ContinuUM Newsletter of the Department of Mathematics at the Summer 2001

On July 31, 2001, Al Taylor stepped down as department Chair after six successful years in the postion. Trevor Wooley has been selected as the new Chair. Due to Trevor’s scheduled sabbatical leave for the 2001-02 academic year, Alejandro Uribe, the current Associate Chair for Academic Affairs, will serve as the interim chair for the coming year. You should hear about Alejandro’s experience as Chair in the next ContinuUM. In the two “Notes from the Chair” columns, Al reflects on his chairmanship, and Trevor lays some plans for the future of the department. Reflections on Six The Future of the Years as Chair Mathematics Department

This is a piece I’ve looked forward to The Mathematics Department at writing for some seven years now, my fi- Michigan has experienced extensive nal one for the “Notes from the Chair” change in virtually all aspects of its mis- column. At the end of July, I’ll have fin- sion over the past several years, and we ished my two terms as Chair and am ex- are fortunate indeed that, through Al cited about returning to my normal career Taylor’s commitment and balanced lead- of teaching and research. Alejandro ership through six of the last seven years, Uribe will assume the chairmanship next almost all of these developments have year, filling in for Trevor Wooley, who been for the good. As Al begins some has agreed to serve a 3-year term as Chair, well-deserved relief from administrative the 2002-2005 academic years, after he duties, it seems an opportune moment to returns from a year’s leave in Cambridge highlight some of the developments and and Bonn. challenges that we expect to see in the fu- I don’t believe the Dean could have ture. Fortunately for me, the “future” does made any better choice of Chairs to keep not begin until July of 2002! The Depart- the department on its upward trend. My opinion is confirmed by ment is very fortunate that Alejandro Uribe has agreed to serve as the selection of three new Associate Chairs to join the leadership Chair during my long-awaited year of leave next year. team, Tony Bloch for graduate affairs, Dick Canary for educa- Competing with Peer Departments tion, and Mel Hochster for faculty appointments. Other major One of my regular complaints in recent years has been that the leadership jobs are being filled by Toby Stafford (Chair of the resources provided to us by the College barely enable us to main- Faculty Recruitment Committee), John Stembridge (Doctoral tain our status within the Big Ten, let alone compete with the top Chair), and Ralf Spatzier (Undergraduate Chair). This leadership ten departments. The good news is that this situation is changing team is remarkable for its youth and vitality! for the better. In the final years of Al’s term as Chair, increased re- While we have for decades been a democratic department with sources were forthcoming from LS&A. In addition, we have just important decisions being made on a near consensus basis, the secured a significant new package of resources that, starting next new team reflects the fact that administrative work and responsi- year, will incrementally address issues involving salary and teach- bility must be shared to a much greater degree than ever before. ing so crucial in a competitive hiring environment. Taken together, The youth of the team reflects the fact that the department has im- these resources will allow us to concentrate our competitive en- proved to one in which almost every faculty member has an active ergy on the top ten departments, and offer prospects of entering research program, most of which are increased in impact by re- the elite five departments nationally. ceiving highly competitive external research funding. Faculty, As one contemplates the difficulties of competing with the especially young faculty, can’t afford to de-emphasize their re- very strongest departments, one is struck by the scale of financial search work for several years to spend large amounts of time on resources available to highly endowed private schools. However, the important administrative work that is necessary to keep a large the size and quality of the department at Michigan provides a criti- department functioning smoothly. Therefore, the new Chairs have cal mass of excellence that offers an extraordinarily stimulating obtained some incremental resources to enable active young fac- environment unavailable to smaller departments, no matter how ulty to take on these tasks while maintaining their research well-endowed. What we seek to do in the future is to exploit this

continued on page 6 continued on page 7 Bioinformatics: Professor Math’s Role in the Life Sciences Initiative Phil Hanlon Bioinformatics sits at the intersection of blueprint under different conditions? Given Collegiate Chair and molecular biology and computer science, the DNA blueprint for a protein, how do two disciplines which have undergone we predict the three-dimensional shape that LSA Associate Dean revolutionary scientific-technological de- this protein will eventually assume, a As described in the article to the left, velopment during the past few decades. Po- shape which largely governs its function in Phil Hanlon is spearheading Math’s par- sitioned on the interface of two rapidly the cell? This growing bank of molecular ticipation in the Bioinformatics portion of developing intellectual arenas, bio- information leaves us well short of under- UM’s life sciences initiative. In addition informatics is experiencing intensive devel- standing the principles that govern the in- to these activities, Hanlon has been opment as well as explosive growth in teractive biological system. named the Donald interest and demand. A key goal of bioinformatics is to con- J. Lewis Collegiate Improving techniques in molecular biol- struct the integrated behavior of the intact Professor of Math- ogy yield extensive information about the organism in relation to its underlying mo- ematics, 2000-05. molecular components of living cells. This lecular determinants (the genome). Mo- He has also been information includes determination of the lecular biology takes the first step towards selected to be the genetic make-up (the DNA) of organisms such an understanding with the measure- Associate Dean of and provides precise information about pro- ment of molecular features of a living cell. Finance and Plan- teins that are active in cells. This informa- The next few steps lie more on the ning for the College tion about DNA and proteins comes as informatics side, steps that may be most of Literature, Sci- exact information about molecular se- readily made by mathematicians, computer ence and the Arts, a position he assumed quences, and also as information about scientists and statisticians. These include in the winter of 2001. three-dimensional structure which is very mining of the molecular data to filter and Hanlon completed his undergraduate important in determining the way in which select out interesting features. Then math- degree at Dartmouth and received his the DNA or protein functions. Technologi- ematical modeling of how the cell/organ- Ph.D. from the California Institute of cal advances have made molecular technol- ism, as an integrated system, is acting on Technology in 1981. He taught at Massa- ogy commonly accessible. The result has the molecular information identified in the chusetts Institute of Technology and Cali- been a flood of information about the mo- previous step as lying in the genome and in fornia Institute of Technology before lecular composition of DNA and proteins protein structure. Computer science is pro- joining UM in 1986. He became a pro- from a wide variety of organisms. Articles viding us with more and more powerful fessor in 1990. Hanlon is an extremely in the popular press about genome sequenc- tools to do this analysis— hardware archi- well regarded mathematician, and has re- ing have given some indication of the revo- tectures and efficient algorithms for sym- ceived recognition over the years to in- lution in available information, but give bolic analysis, scientific computation, clude the NSF Presidential Young little indication of the magnitude of data graphical interpretation and data manage- Investigator Award, a Sloan Fellowship, a available as biologists worldwide produce a ment. Guggenheim Fellowship, and University constant flow of information about the mo- Michigan is one of a few institutions honors including the Henry Russel lecular structure of the genes and proteins that are playing a leadership role in Award, the LS & A Excellence in Educa- that control living cells. bioinformatics. With a truly interdiscipli- tion Award, and a Thurnau Professorship. As valuable and as plentiful as this in- nary effort rooted in the Medical School Considered a world leader in alge- formation is, it only provides a “parts cata- but including faculty in the Departments of braic combinatorics, Hanlon’s expertise log” for a variety of organisms without Mathematics, Biology, Chemistry and the has been used in various arenas. Combi- explaining how these parts work or fit to- Colleges of Pharmacy, Engineering and natorics describes the study of patterns. gether. Little is known about the integrated Public Health, we are launching a graduate Typically Hanlon applies combinatorial system—what makes a living cell, or how a degree in bioinformatics and expanding the methods and results to problems in alge- cell will respond to a novel environment or number of bioinformatics faculty positions bra or alternatively applies algebraic a specific change in its genome. DNA gives by ten to fifteen campus-wide. More about theory to combinatorial problems. His the blueprint for the design of various pro- the newly formed program can be found at leadership and expertise in this area has teins, but what controls the process its web site www.bioinformatics.med. been recognized by (among others) the whereby proteins are expressed from this umich.edu. National Security Agency. He has served -Professor Phil Hanlon on the NSA Advisory Board since 1994, and also chaired the Math Section since 1994. Hanlon served as Chair and author of a report on the technical challenges facing NSA and the role mathematics could play in addressing the fundamental continued on page 8 2 black college in Tyler, and also at the Uni- Successful MLK Day Colloquium versity of Texas at Tyler. In her Colloquium talk entitled The second annual Marjorie Lee sor , a distinguished analyst. In “Strengthening the K-12 Curriculum in Sci- Browne Colloquium was presented as part 1949, Dr. Granville became the first Afri- ence and Mathematics: An Absolute Must,” of the department’s recognition of Martin can-American woman in the history of the Dr. Granville detailed some of her personal Luther King Day. The event honors Dr. United States to be granted the Ph.D. in experiences in past and recent years con- Marjorie Lee Browne, the University of mathematics. cerning mathematics education in this Michigan’s first and the nation’s second Af- Following the receipt of her Ph.D., Dr. country. Private industries and government rican-American woman to earn the Ph.D. in Granville enjoyed a remarkable career agencies in the United States are finding it mathematics. working as a mathematician and educator in impossible to recruit enough technically The department was honored to host Dr. academia, government and industry. She qualified personnel to fill existing job Evelyn Boyd Granville as this year’s held academic positions first at the New openings. Dr. Granville recounted how in speaker. Dr. Granville is the nation’s first York University Institute of Mathematics 1998-99, she partcipated in an outreach African-American woman to earn the Ph.D. (now known as the Courant Institute) and program to middle school students. The in mathematics. , before moving to a position program, sponsored by Dow Chemical, em- Dr. Granville has led an inspirational as a mathematician at the National Bureau phasized to the students the importance of life as a scientist, educator and person. She of Standards, and later at IBM. At IBM, Dr. math and science in their future careers. Dr. was born in Washington, DC in 1924, the Granville played an exciting and fundamen- Granville stressed that math provides stu- second child of William and Julia Boyd. tal role in the dawn of the computer age, es- dents with the skills employers look for She came of age in segregated Washington pecially as it was being applied to celestial when hiring workers: logical thinking, during the Depression, but reports never mechanics. For example, she was part of problem solving abilities along with a vari- having been aware that her family lacked the team of scientists responsible for writ- ety of problem solving strategies, and cre- the basic necessities of life. Instead her par- ing the computer programs that tracked the ative thinking. paths of vehicles in space on NASA’s ents emphasized to her the value of hard While Dr. Granville was showing the Project Vanguard and Project Mercury. work and education. middle school students why math was im- After graduating summa cum laude In 1967, Dr. Granville made a major ca- portant, she wondered if there were enough from Smith College in 1945, Dr. Granville reer change by accepting a professorship in well trained math and science teachers to began graduate school in mathematics at mathematics at California State University, help them develop these skills. The effec- Yale. (Although she’d also been accepted at . Here she discovered a new tiveness of the math and science curricula UM, Yale offered her a scholarship.) At passion: the education of K-6 teachers and was also in question. Are the teacher train- Yale, she was twice awarded a Julius students. She was a key participant in sev- ing programs designed to produce effective Rosenwald fellowship and was also hon- eral special projects for K-6 education, in- teachers in math? Considering that the test ored with a U.S. Atomic Energy Fellowship cluding the Miller Mathematics scores of U.S. students in mathematics and for her final year. Her doctoral dissertation Improvement Program. Her textbook (with science rank low in comparison with stu- on the properties of Laguerre series in the Jason Frand), Theory and Applications of dent performance in many other countries, complex domain was supervised by Profes- Mathematics for Teachers (Wadsworth, the answer is likely NO, particularly in ur- 1975, 1978) became a standard for the ban schools. “new math” and was Students develop an attitude toward adopted at over 50 col- math, good or bad, at an early age. There is leges and universities. a scarcity of well trained, inspiring teachers Upon retiring from to help foster positive attitudes at an early CSULA in 1984, Dr. age. Effective teacher training is a must, Granville and her hus- combined with continued career develop- band moved to a com- ment opportunities. munity near Tyler, Dr. Granville believes that a strong na- Texas. Her talent and tion needs a first rate public educational energy did not go unno- system starting in kindergarten. “Strength ticed: She received invi- comes from…an intelligent citizenry tations to join the trained to think rationally and equipped to faculty at a local public solve problems.” school, at Texas Col- lege, a small historically Institutions of higher learning must work with local and state agencies respon- sible for the K-12 curriculum in math and science and with those institutions respon- Bob Megginson presents a sible for teacher training standards to effect framed poster to Evelyn changes that ensure that the pool of quali- Boyd Granville. Math fied workers will be sufficient to meet fu- Department photo. ture demands. 3 Bass Delivers Collegiate Chair Lecture

