ContinuUM Newsletter of the Department of at the 2007 Bass Wins National View from the Medal of Science Chair's Offi ce

University of Michigan Tony Bloch Mathematics and Educa- tion Professor The 2006-2007 academic year was an received the nation’s highest eventful and exciting one for the Depart- science honor from President ment of Mathematics. The current quality George Bush during a July of the Department is refl ected in the range 27 ceremony at the White and scope of our activities: numerous House. A video of the cere- seminars, exciting colloquia, and interest- mony is available on the U-M ing conferences. During this past aca- website http://ummedia04. demic year we had 21 long-term visiting rs.itd.umich.edu/~nis/Bass. scholars, and more than 160 short-term mov. visitors. In addition our faculty members presented numerous lectures at exciting Bass was one of eight venues all over the U.S. and the world. National Medal of Science laureates honored. He is the Department members organized nu- Collegiate merous conferences on various subjects: Professor of Mathematics , Financial Engineer- in the College of Literature, ing, Teichmueller Theory, and Scientifi c Science, and the Arts, and Computing. There was also the Canary Professor of Mathematics Fest, a series of workshops on Geometry Education in U-M's School of and in celebration of Dick Ca- Education. and researcher in the College of Litera- nary’s 45th birthday. ture, Science, and the Arts working col- Bass is the fi rst U-M researcher to Our weekly colloquium series was laboratively with his colleagues in the very successful, featuring several distin- win the honor in 21 years. Five other School of Education to advance mathe- U-M researchers won the award between guished University of Michigan alumni, matical research and teaching skills,” said as well as fi ve Fields Medalists. 1974 and 1986 for their work in engi- LSA Dean Terrence J. McDonald. “We neering, biological sciences and physical are very pleased that his work is being We were fortunate to have had two sciences. Bass is the only U-M winner to recognized with the prestigious award.” excellent visiting lecture series last year: represent the fi elds of math and educa- Jerrold Marsden, the Carl F. Bruan Pro- tion. Bass said he was “very honored” by fessor of Control and Dynamical Systems the recognition. “My work in mathemat- The award citation for Bass states: at Caltech, gave the Ziwet Lectures in ics education, with Deborah Ball, Dean September 2006, on various topics in me- “For his fundamental contributions to of the School of Education, and her re- pure mathematics, especially in the cre- chanics including invariant manifolds and searchers, is focused on the problem of coherent structures, numerical integrators, ation of algebraic K-theory, his profound helping teachers provide quality mathe- infl uence on , and and geodesic fl ows on fi nite- and infi nite- matics instruction for the full diversity of dimensional groups. Philip Holmes of his service to the mathematics research students in American classrooms,” Bass and education communities. With his presented the Rain- said. “Working together we have focused ich lectures in November, on neural oscil- unique combination of gifts he has had on the mathematical demands at the ele- enormous impact over the course of a lators, stochastic dynamics, and optimal mentary level and what this implies about decisions. half century.” the mathematical knowledge needed for “Professor Bass’s work is a wonder- teaching.” continued on page 2 ful example of a gifted continued on page 2 Notes from the Chair member and as a dedicated teacher and Bass Medal of Honor (continued from page 1) tutor. After his retirement he continued (continued from page 1) his much appreciated work in the Math The 2007-08 academic year also Lab. We are very happy to honor him. After a 40 year career as a faculty promises to be exciting with upcoming We are sad to report that we lost member at , Bass lecture series including those by Curtis two Professors Emeriti this year, Robert joined U-M in 1999. He was named a McMullen and Gang Tian, and a collo- Bartels, who made tremendous contribu- Collegiate Professor shortly after arriv- quium talk by Fields Medalist Vaughan tions to computing at Michigan, and Tom ing at Michigan. His research in Jones, among others. Storer, who will be remembered as a most and geometric theory has shaped We have a remarkable faculty who extraordinary teacher. We would like to the development of these areas in the continue to be recognized both internally remember them here (see page 12). last decades. Bass’s work has enormous and externally. During the 2007-08 aca- No report of the Mathematics Depart- breadth and includes theory, com- demic year, the math department has 68 ment is complete without a mention of mutative algebra, the Jacobian problem, regular tenured/tenure-track members, 5 our student body. This comprises 139 combinatorial , as well non-tenure-track members, and 58 three- graduate students and approximately 340 as his foundational work in algebraic year post-graduate positions. One mea- math concentrators. In the fall 2006 term, K-theory. His recent mathematical re- sure of our excellence is that our faculty 7,119 students were enrolled in math search has emphasized geometric meth- members currently hold more than 141 courses. In the winter term 2007 there ods and group theory, including group federal grants for their research. Other were 5,211 such students. We graduated action on trees and the discrete sub- outstanding accomplishments by our fac- 133 undergraduate math majors in 2007, groups of Lie groups. Bass has received ulty are detailed within this newsletter. and 36 new Ph.D. and Masters gradu- much recognition for his mathematical contributions, including election to As a result of the strength of our ate students started their degrees in the fall of 2007. There are many outstanding membership in the National Academy of faculty, we face intense outside pres- Sciences in 1982. sure in the form of external recruitment. students, several of whom have won the We were sorry to lose members of our prizes which are awarded internally every Bass served a two-year term as number theory group. However I am year. One of our 2006 Ph.D. graduates, President of the American Mathematical happy to report that we were fortunate to Sam Payne, is currently a Clay Research Society from 2001-2003. He was in- retain many of our wonderful faculty in Fellow at Stanford. strumental in the formation and admin- the face of enticing external offers. On Of course, we are very grateful to istration of the Mathematical Sciences the recruitment front we are delighted to the valued alumni of our Department. Research Institute in Berkeley, CA. In welcome as new Assistant Professors in Our development and fund raising ef- recent years, Bass has taken a leadership the fall, Volker Elling, who works in par- forts have been successful thanks to the role in mathematics education, serving tial differential equations, and Victoria much appreciated generosity of our loyal as chair of the Mathematical Science Booth, who works in neuroscience and alumni. Our annual alumni fund-raising Education Board and president of the holds a joint appointment in Anesthesiol- letter consistently raises a much needed International Commission on Math In- ogy. $16,000 to $20,000. This year these struction, which is the educational coun- funds allowed us to provide scholarship terpart of the International Mathematical We are happy to welcome two dis- Union. tinguished Gehring Visiting Professors, support to 2 undergraduate students and Keith Ball from University College, summer support to 3 graduate students. The National Medal of Science, es- London and Blake Temple, from UC What the Department needs more than tablished in 1959, honors individuals for Davis. Joseph Marker has joined the anything else, at the moment, is endowed pioneering scientifi c research in a range Department as the Carl H. Fischer Visit- chairs. We would like to thank Susan of fi elds that enhance understanding of ing Professor in Actuarial and Financial Smith for her funding of an actuarial and the world and lead to innovations and Mathematics. fi nancial mathematics chair (sse page 16). technologies that give the United States its global economic edge. We are proud of our distinguished We continue our affi liation with the retired faculty and staff. Recently we Inquiry Based Learning program, a pro- were pleased to recognize Lee Zukowski gram which funds exciting new innova- at the Emeritus luncheon by dedicating tions in teaching, as detailed on page 10. a plaque for the Mathematics Learning We are extremely grateful to all who, Center (a.k.a. MathLab) in his honor. with their contributions, help to make our Lee served the Department wonderfully Department such an excellent place for for many years, both as a valued staff teaching, learning, and research.

See more news of the University of Michigan Department of Mathematics on our website www.math.lsa.umich.edu

2 CONTINUUM – 2007 Mapping of E8 Professor of Mathematics The magnitude and John Stembridge is a member nature of the E8 calcula- of an international team of 18 tion invites the comparison and computer with the Human Genome scientists who successfully Project, according to AIM. have mapped the Lie group The human genome, which E8, one of the largest and contains all the genetic in- most complicated structures formation of a cell, is less in mathematics. The E8 cal- than a gigabyte in size. The culation is so large it would result of the E8 calcula- cover Manhattan if it were tion, which contains all the written out on paper, accord- information about E8 and ing to the American Institute its representations, is 60 of Mathematics (AIM). gigabytes. This is enough to One of the most sym- store 45 days of continuous metrical mathematical struc- music in MP3 format. tures in the universe, E8 is The computation re- an example of a Lie group. quired sophisticated new Lie groups were invented by mathematical techniques the 19th century Norwegian and computing power not mathematician Sophus Lie to available even a few years study symmetry. Underlying ago. While many scientifi c any symmetrical object, such projects involve processing as a sphere, is a Lie group. large amounts of data, the

Balls, cylinders or cones are A graphic depiction of the E8 plane. Further explation is available E8 calculation is very differ- familiar examples of symmetric at this website: http://www.math.lsa.umich.edu/~jrs/coxplain.html ent, as the size of the input three-dimensional objects. Math- is comparatively small, but ematicians study symmetries in the answer itself is enor- higher dimensions. In fact, E8 is mous and very dense. the group of symmetries of a geometric object like a sphere, cyl- The E8 calculation is part of an ambitious project sponsored inder or cone, but the object in this case is 57-dimensional. E8 by AIM and the National Science Foundation, known as the At- itself is 248-dimensional. For more technical details on E8 visit las of Lie Groups and Representations. The goal of the project is http://www.liegroups.org/AIM_E8/technicaldetails.html. to determine the unitary representations of all the Lie groups (E8 “E8 was discovered over a century ago, in 1887, and until is the largest of the exceptional Lie groups). This is one of the now, no one thought the structure could ever be understood,” most important unsolved problems of mathematics. The E8 cal- says Jeffrey Adams, project leader and mathematics professor at culation is a major step, and signals that the Atlas team is well the University of Maryland. “This ground breaking achievement on the way to solving the problem, mathematicians say. is signifi cant both as an advance in basic knowledge, as well Stembridge says the mapping of E8 also will create oppor- as a major advance in the use of large scale computing to solve tunities for students at U-M. “Students might get to work on a complicated mathematical problems. The mapping of E8 may cool problem as part of this project.” well have unforeseen implications in mathematics and physics which won’t be evident for years to come.” Stembridge received his Ph.D. in 1985 from MIT. He spent three years as an E.R. Hedrick Assistant Professor at UCLA pri- “We’ve determined the basic building blocks that are needed or to joining U-M in 1988, and has held Sloan and Guggenheim to understand how E8 is represented in nature,’’ says Stem- Fellowships, as well as a Presidential Young Investigator award bridge. “This could lead to better understanding of the physical from the NSF. models of the universe.” He is recognized as a leader in the fi eld of algebraic com- Stembridge says the way the calculation was achieved—by binatorics, and has a special interest in representation theory, a group of 18 mathematicians and computer scientists working Coxeter groups, root systems, symmetric functions, and enu- in intensive collaboration for four years—also is a signifi cant meration, as well as in computational problems that arise in breakthrough. “Mathematicians more typically work in groups these areas. of one, two or three,” Stembridge says. “We have a large group spread all over the U.S. and in France. That is unusual.”

