends, family, their visas, and assure Alexander Ziwet Lectures and many members of family members that the mathematical com- students would be taken September 19-21, 2006 munity. Guests were care of at Michigan. He Professor Jerrold Marsden asked to bring bumper really worked hard to stickers for Maxwell fi nd the best students.” California Insitute of Technology which were appropriate Lee donated enough to the occassion and/or money for the fund to supportive of one of G.Y. Rainich Lectures reach endowment status Maxwell’s causes. to begin earning inter- October 31 - November 2, 4:00 A few years ago, for- est. In 2005 the Depart- Room 1360 East Hall mer Mathematics staff ment of Mathematics member Lee Zukowski began actively soliciting Professor Philip Holmes established a fund in donations to the fund. Princeton University Maxwell’s honor. The There was a leadership fund is intended to help gift from an alumnus of support diversity within $15,000, plus gifts from Mathematics Career Conference the Department by pro- faculty members and Friday, November 3 viding funding for student recruiting, direct friends of the Department. While the fund support of students, and other activities has now reached a level where the inter- related to this area. Lee wanted Maxwell’s est can be awarded to a student or used for Michigan Reception past efforts in this area to be remembered support of recruiting, the Department will Joint Meeting of the American and celebrated. “Maxwell did so much for continue efforts to grow the fund to higher so many students over his years as Gradu- levels. Mathematical Society New Orleans, LA Saturday, January 6, 2007 5:30 - 7:00 p.m. Want to get involved with the UM De part ment of Mathematics? 2007 Michigan Math and Science Here are some areas where alumni participation is vital. Let us Scholars Summer Program know if you are interested in working with us on these initiatives. Two Sessions for High School Students: Recommend the UM mathematics program to students inter- June 24 - July 6 and July 8 - July 20 ested in un der grad u ate or graduate studies Participate in our annual Career Day, November 3, 2006 Please visit our website for Visit the Department for afternoon tea (3:45 sharp) if you are in additional information on these and town for the week end, including Homecoming, Parent’s week- other events in the Department. end, or the Pres i den tial Society weekend www.math.lsa.umich.edu. Be a mentor (in person or via email) to a current student Set up a recruiting program with your company for graduating students Offer internships in your company to mathematics students Allow groups of mathematics students to visit your company Give an informal talk to mathematics students about how you have used your math degree Email [email protected] or call 734-647-4462

