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Fall 2007 Newsletter FALL/WINTER 2007-08 Volume 5 - Number 1 Courant Institute of Mathematical Sciences Akshay Venkatesh Awarded 2007 Packard Fellowship and 2007-08 Salem Prize Akshay Venkatesh, Associate He has also been awarded the 2007-08 Salem Professor of Mathematics, is Prize for his contributions to the analytic theory one of 20 researchers awarded of automorphic forms and its applications to clas- a 2007 Packard Fellowship, sical and modern problems in number theory, in established to strengthen uni- particular his introduction of novel methods that versity-based science and combine analytic- and ergodic-theoretic tech- engineering programs by sup- niques to resolve longstanding problems. The porting unusually creative researchers early in their Salem Prize is awarded every year by the AMS to careers. Akshay's award is "to study number theory a young mathematician judged to have done out- ... and to develop techniques to study L-functions, standing work in the field of analysis. which encode the behavior of prime numbers". Faculty: Recent Arrivals Subhash Khot, Associate Professor of Fellowship and a Sloan Research Fellowship. Computer Science. He works in theoretical computer science with an emphasis on computa- Petter Kolm, Clinical Associate Professor of tional complexity theory. His research Mathematics and Deputy Director of the includes probabilistically checkable proof Mathematics in Finance M.S. systems, hardness of approximation results Program. His interests include dele- and lower bounds in restricted models of gated portfolio management, financial computation. He has been awarded a econometrics, quantitative trading Sloan Foundation Fellowship, a Microsoft strategies, risk management, and optimal New Faculty Fellowship, and an NSF portfolio strategies. He coauthored the CAREER Award. books Financial Modeling of the Equity Market: From CAPM to Cointegration Rob Fergus, Assistant Professor of Computer (Wiley, 2006), Trends in Quantitative Science. His work is in the field of computer vision, with Finance (CFA Research Institute, 2006), and Robust Portfolio links to computer graphics and machine Management and Optimization (Wiley, 2007). learning. Specific areas of interest include object recognition, computational Jean-Claude Franchitti, Clinical Associate photography and problems in low-level Professor of Computer Science. His interests vision. He won the best paper award at include database systems and software the IEEE computer vision and pattern engineering, with an emphasis on large recognition conference in 2003, and in scale software architectures and business 2005 he co-taught a prize-winning short solutions. He has over 25 years of expe- course on object recognition at the IEEE rience in the industry, having held international conference on computer vision. executive positions in large US-based corporations and served on several Fengbo Hang, Associate Professor of industry standards committees, and has Mathematics. His research concerns nonlinear analysis conducted research as part of several and its applications to differential NSF and DARPA funded research programs. geometry and mathematical physics. He has worked on topology of Sobolev maps related to variational problems between Inside This Issue: manifolds, problems from conformal Puzzle.....................2 Graduate Research.......5 Paul Garabedian.........2 Student Showcase........ 5 geometry and sharp inequalities in Lakshmi Subramanian..3 Step Back in Time.......5 analysis and geometry. He was a recipient Donor List................4 NSF PIRE Grant...... 6 of the Sokol Postdoctoral Research COURANT INSTITUTE OF MATHEMATICAL SCIENCES FALL/WINTER NEWSLETTER 2007-08 Holiday Puzzle 2007 - Polish Hand Magic unusual at his age to be working with a brain that’s mathe- By Dennis Shasha, Professor of Computer Science matically still incisive. Not only is Prof. Garabedian still working but he is cur- I don't really know the origin of this trick but a smart and rently a groundbreaking leader in the field of magnetic elegant Polish woman taught it to me, whence the title. fusion. He spoke in Toki, Japan on October 18 at the 16th International Stellerator Workshop, the nature of which he In the process of learning multiplication by single digits, says is unusual because it’s in a field of physics, using com- children have an easy time provided one digit is less than putational science. 