U-M DEPARTMENT OF MATHEMATICS 3 Faculty Achievements

Fomin Named Collegiate covery of cluster , made jointly for the fi nite simple groups. It was not Professor with A. Zelevinsky, has impacted several clear how to work with such a large, spe- areas of mathematics. cial fi nite simple group. On his 1979-80 Professor sabbatical from U-M at the Institute for Sergey Fomin Advanced Study, Griess found new theo- has been named Griess Elected to AAAS ries to manage the analysis. The group a Collegiate Professor Robert L. Griess was elect- was constructed as rational matrices in Professor in the ed a member of the prestigious American dimension 196883. A recent book by College of Lit- Academy of Arts and Sciences in April, Mark Ronan entitled “Symmetry and erature, Science 2007. The Academy honors distinguished the Monster, one of the Greatest Quests and the Arts. His scientists, scholars, and leaders in public of Mathematics” concerns the history professorship affairs, business and the arts. Fellows of simple groups and gives more details will be named in are selected about the sporadic groups for a general honor of Robert through a mathematical audience. M. Thrall, who highly com- was a U-M Mathematics faculty member The research of Professor Griess petitive process for 32 years. has involved the classifi cation of fi nite that recognizes simple groups, group cohomology, fi nite R. M. Thrall (1914-2006) joined U-M individuals aspects of Lie theory and algebraic group as an instructor in mathematics in 1937. who have made theory, nonassociative algebras, lattices He became Associate Professor in 1948 preeminent in Euclidean and vertex operator and Professor in 1956. He received the contributions to algebras. The 196884-dimensional alge- Henry Russel Award (1948-49) and the their disciplines bra associated to the Monster has taken Distinguished Faculty Award (1965). and to society on a life of its own, being known as the Thrall left Michigan in 1969 to become at large. Griess algebra. the founding chairman of Rice Univer- The AAAS citation notes that Griess sity's Department of Mathematical Sci- Griess received his Ph.D. from the is best-known for the construction of the ences. in 1971. He came Monster sporadic fi nite simple group. to U-M as a Hildebrandt Research In- Thrall began his career as an algebra- Construction was accomplished by structor in 1971, and was named Profes- ist, making seminal contributions to ring Griess, not only for the fi rst time, but sor in 1981. He received a Guggenheim theory, representation theory, and alge- also entirely by hand without the aid of Fellowship in 1981, presented an invited braic combinatorics. In the 1940s, he be- a computer. Discovery of this group has address at the International Congress of came interested in the emerging fi eld of touched science and mathematics very Mathematicians in 1983 and received discrete applied mathematics, and gradu- deeply. Connections have emerged with the Harold R. Johnson Diversity Service ally became a widely recognized scholar areas as diverse as string theory in phys- Award from the University of Michigan in operations research and management ics and, within mathematics itself, in very in 2003. The latter award was due to science. He was the President of the In- sophisticated number theory. his expanding the Mathematics Depart- stitute of Management Sciences (TIMS) In 1973, Bernd Fischer and Robert ment’s minority outreach program. Math in 1969-70, and received TIMS’s Distin- Griess independently found evidence for students and faculty hosted up to four guished Service Medal in 1985. In 2002, the existence of a sporadic group of order hundred middle school students annu- he became one of the inaugural Fellows 246 320 59 76 112 133 . 17 . 19 . 23 . 29 . 31 . ally in the U-M’s King-Chavez-Parks of the Institute for Operations Research 41 . 47 . 59 . 71 = 80801742479451287588 visitation program. This was the highest and the Management Sciences. 6459904961710757005754368000000000. level of academic unit participation at the Fomin received his Ph.D. in 1982 A sporadic group is a fi nite simple group University. from St. Petersburg State University in outside the known infi nite families (such Russia. He was a faculty member at MIT as classical groups over fi nite fi elds). The for 7 years before joining U-M in 1999 fi rst sporadic groups were the fi ve Ma- Lazarsfeld Named Collegiate as an Associate Professor, and was pro- thieu groups, found in the 19th century. Professor moted to Professor in 2001. During the period 1965-1975, twenty-one Professor Robert Lazarsfeld has been Fomin’s main research area is com- more sporadic groups were found. They named a Collegiate Professor in the Col- binatorics, especially its applications in exist because of special number-theoretic, lege of Literature, Science and the Arts. representation theory, algebraic geometry, combinatorical and algebraic accidents His professorship will be named in honor and other areas of mathematics. In recent or special situations. No single theory of Raymond Wilder, a member of the years, his research has revolved around explains them. A complete and well- UM Mathematics faculty from 1926 to cluster algebras, total positivity, and understood list of fi nite simple groups 1968 who did pioneering research in to- Schubert calculus. In particular, his dis- was important to classifi cation program pology, and was instrumental in bringing

4 CONTINUUM – 2007 the department to international promi- While at U-M, and previously at New Faculty nence. Wilder died in 1982. UCLA, Lazarsfeld directed 16 graduate After receiving his Ph.D. from students, several of whom are themselves Members in 1980, Lazarsfeld becoming leaders in the fi eld. He has was a Ben- been instrumental in developing a strong Assistant Professor Victoria postdoctoral program in algebraic geom- jamin Pierce Booth Instructor at etry, providing mentoring to some of the Harvard. He best young mathematicians starting their Booth came to U-M in 2004 on an joined the fac- careers at U-M. In 1999 Lazarsfeld was NSF ADVANCE ulty of UCLA the leader in designing and writing a grant award with a in 1983, and proposal to the National Science Foun- joint appoint- was promoted dation for a fi ve-year VIGRE (Vertical ment in Math to professor Integration of Research and Education) and Anesthesiol- there in 1987. program that provided $1 million per ogy. She will He moved to year in support for graduate students and continue her Michigan in 1997. Lazarsfeld won an postdocs. He continued as Director of joint appoint- AMS Research Fellowship in 1980, a VIGRE here, designing and administering ment on the ten- Sloan Research Fellowship in 1984, and program activities that were recognized as ure track within a fi ve-year Presidential Young Investiga- innovative by the NSF. More recently he the Applied and tor Award in 1985. He was awarded a was instrumental in securing a Research Interdisciplin- Guggenheim Fellowship in 1998, and Training Grant that will provide $2.5 mil- ary Mathematics program. Booth re- was elected to the American Academy lion over a fi ve year period. ceived her Ph.D. in applied mathematics of Arts and Sciences in 2006. In 2005 from Northwestern in 1993. She was Lazarsfeld was the Colloquium Lecturer a researcher at the National Institutes at the annual meeting of the American Esedoglu Receives Sloan of Health, and then joined the faculty Mathematical Society—the most dis- Assistant Professor Selim Esedoglu of the New Jersey Institute of Technol- tinguished series of lectures sponsored has been awarded an Alfred P. Sloan Fel- ogy. Booth studies mathematical and by the Society. Lazarsfeld has served lowship, an extraordinarily competitive biophysical modeling of the electrical on several editorial boards. Since 2002 award involving nominations of the very fi ring behavior of neurons. She develops he has been one of fi ve editors of the best young scientists from around the and analyzes models based on electro- Journal of the American Mathematical country. physiological data. The research entails Society (JAMS), the premier publication mathematical analysis of neural models using singular perturbation techniques, of the AMS, regarded as one of the most Mustata Receives Packard prestigious mathematics journals and re- bifurcation theory and methods of nonlin- Associate Professor Mircea Mustata cently ranked fi rst in terms of its impact ear dynamics. received a Packard Fellowship for Sci- on mathematics. He became managing ence and Engineering. These extremely editor of JAMS this year. competitive Fellowships, awarded an- Assistant Professor Volker Throughout his career, Lazarsfeld has nually by the David and Lucille Packard Elling been recognized as a leader in the fi eld of Foundation, recognize and support out- Elling received his Ph.D. from Stan- Algebraic Geometry. The fi eld uses geo- standing young scientists early in their ford University metric methods to study systems of poly- careers. Mustata is working on a project in 2005. He was nomial equations in several variables. using techniques such as spaces of arcs, a Prager Assis- In recent years, Lazarsfeld has focused D-modules or positive characteristic tant Professor on applying ideas and techniques from techniques to understand questions on of Mathematics higher-dimensional geometry to a num- invariants of singularities coming from at Brown Uni- ber of concrete algebraic and geometric the classifi cation theory of higher dimen- versity prior to problems. He and his colleagues have sional varieties. coming to U-M. helped to develop the theory of multiplier Elling's research ideals, which are playing an important is concerned with role in the geometry of higher dimen- Faculty Promotions the study of the sions. Lazarsfeld recently published a Peter Miller was promoted to Profes- partial differential two-volume monograph entitled Positiv- sor. equations which occur in the theory of ity in Algebraic Geometry, which sum- Anna Gilbert was promoted to Associ- gas dynamics. He has worked on numer- marizes research development in the area ate Professor wth tenure. ical computation of solutions, rigorous over the past 20 years. The books have Kristen Moore was promoted to As- mathematical analysis of numerical algo- already formed the basis for courses and sociate Professor wth tenure. rithms and on proving existence theorems seminars at several universities through- for solutions. out the U.S. and Europe. Divakar Viswanath was promoted to Associate Professor wth tenure.