Professor Hyman Bass presented the metry may seem a somewhat exotic notion, When addressing university-trained math- inaugural lecture of the Roger C. Lyndon it finds its way into virtually all branches of ematicians, he declared “…what high re- Collegiate Professorship in Mathematics. mathematics and science. gard one must have for the performance of He began with biographical remarks about In his lecture “Mapping the Borderlands the elementary school teachers. Imagine the man for whom this collegiate chair is between Mathematics and Education,” Bass what methodical training is necessary to named, Roger C. Lyndon. Lyndon was explored instances where researchers have indoctrinate…children with the principles educated at Harvard, where he earned a crossed the boundary between mathematics of arithmetic! Try it with your university B.A. in 1939, an M.A. in 1941, and a Ph.D. and education, much as he is doing in his training; you will not have great success!” in 1946. He was an instructor and assistant position at UM. His work with Deborah In his extensive work on the school professor at prior to Ball of the School of Education, crosses the mathematics curriculum, Klein exemplified joining the faculty at the University of borderlands between the mathematical what Bass calls the cultural exchange Michigan as assistant professor. He was knowledge and practices of the discipline, model of interaction. He was respectful and promoted to associate professor in 1956 and those of the mathematics classroom, humble. He sought to bring a unifying dis- and to professor in 1959. Lyndon retired in particularly at the elementary level. He pre- ciplinary perspective to considerations of 1988 and died in June of that year. sented three historically significant ex- curriculum, but did not seek to determine During his career, Lyndon gained amples of work in the borderlands, and that curriculum. worldwide recognition for his seminal con- their impact on the discipline. Bourbaki and the New Math tributions to logic and group theory. As an Felix Klein, Turn of the 20th Century undergraduate he found and corrected a This example also involves mathemati- flaw in philosopher Willard Quine’s foun- Felix Klein was notable for his deep cians developing visions of the curriculum. dations of mathematical logic. His contribu- and enduring interest in mathematics edu- In the 1930s, a group of mathematicians th tions to group cohomology were initiated in cation at the turn of the 20 century. He recognized the need to modernize math- his thesis, where, among other things, he was a great mathematical synthesist work- ematics instruction in the French universi- anticipated spectral sequences, which are of ing at Göttingen, where he devoted substan- ties. They undertook to reform the basic fundamental importance to group tial attention to developing ideas about the courses of instruction. What began mod- cohomology. pre-college mathematics curriculum. He estly quickly escalated into a monumental hoped to provide a vision of school math- enterprise to write collectively a compre- Both Bass and Lyndon devoted much of ematics that would offer teachers a perspec- hensive account of the foundations of all of their research careers to group theory, tive on the discipline that would enable contemporary mathematics. These volumes sometimes described as the mathematical them to make better choices about presenta- were published under the pseudonym of theory of symmetry. Group theory measures tion and representation of important math- Nicolas Bourbaki. Unlike earlier influential the symmetry of an object as the set of all ematical topics. Klein appreciated the encyclopedic productions, Bourbaki under- ways that we can change that object and yet special cognitive complexity of teaching. took to actually develop the mathematics, leave it the same. While mathematical sym- from the foundations up, with detailed rig- orous proofs, and a globally unified con- ceptual and linguistic structure. Bourbaki serves as an incomparable reference work that has greatly influenced university level mathematics education around the world. None of the brilliant mathematical de- velopments of the post WWII period mani- fested themselves in the school curricula. In the 1960s, a number of mathematicians turned their attention to efforts to export to schools the new kinds of mathematical thinking, such as that exemplified by Bourbaki. This was the period that is now referred to as the “new math.” Elementary versions of university level courses were developed, founded on the formalism of set theory, with prominent attention to naming and studying the properties of algebraic op- erations. Calculus descended to the high school curriculum. While the new math was not entirely misguided, pedagogically, it Chair Al Taylor, Professor Hy Bass and LS&A Dean Shirley Neuman prior to the Collegiate Chair lecture. UM Photo Services. continued on page 9 4 Department Hosts Middle School Students

Each fall, the echo of their voices and energetic footsteps can be heard around East Hall. These groups are not incoming freshmen, but middle school students visit- ing the department in conjunction with the University’s King/Chavez/Park (K/C/P) Program. The K/C/P Program is run by the University’s Office of Academic Multicul- tural Initiatives. The goal is to help underrepresented students prepare for col- lege by learning about college admission requirements and procedures, attending presentations by staff and faculty in se- lected academic units, and engaging in other activities designed to expose them to the campus environment. K/C/P is a large state initiative with many programs and components. Students from middle schools in De- troit, Ann Arbor, Willow Run, Ypsilanti, Pontiac, Flint, Adrian, Hazel Park, Monroe, Van Buren Township and other school dis- tricts in southeastern Michigan, visit the University of Michigan for a day long se- A group of students from Barbour Middle School in Detroit work with Bob Griess on a ries of activities. Students also have the op- combinatorics problem. Math Department photo. portunity to participate in a classroom setting at UM. Professor Robert Griess organizes the also thwart any misconceptions the stu- they practiced. Some of the comments on Mathematics Department’s components of dents have about studying math in their their evaluations show that the presenta- the program. Griess sees the opportunities college careers. tions were a success. Here are some of the presented by the program to be long range. One of Griess’s presentations involved students’ responses to the question “what “Minorities are not greatly represented in combinatorics and sequences of numbers. did you learn”: mathematics and math-related fields. There He had the students label four pennies with there is more to math than plus, are many interesting career possibilities. If • the numbers 1 through 4. The students we and our math presentations catch the minus, and divide; were then asked to write down how many imagination of these kids, we would expect different combinations of numbers they • that you need math for a lot of to see increasing numbers of minorities in could make from those four numbers (1-4). things; mathematics.” Next, they were asked to take away the • that you don’t really know how to Once a week during the fall, groups of number 4 penny, and determine how many add like you really think you do, approximately 15 students arrive at the different combinations of numbers they and that it is not as easy as you Mathematics Department for their hour- could make with the numbers 1-3. They did might see it will be. long visits. Department hosts for the pro- the same for 2 pennies and one. In the end, “I think the K/C/P program offers the gram range from graduate students to it was the method of sequencing that the members of this department the opportu- professors. Each host is responsible for students learned, and how it was easier to nity to have an impact on the future of our creating a program for the students that can determine the answers using this method discipline,” Griess says. “If we can reach include a tour of the building, a visit to the than just randomly arranging the pennies. library, visiting classrooms, viewing and young minds and show them the value of The students who participated in the discussion of the computer facilities, and continuing their education—in math or an- mathematics programs this fall formed a usually a demonstration or exercise in other subject—then we have succeeded.” variety of opinions about the mathematics mathematics. It is important that the stu- dents understand the significance of a mathematics education, and how it can be used in many professions. The host can

