ContinuUM Newsletter of the Department of Mathematics at the University of Michigan 2008 View from the Mel Hochster Named Chair's Office New Chair Tony Bloch This has been a busy year for the Department of Mathemat- It is exciting for me to have the chance to serve as Chair of ics. The year was mostly upbeat and filled with interesting math- the Department of Mathematics. ematical occasions. Unfortunately, however, we were saddened In his column, Tony Bloch has spoken of the passing of our by the tragic loss of our esteemed colleague and good friend, colleagues, Juha Heinonen and Wilfred Kaplan. Wiflred contrib- Juha Heinonen, and we mourn the passing of our much loved and uted so much to the admired emeritus professor, Wilfred Kaplan. Department for such During this past academic year we had 21 visiting scholars a long time that it is and faculty members playing an active role within the Depart- hard to imagine be- ment, and more than 160 short-term visitors. In addition, our own ing without him. faculty members presented numerous lectures at venues through- The unexpected out the USA and all over the world. loss of Juha Heino- We had an excellent colloquium series. We also enjoyed two nen this past year superb lecture series, one on Hyperbolic Dynamics by Curt Mc- was a tremendous Mullen and the other on Complex Manifolds by Gang Tian. In shock. He was an addition, our Department members organized numerous confer- amazing man, both ences on various subjects, including a wonderful conference in a renowned math- honor of Juha Heinonen. An exciting conference in honor of the ematician and a 65th birthday of Mel Hochster, our new Department Chair, was wonderful friend. He held in August. personified what it We have a remarkable faculty who continue to be recognized means to lead a bal- both internally and externally. The Math Department has 62 anced life. He will regular tenured/tenure-track members, 5 non-tenure-track mem- be greatly missed bers, and 53 three-year post-graduate positions. We are pleased and long remem- to have hired Professor Roman Vershynin who joined us from bered. UC Davis. Tony has described several of the more upbeat events of the One measure of our excellence is that our faculty members year. Here, I want to look to the future and describe some of the currently hold more than 91 federal grants for their research. things that will be happening over the course of the next three Several of our faculty have received distinguished honors, the years. details of which can be found on page 4. Hy Bass was named a We expect to be doing a significant amount of hiring. There Distinguished University Professor, the highest honor bestowed has been a terrific, albeit unwelcome, testimonial to the quality upon faculty by the UM. We are proud that the Department now of our faculty: many of them have gotten very good offers from boasts two such professorships. As a result of the strength of our other excellent mathematics departments. We have managed to faculty, we continue to face intense outside pressure in the form retain a strong majority of those receiving such offers, but we of external recruitment attempts. I am happy to report that we have also had some losses. We anticipate being able to make a continue to succeed in retaining most of our excellent faculty. substantial number of faculty appointments at the tenure-track Our student body this year comprises 143 graduate students and tenured levels. Rob Lazarsfeld has taken over from Sasha and approximately 415 math concentrators. In the fall 2007 term Barvinok as Chair of the Personnel Committee. I want to thank 7,353 students were enrolled in math courses. In the winter term both of them: Sasha for the work he has done over the previous there were 5,298 such students. We graduated 133 undergraduate two years, and Rob for his willingness to take over. math majors this year, and 31 new graduate students will be start- Dick Canary will be replacing me as Associate Chair for Term ing their degrees in the fall of 2008. There are many outstanding Faculty and Andreas Blass will be replacing Peter Hinman as As- continued on page 2 continued on page 2 Notes from the Chair Mel Hochster the answer that I got was that Michigan is (continued from page 1) (continued from page 1) better. This is encouraging to hear, but I feel that we need to do a more systematic students, several of whom have won the sociate Chair for Regular Faculty. I want analysis. prizes which are awarded internally every to express my appreciation to all of them I am planning to make some changes year as detailed on pages 6, 7, and 9. for their willingness, past and future, to in our website. I would like to give ev- It goes without saying that we are take on these sizable jobs. eryone ever associated with the Mathe- very grateful to the valued alumni of our Our key administrator, Doreen Fuss- matics Department at any level, including Department, whose support has helped to man, served in Iraq this past year. We are current and former faculty, graduate and make our development and fund raising pleased that she has safely returned this undergraduate students, staff, and visi- efforts very successful. Through the gen- fall. Laura Hornbeck has done a great tors, as well as their families, the oppor- erosity of our alumni, faculty, emeritus job filling in, and all of our staff deserve tunity to have some space on our website faculty and Juha’s many friends and col- high praise for stepping up during Do- to give contact information and, if they leagues, we were able to raise more than reen’s absence. wish, describe briefly what they are do- $50,000 for the Juha Heinonen Memorial We are due to have an External Re- ing now. This will enable people to keep Fund. The fund was established after view in March of 2009. A committee of in touch with friends who have been here Juha’s passing and will provide graduate distinguished mathematicians from other at some point in their careers whom they student support. This memorial is appro- institutions will give their advice about might lose track of otherwise. Computer priate given Juha’s dedication to young various aspects of Department opera- memory has become so inexpensive that mathematicians and his extensive men- tions. This review was postponed from I believe we can make such space avail- toring efforts. Our annual fund mailing last year, partly because of the transition able to anyone who is interested. to all alumni this year focused on funding in the Chair and partly so that Doreen I would also like web pages for for- for graduate student support. This was to would be here to help get ready for it. I mer faculty who have retired or passed take advantage of the President’s Initia- have asked the ADVANCE program to away to be maintained for a very substan- tive to match at a 50% ratio contributions do a climate survey for the Department as tial period of time, perhaps fifty years. to funds designated to support graduate part of the preparation for this review. students. Other fund raising allowed us Beyond that, I would like to think to continue our affiliation with the Inqui- Regular faculty, postdocs, staff, and about what information we might make ry Based Learning program, a program doctoral students will all have a chance available on our web page, possibly with which funds exciting new innovations in to voice their opinions about how the some limitations on access, that would teaching. Department operates and what we can do increase its availability to those with a to improve. legitimate interest. I would like to thank the faculty who served on the various Departmental com- During my term as Chair I would like In the course of preparing for the job mittees while I was Chair. Dick Canary, to do a thorough evaluation of our teach- of chairing this Department, I learned Joe Conlon, John Erik Fornæss, Juha ing of Calculus, and, more generally, of a great deal from working with Tony Heinonen, Peter Hinman, Mel Hochster, our Undergraduate Program. I believe Bloch. This was truly an education: I Curtis Huntington and Alejandro Uribe that we are doing an excellent job, but started with very little understanding of served as Associate Chairs. Sasha Barvi- it has been a considerable time since we the magnitude of the tasks the Chair must nok and Mel Hochster chaired the Per- have attempted a substantial assessment assume. sonnel Committee. of the program. The Department may In conclusion, I want to offer my seek external funding to study issues deepest appreciation to Tony, both for I would like to thank my Key Ad- related to the teaching of Calculus. I ministrator, Doreen Fussman, and Laura all that he has done for the Department want to mention that I have informally during his term as Chair, and for all of Hornbeck who did so much work in this asked several graduate students and Post- position while Doreen was away in Iraq. the help he gave me in getting ready to doctoral Assistant Professors who have follow him. I would also like to thank my Executive experience with the teaching of Calculus Secretary, Sallie Kne, and all the wonder- Melvin Hochster, Chair both at Michigan and elsewhere for their Jack E. McLaughlin Distinguished ful faculty and staff members who were opinions of the system here. Uniformly, so helpful to me and to the Department. University Professor of Mathematics I am very grateful to each and every one of them. I would also like to express my thanks for the various messages of appre- ciation that I have received. It has been a See more news of the pleasure Finally, I would like to take this op- University of Michigan portunity to wish Mel the very best in his Department of Mathematics on our website new position. As I start my sabbatical I leave knowing that the department will www.math.lsa.umich.edu be in his good hands.