5. They have much more trouble when both are 5 or over. That is what Polish Hand Magic addresses. In magnetic fusion, hot deuterium and tritium Let me explain the trick with a few examples. Suppose ions are combined to form helium and release that you want to multiply 9 by 7. You represent 9 (= 5 + neutrons intended to provide a commercial 4) by ||||., that is four fingers up and the thumb down. source of energy. The color map of the hydrogen You represent the 7 (= 5 + 2) by ||..., that is two fingers plasma in the figure displays a symmetry up and three fingers down. The total number of fingers property that enhances confinement. Twelve only that are up is 6. That becomes six tens. The product of the moderately-twisted coils generate a magnetic fingers that are down is 3 x 1 = 3. So the answer is 63. field designed to keep the plasma in stable equilibrium separated from material walls. Here is another example: 8 x 6. 8 becomes |||.. and 6 becomes |....; 4 fingers are up in total and the product of the down fingers is 2 x 4 = 8. So the answer is 48. This even works for extreme cases such as 10 x 5. 10 becomes ||||| and 5 becomes .....; we have 5 fingers up in total and the product of the down fingers is 0 x 5 = 0. So the answer is 50. Another interesting case is 6 x 7. 6 becomes |.... and 7 A quasisymmetric stellarator. From Romeo Alexander and Paul R. Garabedian, “Choice of coils for a fusion reactor.” Proceedings of the National Academy of Sciences, July 24, 2007, 104, 12250-12252. become ||...; three fingers are up and the product is 4 x 3 = 12. So we get 30 + 12 = 42. Prof. Garabedian began his career in the late 1950’s The general method follows. working for the U.S. Navy with a research grant for naval Step 1. Take each digit, subtract 5, and put up that many hydrodynamics. The Cold War was in full swing and had fingers. everyone on edge. It was while he was working for the Step 2. Sum the fingers that are up. That's the 10s place. Navy that the Atomic Energy Commission became inter- Step 3. Multiply the fingers that are down. That's the 1s ested in magnetic fusion reactors, which involved similar place; there may be a carry into the 10s place. mathematics but a different type of security clearance. “Through fusion,” Prof. Garabedian says, “scientists were It seems magical I know. You might teach it as magic to trying to design a nuclear reactor that would be a com- your child, but can you yourself explain what's going on? mercially viable source of energy.” In 1958, the U.S. Government declassified the magnetic For the solution email [email protected]. fusion research and Prof. Garabedian felt that this was This puzzle is adapted from The Puzzler's Elusion: A Tale of something he could work on. He taught electromagnetic Fraud, Pursuit, and the Art of Logic by Dennis Shasha, 2006. theory as a math course and says now that he learned the His latest puzzle book Puzzles for Programmers and Pros was material by teaching it, picking up physics as he went published this past spring. along. Returning this fall to the field in which he earned his Ph.D., Prof. Garabedian is teaching a graduate course in complex variables comprised of 35 students. The class has PAUL GARABEDIAN: AT 80 YEARS both master’s candidates and undergrads. He likes to teach YOUNG, IT’S FULL STEAM AHEAD eager faces who want to learn, he says. By M.L. Ball “The agony and the ecstasy” is how Prof. Garabedian describes those moments when great ideas have come to When the rest of us reach our him. In his younger years, these epiphanies might happen 80th year, we should all hope to several times a year; as he’s gotten older, maybe once a be as vibrant and full of bounce year. “These good ideas have come from a lot of hard as Paul R. Garabedian. A highly work; they didn’t come from nowhere,” he explains. “I’m a accomplished professor of mathe- hard worker, not a genius.” matics, at the Courant Institute Speaking of working hard, it’s while describing his pres- since 1959, and now Director of ent work that Prof. Garabedian becomes positively giddy. the Division of Computational The cause of the excitement? “I’m finding that I have to Fluid Dynamics, Dr. Garabedian prove myself again – I’m treated as a newcomer, not as an dives into each day’s work with old duffer, which keeps me on my toes!” It’s a lot of fun the passion of a 20-something. and he’s having a good time, and according to him, “If I While most of his contemporaries have long since retired, rested on my laurels, I’d fall asleep.” he is currently teaching a course in complex variables this Here’s hoping the rest of us can be as awake as Paul. fall and sees no reason to stop. Even he admits that it’s Garabedian, a true professeur extraordinaire. 2 COURANT INSTITUTE OF MATHEMATICAL SCIENCES FALL/WINTER NEWSLETTER 2007-08 HOW CAN ONE MAN IMPROVE THE LIVES OF MILLIONS? JUST ASK LAKSHMINARAYANAN SUBRAMANIAN By M.L. Ball How many of us truly have a chance to change the world? kilometers, all for the low cost of $1000 per link. Recently, Professor Lakshminarayanan Subramanian does. What’s more, he using WiLDNet, the TIER team was able to break the world has the vision, the passion, the commitment to make it hap- record for the longest wireless link spanning 382 kms deliver- pen…and he’s right here at Courant.
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