5 Taylor, continued from page 1 Strengthening and Broadening the proud of the Michigan Math Scholars pro- Department gram, expanded this year to include all the programs. It is very gratifying to me to see We’ve recruited outstanding faculty in natural science departments at Michigan, such high quality teachers and researchers both core areas of mathematics and new ar- intended to give talented high school stu- doing the jobs that will continue to improve eas of applied mathematics. As you have dents a taste of the excitement of doing the quality of our education and research read in this newsletter over the years, fac- math and/or science research. program. ulty honors and recognition for research, I’d like to take credit for all these great When finishing a job, it’s natural to the analog for a math department of the All- things happening, but the truth is that I had look back and think about what’s gone well, America selections for the football team, almost nothing to do with any of them ex- what hasn’t, and what one thought of the have never been greater. Faculty honors for cept to serve as a cheerleader. Instead, I work. Ever since agreeing to serve as Chair outstanding educational work have also must thank all the people who worked as in 1994, I have been waiting for some very never been greater. heads of major committees and programs. A unpleasant disaster to strike that I’d have to Freshman-Sophomore Program far from complete list includes Mel deal with. I’m still waiting and with less Hochster, Ralf Spatzier, Igor Dolgachev, Many faculty continue to work hard at than a month to go (as of this writing), it’s Toby Stafford, David Barrett, Charlie improving our freshman-sophomore pro- pretty clear that none is going to happen! I Doering, Peter Scott, Dick Canary, Rob gram, being sure we have a wide array of attribute this to the great shape and the Lazarsfeld, Curtis Huntington, Mort courses so that every Michigan freshman trends that had been put in place under Don Brown, Pat Shure, Phil Hanlon, Dan has an appropriate course to help them Lewis’s decade of chairing the department. Burns and Carolyn Dean. They did the ac- learn the mathematics they need to succeed Don has the record of being the best Chair tual work. As to “running the department,” in whatever career they choose. We are of a math department I’ve ever known. If most of the credit for this has to go to the working hard to find ways to use the there was a theme to my years as Chair, it Associate Chairs, Paul Federbush, Jim internet to enhance and improve the courses was to continue to support the many good Kister, Andreas Blass, Berit Stensones, as well as teach more of the technology stu- things that were already happening. Alejandro Uribe, and especially Peter dents need to learn. It’s also the case that serving as Chair is Hinman who served so many years as As- Junior-Senior Program a very interesting job. The job of professor sociate Chair for Education and the Under- is good because one can keep learning new We’ve added many new courses (e.g. graduate Program Director. things every day; by this scale, the job of mathematical biology) and give a lot of fac- I can’t forget Jeffrey Rauch, who, as being Chair is very good! One gets to meet ulty attention to the undergraduate major he did once before for Don Lewis, stepped and work with colleagues from around the program, including our annual Career Day in to serve as Chair for a year, perhaps our University to help make Michigan a better (for which we depend on the generous help most successful recruiting year of the last place for students and faculty. I have been of many alums) and Awards Ceremony. decade, when I took a sabbatical leave. In very impressed with the quality and dedica- New degree opportunities have also been fact, Jeffrey has done a big administrative tion of colleagues I’ve met, dealt with, and added as well as the possibility of minoring job just about every year. We have a great learned from. This includes Chairs and in mathematics. faculty and just about everybody pitches in heads of other units as well as the Deans of Graduate Program to do the work. our College. As a faculty member, one of- Much more fellowship support than So, you can see I’ve had a great time ten shares Dean jokes—like the one where ever before is available through our NSF serving as Chair. Nevertheless, I am happy the irate parent calls to complain about the VIGRE grant, the largest such grant in the to turn it over to others, as it is tiring and lousy teacher her child has and demands to country. A new doctoral program in Applied I’m out of ideas. I’ll be taking a term of speak with “no one lower than the Dean;” and Interdisciplinary Mathematics has been leave this fall to concentrate once again on whereupon the Dean’s secretary responds, added along with our participation in the the excitement of doing research in math- “Madam, there is no one lower than the Masters Program in Financial Engineering, ematics and then return to teaching and re- Dean.” But the truth is, at least in the Col- both of which give more opportunities to search in January. However, I’ll be here, lege of LS & A at Michigan, the Deans and Michigan graduate students. ready to help out the new departmental Associate Deans have all been very intelli- leaders when called upon, just as Don Outreach Program gent and committed faculty who highly Lewis has always been there for me when I value and support the educational and re- Many more faculty than ever before are needed help. I’ll do all I can to help Trevor search missions of the University. involved with outreach programs to high and Alejandro continue to make us the very As to what’s gone well, the list is simply school students and teachers, with at least best math department for research AND too long to cover except in the barest detail. three such programs in place. I’m especially education in the country! - Professor B. Alan Taylor

6 Wooley, continued from page 1 Similarly, at the postdoctoral and gradu- will confront us over the next several years. ate level we find ourselves pressured on As a public institution, we have a duty to competitive advantage in order to increase compensation, teaching load and resources, provide mathematical training to meet the the number of our star-rated groups of re- largely on account of the new VIGRE pro- needs of the “New Economy,” broadly con- searchers. Already, we have highly visible gram funded by the National Science Foun- strued. We must train students in areas of such groups in algebraic geometry, number dation. This program has substantially mathematics increasingly demanded by em- theory, several complex variables, and alge- expanded the availability of competitive ployers in computer science, financial braic combinatorics, and we will seek to postdoctoral and graduate student packages mathematics, bioinformatics, etc., both at build new groups, both on long-standing to U.S. citizens, and thus we find ourselves undergraduate and at graduate levels. This strengths as well as in new areas. The more competing for recruits with many more obligation offers challenges, but also pos- recent moves by the department into ap- well-funded programs than hitherto. To sible rewards. In common with departments plied, interdisciplinary and emerging math- compete effectively, we will need to find a across the nation, we are experiencing a ematics (including financial mathematics, way to create additional independently continued decline in the number of math- mathematical biology, computer science, funded postdoctoral and graduate positions ematics majors enrolled in our program. mathematics education) will form an inte- (along the lines of our current Hildebrandt Perhaps by embracing the challenge of gral part of this thrust. Assistant Professorships). training for the above emerging areas, we will make progress on reversing this trend. The increasing competitiveness in the Education quality of our permanent faculty has been Perhaps the biggest and most immediate Summary accompanied by a corresponding increase issue that will influence our educational While it is satisfying to observe that we in the vigor of our Postdoctoral program. mission in mathematics is the increasing are more competitive than ever as a depart- We currently have over 50 postdoctorates role of computers. The future will undoubt- ment, both in research and teaching, we working in the Department, a level one edly bring increased integration of comput- face serious pressure in recruitment, espe- might even consider too vigorous! Such a ers and teaching. Our challenge will be to cially so far as postdoctorates and graduate large pool of energetic young talent pro- enhance the experiences of both student students are concerned. We will seek to be- vides both an attractive research scene for and instructor as this transformation occurs. come leaders in applied, interdisciplinary faculty and graduate students, but also a It is obvious that proper use of technology and emerging areas of mathematics beyond stimulating environment for our under- can enhance our undergraduates’ experi- the core areas more familiar to the depart- graduates—especially those taking part in ences in the classroom (and outside too!). ment, and we will be forced to adapt to our REU (Research Experiences for Under- Faculty, on the other hand, are all too famil- changing technology, both in terms of our graduates) program. It is somewhat hum- iar with the large investment of time, money teaching practices, and in order to address bling to note how large a slice of North and energy involved in designing courses the increasing importance of mathematics America’s future faculty members are that properly exploit available technology. in underpinning the new economy. This all trained here at Michigan. However, following such initial investment, seems quite daunting! However, all of these Our graduate students are increasingly it is possible to achieve the first educational challenges offer excellent opportunities for competitive with the very strongest in goal, and also save time for faculty to in- the Mathematics Department to develop North America, and we will increasingly crease course development. and improve further. Check out your copies seek to find resources to bring the very best Computers also play a role in another of ContinuUM to monitor our progress! here to Michigan. Our new AIM (Applied important aspect of educational change that - Professor Trevor Wooley and Interdisciplinary Mathematics) Ph.D. program, in particular, offers to augment the opportunities available as we look to- wards placing our graduates increasingly outside the academic world. One might surmise from my comments Math Problem thus far that we are on the brink of entering Elysium, and so I offer some cautionary Assistant Professor Harm Derksen has developed math problems for competitions notes (the bad news!). First, we certainly such as the International Math Olympiad. Here is one of his problems to challenge face increasing outside pressure for our your math skills. The answer is elsewhere in this newsletter. best young faculty, and also when we seek

to hire senior faculty, from well-endowed

that 1

and interdisciplinary areas, in which we in-

xc; b2xc; b3xc; b4xc;::: creasingly seek to hire, frequently require b

hiring packages and resources going sub-

tains in nitely manypowers of 2. (For any real stantially beyond those usually available to con

