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The Quaternion The Quaternion Volume 22: Number 1; Fall, 2007 The Newsletter of the Department of Mathematics and Statistics Just a Thought about Poincaré The R. Kent Nagle Lecture Series by Boris Shekhtman The Navier-Stokes (ordinary differential) equations are Andrei Okounkov, Grigori Perelman, Terence Tao, extensions of Newton’s laws of motion to flows of Wendelin Werner. Which of these names sounds liquids or gases. Developed by Claude-Louis Navier familiar? If you circled Perelman you are not alone. I do and George Gabriel Stokes (among others) during the not remember when so many people from different Nineteenth century, these equations are critical in walks of life asked me about a mathematician: modeling weather, air flow around planes and rockets, “Do you know the dude? What’s he done?” motions of stars in a galaxy, and many other physical “Not personally but he solved the Poincaré phenomena. Conjecture.” These equations are very difficult to solve, and the “What’s that?” Clay Institute has offered $ 1,000,000 for a tractable “He proved that a 3-dimensional, simply-connected solution as one of the seven “millennial problems” in manifold is homeomorphic to a sphere” modern mathematics. Then after a pause, “Yeah, whatever, dude. What do Fang-Hua Lin , Silver Professor of Mathematics at you think? Is he nuts?” the Courant Institute of Mathematical Sciences at NYU So who is Perelman and why is he crazy? and recipient of a Sloan fellowship, a Presidential Young Grigori “Grisha” Perelman, WJM, 40, Investigator Award, the Bochner Prize, and the Chern mathematician, lives as a recluse in St. Petersburg, Prize, came to USF last spring to outline some of the Russia, in small one-bedroom apartment with his problems facing mathematicians who try to solve these mother. Favorite activities include opera, long walks equations. through the woods, gathering berries, mushrooms, and The equations start with the “conservation of mass”: thinking. In 2002, posted a proof of Poincaré as a liquid or gas flows, none can appear or disappear. Conjecture. Awarded Fields Medal, the traditional So one starts by formulating the statement the amount of “Nobel of mathematics” in August 2006, but declined to matter does not change; it can only move from one place accept the prize. In search of: Friends. (They don’t have to another . These statements are differential equations to be mathematicians). with unknowns: do solutions for these unknowns exist? Refusing the medal brought him (and the Poincaré And assuming that the equations are correct and Conjecture) the notoriety. The other three people solvable, how might we compute these solutions? mentioned at the beginning of this article also received The Nagle Lecture Series was established in honor of Fields Medals but accepted them and went unnoticed. the late R. Kent Nagle, a mathematician deeply Grisha stole the limelight. In December, 2006, (four interested in mathematics in itself, in education and in years after the discovery but a few months after the society. In this spirit, the NLS invites world renowned refusal) the journal Science recognized Perelman’s proof scholars to speak on mathematics in lectures designed of the Poincaré Conjecture as the scientific for the general public. “Breakthrough of the Year”, the first such recognition in The next Nagle Lecture will be on November 1, when mathematics. John H. Conway will speak at 7:30 pm in BSF 100. His He certainly got more fame than he would had he talk will lead into the Knotting Mathematics and Art accepted. In the minus column, he is out about ten Conference. For more information, consult the event thousand bucks (after taxes). You do the math. web-page Power…? That remains to be seen, but according to The http://www.math.usf.edu/~saito/Nagle/conway.html. see Perelman on Page 2 The Quaternion is an annual publication of the USF Department of Mathematics and Statistics, which can be visited on the web at <http://www.math.usf.edu/ >. Our e-mail address is < [email protected] >, our snail-mail address is Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave., PHY114, Tampa, FL 33620. Our phone number is (813) 974-2643, and our fax number is (813) 974-2700. The Quaternion, volume 22 Fall, 2007 Page 2 Perelman, continued from Page 1 Program Director in Analysis, and before that Distinguished Professor of Mathematics at the New Yorker, another former Fields Medal laureate, University of Arkansas. He received an M.S. from Shing-Tung Yau, attempted to “use” Perelman’s work Moscow State Pedagogical Institute (Moscow, USSR) to gain absolute power over mathematics in China (a in 1978, then, after immigrating to the United States, country of a billion people!). earned his Ph.D. from Brown University in 1983. He Is there a woman? Well…you read his personal. has worked in a broad range of areas of analysis, from Yet there may be a profound wisdom to his actions. approximation theory to potential theory to differential A job in