The Quaternion


Just a Thought about
Poincaré
by Boris
Shekhtman
Andrei Okounkov, Grigori
Perelman, Terence Tao, Wendelin Werner. Which of these names sounds familiar? If
you circled Perelman you are not alone. I do not remember when so many people
from different walks of life asked me about a mathematician:
“Do you know the dude?
What’s he done?”
“Not personally but he
solved the Poincaré Conjecture.”
“What’s
that?”
“He proved that a
3dimensional, simplyconnected manifold is homeomorphic to a
sphere”
Then after a pause,
“Yeah, whatever, dude. What do you think? Is he nuts?”
So who is Perelman and
why is he crazy?
Grigori “Grisha” Perelman, WJM, 40,
mathematician, lives as a recluse in St. Petersburg, Russia, in small
onebedroom apartment with his mother. Favorite activities include opera, long
walks through the woods, gathering berries, mushrooms, and thinking. In 2002,
posted a proof of Poincaré Conjecture. Awarded Fields Medal, the traditional
“Nobel of mathematics” in August 2006, but declined to accept the prize. In
search of: Friends. (They don’t have to be
mathematicians).
Refusing the medal
brought him (and the Poincaré Conjecture) the notoriety. The other three people
mentioned at the beginning of this article also received Fields Medals but
accepted them and went unnoticed. Grisha stole the limelight. In December, 2006,
(four years after the discovery but a few months after the refusal) the journal
Science recognized Perelman’s proof
of the Poincaré Conjecture as the scientific “Breakthrough of the Year”, the
first such recognition in mathematics.
He certainly got more
fame than he would had he accepted. In the minus column, he is out about ten
thousand bucks (after taxes). You do the math. Power…? That remains to be seen, but
according to The New Yorker, another
former Fields Medal laureate, ShingTung Yau, attempted to “use” Perelman’s work
to gain absolute power over mathematics in
Is there a woman?
Well…you read his personal.
Yet there may be a
profound wisdom to his actions. A job in academia awards us the luxury of having
a day or so per week that I like to call “A Thinking Day.” A day, completely
void of anything mundane, spent in joy of thinking about anything that comes to
mind. No guilt, no interruptions, just me and my thoughts. An intellectual
Sabbath if you will. So ... maybe the “dude” is brave enough to give himself a
“Thinking Life.” Have you ever thought of that? I have (on my Thinking Day, of
course).
And then… maybe he is
simply nuts!
The R. Kent
Nagle Lecture Series
The NavierStokes
(ordinary differential) equations are extensions of
These equations are very
difficult to solve, and the Clay Institute has offered $ 1,000,000 for a
tractable solution as one of the seven “millennial problems” in modern
mathematics.
FangHua Lin, Silver Professor of
Mathematics at the Courant Institute of Mathematical Sciences at NYU and
recipient of a Sloan fellowship, a Presidential Young Investigator Award, the
Bochner Prize, and the Chern Prize, came to USF last spring to outline some of
the problems facing mathematicians who try to solve these
equations.
The equations start
with the “conservation of mass”: as a liquid or gas flows, none can appear or
disappear. So one starts by formulating the statement the amount of matter does not change; it can
only move from one place to another.
These statements are differential equations with unknowns: do solutions
for these unknowns exist? And
assuming that the equations are correct and solvable, how might we compute these
solutions?
The Nagle Lecture
Series was established in honor of the late R. Kent Nagle, a mathematician
deeply interested in mathematics in itself, in education and in society. In this spirit, the NLS invites world
renowned scholars to speak on mathematics in lectures designed for the general
public.
The next Nagle Lecture will be on November
1, when John H. Conway will speak at 7:30 pm in BSF 100. His talk will lead into the Knotting
Mathematics and Art Conference. For
more information, consult the event webpage http://www.math.usf.edu/~saito/Nagle/conway.html.
Transitions
Arun
Mukherjea retired
this summer. He received his Master's
degree in Applied Mathematics from
Meanwhile, Catherine
Bènèteau, Brendan Nagle, and Dmitry Khavinson joined our faculty during the
20062007 academic year.