mathematics. We will increasingly need to

umber y , by c denotes the largest integer  y .) find outside sources, in addition to pressur- n ing the College, in our attempts to rise to these challenges. 7 2001 Michigan Math and Hanlon, continued from page 2 problems. His report is being used as the basis for attacking mission-critical issues Science Scholars Program facing the NSA for the next 10 years. More recently, Hanlon’s research has With the support of the Office of the sity is like along with getting to know the involved computational genomics, as de- Provost and the College of Literature, Sci- beautiful city of Ann Arbor and other stu- scribed in the accompanying article. His ence and the Arts, the program formerly dents interested in the same subjects. Both work in biomathematics is bringing new known as Michigan Math Scholars (MMS, MMS and MMSS alumni report that this ideas to search for genetic information in a.k.a., Math Camp) expanded into Michi- program assisted them in selecting their the huge new databases that are emerging. gan Math and Science Scholars (MMSS). college majors and even in selecting an aca- The 2001 summer program offered high demic institution to attend. Many alumni Within the department, Hanlon has school students challenging mathematics are outstanding students today at the Uni- been a caring, challenging teacher and and statistics courses as well as courses in versity of Michigan and plan to pursue ca- mentor. He has had eight students complete astronomy, biology, chemistry, geology and reers in mathematics, science, medicine and their doctoral theses and is currently direct- physics. High school students (ages 14-18) engineering. ing four others. Students flock to his classes. He constructed a new combinato- from both the United States and Canada The MMSS administration, directed by rics curriculum at both the undergraduate found that their courses went well beyond Professor Dan Burns, is working on final- and graduate level, and developed an inno- the basic textbooks and classroom experi- izing the dates for the 2002 summer pro- vative class for non-mathematics concen- ences, giving them a hands-on approach gram and creating an exciting combination trators (Math 175 Cryptography) that was along with a glimpse of the exciting re- of math and science courses for the future the first to utilize the department’s now search possibilities in both mathematics and MMSS curriculum. Some possibilities in- widely recognized interactive group mode scientific fields. MMSS offers high school clude Introduction to Logic, The History of of instruction. In an effort to reach out to students the opportunity to explore math Science and Ethics, Neuro-Psychology and the broader Michigan community, Hanlon and science at the cutting edge, with labora- Abstract Geometry. The more popular conceived and implemented the Michigan tory research, field work and computer courses from 2001 such as The Nature of Math Scholars Program (Math Camp), pro- laboratories. Infinity, Cryptology, Microbiology and viding an intensive summer program for The mathematics courses that were of- Roller Coaster Physics will be offered as high school students. This program has fered in MMSS 2001 included The Nature well in 2002. For future inquires or to be proved to be a superb recruiting tool. of Infinity, taught by Professor Andreas added to the Michigan Math and Science Blass, Interactive Statistics, taught by Pro- Scholars mailing list for a future brochure Hanlon is committed to serving the de- fessor Martha Aliaga, and Mathematical complete with application information, partment, college and University. In the Theory in Biology, taught by Professors please call (734) 764-0335 or send email to college, he has been an Executive Commit- Trachette Jackson and Patrick Nelson. Pro- [email protected]. Visit the MMSS tee Member, and on the Search Committee fessor Sergey Fomin taught Codes, Ciphers website at www.math.lsa.umich.edu/mmss/ for the new Dean. He is a member of the and Secret Messages, an introductory for more information and updates about this Board in Control of Intercollegiate Athlet- course to cryptology, and Professors Hugh amazing summer program for high school ics, and was one of two faculty asked to Montgomery and Carolyn Dean taught students. serve on the search committee for Athletic Director. He has been a member of the number theory to aspiring mathematicians - Annie Marshak Dowling Life Sciences Advisory Committee, mem- in a course titled Exploring Number MMSS Program Coordinator Theory: From Ancient Greece to Internet ber and Chair of the Rackham Divisional Security. Board, and was on the Faculty Advisory Committee on Information Technology. Science courses offered included Envi- ronmental and Medical Microbiology, Ge- nome Sequences and Human Health, Mysteries of Embryology, The Large Scale Structure of the Universe, Michigan Rocks! The Geology of Southeastern Michigan, A Journey through Modern Molecular Sci- ence—an Introduction to Chemistry, and Roller Coaster Physics. All of these courses were taught by outstanding Univer- sity of Michigan faculty members who not only love their subjects of study, but also love teaching their subjects to enthusiastic students. All MMSS participants get a great idea MMSS Program participants study the environmental history of a glacial kettle lake by of what studying at a major research univer- examining the sediment core at Pickerel Lake, MI. Geology Department photo. 8 Bass, continued from page 4 Others aim to generate new fundamen- This approach seems so natural and rea- tal knowledge and understanding about the sonable that one can well ask why it has was naively conceived. It was designed nature of mathematics instruction and its not happened long ago. A major reason is mainly by mathematicians with the subor- entailments. Specifically, the research that teaching is difficult to observe, to rep- dinate participation of educators. It vastly Bass and Ball are leading here at UM is resent, and to analyze. What makes the underestimated the learning opportunities aimed at what has come to be recognized work possible now is the existence of a that teachers would need to work with this as one of the central problems in U.S. rich, digitized data base of primary records radically new mathematical content. Hence mathematics education: the mathematical of teaching practice, consisting of video, the enactment of the new math curricula content knowledge of teachers, particularly transcripts, student work, teacher’s journal, was sometimes ineffectual. at the elementary level. and many other artifacts, for an entire year Reforms, Debates & Collaborations at Research has amply documented the of teaching of a third grade class. the Turn of the 21st Century shallow and fragile mathematical knowl- Analyzing these records in detail ad- We are amid a major period of educa- edge and skills of many U.S. teachers. dresses the following questions: tional reform in mathematics. Widespread What is not well understood is how to ad- • What kinds of mathematical concerns about weak mathematics achieve- dress the problem of teachers’ mathemati- knowledge—ideas and proce- ment have led to claims about the poor cal knowledge in ways that would improve dures, practices, sensibilities—is quality of teachers, teaching, and curricu- student learning. The most natural sound- entailed by the work of teaching? lum. Critics also point the finger at inad- ing approaches—to require more tradi- • In what forms do teachers need to equate professional education and poor tional mathematics courses, for example a hold such mathematical knowl- assessments. A significant difference in mathematics major—have proved disap- edge? Where and how in the the contemporary concerns is the pro- pointing. course of their work do teachers claimed aspiration to achieve high level What is the useful and usable math- use these sorts of mathematical mathematics learning for all students. ematical knowledge that teachers need for knowledge? One stream of activity in this area is a effective instruction? The topics and skills • How can teachers be helped to de- substantial effort at curricular and peda- specified by the curriculum offer a piece of velop such knowledge? gogical reform. The major initiatives, how- the answer, but this is hardly enough. Tra- ever, did not emanate from the disciplinary ditional approaches have been to situate the One focus has been the process of stu- experts in mathematics and science. In- school curriculum within the discipline, dents learning the principles of reasoning. stead, the initiatives came from the teach- and to amplify the ambient mathematical Here it is important to notice the moves ers’ professional organization—the ideas from a broader and deeper math- and guidance furnished by the teacher in National Council of Teachers of Math- ematical perspective. Although this makes the direction of such performance. The ematics (NCTM). Starting in 1989, the sense for the curricular questions, it has not children are able to reason because they NCTM promulgated mathematics standards proved as useful for determining the math- had been learning to do so all year. for curriculum, teaching, and assessment. ematical knowledge that it takes to teach. Among the things that Bass and Ball The National Science Foundation fol- In the Bass and Ball work, instead of are discovering about the mathematical lowed this initiative by funding projects for looking to the discipline, and importing its knowledge needed for teaching are: development of standards-based curricular perspectives into the classroom, they di- • that what matters is its use (for ex- materials for the schools. By the late rectly examine teaching practice. They ample, in hearing and interpreting 1990s these new curricula had been piloted ask, what is the nature of the work of students’ thinking, in revising and were in the first stages of adoption in teaching? What mathematical resources tasks, in managing discussion, schools around the country. It was only does it draw upon, in what forms, and in etc.); what ways are they used? To mathemati- then that their nature and significance be- • that it has to be substantially un- cally prepare mathematics teachers, one came vivid to large numbers of teachers, packed, in contrast with the ways should understand the mathematical entail- students, and parents. Reactions were di- that mathematicians hold such ments of their work. This is how the math- verse and often passionate. Suddenly edu- knowledge; cational improvement in mathematics ematical preparation of physicists, became a widespread concern, entering engineers, economists, and biologists is de- • that knowing connections across politics and the media. signed. Bass and Ball are engaged in a re- topics and stretching out to where lated endeavor by studying the work of students are headed matters. A second, more diffuse, and less pub- mathematics teaching and seeking to un- licly visible development is the gradual The improvement of mathematics edu- cover the mathematical resources—knowl- emergence of interdisciplinary collabora- cation (like that of science education and edge, skills, sensibilities—on which tions of mathematicians with educational literacy) is an urgent national need. The teaching depends. practitioners and researchers. Some of problems are complex and they inherently these are directed at interventions for the demand multi-disciplinary approaches for improvement of instruction—curriculum effective treatment. development, construction of assessment instruments, professional development of teachers, etc.

9 Several Outstanding Young Faculty Members Appointed

The department has made significant first holomorphic actions of reductive the proof of the Margulis conjecture, con- progress in recruiting and hiring many groups on complex affine space which are cerning quasi-isometries of higher-rank young faculty members. This year the de- not holomorphically linearizable. Recently, symmetric spaces. partment welcomed several new tenured or he gave a new proof of the “saturation con- tenure-track faculty. Profiles of the six new jecture” for multiplicities of irreducible rep- Assistant Professor Peter Miller re- department members are below. resentations in a tensor product of ceived his Ph.D. irreducible representations of the general from the University Associate Professor Brian Conrad re- linear group. His teaching background in- of Arizona in 1994. ceived his Ph.D. cludes working with Dutch participants of He studies applied from Princeton Uni- the International Mathematics Olympiad. mathematics, in par- versity in 1996. He ticular nonlinear is considered one of Assistant Professor Trachette Jackson waves. His major the best young alge- received her Ph.D. work has dealt with braic number theo- from the University the nonlinear rists in the field of Washington in Schrödinger equa- today. With col- 1998. She works in tion, particularly in leagues at other uni- biomathematics, par- connection with optics and nonlinear versities, he is ticularly in the waves. His study of optics is important and completing the re- analysis of systems timely, and constitutes one of the main sci- maining cases of the Shimura-Taniyama of nonlinear partial entific foundations of the computer and conjecture of the rational numbers. The im- differential equa- communications revolution. Miller will portance of this result was highlighted tions that model have the opportunity for interdisciplinary when ’s proof of Fermat’s problems in physiology such as cancer and interaction with faculty from electrical en- last theorem hinged on an incomplete proof cellular dynamics. She works on real bio- gineering and computer science. of the Shimura-Taniyama conjecture. His logical and medical problems, using real research in this area is groundbreaking, and data from experimentalists. At UM, Jack- Associate Professor Chris Skinner re- he has the potential to be a truly excep- son will be developing interactions with mi- ceived his Ph.D. tional leader in the field. Conrad is also a crobiology, immunology, and the Cancer from Princeton Uni- superb lecturer and excellent teacher. This Center. She is a gifted lecturer who empha- versity in 1997. He year he has taken over the Undergraduate sizes interactive teaching techniques in her is considered one of Math Club. Each week numerous math ma- classes. the most outstanding jors meet for pizza and pop in the Nesbitt young number theo- Associate Professor Bruce Kleiner re- undergraduate commons room, and hear a rists practicing to- ceived his Ph.D. presentation by a faculty member. It has day. Skinner has from the University grown to a truly successful endeavor. been publishing in of California-Berke- mathematics since Assistant Professor Harm Derksen re- ley, in 1990. He 1989, his freshman ceived his Ph.D. was a faculty mem- year here at UM. His undergraduate thesis from the University ber at the University was solicited for publication in the Duke of Basel in 1997. of Pennsylvania and Mathematical Journal. Upon completion of He has done distin- the University of his Ph.D., he received a three-year appoint- guished work in Utah before coming ment at Princeton’s prestigious Institute for constructive invari- to UM. His initial Advanced Study, where he was awarded an ant theory, represen- field of research was Ostrowski Fellowship and a Clay Math- tation theory, affine differential geometry, and in his thesis he ematics Institute Fellowship. Skinner’s geometry and sym- classified four-dimensional manifolds with most significant contributions are to the bolic computation. positive curvature and a continuous symme- theory of diophantine equations in many Derksen has made try. Soon thereafter he proved a major re- variables over number fields, non-vanishing three major research contributions. He ob- sult about isoperimetric inequalities. He of twists of L-functions, and Galois repre- tained a polynomial bound for the degrees continued his research in the area of sentations and their application to modular- of generators of invariant rings of reductive nonpositive curved manifolds and mani- ity questions associated especially with groups, and introduced a new and simple folds without conjugate points. Kleiner’s elliptic curves. algorithm for finding such generators via a recent work is in the field of combinatorial Gröbner basis calculation. He found the group theory. His main result in the field is