2 CONTINUUM – 2008 Gopal Prasad Named Collegiate Chair Professor Gopal Prasd has been involved an intricate and subtle awarded a Collegiate Professorship. His blend of geometry, number theory, Professorship will be named in honor of and the structure theory of alge- Raoul Bott, a member of the UM Math- braic groups. These results have ematics faculty from 1951 to 1959. Bott attracted a great deal of attention was an admired pioneer in 20th century from the mathematical community. mathematics, particularly in the geometry Prasad has also recently com- and topology of Lie groups, and homoge- pleted pathbreaking research in a neous spaces and representation theory. very different direction, concerning Prasad received his Ph.D. from the whether a Riemannian manifold University of Bombay. After visiting ap- (generalizations of the kinds of pointments at Yale and the Institute for geometric spaces that arise in Ein- Advanced Study, he joined the faculty stein’s theory of general relativity) at the Tata Institute of Fundamental Re- is determined by spectral data such search in Mumbai. His 20 year career as the spectrum of its Laplacian, there culminated in a two year term as or its length spectrum. Using deep Dean of the School of Mathematics. He results from number theory and al- joined the UM faculty in 1992. Prasad gebraic groups, Prasad and Andrei has received significant recognition for Rapinchuk completely analyzed his work. He is a member of the Indian this question for arithmetic locally National Science Academy and the In- symmetric spaces of non-positive dian Academy of Sciences, and in 1989 surfaces are merely assumed to have the curvature. These classical objects received the Mathematical Sciences same numerical topological invariants form a large and extremely important Prize from the Council of Scientific and rather than the same underlying topology. class of Riemannian manifolds, and their Industrial Research in India. He was It follows from a theorem of Yau that work represents a quantum leap in our an invited speaker at the 1990 Interna- such an S that is different from P (a so- understanding of spectral theory. called “fake projective plane’’) must arise tional Congress of Mathematicians. He In the mid-1990s, Prasad and former in a very special way, as the orbit space received a Guggenheim Fellowship in UM colleague Allen Moy wrote two of a discrete subgroup Γ of the Lie group 1998, and a Humboldt Senior Research papers on the representation theory of p- PU(2,1) acting on the two-dimensional Award in 2006. adic groups. These papers established a complex ball. The existence of fake Prasad is recognized as a leading new invariant for representations of p-ad- projective planes was established by the expert in the theories of Lie groups and ic groups, affirmatively answered a very Fields medalist David Mumford in 1979. algebraic groups. The field has deep con- old and important conjecture relating the Since these fake planes are very intricate nections with problems and techniques representation theory of p-adic groups objects having the same numerical invari- in physics (classification of elementary with that of finite Lie groups, and re-in- ants as the simplest surface, they attract- particles); chemistry (crystallographic troduced Bruhat-Tits theory to represen- ed a great deal of attention. However, groups); and geometry, number theory, tation theory. Perhaps more importantly, Mumford’s existence proof was quite and numerous other branches of mathe- the methods introduced in these papers indirect: it did not determine the group matics. The astounding breadth found in have played a central role in the solution Γ, and it did not provide a concrete geo- his past and current work is quite rare in of at least two outstanding problems in metric description of the surface. After the modern era of narrow specializations. the field, leading to explosive progress in twenty-five years of unsuccessful efforts several directions. Prasad’s most famous recent work by many mathematicians, the challenge solved a long-standing problem in alge- of giving a direct construction of these In a recent joint work with a former braic geometry. In the beginning of the surfaces had become one of the major UM colleage Brian Conrad, and Ofer 20th century, the great Italian algebraic open problems in algebraic geometry. Gabber of IHES, France, Prasad has giv- geometer Francesco Severi asked wheth- en a classification of nonabelian pseudo- In a breakthrough paper that appeared er a smooth complex projective algebraic reductive algebraic groups over all fields recently in Inventiones Mathematicae, surface S whose underlying topology is of odd characteristics. This work settles one of the most distinguished journals “the same’’ as that of the complex projec- an outstanding problem in the area and in pure mathematics, Prasad and S. K. tive plane P (the simplest such surface) has several important arithmetic applica- Yeung solved this problem by giving the must be that plane. It took more than fifty tions. first effective construction of a fake pro- years before this question was answered jective plane. In fact, they did something His earlier results on strong rigidity, in the affirmative by the Fields medalist even more remarkable: they obtained strong approximation, the congruence S.-T. Yau. A refinement of this question an almost complete classification of is whether S is the same as P if the two the groups Γ that can occur. Their work continued on page 5

U-M DEPARTMENT OF MATHEMATICS 3 Faculty Kudos Professor Hyman Bass has been named the Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education, LSA and School of Education. This competitive and prestigious award is the highest honor that the University bestows on senior faculty “to recognize exceptional scholarly and/or cre- ative achievement, national and international reputation, and superior teaching skills.” Samuel Eilenberg was on the faculty of the Mathematics Department during the 1940s.

Associate Professor Stephen DeBacker has received an Excellence in Concentra- tion Advising Award from the College of Literature, Science, and the Arts.

Assistant Professor Selim Esedoglu was promoted to Associate Professor of Math- ematics. He also received a 2008 NSF CAREER award for his project “Analysis and modeling for image processing problems.” The CAREER awards provide early career DeBacker development for faculty with outstanding potential.

Assistant Professor Daniel Forger received a Young Investigator Research award from the Air Force Office of Scientific Research. Forger will study physiology model- ing of circadian timekeeping. The Young Investigator awards support recent Ph.D. recipients (<5 years) who show exceptional ability and promise for conducting basic research. The program aims to foster creative basic research in science and engineer- ing, enhance early career development of outstanding young investigators, and in- crease opportunities for the young investigators to recognize the Air Force mission and the related challenges in science and engineering.

Associate Professor Anna Gilbert is the recipient of the 2008 National Academy of Sciences Award for Initiatives in Research. The award recognizes innovative young scientists and encourages research likely to lead to new capabilities for human benefit. She is being recognized for her work with innovative algorithms using wavelets and sampling techniques and their impact on data analysis and sparse approximation. Gilbert Professor Trachette Jackson has been named one of the Emerging Scholars of the Year by Diverse Issues In Higher Education magazine. She was profiled in one of the magazine’s 2008 issues. The scholars are nationally recognized for their research, edu- cational background, publishing record, teaching record, competitiveness and unique- ness of field of study, and recommendations from other faculty members, department chairs and students. Diverse: Issues In Higher Education is America’s preeminent newsmagazine that covers news and information about the ever-changing world of higher education. Jackson was promoted to Professor of Mathematics this year.

Professor Robert Krasny has been elected a Fellow of the American Physical So- ciety in the Division of Fluid Dynamics. Election to fellowship in the APS is limited to no more than one half of one percent of its membership each year.

Krasny Professor Jeffrey Lagarias is one of the recipients of the Lester R. Ford Award from the Mathematical Association of America, awarded at the August Summer Math- Fest in San Jose, CA. Established in 1964, the award, which includes a citation and cash prize, is presented for articles of expository excellence published in the American Mathematical Monthly. Lagarias received the recognition for his article “Wild and Wooley Numbers,” vol. 113, No. 2, 2006.

Professor and LSA Associate Dean Robert Megginson has been named an Arthur F. Thurnau Professor. The Thurnau Professorships recognize outstanding contributions to undergraduate education. Megginson is the winner of numerous campus and na- tional awards for excellence in mathematics education. He is credited with reforming introductory math courses to emphasize real-world problem solving and cooperative learning. He also re-designed the Mathematics Learning Center to focus on mastery of basic skills, leaving classroom time for learning the higher order thinking that is at the Megginson heart of mathematics education.

4 CONTINUUM – 2008 Associate Professor Kristen Moore has been awarded Gopal Prasad the Class of 1923 Memorial Teaching Award from the Col- (continued from page 3) lege of Literature, Science and the Arts. The award rec- ognizes her outstanding teaching abilities and innovative subgroup problem, determination of cen- classroom techniques. tral extensions and the metaplectic ker- nel, and the computation of the covolume Mircea Mustata was promoted to Professor of Math- of arithmetic subgroups are well-known ematics. and widely used. Martin Strauss was promoted to Associate Professor of The enormous diversity of Prasad’s Mathematics. work is evidenced by numerous im- portant papers of his on algebraic and arithmetic groups, algebraic geometry, Bruhat-Tits theory, differential geometry, ergodic theory, number theory, and repre- Moore sentation theory. In the Department, Prasad is recog- nized as a devoted and effective teacher at all levels. He has directed four Ph.D. New Faculty Members theses here, and developed a course on Assistant Professor Juan Souto the theory of Lie groups. His colleagues Souto joined the Department in winter, in the Department have recognized him 2008. He received his Ph.D. from the Rhein- as an invaluable source of advice and in- ische Friedrich-Wilhelms-Universität in Bonn, sight on a wide panorama of mathemati- Germany. From 2001 to 2004 he held the cal subjects, always willing to share ideas position of Wissenschaftlicher Assistent at that and help with problems. institution. In 2005 he held a Research posi- Since 1998, Prasad has been manag- tion at the Université Paul Sabatier in Toulouse, ing editor of the Michigan Mathematical France. He then joined the faculty at the Uni- Journal. Through his leadership, he has versity of Chicago for two years. expanded the breadth of the editorial Souto’s field of research is in geometry/ board to include highly regarded math- topology, specifically in hyperbolic geometry ematicians from around the world. The and Kleinian groups, with broader interest in Journal has risen in stature and impor- 3-dimensional topology and rigidity theory. tance in the mathematical community. His publications include a paper that solved a twenty year old conjecture and contrib- Prasad is also an editor for the Asian uted to the proof of the Bers-Sullivan-Thurston Density Conjecture, and another which Journal of Mathematics and an associ- was influential in the solution of Marden’s Tameness Conjecture. ate editor of the Annals of Mathemat- ics, considered by many to be the most prestigious mathematics journal. He has Professor Roman Vershynin served on the Department’s Executive Vershynin joined the Department in fall Committee several times. 2008. He received his Ph.D. from the Univer- sity of Missouri-Columbia. After one year as a Research Postdoctoral Fellow at the Weizmann Institute in Israel and two years as a PIMS post- Math Problem doctoral Fellow at the Pacific Institute for Math- ematical Sciences and the University of Alberta, A jar contains 600 jelly he came to the University of California, Davis beans: 100 red, 200 green, as an Assistant Professor. He received a Sloan Research Fellowship in 2005, and was promoted and 300 blue. These are to Associate Professor in 2006. drawn randomly from the Vershynin’s research interest is geomet- jar, one at a time, without ric functional analysis, exploring connections among functional analysis, convex geometry and replacement. What is the probability theory. He has established himself probability that the first as a leader in this area, and he has the ability to apply his expertise to a wide variety color to be exhausted is red? of problems, many of them drawn from applied mathematics. Several of Vershynin’s papers contain solutions to long outstanding conjectures, and have been published in Answer elsewhere in the newsletter top journals.