U-M DEPARTMENT OF MATHEMATICS 5 Recent Ph.D. Recipients

Mahesh Agarwal completed the Sukmoon Huh completed the disser- Khachik Sargsyan completed the dissertation “p-L Function for GSp(4) tation “Moduli Spaces of Stable Sheaves dissertation “First Passage Times in the x GL(2)” under the direction of Chris on a Plane and an Embedded Curve” Near-Continuum Limit of Birth-Death Skinner. Mahesh will be a postdoctoral under the direction of Igor Dolgachev. Processes” under the direction of Char- fellow at McMaster University. Sukmoon will be a researcher at Korea lie Doering. Khachik will be a research Amy Bauer completed her dis- Institute for Advanced Study. postdoctoral fellow at Sandia National sertation “A Multi-Scale Cell-Based Paul Jeray completed his dissertation Laborary. Model to Simulate and Elucidate the “Explicit Matrix Representations for Type Matthew Smith completed his dis- Mechanisms Controlling Tumor-Induced D Coxeter Groups” under the direction of sertation “On Solution-Free Sets for Angiogenesis” under the direction of John Stembridge. Simultaneous Additive Equations” under Trachette Jackson. She will be a post- Rizwanur Khan completed the dis- the direction of Trevor Wooley. He will doctoral research associate at Los Ala- sertation “Non-Vanishing of the Symmet- be a postdoctoral instructor at the Univer- mos National Laboratory. ric Square L-function” under the direction sity of Georgia. Bryden Cais completed his dis- of Kannan Soundararajan. Rizwanur will Andrew Stein completed his disser- sertation “Correspondences, Integral be a NSF Postdoctoral Fellow/Hendrick tation “Mathematical Models for Glio- Structures, and Compatibilities in p-adic Assistant Professor at UCLA. blastoma Invasion in Vitro” under the Cohomology” under the direction of Hyekyung Min completed the dis- direction of Trachette Jackson. He will Brian Conrad. He will be a postdoctoral sertation “Stochastic Control Models of be a postdoctoral fellow at the Institute fellow at Centre de Reserches Mathema- Optimal Dividend and Capital Financ- for Math and its Applications. tiques in Montreal, Canada ing” under the direction of Joe Conlon. Janis Stipins completed his disserta- Mark Conger completed his disser- Hyekyung will be a postdoctoral fellow tion “On Finite k-Nets in the Complex tation “Shuffl ing Decks with Repeated at the University of California Santa Bar- Projective Plane” under the direction of Card Values” under the direction of Di- bara. Igor Dolgachev. He will be a software vikar Viswanath. Charles Mueller completed his dis- engineer at Google. Sarah Crown completed her dis- sertation “On the Varieties of Pairs of Ellen Veomett completed her disser- sertation “The Homology of the Cyclic Matrices Whose Product is Symmetric” tation “The Computational Complexity Coloring Complex of Simple Graphs” under the direction of Mel Hochster. of Convex Bodies” under the direction under the direction of Phil Hanlon. She Alvaro Pelayo completed his disser- of Alexander Barvinok. She will be an will be an Assistant Professor at Denni- tation “Symplectic Torus Actions” under assistant professor at California State son University. the direction of Alejandro Uribe. He will University. Hualong Feng completed the dis- be a NSF postdoctoral fellow at MIT. Kevin Wildrick completed his dis- sertation “Vortex Sheet Simulations of Feng Rong completed his dissertation sertation “Quasisymmetric Parameter- 3D Flows Using an Adaptive Triangular “Critically Finite Maps, Attractors and izations of Two-Dimensional Metric Panel/Particle Method” under the direc- Local Dynamics” under the direction of Spaces” under the direction of Mario tion of Robert Krasny. Hualong will John Erik Fornæss. He will be a postdoc- Bonk. He will be a postdoctoral research be an instructor at Huaihai Institute of toral fellow at Syracuse University. fellow at the University of Jyväskylä. Technology in China. Eric Zupunski completed his dis- sertation “A Bound on the Complexity of the JSJ Decomposition in the Bounded Case” under the direction of Peter Scott.

Professor Juha Heinenen with (l-r) Kevin Wildrick, Mark Conger and Feng Rong at the Mathematics Awards Ceremony.

6 CONTINUUM – 2007 2006-07 Graduate Program Fellowships & Awards

Alice Webber Glover Math Fellowships Mathematics Scholarship Fund Hannah Robbins Taeyong Ahn Nicholas Rupprecht Susan Sierra Xueying Hu Joe Stubbs Wansu Kim National Physical Science Consortium Kevin Tucker John Mackay Fellowship Research Training Grant (RTG) Marie Snipes Arthur Herbert Copeland, Sr. Geometry Memorial Scholars National Defense Science and Jasun Gong Russell Golman Engineering Graduate Fellowship Christopher Hammond Diane Vavrichek Darragh Rooney Brian Wyman Marshall Williams Cameron & John Courtney National Science Foundation Fellows Scholarship 2006 Sumner B. Myers Memorial Prize David Constantine for the Best Thesis Nathan Totz Ellen Veomett Crystal Zeager Yann Bernard Natural Science & Engineering Samuel Payne CONACYT Fellowship Research Council of Canada Gerardo Hernandez Scholarship Graduate Departmental Scholarship Spring 2007 Luis Serrano Fulbright Scholarship Xinyun Sun Clara Blakelock Richard Vasques Henry Boateng Rackham International Fellowship Kelli Carlson Sohhyun Chung G. Cleaves Byers Endowment Zhengjie Xu Jiarui Fei Brian Jacobson Jose Gonzalez Craig Spencer Rackham One-Term Dissertation Mark Iwen Hao Xing Fellows Stephanie Jakus Sara Heusel Fidel Jimenez Lucent Fellowship KyungYong Lee Paul Johnson Giancarlo Urzua Shin-Yao Jow Ellen Eischen Brian Jurgelewicz Rackham Predoctoral Fellows Hyosang Kang Luther Claborn Mathematics Fellow Bryden Cais Daniel Kneezel Kyle Ormsby Alvaro Pelayo Marc Krawitz Cagatay Kutluhan Mathematics Alumni Scholarship Rackham Science Award (RSA) Michelle Lee Eugene Einsenstein Michael Lieberman Jonathan Bober Ashley Selegue Victor Lozovanu Aubrey da Cunha Lindsey Selegue Aaron Magid Oscar Gernandez Ray Maleh Tamara Flournoy Mathematics Department Graduate Gregory McNulty Daniel Hernandez Fellowship Ajinkya More Ricardo Portilla Tomoki Ohsawa Catherine Dupuis Felipe Ramirez Jordan Sahattchieve Timothy Ferguson Chelsea Walton Leo Goldmakher Alan Stapledon Elizabeth Twentyman Geri Izbicki Regents’ Fellowship Brian Jennings Giancarlo Urzua Johanna Mangahas Harlan Kadish Liz Vivas Ryan Kinser Ting Wang Austin Shapiro Research Training Grant (RTG) Emily Witt Paul Shearer Algebra Szymon Wojczyszyn Benjamin Weiss David Anderson Qian Yin Nina Shite Kyle Hofmann Hsu-Wen Young Yogesh More

U-M DEPARTMENT OF MATHEMATICS 7 Congratulations to our 2006-07 Mathematics Bachelor of Arts/Science Degree Recipients

Mohd Abd Rahim Ryan Edgar David Kalita Betty McColor Rachel Snider Heather Abraham Brendon Eisner Arman Kayupov Kyle McGuffi n Jiesi Song Ruchir Agarwal Keary Engle Noora Kazanji Timothy McMillen Elena Spatoulas Matthew Arnold Anthony Fader Jacob Ketchum Caitlin McNicholas Nathan Stiennon Thomas Babinec Ryan Fisher Muhammad Khairir Rebecca McQuillan Joseph Stierman Emily Beam Benin Fitzpatrick Katherine Kiefer Michael Miller Ethan Street Matthew Becker Hau Voon Foo Andrew Kirchner Ruth Miller Brandon Strom Marc Bell Ashley Frazier Melinda Kleczynski Alexander Mirkin Zachary Szpiech David Benjamin Jujhar Gahley Nicole Klever Rohin Moza Ya-chin Tang Stephanie Bercaw Yuan Geng Wei Heong Koh Alexander Nagle Cameron Thomas Daniel Blazevski Jennifer Gerber Robert Kovats Danny Ng Ernest Travis Janai Brodnax Joseph Golden Esha Krishnaswamy Mui Keng Oh Stephanie Trezza Bradley Bykowicz Varun Gupta Sudono Kusuma Jeffrey Parker Gina Uhrich Richard Chang Melissa Halfon Lakeita Larkins Anthony Pinter Elisabeth Uible Thomas Choi Thomas Halvorson Edward Lee Nicholas Posavetz Alison VanDerKolk Mi Ra Cho Christopher Hankinson Jaekeun Lee Rupert Pun Nathan Wade Yen Leng Chua Adam Hanlon Ji Hyun Lee Ethan Rein Julie Waldman Andrew Clark Shannyn Hart Sean Lenhard Danielle Rogers Allen Weiss Andrew Coleman Christine Henderson Lisa Lentz David Sabatini Richard White Aalok Dave Daniel Hidlay Wing Ki Leung Hanis Syahrilla Salim Tiffany Wong Fernando Delgado Salas Lisa Huey Fang Lim Ryan Scharwath Erin Wood Michael Dobbs Ashley Hovenkamp Kevin Ly Geum Chu Seo Lindsey Worcester Andrew Douglass Joe Hsieh John Madonna Marc Sherman Natalie Wowk Jeffrey Druce Ann Hughes Christopher Marsh Liza Shiffman Zhenghao Wu Julie Inwood Laura Matney Paul Siegel Lin Ye YuanYuan Jiang Joshua Maurice Daniel Sikora John Yoon Michael Mayhew Nicole Smith Ahmad Idzuddin Yusuf Noah Smith William Zasadny Meng Zhong

Clockwise from top left: Professor Stephen DeBacker with Allison Frayer; Paul Siegel with Professor Stephen DeBacker; Professor Harm Derksen with Jeffrey Madsen; Professor Curtis Huntington with Voon Seng Lai; David Benjamin with Professor Harm Derksen.

8 CONTINUUM – 2007 2007 Undergraduate Award Recipients

The Department’s team for the Paul Siegel received the Leon P. The Otto Richter Memorial Prize William Lowell Putnam Mathemat- Zukowski Prize for outstanding service in Actuarial Science was presented to ics Competition placed 22nd out of 401 in the Mathematics Learning Center (for- Wei Heong Koh. teams in the event. This year’s team was merly known as the MathLab). The CIGNA Award in Actuarial comprised of Fernando Delgado Salas, Science was presented to Kai Kiat Timothy Heath and Jeffrey Madsen. The William LeVeque Award in Chooi. The individual competition included Number Theory was presented to Zach- The Irving Wolfson Award in 3640 students from across North Amer- ary Maddock. The award recognizes a ica. Timothy Heath placed the highest Actuarial Science was presented to student who is at most a junior and excels Voon Seng Lai. of UM students at 140. David Benjamin in the study of number theory. and Jeffrey Madsen also fi nished in the The Lois Zook Levy Memorial top 200. The Sumner Myers Award in Anal- Award was presented to Rachel Snider. ysis was awarded to Richard William th The award recognizes an outstanding The winner of the 24 Annual Uni- Turner. versity of Michigan Undergraduate Mathematics student who plans to pursue Mathematics Competition was Jeffrey Outstanding Achievement in Math- a career in K-12 Mathematics education. Madsen, who also won last year. Timo- ematics Awards went to the following The following students were named thy Heath placed second and Zili Huang seniors: Michigan Mathematics Merit Schol- came in third. Thomas Babinec ars: The following students received Emily Beam Fernando Delgado Salas Mathematics Alumni/Alumnae Schol- Matthew Becker Melinda Kleczynski arships for the 2006-07 academic year: David Benjamin Nathan Stiennon SeHyoun Ahn Daniel Blazevski Zachary Maddock Andrew Clark Michael Miller and Ethan Street were named the Outstanding Graduat- Wei Heong Koh The following students received ing Seniors. Huey Fang Lim Evelyn O. Bychinsky Awards, which Kevin Wilson received the Wirt and recognize underclass students who show Rupert Pun Mary Cornwell Prize, recognizing a exceptional promise in mathematics: Noah Smith student who has demonstrated the great- est intellectual curiosity, given the most SeHyoun Ahn Richard White Sam Espahbodi promise of original study and creative work in math, and also shows an interest Allison Frayer in music. Timothy Heath Jeffrey Madsen

The following students received Margaret S. Huntington Awards in Actuarial Outreach: Hui Ying Chin Athena Eyster Su Jane Ling Johnson Mei Philip J. Minaudo Steven Moses Meelap Shah Rebecca Sunde Tiago Szvarca Wan Ying Teoh Professor Curtis Huntington with Margaret S. Huntington prize winners Wan Ying Teoh, Meelap Shah, Hui Ying Chin, Athena Eyster, Su Jane Ling and Steven Moses.