10 Ronghua Pan - Institute of Mathematics, Three-Year Faculty Appointments Academia Sinica, Partial Differential Equations The department welcomed 29 new as- Mark Dickinson - Harvard, Algebraic Benjamin Richert - University of Illinois, sistant professors for the 2000-01 academic Geometry (Hildebrandt) Commutative Algebra/Algebraic Geometry year—a record! New assistant professors Anton Dzhamay - , Oliver Roth - University of Würzburg, are listed here with their doctoral institu- Partial Differential Equations/Math Physics tions and area of speciality. Hildebrandt Complex Analysis and VIGRE apointments are also indicated Gavril Farkas - University of Amsterdam, Victoria Sadovskaya - Pennsylvania State Algebraic Geometry Mahdi Asgari - Purdue, Number Theory University, Differential Geometry (Hildebrandt) Tatyana Foth - Pennsylvania State Eric Schippers - University of Toronto, University, Automorphic Forms Tibor Beke - M.I.T., Topology Complex Analysis Angela Gibney - University of Texas- Mark Skandera - M.I.T., Permutation Thomas Bieske - University of Pittsburgh, Austin, Algebraic Geometry (VIGRE) Geometric Function Theory (VIGRE) Statistics (VIGRE) Hans Johnston - Temple University, Michael Sullivan - , Gilberto Bini - Universita La Sapienza di Numerical Analysis Roma, Commutative Algebra/Algebraic Differential Geometry (VIGRE) Geometry Boris Kalinin - Pennsylvania State Kaushal Verma - Indiana University, University, Dynamical Systems Marcin Bownik - Washington University, Complex Analysis Harmonic Analysis Tao Luo - Institute of Mathematics, Thomas Weston - Harvard, Algebraic Academia Sinica, Non-Linear Dynamical Number Theory (Hildebrandt/NSF Ana Bravo - Autonomous University of Systems Madrid, Commutative Algebra Postdoctoral Fellow) Patrick Nelson - University of Seattle, Ming Yang - Columbia University, Stephen Bullock - Cornell University, Math Biology Differential Geometry Probability Thomas Nevins - University of Chicago, Daniel Chan - M.I.T., Algebra Gang Yu - University of Georgia, Number Algrbraic Geometry Theory

Faculty Kudos Kristen Moore was awarded the American Fellowship from the American Several faculty members received pro- Fellows are selected from the very best sci- Association of University Women Educa- motions this year. To Professor: Alexander entists of their generation. tional Foundation. This award is highly Barvinok, Dick Canary, Sergey Fomin William Fulton was elected a Foreign competitive, with only 18 fellowships for and Karen Smith. To Associate Professor: Member of the Royal Swedish Academy of all of the arts and humanities, social sci- Brian Conrad. Sciences. ences, and natural sciences. The following faculty members have Angela Gibney was awarded an out- Krishnan Shankar received the Marga- been invited to speak at the next Interna- standing dissertation award from the Uni- ret and Herman Sokol Postdoctoral Fellow- tional Congress of Mathematicians to be versity of Texas for her thesis, one of only ship Award in the Sciences, recognizing his held in the summer of 2002 in Beijing: four so honored out of over 800 graduates outstanding work in research and teaching. Tom Hales, Juha Heinonen, Toby from the University of Texas. Stafford, Trevor Wooley. Pat Shure was awarded the 11th Annual Gene Krause received the Excellence Louise Hay Award for Contributions to Hyman Bass was awarded the Excel- in Concentration Advising Award from Mathematics Education by the Association lence in Research Award from LS&A. LS&A. This award recognizes his long and for Women in Mathematics. The award Anthony Bloch is co-chairing the 2001 exemplary record as a concentration advi- cites Pat “not only on the breadth of her SIAM Conference on Control and its Ap- sor for students pursuing a teaching certifi- contributions to mathematics education, plications. cate in mathematics within the College. but also on her reputation as a superb Daniel Burns and Robert Megginson Robert Megginson was inducted into teacher and an inspiring role model for her received Excellence in Education Awards the Native American Science and Math- colleagues and students.” from LS&A, acknowledging their special ematics Wall of Fame. This is an honor site Karen Smith won the 2001 Ruth Lyttle contributions to undergraduate education. maintained at the Southwest Indian Poly- Satter Prize from the American Mathemati- Brian Conrad was awarded an NSF technic Institute in Albuquerque to recog- cal Society. The prize honors outstanding CAREER Award. nize Native Americans whose careers have contributions to mathematics research by a made significant contributions to both their woman in the previous five years. She re- Brian Conrad and Chris Skinner fields of study and the advancement of ceived the prize for her work in commuta- were named Alfred P. Sloan Research Fel- other Native Americans in science and tive algebra, and her more recent work that lows. An extraordinarily competitive award, mathematics. The site currently honors builds new bridges between commutative twelve Native Americans. algebra and algebraic geometry. 11 solvability for ∂ on a singular surface and Faculty Profile with David Barrett on a problem related to the Bergman kernel of a nonsmooth model Several Complex Variables domain. She credits these collaborations with opening some new horizons in her re- For the past few years the department some control theory and Lie theory (mostly search and forcing her to think in a more has been fortunate to have a special group connected to geometric problems). Varolin geometric way. Vassiliadou’s future re- of assistant professors who are extremely has collaborated with several people in the search projects involve trying to under- active in the general research area of sev- department and elsewhere, including John stand the geometry of singular varieties and eral complex variables. These four have Erik Fornæss, Mattias Jonsson, Rob analyzing symmetric spaces. been responsible for some exciting collabo- Lazarsfeld, Alex Schuster, Karen Smith ration with senior faculty as well as other and Arpad Toth. Vassiliadou is impressed with the stimulating atmosphere of the department. assistant professors. Each has a unique In addition to his many teaching re- background and area of interest. Here we “What I really liked about Michigan is that sponsibilities during his time at UM, you can feel that math is being done in this include brief profiles of the four faculty Varolin has organized numerous seminars, members. place. There are so many seminars and including the weekly Several Complex actvities on various subjects that you can Mattias Jonsson received his Ph.D. Variables seminar, the Quantum Mechanics get an idea of what’s going on in many from the Royal Institute of Technology in seminar and the Nevanlinna Theory semi- fields, not just your own.” Sweden. His current research interests are nar. He was an organizer for two Midwest in the areas of dynamical systems, financial SCV conferences in 1999. “Michigan has Vassiliadou plans to stay in the depart- mathematics, complex analysis and ergodic a very active faculty, and I’ve developed ment for one semester next year, then she theory. His research in higher-dimensional some great research topics with other fac- will join her husband in the Mathematics complex dynamics involves the ergodic ulty members,” Varolin says. Department of the University of Toronto. properties of iterates of holomorphic maps Varolin is active with the Ann Arbor Kaushal Verma is completing his first of complex manifolds, in particular com- Soccer Association. His team placed third year here at UM, after receiving his Ph.D. k plex projective space P . Jonsson has last year, and he hopes to have better luck from Indiana University in 1999. His main worked on joint projects in this area with this year. research interests include mapping prob- colleagues at Notre Dame, Penn State and lems in Cn, holomorphic correspondences, in Paris. In the area of financial mathemat- He will stay in the department next year pluripotential theory and complex dynam- ics, he is studying optimal trading strategies to participate in the Special Year in Com- ics. His thesis work involved understand- and other stochastic control problems. plex Analysis. ing the reflections principle in several During his work here, Jonsson has been Sophia Vassiliadou received her Ph.D. complex variables and its applications to able to participate in numerous interna- from the University of Notre Dame in studying the boundary behavior of tional conferences, including the Ph.D. 1997. Before coming to UM in 1998, she holomorphic mappings and analytic sets. Euroconference on Complex Analysis and was a postdoctoral fellow at the Max More recently his interests have broadened Holomorphic Dynamics in Spain, and the Planck Institute in Germany. Her research to include the dynamical study of Henon 2 International Conference on Dynamical interests are in the areas of several com- mappings in C , in particular their struc- Systems in Brazil. Jonsson was part of the plex variables and partial differential equa- tural stability. organizing committee for the 1999 Mid- tions. In particular, she is interested in Verma is also impressed and enthused west Several Complex Variables confer- proving the existence and regularity results by the research environment at Michigan. th , ence honoring Al Taylor’s 60 birthday. for solutions to the ∂ ∂ b, and ∂ - “There are many dynamic researchers in He is active in the Ann Arbor Juggling Arts Neumann problems on nonsmooth do- the department, and I am impressed by the Club, and can often be spotted on the Diag mains. Vassiliadou has worked with John number and variety of seminars and talks.” plying his art with other club members. Erik Fornæss on a question of local L2- “Michigan has a good research environ- ment for postdocs,” Jonsson said. “I have benefited from the extremely active re- search and the many seminars and oportunities for mathematical discussions.” The department is fortunate that Jonsson has accepted an offer of a tenure- track position. Dror Varolin received his Ph.D. in 1997 from the University of Wisconsin. He is interested in many areas of math- ematics, all centered around some aspect of geometry. His primary work has been in several complex variables, complex dynam- l-r: Kaushal Verma, Sophia Vassiliadou, Dror Varolin, Mattias Jonsson. ics, algebraic and analytic geometry, and Math Department photo. 12 Two Faculty Members Retire Jack McLaughlin 1923-2001 Jack Goldberg, Associate Professor of the local solubility of cubic forms, however, Mathematics, retired from active faculty remains definitive. One of Lewis’s main in- Professor Emeritus Jack E. status in May, 2000. He received his B.S. terests was the development of young math- McLaughlin passed away on January 12, degree from the City College of New York ematicians, and he directed 24 doctoral 2001. Born in Idaho in 1923, McLaughlin and his M.S. and Ph.D. degrees from the theses. received his B.S. from the University of University of Illinois at Urbana- Lewis served as Chair of the department Idaho in 1944, and his Ph.D. from the Cali- Champaign. Goldberg joined the UM math- from 1984-94. He was noted for his leader- fornia Institute of Technology in 1950. ematics faculty in 1961. ship in University affairs. This included McLaughlin joined UM as an Instructor Goldberg’s research has been in com- service on the Executive Committee of the in 1950, was promoted to Associate Profes- plex variables and special functions. He College of Literature, Science and the Arts, sor in 1958 and to Professor in 1963. He directed four dissertations in these areas. on the University Budget Priority Commit- retired from the Department in 1994. He In 1969-70, Goldberg was a visiting associ- tee, and on search committees for the was considered an excellent and demanding ate professor at Robert College in Istanbul, Deans of Literature, Science and the Arts, teacher, especially of honors students who Turkey. In 1981-82, he returned to Turkey of Engineering, and the Vice President for sought his courses to measure their ability. as a Fulbright Scholar at Bugazici Univer- Research. He has received numerous McLaughlin guided these students as chair sity in Istanbul. awards, including a Distinguished Faculty of the honors program for several years. He Best known as a popular, dynamic Achievement Award from UM, an had a unique success in impressing under- teacher involved in curriculum develop- Alexander von Humboldt Pries Award, and graduates with the beauty of math and the ment, Goldberg was active in bringing com- the Distinguished Public Service Award pleasure of discovery after intense effort. puters into the classroom. In 1980 he from the American Mathematical Society. He directed nineteen doctoral theses, and received the Amoco Foundation Good As Chair of the Math Library for many many of his students have become leaders Teaching Award from UM. He has written years, Lewis was instrumental in getting it in their fields of interest. classified as a Level 5 library. four textbooks stemming from his teaching In 1986, he received the Amoco Foun- on linear algebra, matrix theory, differential From 1995-99, Lewis was based in dation Good Teaching Award. In the letters equations and other topics in applied math- Washington, D.C., as the Director of the of recommendation submitted by his former ematics. Division of Mathematical Sciences of the students, a great number of them cited An active member of the department, National Science Foundation. McLaughlin as the best and most inspiring Goldberg was an Associate Chair from He has been granted emeritus status by teacher they had in their academic careers. 1975-77, and served on several University the Regents. The mastery of the subject he displayed in committees, including the Board in Control his teaching influenced many of his stu- of Intercollegiate Athletics. He has been Emeritus Faculty and dents to pursue a career in mathematics. granted emeritus status by the Regents. Friends Gather McLaughlin’s research ranged widely, encompassing several subfields of alge- In May, 2001, the department hosted a Donald J. Lewis, Professor of Math- bra—lattice theory, finite groups, and com- luncheon for emeritus faculty and friends ematics, retired from active faculty status in mutative algebra. He discovered one of the of the department. More than 45 people at- May, 2000. Lewis received his B.S. from sporadic finite simple groups, that of order tended the luncheon, which was an oppor- the College of St. Thomas and his M.S. and 898,128,000, which now bears his name. tunity to renew acquaintances, greet Ph.D. from UM. Prior to joining the UM He also participated in the discovery of a long-time colleagues, and find out about faculty in 1961, he was an instructor at module of finite projective dimension with current departmental happenings. Ohio State, an NSF fellow at the Institute a negative intersection multiplicity. His for Advanced Study in Princeton, and a fac- The program for the day began with work on group cohomology, most of which ulty member at Notre Dame. Lewis was current Chair Al Taylor and incoming passed on through the writings of his stu- promoted to Professor in 1963. Chair Trevor Wooley sharing recent de- dents, has had an important impact on the partmental highlights, and future plans. field. He was well respected by his col- Lewis’s research lies in the area of num- (See the Chair’s Notes columns for further leagues in the field. Paul Halmos, his UM ber theory concerned primarily with details.) Associate Professor Chris Skinner colleague, once said that there are a number Diophantine problems, and encompasses presented the mathematical portion of the of ways to tackle a mathematical problem, the theory of algebraic number fields and program “Right triangles, a million dollars, but when all else fails, ask McLaughlin. function fields, and arithmetic geometry. and number theory at Michigan.” While a number of his results have been While enjoying the intellectual chal- improved in recent times, it is characteristic Everyone in attendance agreed that the lenges of mathematics, McLaughlin had to especially of his earlier work that he was luncheon was a wonderful opportunity to overcome the physical challenges of mul- the first to obtain any kind of result on a share current achievements with the faculty tiple sclerosis. He lived with the disease for problem, and that this decisive progress who helped to make the department what it the last 30 years of his life. McLaughlin’s cleared the way for subsequent develop- is today. Hopefully, an event such as this physical challenges rarely limited him in his ments. The work in his thesis concerning will be repeated on an annual basis. teaching, research or academic activities.