academia awards us the luxury of having a day equations to real analysis to ... all appearing in two or so per week that I like to call “A Thinking Day.” A books and over seventy papers. He has also mentored day, completely void of anything mundane, spent in joy student theses from high school student projects to of thinking about anything that comes to mind. No guilt, doctoral dissertations. no interruptions, just me and my thoughts. An Brendan Nagle received his PhD from Emory intellectual Sabbath if you will. So ... maybe the “dude” University in 1999. The intervening years were spent as is brave enough to give himself a “Thinking Life.” a postdoctoral fellow at Georgia Institute of Have you ever thought of that? I have (on my Thinking Technology, and Assistant Professor at the University Day, of course). of Nevada, Reno. He continues his work in various And then… maybe he is simply nuts! areas of graph theory, especially hypergraph and extremal theory. Transitions Faculty News Arun Mukherjea retired this summer. He received his Master's degree in Applied Mathematics from Calcutta Natasha Jonoska was awarded the DNA Scientist of University in India and his Ph.D. degree in Mathematics the Year Award during the Thirteenth International from Wayne State University in Detroit. After a brief Meeting on DNA Computing this year. This award, stay at Eastern Michigan University as an Assistant also called the Tulip Award because the trophy is a Professor, he joined USF in 1969 as an Assistant crystal tulip, is given in recognition of long-term Professor of Mathematics. He has been a Professor of contributions to molecular computing. Tulips have Mathematics at USF since 1975. During his forty years been awarded annually since 2000, and are awarded at of service, Professor Mukherjea has been one of our the annual DNA Computing conference. most productive research mathematicians – publishing Dima Khavinson’s work in gravitational dozens of books, monographs, and chapters, and microlensing got him an invitation to be a plenary scholarly research papers. His research interests include speaker at New Trends in Complex and Harmonic the study of probability measures on algebraic Analysis in Bergen, Norway, in May. structures, weak convergence of their convolution Wen-Xiu Ma served as President of the Chinese- products, and random walks induced by such measures; American Association of Tampa Bay and co-edited a also, Markov chains, problems in multivariate analysis special issue on Topics on Integrable Systems in the concerning identification of parameters in multivariate Journal of Computational and Applied Mathematics. distributions, and random matrices and limit Manoug Manougian was invited to the Oxford distributions of their products. We wish him well on his Round Table to present a paper on reclaiming trust in further adventures. government; the conference itself was on the waning of Meanwhile, Catherine Bènèteau, Brendan Nagle, and trust in government. Dmitry Khavinson joined our faculty during the 2006- Jogi Ratti and Marcus McWaters have published a 2007 academic year. new text, College Algebra, with “a strong emphasis on Catherine Bènèteau received her Ph.D. from the both concept development and real-life applications.” State University of New York at Albany in 1999. After Published by Pearson/Addison-Wesley, it is designed to a stint at the Center for Talented Youth at Johns help students “find mathematics useful and interesting.” Hopkins University, she went to Seton Hall, where she Vilmos Totik has co-authored a book, Problems and continued her work in complex function theory. Her Theorems in Set Theory, with Peter Komjáth of Eotvas current NSF grant supports the development of a University in Budapest, Hungary. multidisciplinary course in wavelets and their Yuncheng You will be visiting Shanghai University applications. in China as a Ziqiang Distinguished Visiting Professor Dmitry “Dima” Khavinson came to us from the this fall. National Science Foundation, where he was the The Quaternion, volume 22 Fall, 2007 Page 3 USF Math Club Activities parentheses): Kheira Ameur (Masahiko Saito), Gokarna R. Aryal (Chris P. Tsokos), Louis R. Last year, the MAA Student Chapter was led by Camara (Chris P. Tsokos), Edgardo S. Cureg Denise Kalos (President), Michael Grossman (Arunava Mukherjea), Jemal E. Gishe (Mourad E. H. (Secretary), and Nicole Hooper and Ryan Grotheer Ismail), Abdelelah M. Mostafa (Kandethody (Treasurer). The PME was led by officers Egor Ramachandran), Joni B. Pirnot (Natasha Jonoska), Dolzhenko (President), and Christine Fitch (Vice- Joseph O. Quarcoo (Athanassios Kartsatos), Michiru President). The two clubs met jointly 14 times, and Shibata (under Yuncheng You), and Rebecca D. heard presentations by students Brent King and Wooten (Chris P. Tsokos). Clayton Beardsley, Oleg Polupan, Dewey Estep, and Twelve students were awarded masters degrees: Erik Lundberg, as well as former student and current Hari P.
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