U-M DEPARTMENT OF MATHEMATICS 9 Inquiry Based Learning at Michigan

Linear algebra MATH 372. East Hall help of experienced instructors and 931 at 9 am: The students gather for assistants. Actual implementation their class. Professor Algamma enters, of this technique varies greatly. The returns work, states today’s topic, and goal however is always the same: slowly and carefully proceeds with stat- get the students to think and under- ing the theorem of the day and explaining stand mathematics on their own, its meaning. Then Professor Algamma with the help and guidance of the gives its proof. Possibly an application instructors. To achieve this goal, follows. Once in a while a brave student we use enriched homework sets, asks a question which gets a brief answer. group work both inside and outside This is your typical good math class. of class, experimentation with com- Most learning happens when students do puters in a lab as tools. Interaction their homework and try to use the ideas between the students, and with the and tools they heard about in class. It’s instructors is crucial. To make this a good way to learn and excellent at possible, we often have assistants transmitting lots of information. How- help teach these classes. The nu- ever, it's a very passive way of learning, merous benefi ts include increased and provides little opportunity to train availability of instructors and train- in mind. The students are not told pre- mathematical and more generally ana- ing of postdoctoral fellows and graduate cisely what to compute or to prove. This lytical thinking. Real understanding of students in this learning method. class is modeled after one taught by Pro- concepts often falls behind the learning We currently offer fi ve classes in fessor (MIT) who taught of particular techniques. While the latter our IBL program. They are directed at it here while on sabbatical. MATH 389 is important, especially for applications, a wide range of interests: MATH 175: has been very well received, and serves it is really the proper understanding of introduction to Cryptology is a Freshman as a bridge to our undergraduate research the concepts that will allow for creative Seminar. Students learn about encrypting program during the summers. applications of the tools. This is particu- techniques, and en route about various Longer term plans include expansion larly true in this day and age of sophis- number theoretic and combinatorial ideas. of our course offerings at all levels. Ev- ticated computer programs that can do It is widely popular to the extent that we ery mathematics major should be able to even complicated mathematical tasks in are offering two sections this Fall semes- take one of these classes to get the expe- a split second. Understanding the mean- ter. MATH 351: Principles of Analysis rience of thinking mathematics at a high ing of the concepts behind these tech- is a core class for math majors about the level. We also hope to offer a critical niques, what they do for an application, underpinnings of calculus. It is heavily mathematical thinking class to non-math is becoming more and more important. concept oriented and ideal for the IBL ap- majors so that they are better equipped to As an antidote, the Department has proach. Two of these classes, MATH 385 understand important mathematical ideas invested in an alternate way of learning, and MATH 489, are for future elementary and phenomena. Mathematics enters to- Inquiry-Based Learning (IBL), that will and middle school teachers. day's world in a myriad of ways, and our supplement our many traditional classes. Our most experimental and thorough- students need to be educated. Besides About three years ago, the Department ly IBL class is MATH 389: Explorations teaching IBL classes, the Center is heav- started its Center for Inquiry Based in Mathematics. Students at all levels ily involved in training future teachers in Learning. It is one of fi ve national cen- work on open ended yet accessible prob- these methods. The Department has the ters of this kind which were established lems in groups of three or four students. largest postdoctoral training program in with initial funding from foundations, The course shows the students how new the country, and one of the largest gradu- private sources and the universities mathematics is actually created: how to ate programs. Our former students and involved. Other centers are at the Uni- take a problem, make models and guesses, postdocs teach at all levels in universities versity of Chicago, , experiment with them, and search for and colleges throughout the country, and the University of and UC Santa underlying structure. It is suitable for stu- will surely take their IBL experiences Barbara. dents at many levels. This course serves with them. IBL classes engage the students in also to develop useful skills, including Professor Ralf Spatzier ways not normally seen in a typical un- how to write and typeset a math paper, IBL Director dergraduate course. They use discovery, making an oral presentation, and comput- analysis, and investigation to gain so- ing with a mathematics software system such as Mathematica or Maple. The prob- Visit the IBL Website at phisticated understanding of the subject http://www.math.lsa.umich. matter and its applications. Students lems display interesting phenomena, but learn through guided exploration with the do not necessarily have a particular result edu/ibl/index.html

10 CONTINUUM – 2007 Actuarial Program News A Family Actuarial History at U-M Enrollments in both Actuarial Mathematics and Financial Mathematics classes con- tinue at record rates as the number of students declaring these subjects for their major Weltha McLachlan studied math- grows. As a result, all of our classes are running at full capacity and whenever we add ematics and graduated from the Uni- a new section, it fi lls up very quickly. As an example, we have more than 50 students versity of Michigan in 1918. She then enrolled in the core Actuarial Mathematics class (Mathematics 520) in the Fall 2007 became a qualifi ed actuary, married semester. Neil Van Eenam, and in 1936 became To accommodate all of this growth, we continue to welcome new faculty members. the fi rst staff actuary of the newly Last year, Ahmet Duran, Ph.D. (Pittsburgh) and Semih Sezer, Ph.D. (Princeton) joined enacted Social Security system, from the fi nancial mathematics faculty as postdoctoral fellows. In the Fall, 2007, Joseph which she retired in 1959. Marker, FCAS joined the actuarial mathematics faculty as the Carl H. Fischer Visiting Mrs. Van Eenam’s daughter, Professor, and will begin developing courses in the property and casualty insurance Marjorie, also studied mathematics area, an area that we have long hoped to cover more fully. Marker’s career spans over and graduated from the University of thirty years as a practicing actuary. He was Vice President and Chief Actuariy for Michigan with a BA in 1947 and an Citizens Insurance, and Senionr Vice President and Chief Actuary with Pronational MA in 1949 in (actuarial) mathemat- Insurance Company. Most recently he was the visiting Lincoln National Group Distin- ics. She married a fellow graduate guished Professor of Actuarial Science at Ball State University, and a private consul- student, Robert W. Butcher, and they tant through Marker Actuarial Services. both became qualifi ed actuaries—at Using the Weltha McLachlan Van Eenam Memorial Fund, established by Marjorie the time, a relatively rare occurrence. Van Eenam Butcher and her late husband, Robert W. Butcher, A. Haeworth Robert- Weltha and Marjorie became the fi rst, son delivered an address to a joint meeting of the Michigan Actuarial Society and the and so far only, mother-daughter pair Student Actuaries @ Michigan in April 2007. Mr. Robertson, a former Chief Actuary of actuaries in the U.S. of the Social Security Administration titled his address “Uncommon Perspectives on Bob Butcher went on to a 31-year Social Security and Medicare.” The acknowledgment for this address gives a fascinat- career at The Travelers Insurance ing history of the individuals involved and, once again, reinforces the extraordinary Companies in Hartford, CT. Marjorie impact of the Michigan Actuarial Program over the years (see column at right). Copies had a 33-year career at Trinity Col- of Robertson’s address are available from my offi ce upon request. lege (Hartford) teaching mathematics In 1963, Susan Smith graduated, with $75, from the U-M actuarial program and (including actuarial advising) and be- went on to a career at Towers, Perrin. She has recently given $1.5 million to establish came its fi rst-ever female teacher and the Susan Meredith Smith Professorship in Actuarial Science (see story on page 16). female full professor. This creates the third endowed faculty position in Actuarial Mathematics in the De- While the two were graduate partment (the others being the Nesbitt and Fischer professorships) and will allow us to students, both before and after their add strength to our program as we recruit new faculty. Ms. Smith also gave the fi rst marriage, Bob and Marjorie taught Nesbitt Commencement address fi ve years ago. actuarial mathematics at Michigan. Our April 2007 Cecil J. Nesbitt Commencement Lecturer was Gabriel L. Shaheen During 1951-53, one of their students (BA 1976, MAS 1977), Principal, NxtStar Ventures LLC. His message of listening was Haeworth Robertson (see article well and getting along with people as you continue learning and serving the public was at left). In his career, Robertson well-received by an enthusiastic audience of this year’s graduates (and their families). continued Weltha McLachlan Van Ee- This was the fi fth event in this series and is rapidly becoming a highlight of the actu- nam’s work with the Social Security arial academic year. Administration. The student-run club renamed themselves as the Student Actuaries @ Michigan (or SAM) a year ago. SAM maintains an active schedule of academic, sporting and social events. With more 100 members, this group is rapidly becoming one of the more ac- tive academically-focused groups on campus. This past year, CNA in Chicago hosted an on-site visit for members of the club as we continue to seek ways to expand the ca- sualty aspects of the profession. A meeting of the Actuarial Alumni/ae Leadership Council is scheduled for October of this year and we are looking forward to meeting the members and discussing future directions for the Michigan Program. The faculty and students look forward to hearing from you with any comments, questions or suggestions you might have. And, if your travels bring you through Ann Arbor, please let us know so that we can host a visit with us in our East Hall home.

Curtis E. Huntington (BA 1964, MAS 1965), FSA, FCA, MAAA, APM Marjorie Van Eenam Butcher Professor of Mathematics (photo courtesy of Trinity College) Director, Financial & Actuarial Mathematics Programs, Director MPET Program