13 VIGRE Activities Enrich the Department

Fall 2000 marked the first full semester smarts,” with topics including how to sub- beneficial way to learn.” Otero is currently of activities for the VIGRE (Vertical Inte- mit papers for publication, how to apply for developing a student applied math seminar. gration of Research and Education) pro- grants and jobs, what the American Math- He plans on continuing research with Pro- gram in the department. The current ematical Society does, etc. fessor Doering in the area of mathematical program provides financial support for 30 Integrated Working Groups: Faculty, fluid dynamics and problems of heat trans- graduate students and 4 postdoc assistant postdocs, graduate students and under- port in turbulent flows. professors, and allows the department to graduates meet to work on a common area Assistant Professor Angela Gibney’s in- offer professional development activities of mathematics or a problem. The two terest in math was fostered at a young age, designed to foster close contact between groups that were held this year focused on since her mother studied the subject. She students, postdocs and permanent faculty. the topics of Mathematical Fluid Dynamics understood early The program reduces the teaching respon- and Non Linear Systems, and Numerical that mathwas inter- sibilities for participants, allowing them to Analysis. esting, and was at profit more fully from the rich mathemati- Undergraduate REU Summer Pro- the heart of most cal life of the department. Additional ac- sciences. Gibney re- tivities, including a large number of gram: Undergraduate math majors work on research projects with faculty members. ceived her Ph.D. research experiences, will be offered to un- from the University dergraduates. While the activities de- The participants met once a week during the summer and coordinated with two of Texas, Austin. scribed below are designed for and She was recently supported by the VIGRE program, they VIGRE graduate trainees. The graduate coordinators gave talks on mathematics, awarded UTA’s clearly are of benefit to all members of the Outstanding Disser- department. gave advice on applying to graduate school, and organized guest speakers. tation Award. Numerous activities have been de- Undergraduate Math Club: This Gibney feels that the VIGRE program signed and implemented to foster interac- offers an ideal opportunity to teach, while tion between graduate students, postdocs group of undergraduate math majors meets with a faculty mentor who facilitates math- still having the time to participate in the in- and senior faculty within the department, tellectual life of the department. The de- and include opportunities for undergradu- ematical discussion and organizes guest speakers. partment houses some of the premiere ate participation in research. Here is a de- faculty members in her area of interest, al- Graduate student Jesse Otero is an up- scription of the current seminars and gebraic geometry. “Teaching only one per level student participating in the groups developed as part of the VIGRE class per semester makes scholarship VIGRE program. He was a graduate stu- program: easier. I want to get as much as possible dent in the depart- VIGRE Seminar: Intended for ad- out of my experience here, and this allows ment in 1994-5, vanced undergraduates and graduate stu- for the time to do research, as well as expo- and returned to his dents, these talks by internal and external sure to the other mathematicians.” She has graduate studies in speakers are related to diverse applications also enjoyed the non-math presentations 1998. During his of mathematics, career possibilities in the about job seeking and the career planning hiatus, Otero mathematical sciences and important process, that can benefit all members of the taught high school trends within mathematics itself. department. algebra and geom- Open Problem Seminar: Intended for etry in Florida. He Gibney is currently working with Assis- postdocs and advanced graduate students, and Jessica tant Professor Gavril Farkas on research. participants present open problems in their Sidman were the She would like to develop a Saturday area of research. The goal is to help coordinators of the morning math group designed to reach the younger colleagues develop independent undergraduate REU program last summer. general public, including high school stu- research agendas. Seminars are held in dents. “Since VIGRE emphasizes partici- Otero embraced mathematics because each of four areas: algebra, analysis, ap- pation of all levels in the field of he excelled in the subject and enjoyed plied mathematics and geometry-topology. mathematics, this would allow us to reach studying it. He is currently working with students prior to their enrollment in col- Graduate Student and Postdoc Pro- Charlie Doering and has benefited greatly lege, as well as emphasize to the commu- seminars: The two separate seminars are from the various VIGRE activities. “The nity the significance of math in all areas of informal meetings under the leadership of a support provided by the program allows me science.” senior faculty member. The basic idea of more time to work on research and other the graduate student seminar is to expose activities. I have particularly enjoyed the participants to different aspects of the Integrated Working Group in Mathematical mathematical profession, and are largely Fluid Dynamics and Non Linear Systems. cultural and non-technical in nature. The The group is class-like, and allows for par- postdoc seminar leader helps younger col- ticipation of all levels. I found it a very leagues development professional “street