U-M DEPARTMENT OF MATHEMATICS 5 2007-08 Graduate Program Fellowships & Awards

A.V. Flint Memorial Scholarship Mathematics Department Graduate Rackham Predoctoral Fellow Brian Jennings Fellowship Susan Sierra Samuel Altschul Alice Webber Glover Math Timothy Ferguson Rackham Science Award (RSA) Fellowships Aurel Fulger William Gignac Jonathan Bober Clara Blakelock Geri Izbicki Aubrey da Cunha Sohhyun Chung Brian Jennings Daniel Hernandez Ajinkya More Nicholas Rupprecht Ricardo Portilla Lei Wang Austin Shapiro Chelsea Walton Paul Shearer Allen L. Shields Memorial Scholarship Sourya Shrestha Gabrielle & Sophie Rainish Fellowship Katarina Bodova Katarina Bodova National Physical Science Consortium Alta B. West Math Scholarship Fellowship Regents’ Fellowship Julian Rosen Marie Snipes Johanna Mangahas

Arthur Herbert Copeland, Sr. National Defense Science and Research Training Grant (RTG) Memorial Scholars Engineering Graduate Fellowship Algebra Henry Boateng Brian Wyman David Anderson Jose Gonzalez Elizabeth Chen Ross Kravitz National Science Foundation Fellows Kyle Hofmann Nina White Ryan Kinser Brian Jurgelewicz Zachary Scherr Yogesh More Wirt and Mary Cornwell Prize Kelli Talaska Kevin Tucker Susan Sierra Natural Science & Engineering Research Council of Canada Scholarship Research Training Grant (RTG) Cameron & John Courtney Geometry Scholarship Luis Serrano David Constantine Fidel Jimenez Jasun Gong Benjamin Weiss Carroll V. Newsom Scholarships Christopher Hammond Oscar Fernandez Paul Johnson CONACYT Fellowship Steven Flores Aaron Magid Ricardo Portilla Gerardo Hernandez Johanna Mangahas Crystal Zeager Felipe Ramirez Diane Vavrichek Fulbright Scholarship E.S. & A.C. Everett Memorial Marshall Williams Richard Vasques Scholarship Catherine Dupuis Royal Thai Government Scholarship G. Cleaves Byers Endowment Panu Sam-ang Jennifer Beichman Edwin Wilkinson Miller Scholarship Harlan Kadish Eugene Eisenstein Graduate Departmental Scholarship Zian Yin Taeyong Ahn Rackham International Fellowship Peter Bosler Lucent Fellowship Florian Block Jiarui Fei Ellen Eischen Huaiying Gu Rackham One-Term Dissertation Shawn Henry Luther Claborn Mathematics Fellow Fellows Bich Hoai Xueying Hu Russell Golman Tigran Ananyan Geri Izbicki Henry Boateng Stephanie Jakus Craig Spencer Johnson Jia

6 CONTINUUM – 2008 Shin-Yao Jow Hyosang Kang Recent Ph.D. Recipients Wansu Kim Marc Krawitz Oscar Felgueiras completed his will be a Doob Research Assistant Pro- Cagatay Kutluhan dissertation “The Ample Cone for a Mor- fessor at the University of Illinois. Sara Lapan phism” under the direction of Robert Jared Maruskin completed his dis- Robin Lassonde Lazarsfeld. He will be an Assistant Pro- sertation “On the Dynamical Propaga- Michelle Lee fessor at Universidade do Porto. tion of Subvolumes and on the Geometry Ray Maleh Sara Gentry completed her disserta- and Variational Principles of Nonholo- Jeffrey Meyer tion “Mathematical Modeling of Muta- nomic Systems” under the direction of Andrey Mishchenko tion Acquisition in Hierarchical Tissues: Tony Bloch. He will be an Assistant Pro- Alexander Mueller quantification of the Cancer Stem Cell fessor at San Jose State University. Tomoki Ohsawa Hypothesis” under the direction of Tra- Yogesh More completed the disserta- Kyle Ormsby chette Jackson. She will be a Lecturer at tion “Arc Valuations on Smooth Variet- Kristofer-Roy Reyes the University of Michigan. ies” under the direction of Karen Smith. Joseph Roberts Jose Gomez-Guerra completed his Yogesh will be a Postdoctoral Research Darragh Rooney dissertation “Models of Twisted K-Theo- Fellow at the University of Missouri. Jordan Sahattchieve ry” under the direction of Igor Kriz. He Ashley Selegue Hannah Robbins completed her will be a Postdoctoral Research Fellow at Lindsey Selegue dissertation “Finiteness of Associated the University of British Columbia. Alan Stapledon Primes of Local Cohomology Modules” Nathan Totz Jasun Gong completed the disserta- under the direction of Mel Hochster. She Michael Von Korff tion “Derivations on Metric Measure will be Postdoctoral Fellow at Wake For- Ting Wang Spaces” under the direction of Juha est University. Jordan Watkins Heinonen and Mario Bonk. He will be Susan Sierra completed her disserta- Jared Whitehead Postdoctoral Associate at the University tion “The Geometry of Birationally Com- Szymon Wojczyszyn of Pittsburgh. mutative Graded Domains” under the Hao Xing Mark Iwen completed his disserta- direction of Toby Stafford. She will be a Qin Qing Xue tion “Algorithmic Compressed Sensing NSF Postdoctoral Fellow at the Univer- Hsu-Wen Young with Applications” under the direction of sity of Washington. Martin Strauss. He will be a Postdoctoral Craig Spencer completed his disser- Member at the Institute for Mathematics tation “Analytic Methods for Diophantine Sumner Myers Award and its Applications. Problems” under the direction of Trevor Harsh Jain completed the disserta- Wooley. He will be a member at the In- tion “Quantitative Modeling of Molecular stitute for Advance Study. Pathways Associated with Intratumoral Joe Stubbs completed his disserta- Angiogensis” under the direction of tion “Potent Elements and Tight Closure Trachette Jackson. Harsh will be a Re- in Artinian Modules” under the direction search Fellow at the Frankfurt Institute at of Mel Hochster. He will be an Informa- Goethe University, Germany. tion Analyst at the University of Texas. Jason Kutch completed his disserta- Giancarlo Urzua completed his dis- tion “Signal in Human Motor Unsteadi- sertation “Arrangements of Curves and ness: Detecting the Action and Activity Algebraic Surfaces” under the direction of Muscles” under the direction of Tony of Igor Dolgachev. He will be a Postdoc- Bloch. He will be a Postdoctoral Re- toral Research Fellow at the University search Associate at the University of of Massachusetts. Southern California Diane Vavrichek completed her dis- KyungYong Lee completed the sertation “Accessibility and JSJ Decom- dissertation “On Realization of Line positions of Groups” under the direction Bryden Cais, above, received the Arrangements as Multiplier Ideals” un- of Peter Scott. She will be a Visiting As- Sumner Myers Award for best Ph.D. der the direction of Robert Lazarsfeld. sistant Professor at SUNY Binghamton. Kyung will be a Research Assistant Pro- thesis in 2007. Bryden is now a fessor at Purdue University. Bo Yang completed the dissertation CRM-ISM Postdoctoral Fellow in “Application of Perturbation Methods to the Department of Mathematics at John Mackay completed his disserta- the Development of a Unified Framework tion “Conformal Dimension and the Qua- McGill University in Canada. for Pricing Credit and Equity Deriva- sisymmetric Geometry of Metric Spaces” tives” under the direction of Erhan Bay- under the direction of Bruce Kleiner. He raktar.

U-M DEPARTMENT OF MATHEMATICS 7 Congratulations to our 2007-08 Mathematics Bachelor of Arts/Science Degree Recipients

April 2008 Sohair Abdelrahman Jonathan Acker SeHyoun Ahn Ryan Allen Lisa Aronovsky Brian Baisa Haikal Fikri Abu Bakar Dana Barhoumeh Douglas Barritt Dominick Bartelme Andrew Birch Andrew Bleeker Michael Bliss Michael Bommarito Caroline Bowden Some recipients of the Outstanding Achievement in Mathematics Award: l-r, Bernard Yiu, Peter Nikolai Brendler Troyan, Zhe Tan, Dominick Bartelme, Thomas Fai, Elizabeth Otto, Professor Curtis Huntington. Andrew Brod Jonathan Buck Lisa Carpenter Hasan Cheema Victor Chen Timothy Kang Mohamed Mukhriz Guido Sofo Daniel Cheong Seulgi Kim Mohamed Hashim Samuel Soichet Andrew Chew Tai Il Kim Corina Mommaerts Smrithi Srinivasan Kai Kiat Chooi Cory Knill Shi Ting Ng David Swenson Eugene Chung Manpreet Kochhar Philip Ngan Zhe Tan Sung Hun Chung Rachel Kraft Jin Ye Ngu Ya-chin Tang Allison Cole Matthew Kuhlman Baonguyen Nguyen Brian Timm Britain Cox Lisa Kurtz Hui Fen Ooi Ernest Travis Laura Distelrath Matthew Laeder Elizabeth Otto Peter Troyan Heather Dougherty Voon Seng Lai Keng Yang Phua Richard Turner Thomas Fai Yin Jing Lai Anthony Pinter Taichi Udo Edward Fletcher Ka Yan Lam Andrew Preston Arthur Urban Jessica Fornari Brett Larsson Lindsay Pushies Derek Van Farowe Eric Fu Melissa Mei Yen Lee Kah Wai Putt Rajeev Vijay Brandon Gipper Nora Lewandowski Asha Radhamohan Paige Warmker Nathan Green Kwan Ho Li David Randazzo Joshua Welling Garrison Grove Yiqiao Li Matthew Rosenberg William Wilcox Jiong Gu Li Li Lim Christian Santos Kevin Wilson Brian Haber San Lo Andrew Sardone Jonathan Wiseman Rachel Harrison Zachary Maddock Ren Jie Saw Poh Yi Wong Thomas Hartsig Vrinda Mahishi Nicolas Scheiblauer Stephen Wu Gregory Haskins Caitlin Marlatt Rahul Shah Wai Ling Wu Yuen King Ho Christopher Marshall You Jin Shin Chia Chye Yee Todd Jarema Marshall Mawson Laurel Shipley David Yee Xiaoyin Jia Betty McColor Shanna Singer Ying Ki Yim Zhangli Jiang Timothy McQuade Patrick Smalley-Wall Bernard Yiu Paul Johnson Hoi Ying So Christopher Young