U-M DEPARTMENT OF MATHEMATICS 11 In Memoriam

Professor Bob Bartels ment of Computer Science education and recognition and directed the thesis Robert C. F. Bartels was a Professor and research. Important advances in work of numerous doctoral students. Emeritus of Mathematics at the Univer- programming languages and operating Tom is most remembered in the sity of Michigan and retired director of systems were nurtured in the computing Mathematics Department as an outstand- the University of Michigan Computing environment he established. Bartels was ing teacher and counselor who inspired Center. Bartels was born the second of also responsible for organizing an impor- his students and left a lasting impres- three sons to German immigrant parents tant series of short courses and lectures sion. He was a dedicated instructor for in New York, and he grew up in humble during a 15-year period with the U-M Honors Calculus for many years. His surroundings both in Brooklyn and in Engineering Summer Conferences in the courses were among the most rigorous, rural New York. His mother’s strong late 1950’s and early 1960’s that encour- and his distinctive teaching style, coupled will that her children should be educated aged some important early developments with great intellectual excitement, drew led to the three brothers each earning a in the theory and software for computer students to his classes. In recognition Bachelor’s degree, Robert Bartels’ de- mathematics. of his teaching skills, he was awarded gree being in engineering. In 1978, when he retired, he took the Amoco Foundation Good Teaching Because of his training, he was able up an interest together with his wife Award in 1985. to fi nd a position as a junior technician in American Art Glass, and during the Tom also had a great impact on stu- with Bell Telephone Laboratories in New course of the next 20 years they es- dents in his role as an undergraduate Jersey, a prize of some consequence tablished an impressive private glass counselor in the Honors Program, a posi- during the Depression. When Bell insti- collection, guided by the considerable tion he held for 32 years. It was in that tuted a program of educational support historical knowledge of American Art role where his integrity, sensitivity, pa- that offered people at his rank the op- Glass that they acquired. Robert Bar- tience, and empathy for students enabled portunity to return to college and earn a tels departed peacefully in his sleep at him not only to guide them academically, post-graduate degree, he took advantage the Swan Creek Retirement Village in but also to help them become well- of this to enter the graduate program in Toledo, Ohio, on the night of Septem- rounded individuals. He touched the electrical engineering at the University ber 9, 2006. He is survived by his wife, lives of students in many fi elds, and is of Wisconsin in Madison. Unfortunately Virginia; by his sons, Richard (Renate) well remembered as a strong infl uence in for Bell, he dropped into a mathematics Bartels and Albert (Jacqueline) Bartels, their lives. “Tom Storer took a personal lecture one day on the advice of a friend, by his grandchildren, Robert, Adrienne, interest in his students’ lives; you knew became interested in what he saw, and and Ainslee; by his great-grandchildren, it was genuine even if you never had changed his major. Ziggy, Ansel, and Isabel and by numer- the pleasure of meeting him outside the ous nieces and nephews. In 1938 he earned a Ph.D. in math- classroom,” writes Susan Kolodziejczyk ematics, married Virginia F. Terwilliger, (BA 1993, Senior Researcher, National of Madison, Wisconsin, and accepted Professor Tom Storer Geographic Society). “Anywhere you his fi rst academic position at the Univer- Thomas F. Storer, Professor Emeri- found him—in his offi ce, on a bench in sity of Michigan. From that year until tus of Mathematics in the College of the sun, at a favorite corner of the Brown the summer of 2006, with a time-out in Literature, Science and the Arts, passed Jug—he welcomed every smiling face.” World War II to work on research with away on November 9, 2006. It has been said that Tom was always the Navy in Washington DC, he has been A familiar face on campus for 35 teaching. He himself left the follow- a resident of Ann Arbor and a Profes- years, Tom was one of the fi rst Native ing legacy on his door upon retirement: sor of Mathematics (active or retired) Americans to receive a Ph.D. in math- “From where the sun now stands, I will with the University of Michigan. In late ematics. He joined the University of teach no more forever.” Besides math- 1958, when the University of Michigan Michigan faculty as a T.H. Hildebrandt ematics and the honors program, Tom planned to move its small computer Research Instructor in 1965 after receiv- was an educator in U-M courses on Na- operation off campus and discontinue ing his M.A. and Ph.D. degrees from the tive American culture and the Ojibwa general computer access to students and University of Southern California, and language. faculty, he embarked on a successful a B.A. degree from the University of Robert Megginson, Professor of campaign to reverse this decision and California at Los Angeles. He was pro- Mathematics and Associate Dean for to establish a viable central computing moted through the ranks to Professor in Undergraduate and Graduate Education facility to support teaching, research, and 1979. Tom’s research area was primar- in the College of Literature, Science, and administration. He became the Comput- ily in combinatorics, more specifi cally the Arts, remembers Tom fondly. “Tom ing Center’s fi rst director in 1959 and cyclotomy. His monograph “Cyclotomy was a remarkable individual who cared remained at its helm until his retirement and Difference Sets” (1967) became a deeply about students. In my travels I in 1978. During that time he actively standard reference. He also conducted re- have found it amazing how many former promoted the University’s develop- search in modeling of long-term memory U-M students, American Indians and others, will fi nd out that I am a U-M

12 CONTINUUM – 2007 mathematician and then tell me of the difference Tom made in their lives and Share Your Stories careers. We have lost one of our great educators and mentors, and he will be Did you know that the fi rst math classes were taught at U-M sorely missed.” in 1841 by Reverend George P. Williams? Which member of For many years, Tom was the prin- the U-M Department of Mathematics faced charges from the cipal faculty spokesman for Native House Unamerican Affairs Committee in the 1950s, and was Americans. He worked closely with the dismissed from the University because of it? How did a “se- U-M and Ann Arbor Native American cret” weekly meeting of faculty members evolve into the Math- community. His commitment to diver- ematics Colloquium? sity and dedication to promoting equity You can fi nd these and other fascinating historical informa- and justice for all people was refl ected in tion on our newly established history webpage www.math.lsa. his receipt of the Dream Keeper Award. umich.edu/information/depthistory.shtml. We have recently Throughout his life, Tom shared his love begun in earnest to collect and share some of our Department’s and knowledge of string fi gures from history. Over the years many documents have been written around the world and became a leading about the educational, scholarly, administrative and research authority. He pursued many different activities of U-M mathematics, and we invite you to share the athletics during his lifetime, and taught history. several Mathematics Department mem- Beyond the facts, fi gures and remembrances of faculty bers to play tennis. He had a deep love members, the history of the Department is contained in its stu- for freestyle Frisbee, and displayed his dents. We are interested in your memories of your time as a prowess regularly on the Diag. His Dal- student. What impressed you about your fi rst or hardest math matians were his constant companions. class? Did a discussion during a seminar help to establish the Tom leaves behind his wife, Karen; direction of your signifi cant research? Who were your most children, Eileen (Charles) Storer Smith memorable instructors? Do you have a story about one of the and Jeannie (Trevor) Thrall; mother, faculty members that might enlighten others to their spirit? Betty Tauer; and six grandchildren. He How did they help shape your educational career and infl uence will always be remembered as being a your life? Do you have a story about Tom Storer, Maxwell true “Renaissance Man” fi lled with deep Reade, T.H. Hildebrandt, George Piranian, or any other Depart- passion and joy. Several years ago, a ment member that stands out in your memory? fund was established in the Department Don Lewis (PhD 1950) recounts this story about the fi rst of Mathematics in Tom’s name. The course he had with T.H. Hildebrandt: “He had given us our Thomas F. Storer fund supports math- second problem set, and I noted that one problem was false, ematics honors program and its students. it didn’t make sense. When I told him about it, Hildebrandt Donations can be sent to the Department giggled and scratched his head. Then he said ‘There’s a true of Mathematics, University of Michigan, theorem there somewhere, go fi nd it and prove it!’” Ann Arbor, MI 48109-1043. Please send us your remembrances and we will make an effort to share them with others. We will include a history col- umn in this newsletter. We will also fi nd a spot on our website to include memories from alumni. The newly designed enewsletter Michigan Today is also seeking your stories. You can share them on this website http:// michigantoday.umich.edu/heritage.php. Math Problem Honors Math Students from the A UFO lands at a random spot on a large square, ‘50s, ‘60s, and 70s which is paved with square tiles of size 1ft × 1ft. If you took the 90s sequence of Honors Math The UFO leaves a disc-shaped burn mark of ra- during that era, we’d like to hear from you. If you dius 10ft. What is the expected number of tiles are interested in getting together for a reunion to discuss the trials, tribulations and triumphs of that have to be replaced because they are dam- honors math students, please contact the math aged by the UFO? department at [email protected], (Answer elsewhere in the newsletter) or Don Lewis at [email protected]. We’d love to hear from you!

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 June 1, 2006 and September 1, 2007

Financial Mathematics Development The David & Kitty Hartman Fund Ms. JJ Lane Carroll Fund Mr. and Mrs. David G. Hartman James and Patricia Case Mr. Marc N. Altschull Mr. and Mrs. Samuel L. Chappell Mr. and Mrs. David G. Hartman Mathematics Department Special Fund Miss Lorraine A. Chorkey Miss Linda Marie Clark John L. Marakas Dr. Judith M. Arms Dr. Todd E. Cochrane Gregg A. Schwab R. James Bennett Mrs. Lee S. Cooper Dr. Yue Wang Mr. Trevor J. Fast Dr. Bruce Nathan Cooperstein Paul and Ruthann Weiss Anjela and Vincent Govan Natalie and George Creed Laura and Leo Kornfeld Philanthropic Dan and Gail Dall’Olmo Margaret S. Huntington First Year Fund Fazli Datoo and Yasmin Kassam Actuarial Scholarships Dr. George A. Kozlowski, Jr. Dr. Sandra J. DeLoatch Mr. and Mrs. Herald Hughes, Jr. Dr. William E. Lakey Richard W. Dernberger Professor Curtis E. Huntington Lannen Investment Trust Susan J. Devencenzi William and Carolyn J. Lucas Mr. Robert V. DeVore Inquiry Based Learning Mr. and Mrs. David T. Morrison Henry Albert Dihm, Jr. Dr. Albert E. Nordgren Mr. Harry Lucas, Jr. Mr. Spencer Dowdall Mr. Matthew A. Posthuma Ms. Nancy J. Dynes Dr. G. Robina Quale-Leach Mathematics Strategic Fund Ruth Engel and Zevi Miller Ellen R. and Richard G. Racusin Elsbeth T. Falk Pamela and Harvey Allen Dr. David A. Sanchez Dr. Arnold D. Feldman Thomas M. and Sallee M. Anderson Michael Sattinger and Ulla Jensen Dr. Eitan Moshe Fenson Mr. and Mrs. C. Philip Bartlett Ms. Mary A. Savas Dr. Vincent J. Ferlini Dr. and Mrs. Denis L. Bourke Mr. and Mrs. Richard A. Scabich David and Susan Flesner Alfred and Elizabeth Bown Mr. David A. Scott Dr. Robert Samuel Fortus James and Yvonne Bray Victor L. Smith Dr. C. Allan Foy, Jr. Timothy and Teri Buchowski Charles and Marianne Snygg Michael L. Frank Mr. Kelly D. Clevenger Mr. Thomas E. Stolper Judy and Mark Gavoor Dr. Bruce Nathan Cooperstein Drs. Emil and Judith Sunley John T. Glass Gene and Luci De Fouw Professor B. Alan Taylor Roberta and Thomas Glassman Dr. C. Allan Foy, Jr. Dr. Gerald L. Thompson Jonathan and Barbara Glauser Denise Yee Friedrich Lee Lynn Zia Dr. and Mrs. David M. Gay Mrs. Suzanne D. Goodrich Mr. Dale L. Haakenstad Mr. William H. Hooben Michigan Math & Science Scholars Charles D. and Sharon J. Wall Dr. Robert C. Hagwood McLaughlin Harold and Sheila Cumberworth Thomas J. Haines Michael J. Merscher Martha and Robert Hanna Michael and Katherine Plantholt Mathematics Alumni/Alumnae Mr. and Mrs. John A. Hartman III Dr. Cris T. Roosenraad Scholarship Fund Cathy and Robert Helton Dr. Donald E. Sarason Dr. Judith M. Arms Drs. Thomas and Carol Herbig Anne and Mitchell Saywitz Dr. Bernice L. Auslander Dr. Jeffrey A. Furst Hittinger Elena and Ronald Schauer Matthew Ryan and Dorothy Bambach Charles and Susan Holmes Mark and Anelly Schwab Felice D. and Paul T. Bateman Merrill Hudson Dr. Thomas W. Shields Michael L. Beeson Dr. and Mrs. Fredrick W. Humburg Kathleen Marie Trock Living Trust Steven and Cheryl Bennett Gudmund R. and Roberta R. Iversen Dr. Nianqing Wang Mr. Jacob Bernstein Charles and Geraldine Keene Mr. Charles A. Weibel Bradley J. Biggerstaff Mary A. Kelly William P. & Suzanne R. White Fund Mr. Craig J. Blumenfeld Dr. Eduard-Wilhelm Kirr Mrs. Margaret M. Bondarew James T. and Pamela Kohan Michigan Pension Education Training Steven J. Bowman Dr. George A. Kozlowski, Jr. Program Dr. and Mrs. Laurence R. Boxer Melanie and Phillip Kraft Kay Kuenker ASPPA Pension Education Research Ruth and Stanley Briggs David L. Kuniansky Foundation, Inc. Mr. Andrew I. Brown