14 Recent PhD Recipients Graduate Dariush Ehsani completed his disser- Ian Pulizzotto completed his disserta- Program News tation “The Solution of the d-bar Neumann tion “Heat Flow in a Random Medium and Problem on Non-Smooth Model Domains” Homogenization” under the direction of The Mathematics Graduate Program under the direction of David Barrett. He Joe Conlon. continues its success in recruiting and re- will be an assistant professor at Texas completed his disserta- taining students. For the 2000-01 academic A&M University. tion “Linear Series on Moduli Space of year, there were 116 active students in the Florian Enescu completed his disserta- Vector Bundles on Curves” under the di- Ph.D. and Masters programs. In March tion “A Study of F-Rationality and F- rection of Robert Lazarsfeld. He will be an 2001, the Department hosted another Injectivity” under the direction of Mel assistant professor at Harvard. Graduate Recruiting weekend. Fourteen students attended the weekend, and ten ad- Hochster. He will be an assistant professor Kimberly Retert completed her disser- at the University of Utah. ditional students visited the department at tation “Noncommutative Curves in other times. Twenty students have been ac- Sara Faridi completed her dissertation Grothendieck Categories” under the direc- cepted to the graduate program for fall “Closure Operations on Ideals” under the tion of Toby Stafford. She will be an assis- 2001. direction of Karen Smith. Faridi is an as- tant professor at Texas A&M University. Rackham Predoctoral Fellowship sistant professor at George Washington Timothy Schwider completed his dis- University, in Washington, D.C. sertation “The Classification of Essential A mathematics student has again been Patrick Hagerty completed his disser- Laminations in Dehn Surgeries on the Fig- awarded a Rackham Predoctoral Fellow- tation “Radiation Induced Instability” un- ure Eight Knot” under the direction of ship for the 2001-02 year. An extrememly der the direction of Anthony Bloch. He Peter Scott. competitive fellowship, only 60 are awarded each year. Eduard-Wilhelm will be an assistant professor at the Univer- Kendrick Smith completed his disser- Kirr, who is studying under the direction sity of Arizona. tation “The Mod 2 Cohomology of some of Anthony Bloch, received the fellowship Eric Hall completed his dissertation Classifying Spaces of Compact Lie for his dissertation “Resonance Phenom- “Generic Extensions of Permutation Mod- Groups” under the direction of Igor Kriz. ena in Hamiltonian Partial Differential els of Set Theory” under the direction of He is an assistant research scientist in the Equations.” Kirr is developing a method of Andreas Blass. He is a postdoc at Purdue University of Michigan Information Tech- investigating autonomous Hamiltonian sys- University. nology Division. tems subject to time dependent perturba- Jason Howald completed his disserta- Craig Sutton completed his disserta- tions. His study analyzes the coupling tion “Calculations with Multiplier Ideals” tion “Applications of Representation between the bound states and the radiation under the direction of Robert Lazarsfeld. Theory to Dynamics and Spectral Geom- modes of the unperturbed Hamiltonian. In- Howald will stay on as a lecturer at Michi- etry” under the direction of Ralf Spatzier. stability of the natural oscillations and their gan for one more year. Sutton will be an assistant professor at decay rate is obtained, and concrete appli- Melinda Koelling completed her dis- Dartmouth University. cations in quantum mechanics, optics and sertation “Dynamics of Generalizations of Rachel Weir completed her disserta- telecommunications are presented. the Toda Lattice” under the direction of tion “Canonical Divisors and Invariant Outstanding Graduate Student Anthony Bloch. She will be an assistant Subspaces in Weighted Bergman Spaces” Instructors professor at Rensselear Polytechnic Insti- under the direction of Peter Duren. She tute. will be an assistant professor at Virginia Elliot Lawes and Rachel Weir were Polytechnic Institute. awarded the department’s Outstanding Graduate Student Instructor award for the year 2000-01. Elliot has taught three differ- ent introductory calculus classes during the Outstanding Dissertation Recognized past four years. He is studying under the direction of Tom Hales. Rachel, who suc- Dennis Keeler received the Sumner B. Myers Prize for the best Ph.D. thesis in cessfully defended her dissertation under mathematics for the year 2000. He was also one of only nine recent Ph.D. recipients the direction of Peter Duren, has also university-wide to receive a Rackham Distinguished Dissertation Award. Keeler is taught three different intoductory calculus currently a Moore Instructor/NSF Postdoctoral Fellow at MIT. classes during various semesters in her aca- For his dissertation “Noncommutative Ample Divisors,” Keeler examined ample demic career. divisors in ordinary commutative algebraic geometry. The ample divisor is used to rep- Million Dollar Friend resent the variety in a particularly useful form and can be used as an analytical starting point. Keeler tackled the following questions that have been raised regarding ample Graduate student Haggai Elitzur was divisors: Under what conditions can an algebraic variety be expected to have a divi- the “phone a friend” for a contestant on sor? Are “left-handed” and “right-handed” noncommutative ample divisors different? “Who Wants to be a Millionaire” this year. Keeler proved that there are no differences between these two types of noncommuta- He correctly answered the final $1,000,000 tive ample divisors. He also outlined criteria for an ample divisor. Many of his results question and his friend won the top prize! have been published in the Journal of the American Mathematical Society. 15 New Undergraduate Program Solution to Math Problem by Harm Derksen

in Risk and Finance Define for all n. Then for all n and we

n n

De ne a := 2 =x b2 =xc

have n

for all n. Then 0  a < 1 for

The Departments of Mathematics and Students in this program will receive . n

n and wehave

Economics have developed a new interdis- the benefits of a liberal arts degree, which If allfor some n, then for all and we 

ciplinary undergraduate concentration in include exposure to a wide range of disci- are done. 1

2a if a < ,

n n

2

a =

n+1

financial economics and mathematics. plines and the central role of language and 1

2a 1 if a  : n We may assumen that for all . expression as part of the educational expe- 2

Modern finance uses mathematical meth- Suppose that there exists a con-

If a = 0 for some n, then

rience. n

ods to study the behavior of firms and indi- stant N such that for all . This m

viduals in asset markets, the market m

2 =xcx =2 The new concentration will require sub- leads to a contractionb because as

determination of asset prices, and links be- stantial resources. Funding is needed to and for all m. We conclude that

m  n and we are done. tween financial market outcomes and the hire faculty with broad interests in teaching for forinfinitely all many positive integers

overall economy. Finance addresses how and research in finance and the analysis of m.

We may assume that a 6=

firms and households manage their affairs risk. n

for all n  0. Supp ose that when faced with risk and uncertainty. It 0If , then

New specialized courses and a program

exists a constant N such also addresses how risk affects overall eco- there

of internships will be offered to build on and where .

a  1=2 for all m  N . nomic outcomes. that

the departments’ strong base of existing m tradiction b e-

The area of risk and finance is a natural courses and programs. This leads to a con

mN

a ! 1 as a = 2

subject for a joint program between eco- cause N

There is widespread student interest in m

! 1 and a < 1 for all nomics and mathematics. m

the economics and mathematics of risk and m

m. Thus we conclude that a >

The disciplines share a common meth- finance, and our alumni/ae have urged us to m

=2 for in nitely many p ositive odological perspective that uses rigorous develop such a program to respond to and 1

modeling in the formulation and solution

tegers m. support that interest. in

of problems.

1

If a  , then m

The economic questions of finance— 2 m

which involve the simultaneous modeling m

0 < ( b2 =xc +1)x 2

of risk and choices over time—require spe-

1

=(1 a )x< x<1: m

cific advanced mathematical techniques. 2

m

and bb xc = 2 where b = m

Finance is an area in which the applica- m

m

2 =xc +1. tion of mathematics to understanding hu- b man behavior has been especially successful. Principles derived from math- ematical reasoning have become a standard part of the tools used on Wall Street and in Career Day 2000 financial centers around the world. The department hosted another successful Mathematics Career Day conference in A concentration in risk and finance October. Over 75 students participated in the event. Both graduate and undergraduate links well with the departments’ existing students were able to meet with representatives from business, education and strengths in areas such as actuarial science academia, and discover the opportunities available in business for mathematicians. Ev- and macroeconomics. eryone involved in the event agreed that it was a successful and worthwhile afternoon. The Departments of Mathematics and Alumni participants: Economics have collaborated to develop a Eric Breck '98 - Computational Linguist, Boston, MA new curriculum. It will be directed at top students who combine an interest in risk Julie Frohlich '97 - Math Teacher, Troy School District and finance with strong motivation for rig- Kimberly Hartzfeld '93 - Manager, Anderson Consulting orous analysis. A special feature of the program, which distinguishes it from busi- David Kaprelian '85 - Consultant, Towers Perrin ness school programs, is that it will be situ- Ed Kimball '71 - Principal Consultant, PricewaterhouseCoopers ated within a broader liberal arts context. Daniel Maki '66 - Chairman, Mathematics Department, Indiana University, Vice- The program will be staffed by eco- President, CDT nomics and mathematics professors who have an interest in finance, but who are Dick McLaughlin '62 - Technical Supervisor/Software Engineer, Bell Laboratories closely integrated into their respective dis- (retired) ciplines. Robert Nelson '75 - President, Airflow Sciences Corp. Andrew Nobel '97 - Consultant, Anderson Consulting Carmen Saleh '95 - Management Consultant, PricewaterhouseCoopers 16 Undergraduate Award Recipients Actuarial Program