8 CONTINUUM – 2008 2008 Undergraduate Award Recipients

The Department’s team for the Samuel D. Faught William Lowell Putnam Mathemat- Ellyn Gendler ics Competition placed 14th out of 413 Jin Sheng Ooi teams in the event. The members of this Vinay Patel year’s team were Daniel Echlin, Timo- Syed Nabil Shahabudin thy Heath, and Jeffrey Madsen. The Spencer Smith individual competition included 3640 Rosaline Tio students from across North America. Chenli Zhu Timothy Heath placed the highest of Eric Fu received the Leon UM students at 126. SyHoun Ahn, P. Zukowski Prize for outstand- Daniel Hermes, and Jeffrey Madsen ing service in the Mathemat- also finished in the top 200. ics Learning Center (formerly The winner of the 25th Annual Uni- known as the MathLab). versity of Michigan Undergraduate The William LeVeque John Shepard, Elizabeth Lee & Professor Curtis Huntington. Mathematics Competition was Jeffrey Award in Number Theory was Madsen, achieving his third win. Zili presented to Jeffrey Madsen. The award Huang placed second. The CIGNA Award in Actuarial recognizes a student who is at most a Science was presented to Elizabeth Lee The following student received the junior and excels in the study of number and John Shepard. Mathematics Alumni/Alumnae Schol- theory. arship for the 2007-08 academic year: The Irving Wolfson Award in The Sumner Myers Award in Anal- Actuarial Science was presented to Mendel Feygelson ysis was presented to SeHyoun Ahn. Christopher Kurdelski. The following students received Outstanding Achievement in Math- The Lois Zook Levy Memorial Evelyn O. Bychinsky Awards, which ematics Awards went to the following Award was presented to Rachel Kraft. recognize underclass students who show seniors: The award recognizes an outstanding exceptional promise in mathematics: Dominick Bartelme Mathematics student who plans to pursue Daniel Echlin II Britain Cox a career in K-12 Mathematics education. Daniel Hermes Thomas Fai The following students were named Wade Hindes Elizabeth Otto Michigan Mathematics Merit Schol- Zili Huang Anthony Pinter ars: Andrew Kiluk Zhe Tan Steven Moses Peter Troyan Zachary Maddock Alfredo Wetzel Paige Warmker Timothy McQuade Richard William Turner The following students received Bernard Yiu Margaret S. Huntington Awards in The Otto Richter Memorial Prize in Kevin Wilson was named the Actuarial Outreach: Actuarial Science was presented to Paul Outstanding Graduating Senior. Shulamite Chiu Johnson. James Cooper

Above: Professor Hendrikus Derksen with Jeffrey Madsen. Right: Zili Huang with Professor Stephen DeBacker.

U-M DEPARTMENT OF MATHEMATICS 9 lessons learned from her experiences Actuarial Program News after graduation from Michigan in both large companies and her current assign- Those of you who graduated more involved in a number of inter-disciplinary ment was well-received by an enthusias- than a few years ago may not be famil- initiatives. tic audience of this year’s graduates (and iar with the frequent, and significant, At the same time, interest in courses their families). This was the sixth event changes that have been occurring in the in financial mathematics from students in this series. This is a fun event for the educational syllabus of both the Casualty with other declared concentrations has faculty to plan and is the highlight of the Actuarial Society (CAS) and the Soci- shown significant growth throughout the actuarial academic year. ety of Actuaries (SoA) in recent years. University. Virtually every course that Finally, we are actively planning a These changes have a direct impact on we offer in this field fills up with students new actuarial alumni/ae directory. This the students, and on the curriculum these eager to enter this new area. Our major will be a time-consuming activity and students take, while at the University. problem here is finding enough instruc- will involve a number of students. Dur- The Michigan Actuarial Program tors to be able to run classes with reason- ing the process, you may receive a call has never been designed to ‘teach to the able enrollment numbers, rather than from one of the students asking to verify professional syllabus.’ Rather, it has em- merely offering a large lecture course. information for the directory. If you do phasized the learning of basic principles The student-run club, the Student Ac- get such a call, I hope that you will take along with developing a set of problem tuaries @ Michigan (or SAM) maintains the opportunity to talk with the student solving skills. Nevertheless, we have an active schedule of academic, sporting about what is happening in Ann Arbor made a number of changes in the curricu- and social events. With more 100 mem- and get a feel for the dynamics of the cur- lum to reflect the new environment. bers, this group is rapidly becoming one rent environment. Also, please let them The most significant changes have oc- of the more active academically-focused know what is happening in your life so curred in the field of financial economics. groups on campus. Students pay annual that we can report that in future issues on Some changes are simple—the name of dues to be a member of SAM and the ContinuUM. the Theory of Interest examination is now group is run by an Executive Committee The faculty and students look forward ‘Financial Mathematics.’ Other changes of 9 students. to hearing from you with any comments, are more extensive—Examination MFE Students who are members of SAM questions or suggestions you might have. (called Examination 3F by the CAS) cov- and have completed courses related to the And, if your travels bring you though ers the topic of mathematical economics professional examinations (for example, Ann Arbor, please let us know so that we and was designed also to be used to test Mathematics 425—Probability for the can host a visit with us in our East Hall candidates for the new CERA (Chartered first examination—Exam P/1) become home. Enterprise Risk Analyst) designation. eligible for a subsidization of their exam- Curtis E. Huntington (BA 1964, MAS 1965), Existing courses have been changed ination fees. These fees, particularly for FSA, FCA, MAAA, APM to reflect new content and several new college students are not trivial. The first Professor of Mathematics courses have been added. two examinations cost $175 each; the Director, Financial & Actuarial Mathematics Programs The actuarial societies have also re- next ones are in the $360-400 range. Director MPET Program cently re-characterized some of the old For the Spring, 2008 examination examination subjects as being part of a sessions, the Department paid more than preliminary education component that $16,000 in subsidized examination fees. is no longer tested but is still required. With increased enrollments and increased Honors Math A process, called ‘Validation by Educa- examination fees, the subsidization pro- tional Experience’ (VEE), has been es- gram has become a significant recurring Students from the tablished for the three subjects involved expense. —Economics, Corporate Finance and ‘50s, ‘60s, and 70s

Applied Statistical Methods. Students Members of SAM visited several area If you took the 90s sequence who take pre-approved college courses high schools as part of our continuing and successfully complete these courses outreach to let local students and teachers of Honors Math during that era, with a grade of B- or higher are assumed become more aware of the actuarial field we’d like to hear from you. If to have gained the required knowledge in and the opportunities that are available. you are interested in getting these three subjects. SAM also donated $1,000 of funds at the together for a reunion to dis- end of the academic year to sponsor one cuss the trials, tribulations and Most of our current students seek to of the annual Margaret S. Huntington triumphs of honors math stu- maximize their Michigan experience by Awards in Actuarial Outreach. also fulfilling all of their VEE require- dents, please contact the math ments while undergraduates. This has Our April 2008 Cecil J. Nesbitt Com- department at math.mich@ mencement Lecturer this year was Karen had a direct impact on the enrollments umich.edu, or Don Lewis at Olsen MacDonald (BA 1975, MA 1976), in some other UM Departments and pro- [email protected]. We’d love vided opportunities for the faculty to get Vice President and Actuary at WellPoint (Woodland Hills, CA). Her message of to hear from you!

10 CONTINUUM – 2008 Alumni News Tom Wilkerson (BS 1953, PhD Physics 1962) received evidence, and suggestive connections with disparate branches the 2007 Utah Governor’s Medal for Science and Technology. of mathematics and theoretical physics. Conrey is currently a Wilkerson is a professor in Utah State University’s Physics De- Professor of Mathematics at the University of Bristol. He is the partment and its Center for Atmospheric and Space Sciences, founding executive director of the American Institute of Math- and is a senior scientist with Utah’s Space Dynamics Labora- ematics, and formerly was a member of the mathematics facutly tory. He taught Physics and Mathematics at the University of at Oklahoma State University. Maryland for 24 years prior to joining Utah State. Wilkerson is an internationally recognized expert in the use of lasers to David W. Centner (BS 1986, JD Indiana University) is a perform remote sensing of the atmosphere—known as light founding member of the West Michigan office of Clark Hill, detection and ranging or LIDAR. He has also been responsible PLC. Clark Hill has approximately 175 lawyers in five offices for numerous advances in the fields of high temperature shock located throughout the state of Michigan and in Chicago. He waves, the “solar wind” plasma, and the optical spectroscopy of continues to practice litigation, with a specific emphasis on ionized gases. The State of Utah awards the Governor’s Medal complex commercial litigation, creditor’s rights and bankruptcy, to recognize individuals who have provided distinguished ser- and intellectual property litigation. David has been married for vice to Utah in the fields of science and technology. It is the 18 years, has four children, and is active in a number of profes- highest honor awarded by Utah for scientific and technological sional and nonprofit organization. achievements. Michael Frank (BS 1987) is President and Actuary at Steven D. Bennett (BA 1965, MBA Kent State 1977) is a Aquarius Capital in New York. In 2007, he was elected to the high school math teacher with Cleveland Metropolitan Schools Society of Actuaries Reinsurance Section Council, and he was and the SuccessTech Academy. appointed Chairperson of the Continuing Education Committee of the Actuarial Society of Greater New York. Herb Hethcote (PhD 1968) retired from the University of Iowa after 37 years as a Professor of Mathematics. He was Martin Erickson (PhD 1987), Professor of Mathematics at the Director of the interdisciplinary Ph.D. program in Applied Truman State University, and Anthony Vazzana (PhD 1998), Mathematical and Computational Sciences. His major research Associate Professor of Mathematics at Truman State University, focus was mathematical modeling of the spread and control of have recently written the textbook “Introduction to Number infectious diseases. He coauthored two books and had over 80 Theory” (Chapman & Hall/CRC Press, 2008). research papers. He and his wife now live on Bainbridge Is- land, Washington, near their two married sons. Patrick Bidigare (PhD 1997) is the Technology Director for BBN Technologies in Virginia. Barry Garelick (BA 1971), is an Environmental Protection Specialist with the U.S. Environmental Protection Agency. He is involved in the issue of K-12 math education, and has written Sarah-Marie Belcastro (PhD 1997) and Carolyn Yackel several articles on the subject. (PhD 1998) are editors of the book “Making Mathematics with Needlework” (A.K. Peters. Ltd., 2007). The book successfully connects the worlds of mathematics and fiber arts. Each chap- James C.R. Burns (BS 1971, MS Radiological Physics, ter covers a different mathematical paper and corresponding University of Colorado, 1973) is the Chief Medical Physicist in needlework project and includes mathematical explanations, Oncology with Promedica Health Systems in Sylvania, OH. needlework instructions, educational materials, and specific projects to demonstrate the principles discussed. The colorful J. Brian Conrey (PhD 1980) has received the 2008 Conant collection presents examples of current research and issues still Prize from the American Mathematical Society. The Conant to be investigated, using topology, graph theory, number theory Prize recognizes an outstanding expository paper published in and algebra, very basic combinatorics, observations of sym- either the Notices of the AMS of the Bulletin of the AMS in metry, and brute force. Belcastro co-directs the Hampshire Col- the previous five years. Conrey’s article “The Riemann Hy- lege Summer Studies in Mathematics and is currently a Visiting pothesis” was published in the Notices of AMS, March 2003, Assistant Professor of Mathematics at Smith College. Yackel pp. 341-353. The article outlines the mathematical context that teaches Mathematics at Mercer University, where she has de- justifies the importance of the Riemann Hypothesis, key mo- veloped a general-education course in mathematics through ments in the problem’s 140 year history, known partial results fiber arts and regularly teaches for the Interdisciplinary Studies and blind alleys, various threads of numerical and theoretical program.