14 CONTINUUM – 2007 Michael M. and Linda Kurpinski Dr. Ruth E.M. Wong Allotta Family Scholarship Fund Jonathan L. and Lourdes U. Wooley David and Cathie LaBeau Allotta Family Foundation Dr. Maureen Lahiff Susan Meredith Smith Professorship in June and Patrick Lee Cecil J. and Ethel M. Nesbitt Actuarial Sciences Ms. Wendy Lichtman Professorship Naomi Gurt Lind and William Lind Ms. Susan M. Smith Rose M. Lowe Mr. and Mrs. Clay Richard Cprek Howard and Marjorie Fosler John L. Marakas Leon Zukowski Prize Mr. David C. Marty Sam and Peggy Gutterman Professor Emeritus and Mrs. James M. Donald E. Masters Mr. and Mrs. John B. Kleiman Kister Ms. BeLinda I. Mathie Karen Olsen MacDonald Dr. Ernst W. Mayer W. James and Barbara MacGinnitie Leonard Rand Fund Edmund B. McCue Jeffrey S. Paciero Mr. and Mrs. Stephen McGrath Stone/Rand Philanthropic Fund Mr. and Mrs. Jerome M. Powell John D. McKenzie, Jr., Ph.D. James and Ann Richhart Mr. Kelly K. Miller Professor Emeritus Thomas Storer Jack and Marguerite E. Seigel Mr. Kurt M. Miller Fund Mr. and Mrs. Clifford R. Simms Mr. and Mrs. Donald R. Sondergeld Zevi Miller and Ruth Engel Professor Anthony M. Bloch John and Earlene Taylor W. Reynolds and Diane Monach Professor Joseph G. Conlon Wendell C. True Professor M. Susan Montgomery Professor Brian D. Conrad William D. Ward Charles and Sonya Moore Professor Peter L. Duren Louis and Rosalyn Weisz David and Carrie Morton Professor Daniel B. Forger Dr. and Mrs. Rogers J. Newman Professor William E. Fulton Irving S. Wolfson Fund Ms. Kristin M. Newton Thomas J. Hansen Brad and Rebecca Osgood Professor Robert Krasny Michael P. and Susan W. Bowden Harriet Parsons and John Brundage Dr. William. J. LeVeque James and Edith Wolfson Mr. Michael L. Quinn Professor Emeritus Donald J. Lewis Dr. Lester M. Wolfson John G. and Susan K. Ratcliffe and Carolyn Dana Lewis Mr. and Mrs. Peter Rothmaler Professor and Mrs. Robert Megginson Carl H. Fischer Fund Thomas and Carrie Ruehle Professor Emeritus M.S. Ramanujan Jane and Dan Arnold Betty Salzberg and Lawrence Morris Professor Peter Scott Miss Lynn J. Sapoff Professor B. Alan Taylor Mathematics Special Endowment Dr. Donald E. Sarason Professor Divakar Viswanath Drs. Jean A. Lawton and James H. Mr. Joseph M. Saunders Professor David J. Winter Ellis Mark and Anelly Schwab Mrs. Gloria M. LaPontney Thomas and Maryellen Scott Professor Emeritus Maxwell Reade Lisa Sensat Fund Sumner B. Myers Memorial Prize Fund Professor Alan Shuchat Professor Hyman Bass Janine and Jonathan Silver Professor Stephen M. DeBacker Professor Anthony M. Bloch Dr. Stan Stahl Professor Ralf Spatzier Professor Brian D. Conrad James and Ann H. Stasheff Professor Stephen M. DeBacker Mr. Elliot M. Steiner Allen L. Shields Memorial Fellowship Professor Igor V. Dolgachev Dr. Clarence F. Stephens Professor Peter L. Duren Dr. Ward D. Bouwsma Melbourne and Nancy Stewart Professor Daniel B. Forger Gerald and Barbara Cargo Wen-Kuan Sun Professor Emeritus Peter G. Hinman Dr. Wayne Carter Ellis Dr. E. Ramnath Suryanarayan Professor Curtis E. Huntington Alan Kaufman and Iris Lopez William and Sally Sutcliffe Professor Emeritus Wilfred M. Kincaid Dr. Yuk J. Leung Dr. Khyson Swong Professor and Mrs. James M. Kister Mr. and Mrs. Clayton Timmons Jean and Ronald Tidball Professor Robert Krasny Dr. Smilka Zdravkovska John R. Tomlinson, Jr. Dr. William J. LeVeque Mrs. Ching-Shung Tu Professor Gopal Prasad Ms. Angela M. Valdick Professor Emeritus Frank A. Raymond Philip and Carolyn VanDecar Mrs. Pat Shure Ms. Susan E. Veach Professor John Stembridge Mr. James A. Verhanovitz Professor Divakar Viswanath Dr. Hugh Eugene Warren Professor David J. Winter John C. and Sally Wenger Professor Trevor Wooley Joel and Katherine Wisdom Professor Sijue Wu

U-M DEPARTMENT OF MATHEMATICS 15 Alumna Endows Professorship

Susan M. Smith is giving $1.5 million to U-M to establish President in 1984. Smith joined the Detroit Offi ce of Towers the Susan Meredith Smith Professorship in Actuarial Sciences in Perrin in 1987, and retired in 1992 after nearly thirty years of the Department of Mathematics. She started the fund modestly service. several years ago and had originally planned to fund the profes- A long-time supporter of U-M and actuarial mathematics, sorship through a bequest gift. When Smith learned that the Smith has been an active member of the Department’s Actu- U-M President’s Donor Challenge would match her $1.5 million arial Alumni/ae Leadership Council. She was recognized for gift with an additional $500,000, she decided the opportunity to her giving to U-M with membership in the President’s club in fulfi ll the Professorship now was too good to miss. “Doing it 1984 and the Angell Society in 2007. Her U-M legacy counts now gives the University that many more years of an endowed 47 U-M graduates in her extended family, as well as four others professorship,” she said. who are currently working on their degrees. “The University After earning a Regents’ Scholarship for tuition, Smith of Michigan has been good to me and my family,” Smith said, started at U-M in 1959. She put herself through school, work- “and it was time to give something back.” ing a part time job and summers. She graduated in 1963 with a Since retirement, Smith met and married Robert H. Gray, B.S. degree in mathematics and $75 to her name. Having taken who is a Professor Emeritus of the U-M School of Public nearly all of the actuarial courses required for a Master’s degree, Health. She stays active volunteering in many local organiza- she interviewed for actuarial positions in the spring of 1963. “It tions, gardening and entertaining their friends and family. was diffi cult to be considered a serious candidate,” Smith said. “One interviewer told me, ‘You will just get married and have “This gift is important,” said Curtis Huntington, Actuarial babies’.” At that point, Smith ended the interview. Program Director and Professor of Mathematics, “because it provides the resources to enable us to compete with industry Smith joined Towers Perrin in Philadelphia in July 1963 as to recruit another top professional to the program to teach and part of their actuarial support staff, and was transferred to the conduct research.” Chicago offi ce in late 1965. In 1978, she became an Associate in the Society of Actuaries and was named a Consultant in 1978. The Actuarial Mathematics program in U-M’s College of She was soon named a principal and was one of the fi rst women Literature, Science, and the Arts (LSA), is the oldest in the na- to have worked her way up from a support staff position. Smith tion and prepares students to enter a fi eld that the Wall Street became Assistant to the fi rm’s Chief Actuary, which necessitated Journal ranks as one of today’s “best” career choices in terms a move to Philadelphia in May 1983, and was named a Vice of job security and lucrative salaries.

Professor Curtis Huntington, Susan Smith, her husband Robert Gray, and Chair Tony Bloch at a luncheon honoring our emeritus faculty and friends of the department.

16 CONTINUUM – 2007 Development Updates Upcoming The Department is continuing with The Alumni/ae Scholarship Fund pro- its fundraising initiative for various vides direct support to undergraduate and Events causes. We are happy to have the new graduate students. It is not an endow- Susan Smith Professorship, helped via ment, and any funds collected provide Department Colloquium the President’s Challenge program. In direct support to students. Following is Every Tuesday at 4:00 addition to providing support to endowed some information on some of the students professorships at U-M, the President’s supported this year. Michigan Reception challenge will match donations to needs SeHyoun Ahn is a senior this year. based scholarship funds for undergradu- He studies math because of “the simplici- Joint Mathematics Meetings ates. To qualify for the match, gifts and ty wrapped in complexity. Many things in American Mathematical Society pledges must be made by December 31, math are hard and complex. For example, San Diego, CA 2007. how can one know that every number can January 8, 2008, 5:30-7:00 p.m. Phase 2 of the President’s Challenge be written as a sum of four squares? Once will target funding for graduate and pro- one proves something, then it becomes fessional student fellowships. A 50% simple.” SeHyoun appreciates the per- G.Y. Rainich Lectures match will be provided for expendable or sonal attention he has received from the January 15-17, 2008 endowed gifts to funds supporting these mathematics faculty, as well as the staff students. This match is available for gifts in the offi ce. Professor Gang Tian and pledges made through December 31, Zachary Maddock is a 4th year Princeton University 2008. More information is available on undergraduate from Brighton, MI. His the Michigan Difference website www. father is a math teacher, so he always giving.umich.edu/where/presidents_chal- liked solving problems and working on Alexander Ziwet Lectures lenge.htm. During the coming year we math. “It wasn't until I took Math 295 February 5-7, 2008 will begin fundraising for graduate stu- here at the University when I realized that Professor Curt McMullen dent support so that we may fully realize learning rigorous mathematics was both Harvard University the benefi t and generousity of the Presi- challenging and rewarding,” Zach says. dent’s Challenge matching funds. He also notes that the faculty and staff The Pension Protection Act of 2006 have been very support and helpful in his 2008 Michigan Math and has created an extraordinary, cost-effec- undergraduate career. The fi nancial sup- Science Scholars Summer tive way to support U-M. Through the port has helped Zach and his family with end of 2007, donors may make IRA gifts tuition and expenses. “With two younger Program to charity and exclude these contributions brothers, my family is ever grateful for Two sessions for qualifi ed from their gross income. Donors must be the scholarship.” high school students: 70½ years of age or older. The transfers Ashley Selegue is a second year grad- June 29 - July 11 and must go directly from IRAs to qualifi ed uate student from Ohio studying fi nancial July 13 - July 25 charities. The gifts must be outright, and and actuarial math. She has found that cannot exceed $100,000 per taxpayer studying math is fun while still challeng- per year. For further details, contact the ing. Ashley also credits the department Mathematics Career Gift Planning Offi ce at 866-233-661. as having very supportive professors and Conference Combining this option with the matching staff, and welcomes the encouragement incentives above provides a unique op- of the other graduate students. The schol- Fall, 2008 portunity to maximize the potential of a arship allowed her to continue her studies signifi cant contribution. during the summer. Department Annual Giving Lindsey Selegue is a second year Please visit our website for The annual solicitation of faculty, graduate student from Ohio studying fi - additional information on nancial math, and is Ashley’s twin sister. emeriti and friends received gifts from these and other events in the 28 individuals. The funds collected were She credits some great high school math Department. contributed mainly to the Maxwell Reade teachers for helping her to develop an in- fund and the Tom Storer funds, although terest in math. Ashley fi nds the program www.math.lsa.umich.edu. some faculty supported other initiatives. in the department interesting and chal- lenging, and all of the people have been friendly and supportive.