The department’s team for the William Stacey Barbosa received the Leon P. Highlights Lowell Putnam Mathematics Competition Zukowski Prize for outstanding service in placed 14th out of more that 434 teams par- the Math Lab. It was another eventful academic ticipating in the event. The individual com- year for the Actuarial students. A Outstanding Achievement in Mathemat- record number of firms visited the petition included 2818 students from across ics Awards went to the following seniors: North America. This year’s team was com- campus during the fall semester pro- Nicholas Ehart prised of Chetan Balwe, who received an viding a number of interesting infor- Alan Grant honorable mention distinction for placing mation sessions. The second annual Joseph Marsano in the top 50 in the individual competition, “Mathematics Pizza Party for Under- Diana Murray Robert Easton, who individually placed in graduates,” sponsored by CIGNA, was Jonathan Ng the top 500, and Rishi Raj, who also re- held in October. In addition, students Megan Powell ceived an honorable mention distinction for went on a day trip to visit Lincoln Na- Brian Reed placing in the top 50 in the individual com- tional in Fort Wayne in November (af- Belal Sabki petition. UM student Thomas Dunlap also ter the examinations!). Recruiting was Jennifer Single placed in the top 500. very active during the winter semester Ludmilla Teng with most employers emphasizing Winner of the 18th Annual University of The Margaret S. Huntington Prize in summer internship programs. Michigan Undergraduate Mathematics Actuarial Science was awarded to the fol- th Competition was Tomas Sirgedas. Tied In conjunction with the 50 Anni- lowing first year students: for second place were Justin Altman, versary of the Conference of Consult- Amy Kimball, and Vivek Shende. Kristen Barbosa ing Actuaries, the American Academy Brian Chi Yan Chan of Actuaries sent a gift to the Univer- The William LeVeque Award in Num- Valerian Jone sity of Michigan, which was used to ber Theory was presented to Jesse Kass. Zubin Kapadia help fund fees for the professional ex- The award recognizes a student who is at Jessica Lobenherz aminations of the Casualty Actuarial most a junior and excels in the study of Fatih Ozsolak Society and the Society of Actuaries. number theory. Anne Piontek Because of gifts like this, we are able The following students received Evelyn Marina Polishchuk to encourage more students to start O. Bychinsky Awards, designed to recog- Tyler Richardson their professional examinations. nize underclassmen who show exceptional Shiu May Young The students helped to organize tu- promise in mathematics: The Irving S. Wolfson Award in Actu- toring sessions at a middle school in Jeffrey Allotta arial Science was presented to Gary Ann Arbor in the fall, and participated Robert Easton Levenbach. in the Detroit project during the winter Andrew Johnson semester. In addition, there was active Paul Kardosh received the Otto Rich- Kalman Nanes participation in a number of intra-mu- ter Memorial Prize in Actuarial Science. Vivek Shende ral sports. Unlike previous years, the Benjamin Singer received the Wirt The award for Outstanding Graduating “Underpaids” were victorious for the and Mary Cornwell Award, recognizing a Senior went to Gabriel Kerr. first time in a new sport for us—co-ed student who, during the four previous inner tube water polo—where we won Bertrand Guillou received the Sumner years, has demonstrated the greatest intel- some richly deserved IM t-shirts. Myers Award in Analysis, which recog- lectual curiosity, given the most promise of - Professor Curtis Huntington nizes a student who is at most a junior and original study and creative work in math. excels in the study of analysis.

Undergraduate Degree Recipients: December 2000, May 2001, August 2001 Yamina Acebo Nathan Fredericks Rebecca Jurva Tim McMillen Brian Poppen Jeffrey Steinkraus Daniel Allen William Gifford Kathy Kam Michael McNamara Megan Powell Bradley Stetson Justin Altman Dana Goldberg Paul Kardosh Cherianne Milne Anish Ramachandran David Stirrup Keith Andrews Anjela Govan Gabriel Kerr Brian Monteith Joe Ray Junichi Takayama Daniel Berebitsky Alan Grant James Kim Siwatu Moore Brian Reed Kuang Tan Rebecca Branch Lamont Hamilton Emily Konzen Diana Murray Belal Sabki Sze Tan Matthew Buckman Tawni Harrington Garret Koski-Budabin Jayjit Nandwana Richard Schierloh Ludmilla Teng Jennifer Cha Nobuya Hayashi Lok-Yi Kwok Stefan Neboyskey Joshua Schore Nicholas Trombetta Emily Cheng Kimberly Henlotter Paul Lam Jonathan Ng Susan Shortreed Wei Voo Hendrik Doorn Carl Horwitz Susan Lee Sara Parent Jennifer Single Nicole Vulcano Jonathan Efron Ryan Hutchinson Joseph Marsano Himani Patel Sarah Snyder Chad Williams Nicholas Ehart Edwin Jung Marcus Matthews Matthew Perry Sarvesh Soi 17 LeVeque Gift Funds Number Theory Alumna Receives William (Bill) J. LeVeque, former UM views in number theory that appeared in Medal professor of mathematics (1949-1971) and Mathematical Reviews (MR) from 1940- department Chair (1967-1970) has made a 1972 assembled by topic, for easy reference Alumna Karen K. Uhlenbeck (BS '64, gift to the department to establish an Excel- and for ease in seeing historical develop- PhD '68 Brandeis) was awarded the Na- lence in Number Theory Fund. This endow- ments. The Special Libraries Association tional Medal of Science. She was one of 12 ment will be used to enhance the number gave him an award for this effort. American scientists and engineers to re- theory program at Michigan by providing The Reviews were updated in 1984. ceive the medal, that was presented at a cer- funds for travel, seminar speakers, confer- This collection had a profound impact on emony in December in Washington, D.C. ences and related activities. the subject and was referenced almost daily In announcing the National Medal of LeVeque, the first number theorist on by researchers. Science winners, former President Bill the faculty, was instrumental in recruiting In 1964, when Ann Arbor was chosen Clinton declared “These exceptional scien- the second, D. J. Lewis. Together they de- as the new site for MR, LeVeque took on tists and engineers have transformed our veloped a very strong program that is now the task of relocation, finding space, as well world and enhanced our daily lives. Their one of the world’s best. A steady stream of as recruiting and training a staff. In June imagination and ingenuity will continue to long term visitors from England, Hungary 1965, MR moved and LeVeque served as inspire future generations of American and Poland gave decided breadth and inter- Executive Director for the next 15 months, scientists to remain at the cutting edge of national impact to the program. guiding MR to stability. scientific discovery and technological inno- vation.” LeVeque’s research areas included tran- In 1977, LeVeque became Executive scendental numbers, uniform distribution, Director of the American Mathematical So- Uhlenbeck, who holds the Sid W. and Diophantine approximation. His two ciety—a position he held until his retire- Richardson Foundation Regents Chair in volume 1956 monograph “Topics in Num- ment in 1988. As Director he led the society Mathematics at the University of Texas at ber Theory” was highly influential in the to become a major publisher of books and Austin, conducts research in geometry and development of number theory in this coun- journals, thereby putting it on sound finan- partial differential equations and studies ap- try, as was the MAA monograph “Studies cial standing. He pioneered the use of com- plications of geometry to large-scale prob- in Number Theory” that he edited. puters in printing, funded the development lems in high-energy physics. She is In 1960 he conceived the idea of updat- of LaTex, and played an encouraging role interested in the ways complex mathemati- ing L. E. Dickson’s “History of the Theory in the computerization of the MR data base, cal concepts find uses in research in other of Numbers” that covered the subject from which made MathSciNet possible. areas of science, such as ecology, molecular biology and the structure of materials. antiquity to 1910. LeVeque assembled a While an immensely imaginative and Who’s Who in number theory, including successful administrator, LeVeque never Uhlenbeck received the National Medal Davenport, Mahler, Erdos, Linnik, Turan, lost his love and interest in number theory. for Honor, the highest honor conferred on Renyi, and Deuring to work on the project, His generous gift will help number theory U.S. scientists, for her pioneering contribu- but the effort failed for lack of funding. In to flourish at Michigan, and the current fac- tions to global analysis and gauge theory 1974 he accomplished part of his goal by ulty members in number theory greatly ap- resulting in advances in mathematical phys- publishing a six volume collection “Re- preciate his contribution. ics and the theory of partial differential views in Number Theory” containing all re- equations. Cited as one of the founders of geometry based on analytical methods, she was also recognized for her leadership as a mentor for women and minorities in math- ematics education. “I feel very humble, as many greater New Graduate Fellowship Established scientists have received this award,” Professor and Mrs. Cameron Flint and Dearborn campuses. When he de- Uhlenbeck said. “I hope that my acceptance Courtney have established the Cameron cided to pursue his graduate education at will serve as encouragement to young and Jack Courtney Graduate Fellowship in UM, he was married with a child. He is women scientists and mathematicians.” the Department of Mathematics. The fel- grateful for the financial assistance he re- Uhlenbeck has taught at UT Austin lowship is named after Cameron Courtney, ceived during his studies, and that is the since 1987. She was born in Cleveland and who received his Ed.D. in 1965, and his reason he has established a graduate fellow- grew up in New Jersey. Prior to her ap- son John (Jack) Courtney, who received ship. pointment at UT Austin, she held faculty his Ph.D. in 1993. Funded through a chari- Jack Courtney worked with Christoph positions at University of California Berke- table remainder trust, the fellowship will Borgers in Numerical Analysis. Jack was ley, University of Illinois and University of provide financial assistance to a deserving the first student to finish in the Scientific Chicago. In addition to receiving numerous graduate student. Computing option that had just been estab- awards, honors and fellowships, including Cameron was a student of Phil Jones at lished. He is now on the faculty of Michi- most recently a Guggenheim Fellowship for UM, and spent 24 years teaching at UM- gan State University. 2002, Uhlenbeck received the UM Alumna of the Year Athena Award in 1984. 18 Considering a Alumni/ae Reply Form Donation to UM? We’d like to hear from you! Please complete and return this form for our alumni/ae files. You may mail it to the address below, fax it to 734-763-0937, or email the information to [email protected]. If you are contacted by the University of Michigan for a donation, you can ear- Name______mark your gift to the Department of Math- ematics. Simply tell the caller to designate University/Degree/Year______your gift to Mathematics or write Math- University/Degree/Year______ematics Department on the pledge card you University/Degree/Year______are sent. We greatly appreciate all of your Home Address______support, and we hope we can count on you to support future fund-raising projects. City, State Zip______Home Phone______Business Phone______Firm/Institution______Estate Gifts Position______Email Address______You can include the Department of This is a new address Mathematics in your estate plan. For infor- mation on charitable trusts and bequests to Information about yourself or comments on the newsletter: the department, contact:

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