Catherine Bènèteau received her Ph.D.
from the State University of New York at
Dmitry “Dima” Khavinson came to us from
the National Science Foundation, where he was the Program Director in Analysis,
and before that Distinguished Professor of Mathematics at the
Brendan Nagle received his PhD from
Faculty
News
Dima
Khavinson’s work in gravitational
microlensing got him an invitation to be a plenary speaker at New Trends in
Complex and Harmonic Analysis in
WenXiu Ma served as President of the
ChineseAmerican Association of Tampa Bay and coedited a special issue on
Topics on Integrable Systems in the Journal of Computational and Applied
Mathematics.
Jogi
Ratti and Marcus McWaters have published a new
text, College Algebra, with “a strong
emphasis on both concept development and reallife applications.” Published by Pearson/AddisonWesley, it
is designed to help students “find mathematics useful and
interesting.”
Vilmos Totik has coauthored a book, Problems and Theorems in Set Theory,
with Peter Komjáth of
Yuncheng You will be visiting
USF Math Club
Activities
Last year, the MAA Student
Chapter was led by Denise Kalos (President),
Members attended the
2006 MAA Suncoast Meeting at Hillsborough Community College, the 2007 MAA
Florida Section Meeting at FSU (where Matthew Williamson gave a talk), and the
2007 MAA/AMS Joint Meetings at New Orleans; we are grateful to the USF Student
Government, the Math & Stat Department, and generous donors for financial
support.
PME and the Math &
Stat Department twice hosted the biannual Hillsborough County Math Bowl, to
which all Hillsborough County High Schools send their best math students to
complete in individual and as team categories. About 400 students and teachers
showed up at the USF Sun dome in November, 2006 and April, 2007 for a halfday
of mathematical competitions in algebra, geometry, precalculus and calculus.
Overall winner bragging rights went to
Sandra Bird, Egor
Dolzhenko, Dewey Estep, Lisa Fazio, Amanda Griffith, Elizabeth Kieran and Oleg
Polupan reviewed a chapter of a new calculus book published by Freeman
Publishing Co., which awarded the
Math Club $500.00 for this work.
The PME’s annual
banquet in April featured thirteen new members: Joy D’Andrea, Gary Dowd, Zach
Jett, Dahomey Kadera, Kenneth Killian, John M. Kowalik, Jill Lusk,
Student
News
Ten students were awarded
doctorates between June 2006 and June 2007 (the dissertation director is in
parentheses): Kheira Ameur
(Masahiko Saito), Gokarna R. Aryal (Chris P. Tsokos), Louis R. Camara (Chris P.
Tsokos), Edgardo S. Cureg (Arunava Mukherjea), Jemal E. Gishe (Mourad E. H.
Ismail), Abdelelah M. Mostafa (Kandethody Ramachandran), Joni B. Pirnot
(
Twelve students were
awarded masters degrees: Hari P. Adhikari, Anand Ravindra Bhat, Chunling Cong,
Natalie Davis, Sandra D. Draper, Sasko Ivanov, David Paul Nezelek, Thucdoan T.
Nguyen, Wilkistar Otieno, Andrew Purcell, Arnut Paothong, and Yiting
Yu.
Twentyfive students
were awarded baccalaureate degrees: Eric Adams; Nichole Blaquiere; Oscar
Castro; Jason Copenhaver, Magna Cum Laude; Daniel Cordeiro; Lisa Fazio, Cum
Laude; Casey Garrett; Melody Goodenough, Magna Cum Laude; Amanda Griffith, Cum
Laude; Matthew Grace; Melissa Holmes; Crystal Johns; Juliana Kamenica; Elisabeth
Kieran, Magna Cum Laude; Sherry Lashley, Magna Cum Laude; Jason Paradis; Oleg
Polupan, Magna Cum Laude; Uriana Ponson; Marcus Rodriguez; Cassaundra Slessman;
Sherry Taylor, Magna Cum Laude; Aichuc Truong; Vien Truong; Shannon Watkins; and
Rachel Zemetres.
Center for
Mathematical Services
The thirtieth consecutive
USF summer program for gifted and high ability students ran from July 3 to
August 10. The program was divided
into two levels, each level having three components: Mathematics, Computer
Science, and Environmental Science.
Level I, for students entering grades 810, had 37 students and was
coordinated by
Justin Norris of
We had a very
successful program in 2007 and look forward to an even better program in
2008.