U-M DEPARTMENT OF MATHEMATICS 17 The Story of Two Alumnae in the High Tech World

In the world of corporate high- computing successful. Her pioneering Allen is also the 2002 recipient of the technology today, women still account compiler work culminated in algorithms Ada Lovelace award for her “outstanding for less than 25% of the workforce. Two and technologies that are the basis for scientifi c and technical achievements and U-M math alumnae have achieved signif- the theory of program optimization to- extraordinary service to the computing icant success in the fi eld, albeit in differ- day and are widely used throughout the community through her accomplishments ent generations and roles. Frances Allen industry. and contributions on behalf of women (MA 1957), a pioneering researcher at By the mid-1960s, as computer sci- in computing.” Most recently, Allen IBM, and Elizabeth Charnock (BS 1987), ence emerged as a profession, Allen saw was honored with the 2006 A.M. Turing a successful entrepreneur, had vastly dif- the percentage of women in the fi eld Award from the Association for Comput- ferent experiences and paths to success. shrink. “New hires were expected to ing Machinery. Considered the Nobel The Fair Lady of Big Blue have professional credentials and the Prize of computing, the Turing Award engineering schools were the primary cited her contributions that fundamen- Frances Allen received her bachelor’s tally improved the performance of com- degree in education from the New York source of trained people. That meant that many of the new hires were men. That puter programs in solving problems, and State College for Teachers. She wanted accelerated the use of high performance to teach led to a big change in the workplace—in who was doing what.” By the end of the computing. She retired from IBM as a math, and Fellow Emerita in 2002. went to the 1960s, Allen says, “I’d go into a full au- University ditorium (for a meeting or lecture), and I The Possibilities of Math of Michi- could count the women on one hand. It Elizabeth Charnock came to the gan for her was a tough period for women.” University of Michigan at the age of 16, master’s in During her tenure at IBM, Allen had enrolling in the Honors Program. At the math. As a long career of personally imprinting urging of a former classmate who at- the comput- the lives of her colleagues. Her ability to tended U-M, Elizabeth began the “90s ing fi eld cultivate relationships was a stepping- sequence” of honors theoretical math- was taking stone to her success. Allen considers ematics. She found the courses to be fl ight at herself lucky to have had many mentors exciting and knew after a short period that time, to provide guidance along her 45-year that she tech com- journey at IBM Research. Allen prides would panies were herself on her involvement with IBM’s major recruiting mentor program. She recalls that when in math. heavily from college campuses. Al- she fi rst joined IBM Research the idea of “I took len, who had taken a single engineering mentoring was not widespread outside honors course at U-M, was hired as a program- of the executive track. However, through courses mer for IBM at their research center formal and informal mentoring, Allen be- in many in New York. “I had that one course, gan seeking out new employees to guide other and I was probably more experienced them along their own personal paths to subjects, than most of the people they hired,” Al- success. IBM was so overcome with Al- but none len says. “I took the job to help pay off len’s commitment to mentoring that they of them debts, and then go back to my fi rst love, established an award in her name, as an were as teaching.” At that time, there were many effort to promote the careers of techni- good or women programmers in the workforce at cal men and women in IBM who have as well IBM. demonstrated “exemplary commitment presented Because of her teaching background, to mentoring of technical women.” In as the math courses,” she says. Allen was asked to teach the just-invent- 2000, Allen, herself, was the fi rst recipi- After graduating in 1987, Charnock ed computer language Fortran to IBM’s ent of the “Frances E. Allen Women in began applying for jobs in Michigan, scientists. To teach it, she had to learn it, Technology Mentoring Award.” and secured an interview with Unisys and that made her fascinated with how Allen’s pioneering contributions to Corporation. Surprisingly, the manager software worked. In the late 1950s, she the fi eld of computing have received with whom she interviewed was familiar started working on compiling systems— signifi cant recognition. In 1989, she with the U-M honors math program, in software that translates the computer lan- was the fi rst woman to be named an particular the requirements of the theo- guages used by programmers into code IBM fellow, the highest technical honor retical math option, as his son had been the computer’s hardware can understand. bestowed by the company. She received researching universities. Charnock was Allen eventually developed ways for the Grace Hopper Celebration of Women hired, and considered herself lucky at compilers to produce much faster codes, in Computing Award as one of the most the time. “I had no computer science or and that helped make high-performance successful women in the computing fi eld. engineering classes at U-M,” Charnock

18 CONTINUUM – 2007 notes. “It was somewhat discouraged through the 90s sequence math at U-M. related items and events into searchable for honors students since the quality of The company was funded through ven- units or discussions. Charnock says of the classes was not at the level of other ture capital, and she sold it in 2001. her work “We actually use a signifi cant honors offerings. Had I known how hard In 2002, Cataphora was founded by amount of math in the analysis of data, it was to get a job with a degree in math, Charnock and three other employees, patterns, and graphs.” Her members of I might have reconsidered. Many of including her partner in Troba. The com- her staff regularly explore combinatorial my friends and colleagues were waiting pany’s genesis was a fundamental insight theory, especially graph theory, and also tables at the time.” At Unisys she ran the that she had about a revolutionary ap- does work in linear algebra, category human factors laboratory. proach to information retrieval. Funded theory, and probability theory. Charnock After Unisys, Charnock moved on entirely by revenues from clients and is proud that over 20% of the Cataphora to management and senior engineering without outside investment, the company workforce hails from U-M. positions at large international high tech has grown to over 100 employees with Charnock laments that the number companies such as Hewlett-Packard and offi ces in California and Washington, DC. of women she sees in her industry is Sun Microsystems. With those compa- Cataphora was recognized as one of the small—in her experience, she estimates nies she survived the “bubble bursting” in top 25 start ups of 2002 and has reached less than 10%. She is unsure of the im- Silicon Valley, and witnessed the decline annual revenue of $30 million. pact her gender has had on her success. of their industry infl uence. “It was ap- Cataphora is both the pioneer and “I guess that, as a woman, I was seen as parent that we were doing good work at industry leader in the burgeoning fi eld ‘different’ in large companies, but I don’t those companies, but the work would not of evidence analytics, or the manage- know if being different was a help or a signifi cantly infl uence anything. I was at ment and analysis of electronic data from hindrance.” Charnock is still a big fan of a point where I wanted my work to make an evidentiary perspective. They are the honors theoretical math sequence, and a difference in a real world sense.” considered the world’s authority on the the opportunities it presented. “Because Charnock’s fi rst venture as an en- implications of personal and organiza- of my theoretical and analytical back- trepreneur was as CEO and founder of tional behavior as evidenced by the use ground, I had something that other people Troba, an industry leading customer rela- of electronic media. In 2006, Cataphora didn’t. It made many more things pos- tionship management software company. was awarded a broad patent for funda- sible in my career.” Her partner in that company also went mental technology to reconstruct causally

Alumnus Smale Receives Wolf Prize The 2007 Wolf Prize in Mathematics was awarded to Ste- dimensions bigger or equal to 5 is one of the great mathemati- phen J. Smale (BS 1952, PhD 1957). Smale was recognized cal achievements of the 20th Century. His h-cobordism theorem for his ground breaking contributions that have played a funda- is probably the most basic tool in differential geometry. Smale mental role in shaping differential topology, dynamical systems, reshaped the view of the world of dynamical systems. His theo- mathematical economics, and other subjects in mathematics. ry of hyperbolic systems remains one of the main developments The Prize is awarded by the Wolf Foundation of Israel to pro- on the subject after Poincaré, and the mathematical foundations mote science and art for the benefi t of mankind. of the so-called “chaos-theory” are his work as well. Smale’s Smale held appointments at the University of Chicago and work contributed dramatically to change in the study of the to- the Institute for Advanced Study before joining the University pology and analysis of infi nite-dimensional manifolds. of California, Berkeley, in 1964, where Smale’s later research turned to mechanics and economics, he continues as a Professor of Math- to which he applied his ideas on topology and dynamics. For ematics in the Graduate School. He is instance, his notion of “amended potential” in mechanics plays currently at the Toyota Technical Insti- a key role in current developments in stability and bifurcation tute in Chicago. A highly recognized of relative equilibria. In economics, Smale applied an abstract mathematician, Smale’s honors include theory of optimization for several functions, which he devel- the 1966 Fields Medal, a Veblen Prize oped, to provide conditions for the existence of Pareto optima from the American Mathematical So- and to characterize this set of optima as a sub-manifold of dif- ciety, the 1967 University of Michigan feomorphic states to the set of Pareto equilibria. Sesquicentennial Award, Membership Most recently Smale has been working on the theory of in the American Academy of Arts and Sciences and the National computation and computational mathematics. Against main- Academy of Science, the Chauvenet Prize from the Mathemati- stream research on scientifi c computation, which focused on cal Association of America, and the Von Neumann Award from immediate solutions to concrete problems, Smale developed a the Society for Industrial and Applied Mathematics. theory of continuous computation and complexity (akin to that Early in his career, Smale contributed greatly to the devel- developed by computer scientists for discrete computations), opment of differential topology, a fi eld then in its infancy. His and designed and analyzed algorithms for a number of specifi c results of immersions of spheres in Euclidean spaces still in- problems. Some of these analyses constitute models for the use trigue mathematicians. His proof of the Poincaré Conjecture for of deep mathematics in the study of numerical algorithms.