U-M DEPARTMENT OF MATHEMATICS 11 In Memoriam Professor Juha Heinonen seven years he was an editor of the Pro- Ann Arbor as tenured professors in 1996, ceedings of the American Mathematical settling into a satisfying marriage and Professor of Mathematics Juha Hei- Society. In 2002, he was invited to give productive careers. They welcomed their nonen passed away on October 30, 2007, a talk at the International Congress of daughter Sanelma in 1998, and their boy- after a courageous battle with kidney Mathematicians in Beijing. Juha became girl twins, Tapio and Helena, in 2003. cancer. Born July 23, 1960 in the small town of Toivakka in central Finland, A gifted athlete, Juha was the 1976 Juha was raised in the village’s old-age Finnish national champion in his class for home where his mother served as the 5 km cross-country skiing. Although he sole staff member. His father Vilho was gave up professional sports to pursue a a lumberjack and well-respected socialist career in mathematics in the early 1980s, politician in the tiny town. After gradu- Juha’s love of competitive sports never ating high school, Juha served one year waned. He participated in many running, as an officer in the Finnish army, and cross-country skiing and orienteering then enrolled as a student of mathematics events around the country. In his class he at the University of Jyväskylä. His 1987 won both the U.S. and the North Ameri- Ph.D. thesis, directed by Olli Martio, can gold medal in orienteering in 2000. was in non-linear potential theory. Juha was a vibrant, balanced, satis- Juha first came to the University of fied person who enjoyed many things in Michigan for a semester as a visiting life besides mathematics and sports. He graduate student in 1985. His first ap- spent his free time studying foreign lan- pointment in the Department of Math- guages, or reading history, biographies, ematics began in 1988, when he returned and political commentary. He loved the as a three year post-doctoral assistant outdoors, particularly Michigan autumns professor. In 1992 he accepted a tenure and Finnish winters. A devoted husband track assistant professorship, and in 2000 a member of the Finnish Academy of and father, Juha enjoyed the company he was promoted to professor. He served Science and Letters in 2004. of his children and was often spotted as Associate Chair for Graduate Studies A dedicated thesis advisor, Juha on errands around town with a child on in the Department of Mathematics from directed eight doctoral students. Many the bus, on his bike-seat, or in his arms. 2004 to 2007. students, junior faculty, and young re- Each time he spoke of his family, the pride was evident through the twinkle in Considered a scholar possessing high searchers greatly benefited from his pa- his eye and his broad grin. professional standards, Juha was a lead- tient mentorship and wise tutelage. Juha ing figure in geometric function theory, was very grateful for the excellent men- His Finnish origins remained deeply his main research area. His two books toring he himself received as a young important to him throughout his life. Juha “Nonlinear Potential Theory of Degen- mathematician, and was happy to repay maintained close contacts with his Finn- erate Elliptic Equations” (co-authored in kind. In addition to his advisor, he ish friends and colleagues, and traveled with T. Kilpeläinen and O. Martio) and especially acknowledged U-M Professor to Finland at least once a year. He taught “Analysis on Metric Spaces” have be- Emeritus Fred Gehring whom he met in his children and his wife to speak Finnish come standard references in their fields. 1985, and Jose Fernandez, to whom Fred and to share his love of his native land. introduced him later that academic year He co-authored more than 60 research Juha was widely loved for his posi- at the Mathematical Sciences Research papers, many of which contributed to the tive attitude, sparkling sense of humor, Institute in Berkeley. Later he was deep- creation of a new branch of mathematics, and genuine kindness towards others, ly influenced by Dennis Sullivan who now called analysis on metric spaces. traits that he maintained throughout the directed his attention to analysis in more Juha was a generous and enthusiastic difficult trials of his illness. He is deeply abstract settings. collaborator who was proud of the fact mourned by his family, friends and col- that nearly all of his research publica- When Juha originally came to the leagues. Besides his wife and children, tions were joint works. His collaborators United States, his intention was to Juha is survived by his mother Liisa Hei- admired him for his erudition, his deep stay for only a short period. His plans nonen and his sister Maritta Nukarinen. A mathematical insights, and his never- changed when he met his future wife, memorial service held in December was ending scientific curiosity. Karen Smith, a first-year graduate stu- attended by nearly 400 people. The De- Juha’s expertise was recognized with dent of mathematics, who also arrived in partment of Mathematics has established many awards and fellowships, includ- Ann Arbor in the fall of 1988. They were the Juha Heinonen Memorial Graduate ing a Sloan Fellowship, numerous NSF married in 1991. Juha put his own ca- Student Fellowship. Information is avail- grants, several visiting appointments, reer on hold to follow his wife to Boston able at http://www.math.lsa.umich.edu/ and an Excellence in Research Award when she obtained a post-doctoral posi- events/juhaMem.html from the University of Michigan. For tion at MIT. The couple came back to

12 CONTINUUM – 2008 Professor Wilfred Kaplan mathematics; and he supervised 8 Ph.D. played an important role in faculty gov- students. He was an outstanding teacher ernance, serving as vice-chair of the Fac- Wilfred Kaplan, Professor Emeritus and the author of a series of important ulty Senate (SACUA) and as as chair of of Mathematics at the University of and influential textbooks. His text Ad- an AAUP committee for annual review Michigan, died on December 26, 2007 vanced Calculus, first published in 1952, of the UM budget. In 1986, he was one after a short illness, at the age of 92. He has been translated into many languages of the inaugural recipients of the Distin- was born in Boston, Massachusetts on and continues to be used in many univer- guished Faculty Governance Award pre- November 28, 1915, the sities worldwide. sented by SACUA. In 1990 he helped to son of Jacob and Anne Among his other establish the Academic Freedom Lecture (Levenson) Kaplan. After texts are Ordi- Fund (AFLF), which sponsors an annual graduation from Boston nary Differential lecture in honor of three University of Latin School, he entered Equations (1958), Michigan professors fired or suspended Harvard University, where Operational Meth- for political reasons during the McCarthy he completed his A.B. ods for Systems era, and he remained on the AFLF Board degree in mathematics (1962), Calculus of Directors until his death. summa cum laude. With and Linear Algebra a traveling fellowship he Wilfred and Heidi’s children Roland (with D. J. Lewis, then spent the year 1936-37 and Muriel were born and raised in 1968), Advanced in Europe, where his flu- Ann Arbor. Wilfred and Heidi greatly Mathematics for ency in German and French enjoyed playing music together and in Engineers (1981), helped him to meet and various chamber groups. He played the and Maxima and confer with many leading violin, piano, viola, and zither; she the Minima with Ap- mathematicians. He met cello and piano. Wilfred did much to plications: Practi- Heinz Hopf in Zürich; Le- promote the arts, especially music and cal Optimization vi-Civita in Rome; Pontry- drama, in the Ann Arbor area. He served and Duality (1999). agin, Kolmogorov, and P.S. as president of the Dramatic Arts Center, In 2007, Calculus Alexandrov in Moscow; president of Ars Musica, and president and Linear Algebra Kuratowski and Borsuk in Warsaw; Had- of the Washtenaw Council for the Arts. was reprinted by the UM Library to be amard, Borel, Denjoy, and Elie Cartan in In addition to music, Wilfred and Heidi used again in UM Mathematics courses. Paris; Kerékjártó and Fejér in Hungary. devoted their leisure time to avid reading “First and foremost, Wilfred Kaplan was While attending lectures at the E.T.H. of classical literature in many languages. a teacher,” says colleague Don Lewis. in Zürich, he met another mathematics They never owned a television set. “He enjoyed conveying the beauty and student, Ida (“Heidi”) Roettinger, who usefulness of mathematics, and his stu- In recent years, Wilfred Kaplan would become his wife of 66 years. In dents responded enthusiastically. He served as President of the University of addition to mathematics, they shared a was a superb expositor, and his ability Michigan Retirees’ Association, and his passionate interest in music and litera- to elegantly convey mathematical ideas work greatly strengthened that organiza- ture. They were married in 1938 and explains the enormous impact of his text- tion. Following the loss of his beloved lived for a year in Houston while Wilfred books. When we were writing our joint wife Heidi in 2005, Wilfred worked to taught at Rice Institute. Wilfred obtained texts, he never came to a meeting without edit and translate their collection of cor- his Ph.D. from Harvard in 1939, as a a new idea to be incorporated.” respondence with each other and with student of Hassler Whitney, then taught family and friends. Two volumes of these for a year at William and Mary before Throughout most of his professional edited letters have been printed, and an- joining the faculty at the University of career, Wilfred was active in the affairs of other is forthcoming. Michigan in 1940, where he served until the American Association of University Wilfred Kaplan will be remembered his retirement in 1986. Professors (AAUP), a national organi- zation dedicated to defending faculty as a cultured man with many talents During the war years 1944 to 1945, rights, especially academic freedom and and a broad range of interests and ac- the Kaplans were away from Ann Arbor tenure. He served as president of the complishments. He dedicated much of while Wilfred did military research in UM Chapter, president of the Michigan his life to the service of his profession, a group of mathematicians at Brown Conference, and member of the national his university, and his community. He University. After the war they made fre- AAUP Council. He was helpful in bring- is survived by his brother Robert Kaplan quent trips to Switzerland for extended ing collective bargaining to several uni- of New York, his sister Esther Kaplan stays with Heidi’s family. They spent versities in Michigan, with the AAUP as Braun of Boston, his children Roland the year 1949-50 in Zürich while Wilfred agent. “Wilfred’s AAUP contributions Kaplan of San Jose and Muriel Kaplan held a Guggenheim Fellowship. were solid, significant, and sometimes in- Zwiebel of Minneapolis, four grandchil- Wilfred Kaplan had extraordinary novative,” says colleague Ralph Loomis, dren, four great-grandchildren, numerous mathematical talent. He published about Professor Emeritus of English. “His de- nieces and nephews, and a large commu- 30 research papers on topological behav- votion to University governance was un- nity of colleagues and friends. All were ior of solutions of differential equations, stinting and unflagging.” At the UM he witness to his intelligence, compassion, complex function theory, and applied generosity, and love of life.