17 Alumni/ae Updates Considering a

Sister M. Bibiana Lewis (MS 1940) empirical repurchase probabilities to make celebrated her 100th birthday in April, retention versus disposal decisions for spare Donation to UM? joined by more than 80 nieces, nephews, parts, and a hybrid analytical-parametric If you are contacted by the Univer si ty of grandneices and grandnephews. She spent model for estimating the mass and volume Michigan for a do na tion, you can ear mark her career teaching in the colleges and high of spares for future space missions. your gift to the Department of Math e mat ics. schools in Minnesota. In retirement she en- Ernst Mayer (MA 91, PhD Aero 93) Simply tell the caller to des ig nate your gift joyed bowling, ping-pong and bridge, and moved to Silicon Valley in 1999 and has to mathematics or write Math e mat ics De- was the subject of several Novi programs. been doing algorithm and software devel- part ment on the pledge card you are sent. William R. Averill (BA 1946) writes “I opment for a series of high-tech program- We greatly ap pre ci ate all of your sup port, never really felt confi dent in my math abil- mable-logic startups there. In the plentiful and we hope we can count on you to sup- ity, so after graduation I took a job working spare time that leaves him, he tries to fi nd port fu ture fundraising projects. as an advertising copywriter, a far cry from time for his other mathematical avocation, math.” He feels he made the right decision, computational number theory. The highlight as he has had a successful career. “My of his work in the latter area was (together Estate Gifts math training was EXTREMELY valuable, with Crandall and Papadopoulos) establish- You may include the Department of however, as it ingrained in my brain an atti- ing the composite character of the twenty- Math e mat ics in your estate plan. Please tude that there is an answer for every prob- fourth Fermat number a few years ago. call us at 734-647-4462 for in for ma tion on lem! That math attitude helps me every More information about his recent personal char i ta ble trusts and be quests to the depart- single day. Thanks, UM!” and professional doings is available at his ment, or contact: Roger H. “Si” Simonsen (MS 1960) homepage, http://hogranch.com/mayer/ University of Michigan retired in 1995 from his position as Man- home.html. Development/Planned Giving ager of Advanced Technology Assessment Professor Emeritus Wilfred Kaplan 734-647-6000 with Boeing. His avocations include direct- has published a biography of his life with ing a choral group for 35 years and singing his wife Heidi (PhD 1944). The fi rst vol- with the Seattle Symphony Chorale. Si ume, entitled “Heidi and Bill: Beginning of bred and raised Whippets for 25 years, our lives together,” highlights two years of achieving top dog in U.S. three times and their courtship. The books is being distrib- over 30 AKC champions, with many dual uted by Kolossos Printing, and can be pur- champions. He moved to Oregon where he chased online at the following webste: is still active in the church choir, and enjoys www.kolossosprinting.com. riding horses and fi shing in the beautiful high desert. Alan Wilde (BS 1970, MS 1973) is a member of six scientifi c organizations and will be in the 2006 Empire Who's Who. Tovey C. Bachman (PhD 1985) is currently a research fellow with LMI Government Consulting. He was recently awarded the Barchi Prize for the best paper presented at the 72nd Military Operations Research Society Symposium. His paper, “Reducing Aircraft Down for Lack of Parts with Sporadic Demand,” describes an ordering policy he developed for repair parts with sporadic demand patterns. The Military Operations Research Society, or MORS, seeks to enhance the quality and ef- fectiveness of military operations research to better support decision making in the De- partment of Defense. Since joining LMI in 1989, Tovey has been extensively involved in developing mathematical models for Pat Shure (BA 1958, MA 1960, pictured above third from left) retired this year from the analyzing complex systems. They include a University of Michigan Department of Mathematics. Pat is celebrating her 100th exam simulation model for analyzing the perfor- with some instructors for the introductory calculus courses. l-r: Graduate Student mance of large-scale inventory and fi nan- Instructors Tomoki Ohsawa, Marshall Williams, Pat, Jose Gonzales, Hyosang Kang, and cial systems, an economic model that uses Dr. Nkem-Amin Khumbah of the Comprehensive Studies Program. 18 What Are You Doing? We’d like to hear from you! Please complete and return this form for our alumni/ae fi les. You may mail it to the address below, fax it to 734-763-0937, or email the information to [email protected].

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Please mail to Alumni Updates, Uni ver si ty 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/alum ni/

The University of Michigan, as an equal op por tu ni ty/ affi rma tive action employer, com plies with all ap pli ca ble fed er al and state laws regarding nondis crim i na tion and affi rma tive action, including Title IX of the Ed uca tion The Regents of the Amend ments of 1972 and Section 504 of the Re ha - ContinuUM Editorial Board: University of Mich i gan: bil i ta tion Act of 1973. The University of Mich i gan is Anthony Bloch, Chair com mit ted to a policy of nondis crim i na tion and equal Suzanne H. Rogers, Editor David A. Brandon, Laurence B. Deitch, op por tu ni ty for all persons regardless of race, sex*, color, re li gion, creed, national origin or ancestry, age, marital Doreen Fussman Olivia P. Maynard, Rebecca McGowan, sta tus, sex u al orientation, dis abil i ty, or Vietnam-era vet- eran sta tus in employ ment, educational programs and ac- Curtis E. Huntington Andrea Fischer Newman, An drew tiv i ties, and ad mis sions. Inquiries or complaints may be Donald J. Lewis C. Richner, S. Mar tin Tay lor, ad dressed to the Senior Director for In sti tu tion al Equity and Ti tle IX/Section 504 Coor di na tor, Offi ce for In sti tu - Photos by UM Photo Services, Katherine E. White; tion al Eq ui ty, 2072 Ad min is tra tive Ser vic es, Ann Ar bor, MI 48109-1432, 734-763-0235, TTY 734-647-1388. For the Michigan Daily, and Ex offi cio: Mary Sue Coleman oth er UM in for ma tion call 734-764-1817. the Department of Mathematics *Includes discrimination based on gender identity and gender expression. 19 Department of Mathematics NONPROFIT University of Michigan ORGANIZATION U.S. POSTAGE 530 Church Street, 2074 East Hall PAID Ann Arbor, MI 48109-1043 Ann Arbor, Mich 734-764-0335 • www.math.lsa.umich.edu Permit No. 144