U-M DEPARTMENT OF MATHEMATICS 19 Alumni/ae Updates Considering a Donation to UM? Wendy Lichtman (BA 1966) has written a math novel for teens that was published by HarperCollins. “Do The Math: Secrets, Lies and Algebra” is written from the If you are contacted by the Univer- perspective of an 8th grade girl who sees the world through mathematical metaphors. sity of Michigan for a donation, you can Wendy says “Although I graduated from Michigan, in December 1966 with a major earmark your gift to the Department of in mathematics, I became a writer, so I surprised myself when I returned to my math Mathematics. Simply tell the caller to training to write this book.” It is the fi rst in a series—the second one, “Do The Math: designate your gift to mathematics or The Writing on the Wall” will be published in summer 2008. You can fi nd more infor- write Mathematics Department on the mation at www.wendylichtman.com pledge card you are sent. We greatly ap- preciate all of your support, and we hope Dr. Renate McLaughlin (PhD 1968) recently retired as Provost and Vice Chan- we can count on you to support future cellor for Academic Affairs and Professor of Mathematics in the College of Arts and fundraising projects. Sciences (CAS) at U-M-Flint. She joined the University in 1968. She was a dedicated teacher and role model for women students of mathematics, teaching nearly every course offered by the math department. In 2005, the student government honored her Estate Gifts by establishing the Renate McLaughlin Academic Achievement Award. McLaughlin is You may include the Department of currently studying organ at U-M with Marilyn Mason. Mathematics in your estate plan. Please call us at 734-647-4462 for information George H. Brown, Jr. (BA 1971, MA 1973) passed away last year. His brother, on charitable trusts and bequests to the James Ward Brown (PhD 1964), who is on the faculty at U-M Dearborn, shared this department, or contact: sad news. University of Michigan Development/Planned Giving J. Paul Austin (BS 1973, MA 1975) has received the Distinguished Leadership 734-647-6000 Award from Leadership Michigan, a program of the Michigan Chamber Foundation. He was selected because of his exceptional leadership qualities; his achievement in both professional and civic activities; his ability to create and articulate a vision and effect change; and his signifi cant contribution to the development of future leaders. Austin is a Senior Vice President at Blue Cross/Blue Shield of Michigan. ContinuUM Editorial Board: Dr. Christopher Swanson (PhD 1999), associate professor of mathematics at Anthony Bloch, Chair Ashland University, received the Henry L. Alder Award for Distinguished Teaching by a beginning college or university mathematics faculty member. The award was pre- Suzanne H. Rogers, Editor sented by the MAA at MathFest in Knoxville, TN. The award was established in 2003 Doreen Fussman to honor extraordinarily successful teachers whose infl uence extends beyond the class- Curtis E. Huntington room. Winners must have taught full time in one of the mathematical sciences in the Donald J. Lewis United States or Canada for at least two, but not more than seven, years since receiving Agnes Soderbeck, Graphics a Ph.D. Swanson, who just completed his seventh year at AU, has created new courses Photos by UM Photo Services, the and has introduced Ashland students to the Putnam competition and to Pi Mu Epsilon. Department of Mathematics, or Despite a four-course teaching load each semester, he has directed four honors theses personally submitted by the subjects. (two of which received awards) and has had the theses writers present their work at conferences. He was invited to give both a plenary and after-dinner talk at the Spring 2005 meeting of the Ohio Section of the MAA, and is now serving as co-chair of Ohio NExT. The biographical note in the prize booklet distributed at MathFest listed one of his spare time activities as “annoying Ohio State Buckeye fans by fl ying his University The Regents of the of Michigan car fl ags while blaring ‘Hail to the Victors’ with his car windows down.” University of Michigan: Julia Donovan Darlow, Laurence In 2006, the editors of all three of the Mathematics Association of America journals B. Deitch, Olivia P. Maynard, Rebecca were mathematicians who had received their doctorates from Michigan: McGowan, Andrea Fischer Newman, American Mathematical Monthly: Bruce Palka (PhD 1972) University of Texas, Andrew C. Richner, S. Martin Taylor, and currently at the Division of Mathematical Sciences, National Science Foundation. Katherine E. White Mathematics Magazine: Allen Schwenk (PhD 1973), Western Michigan Univer- Mary Sue Coleman, ex offi cio sity. College Mathematics Journal: Lowell Beineke ( PhD 1965) Indiana University- Purdue University Fort Wayne.

20 CONTINUUM – 2007 We Need You!

Want to get involved with the UM Department of Mathematics? Here are some areas where alumni participation is vital. Let us know if you are interested in working with us on these initiatives.

• Recommend the UM mathematics program to students interested in undergraduate or graduate studies • Participate in our annual Career Day, held each year in late October or early November • Visit the Department for afternoon tea (3:45 sharp) if you are in town for the weekend, including Homecoming, Parent’s weekend, or the Presidential Society weekend • 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

Answer to Math Problem

Assume that the center (p, q) of the disc is uniform distributed over [0, 1]×[0, 1]. The tile Tx,y := [x, x + 1] × [y, y + 1] (x, y ÎZ) intersects the disc if and only if the point (p − x, q − y) has at most distance 10 to [0, 1] × [0, 1]. So the probability that Tx,y intersects the disc is the area of T-x,-y ∪ S where S is the set of all points with distance ≤ 10 to [0, 1] × [0, 1]. Summing over all x, y ÎZ shows that the expected number of tiles intersecting with the disc is the area of S. The set S is the union of a cross-shaped region

{(x, y) | 0 ≤ x ≤ 1,−10 ≤ y ≤ 11} ∩ {(x, y | 0 ≤ y ≤ 1,−10 ≤ x ≤ 11}

which has area 41 and its complement, consisting of four quarter discs of radius 10, whose area together is 100π. So the expected number of tiles that have to be replaced is 100π + 41.

The University of Michigan, as an equal opportunity/affi rmative action employer, complies with all applicable federal and state laws regarding nondiscrimination and affi rmative ac- tion, including Title IX of the Education Amendments of 1972 and Section 504 of the Rehabilitation Act of 1973. The University of Michigan is committed to a policy of nondiscrimi- nation and equal opportunity for all persons regardless of race, sex, color, religion, creed, national origin or ancestry, age, marital status, sexual orientation, gender identity, gender expression, disability, or Vietnam-era veteran status in employment, educational programs and activities, and admissions. Inquiries or complaints may be addressed to the Senior Di- rector for Institutional Equity and Title IX/Section 504 Coordinator, Offi ce of Institutional Equity, 2072 Administrative Services Building, Ann Arbor, Michigan 48109-1432, 734-763- 0235, TTY 734-647-1388. For other University of Michigan information call 734-764-1817.

U-M DEPARTMENT OF MATHEMATICS 21 2007-2008 Mathematics Department Faculty

Professors Associate Professors Daniel Meyer (NSF/Hildebrandt) David E. Barrett Jinho Baik Djordje Milicevic (Hildebrandt) Alexander Barvinok Stephen DeBacker Carl Miller (Research Training Grant) Hyman Bass, Roger Lyndon Collegiate Hendrikus Derksen Sophie Morier-Genoud (Hildebrandt) Professor Anna Gilbert Carl Mummert Andreas R. Blass Trachette Jackson Lan Nguyen Anthony Bloch, Chair, Alexander Ziwet Mattias Jonsson Pekka Pankka Collegiate Professor Kristen Moore Thomas Petersen (IBL Postdoc) Mario Bonk Mircea Mustata Ivan Petrakiev (Research Training Grant) Daniel Burns Divakar Viswanath Pavlo Pylyavskyy (Hildebrandt) Richard Canary Nicholas Ramsey (NSF/Hildebrandt) Joseph G. Conlon Assistant Professors Sonmez Sahutoglu (Research Training Brian Conrad Grant) Erhan Bayraktar Charles Doering Karl Schwede (NSF/Hildebrandt) Victoria Booth Igor Dolgachev Semih Sezer Volker Elling Peter Duren Anna Siano Selim Esedoglu Sergey Fomin, Robert Thrall Collegiate Loren Spice (NSF/Hildebrandt) Daniel Forger Professor Jack Waddell Aaron King John Erik Fornæss, Frederick W. Gehring Katherine Walker Patrick Nelson Collegiate Professor Richard Yamada Martin Strauss William S. Fulton, M.S. Keeler Professor Stephanie Yang (NSF/Hildebrandt) Juan Souto Robert L. Griess Zhou Zhang Dale Winter Philip J. Hanlon, Associate Provost, Xiaoming Zheng Donald J. Lewis Collegiate Professor Juha Heinonen Lecturers Research Fellows Mel Hochster, Jack E McLaughlin Irina Arakelian Rina Ashkenazi Distinguished University Professor Mark Conger Tom Mestdag Curtis E. Huntington Carolyn Dean Lizhen Ji James Epperson Carl H. Fischer Visiting Professor Smadar Karni Gavin LaRose Robert Krasny Karen Rhea Joseph Marker, Ball State University/ Igor Kriz Marker Acutarial Services Jeffrey Lagarias Postdoctoral Assistant Professors Gehring Visiting Professors Robert Lazarsfeld, Raymond L. Wilder Robert Buckingham Collegiate Professor Renzo Cavalieri Keith Ball, University College of London John W. Lott Xiaojun Chen Blake Temple, University of California- Robert Megginson, Associate Dean, LSA Bin Cheng (Hildebrandt) Davis Peter Miller Tatyana Chmutova Hugh L. Montgomery Cecilia Diniz Behn Emeriti Gopal Prasad Ahmet Duran Morton Brown Jeffrey B. Rauch Neil Epstein (NSF/Hildebrandt) Paul Federbush Yongbin Ruan Farkhod Eshmatov Frederick W. Gehring, Distinguished G. Peter Scott Joel Fish (Research Training Grant) University Professor Carl P. Simon David Gammack Jack Goldberg Peter Smereka Mohar Guha Peter Hinman Karen Smith Jonathan Handy (Research Training Grant) Wilfred Kaplan Joel A. Smoller, Lamberto Cesari Kenneth Harris Wilfred Kincaid Collegiate Professor Benjamin Howard (NSF/Hildebrandt) James Kister Ralf J. Spatzier Tatiana Howard (Research Training Grant) Eugene F. Krause J. Tobias Stafford Valentina Joukhovitski James S. Milne John Stembridge Amanda Knecht (Research Training Grant) M. S. Ramanujan Berit Stensones Richard Kollar Frank A. Raymond B. Alan Taylor Radu Laza Maxwell Reade Alejandro Uribe Lina Lee Ronald Rosen Arthur Wasserman Anna Lenzhen Art Schwartz David J. Winter Peijun Li Chung-Tuo Shih Sijue Wu, Robert W. and Lynn H. Browne Zhi Lin Patricia Shure Professor Larsen Louder (Hildebrandt) Charles Titus Virginia Young, Cecil J. Nesbitt Professor Michael Ludkovski Howard Young Hannah Markwig

22 CONTINUUM – 2007 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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University of Michigan Degree(s) with years & advisors

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Degrees from other Universities/Years

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

U-M DEPARTMENT OF MATHEMATICS 23 Department of Mathematics NONPROFIT University of Michigan ORGANIZATION 530 Church Street, 2074 East Hall U.S. POSTAGE Ann Arbor, MI 48109-1043 PAID 734-764-0335 • www.math.lsa.umich.edu Ann Arbor, Mich Permit No. 144