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, 2007 and August 31, 2008

Cigna Life Actuarial Science Michigan Pension Education Mr. & Mrs. Thomas C. Scott Mathematics Alumni/ae Fund Training Program Dr. Eli E. Shapiro, D.O. Scholarship Fund Dr. Harry E. Spain, Jr. Gary M. Fotiu ASPPA Pension Education Mrs. Deborah P. Badgett Mary Huetteman & Chad H. Research Foundation, Inc. Amy M. & Michael J. Biersack Stone Dr. & Mrs. Denis L. Bourke Financial Mathematics Jeffrey Alan Taras Mrs. Mary E. Boynton Development Fund David & Kitty Hartman Fund Steven J. Thompson Mr. Andrew I. Brown Marc N. Altschull Mr. & Mrs. David G. Hartman William C. Thompson Ms. JJ Lane Carroll Sam Gutterman Jean McLarty & Ronald R. Dr. James H. & Patricia Case Mr. & Mrs. David G. Hartman Tidball Mathematics Graduate Dr. Todd E. Cochrane John L. Marakas Ms. Kathleen A. Tweney Student Support Fund Carl de Boor Merck Company Foundation Richard J. Weiland Mr. Kenneth D. Adema Dr. Sandra J. DeLoatch Gregg A. Schwab Dr. Barbara Gail Weinstein Mrs. Phyllis J. Archambeau Richard W. Dernberger Dr. Yue Wang John C. & Sally Wenger Mr. & Mrs. James W. Arney Mr. Robert V. DeVore Jean M. Wersching Anjana Baluja Henry Albert Dihm, Jr. Dr. Lori J. Williams Margaret S. Huntington First Ms. Donna C. & Dr. Roy G. Jeffery T. & Jean S. Dukes Mr. & Mrs. Henry N. Winslow Year Actuarial Scholarships Belville Mr. & Mrs. Blair M. Duncan Dr. Ruth E. M. Wong Mr. Craig J. Blumenfeld Ms. Nancy J. Dynes Marc N. Altschull, Valerie & Edward Zablocki CNA Insurance Foundation Dr. & Mrs. Alfred J. Bown Soroor Ebnesajjad Mr. & Mrs. Herald H. Hughes, Mr. Michael Persons Braun Dr. Arnold D. Feldman Mathematics Department Jr. Miss Lorraine A. Chorkey Dr. Vincent J. Ferlini Robert Calvin Clark Special Fund Professor & Mrs. David E. Lois Zook Levy Memorial Dr. Todd E. Cochrane Dr. Ian M. Aberbach Flesner Award The Ron & Kathy Colby Family R. James Bennett Mrs. Susan Zinck Flesner Foundation Miss Linda Marie Clark Dr. Robert Samuel Fortus Hiram Levy, II Mrs. Lee S. Cooper Dr. Alan K. Cline Michael L. Frank Dr. Kourosh Danai Deloitte Foundation Jonathan M. Glauser, M.D. Inquiry Based Learning Mr. Fazli M. Datoo Mr. Craig M. Evans Ms. Teow Lim Goh Mr. Harry Lucas, Jr. Mr. Paul G. Eitner David M. Gay Mr. Dennis P. Graham Peggy A. & Larry D. Elliott Mrs. Karen Gold Cathy M. & Robert A. Helton Mathematics Strategic Fund Ruth F. Engel Anjela & Vincent Govan Dr. & Mrs. Jeffrey A. Furst Dr. Eitan Moshe Fenson Douglas G. Hakala Hittinger Mr. Kelly D. Clevenger Dr. Robert Samuel Fortus Thomas J. Hansen Mary A. Kelly Dr. Todd E. Cochrane Mr. S. Nicholas Frontczak Dr. Charles S. Holmes Mr. & Mrs. Edward M. Kimball Dr. & Mrs. Allan Lee Edmonds Roberta & Thomas Glassman Dr. George A. Kozlowski, Jr. Dr. George A. Kozlowski, Jr. Dr. C. Allan Foy, Jr. Mr. Dale L. Haakenstad Professor Robert Krasny Dr. Maureen Lahiff Mr. John D. Gabel Nooshin Haghparast Dr. William E. Lakey Ms. Kelli M. Lauer Dr. H. Mark Hildebrandt John J. Iskra James R. Lannen John L. Marakas William R. Hintzman Drs. Gudmund R. & Roberta R. Lorraine D. Lavallee, Ph.D. Mr. David C. Marty Mr. Todd A. Lanski Iversen Lockheed Martin Corporation Mr. Luke Masselink Lincoln Financial Group Dr. & Mrs. Edward L. Keller Dr. William F. Lucas Edmund B. McCue Jennie A. & James S. Lombard Dr. Parviz Khalili Dr. Michael J. Plantholt Virginia D. McCulloh Marcy Jan & David Marcus Ms. Firuzeh Khorasanizadeh Qualcomm Incorporated Mr. & Mrs. Stephen E. McGrath Michael J. Merscher Melanie S. & Phillip L. Kraft Dr. G. Robina Quale-Leach John D. McKenzie, Jr., Ph.D. Mr. Kelly K. Miller Mr. Thomas E. Kruger Mr. Michael L. Quinn Mr. Kurt M. Miller Dr. & Mrs. W. Reynolds Dr. Harris Kwong Dr. Michael J. Sattinger Dr. & Mrs. W. Reynolds Monach, Ph.D. Naomi Gurt & William H. Lind Mr. Benjamin H. Singer Monach, Ph.D. Joseph L. Murphy III Marsh & McLennan Compa- Victor L. Smith John G. Ratcliffe, Ph.D. Steph H. Oppenheim nies, Inc. Mr. Thomas E. Stolper Dr. Robert Gene Reynolds Professor Emeritus & Mrs. Donald E. Masters Drs. Emil M. & Judith S. Ms. Katherine A. Savatsky Frank A. Raymond Mr. John F. McNamara Sunley, Jr. Mark A. & Anelly A. Schwab Dr. Donald E. Sarason Dr. Zevi Miller Dr. John C. & Sally Wenger Dr. Uriel K. Scott Anne Lattin Saywitz Victor T. Norton, Jr., Ph.D. Prof. Alan Shuchat Mark A. & Anelly A. Schwab Dr. Donna L. Prince Dr. & Mrs. Albert R. Stage Frederick W. Silverman, M.D., Michigan Math & Schience Dr. Albert Ratner Dr. Clarence F. Stephens J.D. Scholars Mrs. Carolyn J. Reif Dr. & Mrs. Melbourne G. John C. Tien Mr. Ethan A. Rein Sheila & Harold Cumberworth Stewart, Jr. William P. & Suzanne R. White John S. & Barbara Mode Rose Mrs. Ching-Shung Tu Lee Lynn Zia Denise Rose Roy Dr. Hugh Eugene Warren John E. Zline

14 CONTINUUM – 2008 Susan Meredith Smith Elsbeth T. Falk Professor & Mrs. Gopal Prasad W. James & Barbara MacGin- Professorship in Actuairal Professor Carol E. Fan Professor Emeritus & Mrs. M.S. nitie Sciences Dr. Jose L. Fernandez Ramanujan MetLife Foundation Professor Daniel B. Forger Professor Emeritus & Mrs. Jeffrey S. Paciero Ms. Susan M. Smith Professor William E. Fulton Maxwell Reade Mr. & Mrs. Jerome M. Powell Ms. Doreen J. Fussman Suzanne H. Rogers PricewaterhouseCoopers Leon Zukowski Prize John Garnett Mr. John F. Rossi Mr. & Mrs. Richard G. Roeder, Professor Daniel M. Burns, Jr. Professor Emeritus & Mrs. Dr. Khachik V. Sargsyan F.C.A. Dr. Smilka Zdravkovska Frederick W. Gehring Professor G. Peter Scott Jack & Marguerite Seigel Professor Anna C. Gilbert Sharon R. Silver Mr. & Mrs. Clifford R. Simms Leonard Rand Fund Professors Kari & Per Hag Ms. Carol Smith Mr. & Mrs. Donald R. Son- Stone/Rand Philanthropic Fund Judith E. Halloran Professor Karen E. Smith dergeld Dr. Aimo Hinkkanen Professor Joel A. Smoller Wendell C. True Professor Zheng Huang Southern Michigan Orienteer- William D. Ward Professor Emeritus Thomas Ms. Dorothy A. Hudock ing Club Mr. & Mrs. Paul S. Weiss Storer Fund Professor Craig L. Huneke Professor Ralf Spatzier Louis M. Weisz Dr. Brian R. Haag Professor Curtis E. Huntington Professor J. Tobias Stafford Ms. BeLinda I. Mathie Alexander John Izzo Dr. Susan G. Staples Irving S. Wolfson Fund Mr. & Mrs. Charles D. Professor Tara Javidi Mr. Jeffrey E. Steif Michael and Susan Bowden McLaughlin Mrs. Agnes C. Jensen Professor John Stembridge Mr. & Mrs. James S. Wolfson Prof. Bart M. Taub Professor Mattias Jonsson Professor Martin J. Strauss Dr. Lester M. Wolfson Professor B. Alan Taylor Mrs. Elizabeth M. Joseph Professor Neil Strickland Mr. David J. Venzon Professor Smadar Karni Ms. Fruma Taub Mr. Leon P. Zukowski Professor Navin Kashyap Professor B. Alan Taylor Carl H. Fischer Fund Robert Kaufman Professor Zachariah C. Teitler Jane and Daniel Arnold Professor Emeritus Maxwell Mr. Anton K. Kim Mr. David Tello Patrick & Charlotte Fischer Reade Fund Mr. Ryan D. Kinser Dr. Mary L. Thompson Charitable Fund Professor Janos Kollar Dr. Thomas R. Transue Professor Daniel M. Burns, Jr. Mr. Sandor Kovacs Mr. William Traves Mathematics Department Professor Stephen M. DeBacker Mr. Leonid V. Kovalev Professor Joel A. Tropp Mr. J. Scott Grannan Special Endowment Professor Robert Krasny United Technologies Corp. Dr. James T. Renfrow James H. Ellis, M.D. Professor Catherine E. Kriloff Professor Divakar Viswanath Dr. Smilka Zdravkovska Mrs. Gloria M. LaPontney Professor Igor Kriz Dragan Vukotic, Ph.D. Mr. Leon P. Zukowski Paul Renard Professor Si Ho Kwok Ms. Leslie Ward Willard D. Larkin Professor & Mrs. Arthur G. Allotta Family Scholarship Professor Robert Lazarsfeld Wasserman Sumner B. Myers Prize Fund Ms. Ann M. Leahy Mr. Alan Weiss Professor Stephen M. DeBacker Mr. Joseph J. Allotta Professor Emeritus & Mrs. Mr. Michael K. Weiss Professor Ralf Spatzier Allotta Family Foundation Donald J. Lewis Dr. Lori J. Williams Mr. John Lewis Professor & Mrs. David J. Allen L. Shields Memorial Juha Heinonen Memorial William V. Luitje Winter Fellowship Mr. John M. Mackay Eric W. & Jennifer K. Wolf Graduate Student Fellowship Dr. & Mrs. Donald P. Ballou Mr. Juan J. Manfredi Ms. Judy A. Wood Dr. Ward D. Bouwsma Professor Ian M. Aberbach Mrs. Katsuhiko Matsuzaki Professor Jang-Mei Wu Dr. & Mrs. Robert F. Brammer Professor Martin K. Albert Mr. Sean A. McGhee Professor Sijue Wu Professor Daniel M. Burns, Jr. Professor Jinho Baik Professor Jean McKemie Dr. Smilka Zdravkovska Professor & Mrs. Gerald T. Professor & Mrs. Anthony M. Professor & Mrs. Robert E. Mr. Leon P. Zukowski Cargo Bloch Megginson Professor Eric J. Zupunski Dr. Todd E. Cochrane Professor Mario Bonk Dr. Sergiy Merenkov Dr. Michael L. Cohen Ms. Dorothee Brand Mrs. Lee Yen Miao LeVeque Excellence in Mr. Dennis A. Darch Professor Daniel M. Burns, Jr. Dr. Zevi Miller Number Theory Fund Mr. Fazli M. Datoo Mr. Luca Capogna Mr. Carl D. Minda Mr. Leon P. Zukowski Dr. & Mrs. Andrew C. Dempster Professor Jeff Cheeger Professor Kristen S. Moore Susan J. Devencenzi Mr. William Cherry Mrs. Jacquelyn Murphy Professor Peter L. Duren Professor Todd E. Cochrane Thomas B. Murphy Cecil J. Nesbitt Commence- Mrs. Suzanne D. Goodrich Professor Michael L. Cohen TB Murphy Foundation ment Lecture Fund Alan L. Kaufman & Iris Lopez Professor Mark A. Conger Professor Mircea I. Mustata Mr. & Mrs. John B. Kleiman Mr. & Mrs. David C. Linnen Professor Joseph G. Conlon Professor Thomas Nevins Mr. James Marker Professor Brian D. Conrad Ms. Nancy Oswald Cecil J. and Ethel M. Nesbitt Dr. Eric Albert Nordgren Professor Serban M. Costea Dr. Bruce A. Palfey Professorship Dr. Demetrios Serakos Professor Susan E. Cutler Dr. & Mrs. Bruce Paul Palka Dr. Gerald D. Taylor Professor Carolyn Dean Professor Pekka J. Pankka Aetna Foundation, Inc. Dr. & Mrs. Layne T. Watson Professor Igor V. Dolgachev Mr. Kirsi Peltonen Aon Foundation Dr. & Mrs. Martin C. Weinrich David Drasin Karen J. Pender Ernst & Young Foundation Dr. Lori J. Williams Professor & Mrs. Peter L. Duren Professor Pietro Poggi-Corradini Sam & Peggy Gutterman Ruth F. Engel Karen Olsen MacDonald Dr. Smilka Zdravkovska

U-M DEPARTMENT OF MATHEMATICS 15 Alumni Voices Algebraic Equations and Finite Simple Groups: What I learned from graduate school at the University of Michigan, 1964–1967, by Michael Fried Michael Fried (PhD 1967) spent 26 years as a member of and group theory. the Mathematics faculty at the University of California, Irvine. Chuck MacCluer’s thesis, under Lewis, showed—for special During his career, he received a Fulbright Fellowship and a f—a geometric statement gave Schur’s one-one mapping hy- Humboldt Award. He has contributed this story as part of our pothesis. Later, by extending the Chebotarev density theorem, ongoing history project, and an expanded version of the article I formulated a general context including Davenport and Schur. is available on our History webpage www.math.lsa.umich. There, pure group theory translated the number theory. edu/information/depthistory.shtml. The full detail of this story is available on Fried’s webpage: www.math.uci.edu/~mfried/ Formulations, paplist-cov/UMStory.html. however, are not conclusions. PRELUDE: After three years of Graduate School in Math- Could you invert ematics at University of Michigan (1964-1967), writing a thesis the direction poly- under the direction of Don Lewis, I left for a postdoctoral at the nomials to groups, Institute for Advanced Study. There I studied with Goro Shimu- as in Schur’s Prob- ra. My first year was extended to two years (1967-1969). Then, lem? I went with James Ax to SUNY at Stony Brook. After receiving tenure and a Sloan Fellowship, I left. That bare bones outline of A rational a beginning career tells little mathematically. function not com- posed of lower It has no hint that the work inspired by my time at UM degree functions is connected resolutely with the simple group classification— indecomposable. I through conversations with John Thompson—and with modular state lightly what curves—interactions with J.P. Serre. Nor, that problems of An- I found powerful drzej Schinzel and Harold Davenport, (visitors to UM my sec- in practice: (i) A ond year) in papers with Lewis, were the inspiration. Not even rational function’s that technical tools came from assiduous use of Grothendieck’s covering group is fiber product approach to algebraic equations. Yet, fulfilling primitive exactly those connections required–no word better–tutoring from many when the function UM-affiliated faculty during my formative years. is indecompos- This short version of the story relates Davenport’s Problem, able; (ii) A poly- the steps in its solution, and how the connections above came nomial’s covering about. I never lost my youthful enthusiasm for completing group always con- programs of Abel, Galois and Riemann, as recorded in “What tains an n-cycle. Michael Fried, circa 1968. Photo courtesy Gauss told Riemann about Abel’s Theorem” (http://www.math. From that I of the American Mathematical Society. uci.edu/~mfried/paplist-cov/Wh-Gauss-Tld-Riem-ab-Abel.pdf). learned, that if f was DAVENPORT’S PROBLEM AND FIBER PRODUCTS: indecomposable, its covering group was either doubly transi- When number theorists say almost all primes p, they mean tive, or f was in the Schur conclusion. That finished the Schur all but finitely many. Davenport sought relations between two story and deepened the Davenport story. polynomials f(x) and g(y) with rational coefficients—where no I now knew Davenport’s hypothesis on f and g produced change of the variable in f gives g—having the same ranges on a difference set mod n that encoded how zeros of g(y)-z=0 integers mod p for almost all p. He liked this style of question, summed to a zero of f(x)-z. Not only did the distinct permutation and often used exponential sums to interpret it. representations for f and g have the same degree, their group Changing “almost all” to “infinitely many” and taking representations were identical. g(y)=y, restates the hypothesis of Schur’s 1921 conjecture. The I had seen Brumer pepper Jack McLaughlin with group conclusion of Schur: f must be composed of linear, cycle and theory questions. When Brumer left for Columbia in 1966, Chebychev polynomials. Richard Brauer was a student of Schur, I took his place with McLaughlin, from whom I learned the and advisor of Don Lewis. When I met him he asked if I knew distinction between doubly transitive and primitive. Richard he had worked on Schur’s conjecture. I hadn’t. Misera, a fellow grad student working with Donald Higman, A variables-separated algebraic equation looks like f(x)- saw this interaction and gave me a propitious example, coming g(y)=0. Writing this as f(x)-z=0 and g(y)-z=0 opened the terri- from projective linear groups. I applied this, modulo something tory. Fiber products of f and g over the z-line allowed me to use that I learned very much on my own—R(iemann)’s E(xistence) groups to draw conclusions. I’ll use n for the degree of f. Visit- T(heorem)—to produce polynomial pairs having almost simple ing Assistant Professors Armand Brumer and Richard Bumby groups with special projective linear core. The three propitious guided my mastering Grothendieck’s Tohoku paper and pieces points were these: of his EGA. There I learned to go between algebraic equations

16 CONTINUUM – 2008 1. Without writing equations, I was able to see the Galois action of the cyclotomic field ofn -th roots of 1, acted on the Share Your Stories difference set relating f and g. The elements that preserved that difference set, up to translation (so-called multipliers), gave the We would like to include your stories and remembrances definition field of the pairf,g ( ). Further, -1 was never a multi- on our History website www.math.lsa.umich.edu/information/ plier, so that definition field was neverQ . depthistory.shtml. We have recently begun in earnest to collect 2. Because the covers given by f and g had genus 0, the only and share some of our Department’s history. Over the years possible degrees for f and g were n=7, 11, 13, 15, 21, 31. many documents have been written about the educational, schol- arly, administrative and research activities of U-M mathematics, 3. The cases with infinitely many essential pairs (f,g) modulo and we invite you to share the history. mobius action on z, x and y appearing in #2, had degree 7, 13 and 15. Further, in these cases those essential parameters Beyond the facts, figures and remembrances of faculty mem- formed a genus 0, upper half-plane quotient, that wasn’t a bers, the history of the Department is contained in its students. modular curve. We are interested in your memories of your time as a student. What impressed you about your first or hardest math class? Did Tom Storer, newly at UM when I visited it from IAS, a discussion during a seminar help to establish the direction of worked with me on the last statement of #1. This completed your significant research? Who were your most memorable Davenport’s Problem over Q for indecomposable polynomi- instructors? Do you have a story about one of the faculty mem- als f. There were no nontrivial examples. It used nothing from bers that might enlighten others to their spirit? How did they the simple group classification. The offshoot of that technique help shape your educational career and influence your life? Do became the Branch Cycle Lemma, the most practical tool by you have a story about Tom Storer, Maxwell Reade, T. H. Hil- which to relate geometric covering groups and definition fields. debrandt, George Piranian, or any other Department member The longer version of this article has these further sections: that stands out in your memory? Using the classification and the genus 0 problem; UM seminars Please send us your remembrances and we will make an and modular curves; The significance of Davenport’s problem. effort to share them with others. If you would like your remem- These tell why Davenport’s problem had an impact (in order) in brances to be included in ContinuUM or on our website, we will well-known papers of Thompson, Serre, and Denef and Loeser. work with you to include your memories. Of the others who got PhDs in 1967, one became much Michigan Today is also seeking your stories. You can share more famous than anyone who might be reading this. That was your stories and read those of others on this website “The Unabomber,” a no-show at the going away party Paul Hal- http://michigantoday.umich.edu/heritage.php. mos gave us. The picture on the opposite page is from Halmos’ “I Have a Photographic Memory” (American Mathematical Society, Providence, RI, 1987). I was standing in front of my diagram for the Schur Conjecture proof at the end of my 1968 We Need You! UM lecture on it. I didn’t know about that picture until years later. Still, either Want to get involved with the UM Department of Mathematics? I, or the Schur Conjecture, must have been funny. A New Yorker Here are some areas where alumni participation is vital. Contact not long afterwards had a cartoon based on it. I have seen only us if you are interested in working with us on these initiatives. one person from my graduate years more than once after grad school. That was the topologist Bob Edwards who twice sat in • Recommend the UM mathematics program to students interested in on talks of mine at AMS conferences. undergraduate or graduate studies • Participate in our annual Career Day, held each year in early No- Solution to Math Problem vember • Visit the Department for afternoon tea (weekdays at 3:45 sharp) if There will be a final string of beans of the same you are in town for the weekend, including Homecoming, Parent’s color (the color of the last bean drawn), and then a weekend, or the Presidential Society weekend bean preceding it of a different color. The desired • Be a mentor (in person or via email) to a current student probability p is that these two colors are blue and • Set up a recruiting program with your company for graduating green or green and blue, respectively. The prob- students ability that the last bean drawn is blue is 300/600 = • 1/2, and, no matter how long the final string of blue Offer internships in your company to mathematics students beans is, the probability that the bean of preceding • Allow groups of mathematics students to visit your company color is green is 200/(100+200) = 2/3. For green • Give an informal talk to mathematics students about how you have and blue these numbers become 200/600 = 1/3 and used your math knowledge 300/(100 + 300) = 3/4. Thus, p = (1/2)(2/3)+(1/3) Email [email protected] (3/4) = (1/3)+(1/4) = 7/12. or call 734-647-4462

U-M DEPARTMENT OF MATHEMATICS 17 Where’s Your Considering a Upcoming Math Department Donation to UM? Events T-shirt Been? Matching funds still available Department Colloquium There is still time to take advantage Every Tuesday at 4:00 of the President’s Challege for Gradu- ate Student Support. Until the end of 2008, all gifts to funds designated to sup- Mathematics Career port graduate students will be matched Conference at a 50% level. For every two dollars given to a fund supporting graduate November 14, 2008 students, one dollar will be endowed in a departmental fund for future gradu- Alexander Ziwet Lectures ate student support. The Mathematics Department has an expendable graduate November 18-20, 2008 student support fund (code 312378) or Ioannis Karatzas several named endowments that also are University of Columbia designated for graduate student support. If you are contacted by the University “Some Stochastic Control Prob- of Michigan for a donation, you can lems in Mathematical Finance” earmark your gift to the Department of Mathematics. We greatly appreciate all of your support, and we hope we can Michigan Reception count on you to support future fundrais- Joint Mathematics Meetings ing projects. American Mathematical Society We’d like to know where you show off your your Math affiliation. Above, Washington, D.C. Department Administrator Doreen Fuss- January 6, 2009 man shows her spirit while serving in Estate Gifts You may include the Department of Iraq. Wear your Math t-shirt while trav- Mathematics in your estate plan. Please elling, snap a photo, and email the picture call us at 734-647-4462 for information 2009 Michigan Math and and a description of where you are to on charitable trusts and bequests to the [email protected]. We’ll try to Science Scholars Summer department, or contact: Program include it in the next newsletter, and in- Two sessions for qualified clude it on our webpage here http://www. University of Michigan math.lsa.umich.edu/undergrad/Tshirts/ Development/Planned Giving high school students: Tshirts%20destination/ 734-647-6000 June 28 - July 10 and Don’t have a Math t-shirt? Stop in July 12 - July 24 the Department some time and pick one up for just $5. Or email math-ugrad- [email protected] to arrange to order one Please visit our website for and have it sent to you by mail. They additional information on are available in several colors and sizes. these and other events in the Your purchase will help support under- Department. graduate program activities. The University of Michigan, as an equal opportunity/ www.math.lsa.umich.edu. affirmative action employer, complies with all appli- cable federal and state laws regarding nondiscrimina- tion and affirmative action, including Title IX of the ContinuUM Editorial Board: Education Amendments of 1972 and Section 504 of the Rehabilitation Act of 1973. The University of Michi- The Regents of the Melvin Hochster, Chair gan is committed to a policy of nondiscrimination and University of Michigan: equal opportunity for all persons regardless of race, Suzanne H. Rogers, Editor sex, color, religion, creed, national origin or ancestry, Julia Donovan Darlow, Laurence Doreen Fussman age, marital status, sexual orientation, gender identity, gender expression, disability, or Vietnam-era veteran B. Deitch, Olivia P. Maynard, Rebecca Curtis E. Huntington status in employment, educational programs and activi- Donald J. Lewis ties, and admissions. Inquiries or complaints may be McGowan, Andrea Fischer Newman, addressed to the Senior Director for Institutional Equity Andrew C. Richner, S. Martin Taylor, Al Taylor and Title IX/Section 504 Coordinator, Office of Institu- tional Equity, 2072 Administrative Services Building, Katherine E. White Photos by UM Photo Services, the Ann Arbor, Michigan 48109-1432, 734-763-0235, TTY Department of Mathematics, or 734-647-1388. For other University of Michigan infor- Mary Sue Coleman, ex officio mation call 734-764-1817. personally submitted by the subjects.

18 CONTINUUM – 2008 Conference in Honor of Mel Hochster In August 2008, over 100 mathematicians gathered to celebrate Mel Hochster’s 65th birthday at a conference titled “Commu- tative Algebra and its Interactions.” Conference participants included Mel’s students, collaborators, former post-docs, and other colleagues from around the world. The conference included six days of talks on commutative algebra, a reception, a conference banquet, and of course a Sunday afternoon gathering to play bridge. Information about the conference proceedings is available on our website here http://www.math.lsa.umich.edu/conferences/hochster/index.html. In conjunction with the conference, the Michigan Mathematical Journal published a special 755 page special volume in honor of Mel. The volume includes 44 articles from over 80 authors. The volume may be purchased for $50 from the Michigan Mathemati- cal Journal ([email protected]).

Conference participants included many of Mel’s 33 graduate students. Some of the students who attended the conference are pictured above, from left to right: Emily Witt, Hailong Dao, Geoffrey Dietz, Adela Vraciu, Florian Enescu, Bruce Fields, Mel Hochster, Anurag Singh, Moira McDermott, Karen Smith, Ian Aberbach, Sankar Dutta.

Right: Conference organizers Karen Smith, Craig Huneke, and Anurag Singh are pictured with Mel and the special volume published in his honor by the Michigan Mathematical Journal.

U-M DEPARTMENT OF MATHEMATICS 19 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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