Academic Visitors
Distinguished Ordway Visitors (2004-2005)
The following leading mathematicians accepted our invitations to visit the School during the current academic year under the Distinguished Ordway Visitors Program. The program brings highly distinguished mathematicians to Minneapolis for prolonged periods, significantly enhancing the creative environment of the School. The visitors typically give several lectures, including a colloquium lecture and several seminars, and the exchanges of ideas with our faculty and students often result in research collaborations.
Professors:
Stuart Antman, University of Maryland, College Park, analysis and mechanics, March 2005
Louis Billera, Cornell University, discrete geometry and combinatorics, October 2004
Erwin Bolthausen, Universitat Zurich, probability theory, September 2004
Alain Chenciner, University of Paris VII, dynamical systems, April 2005
Jack Hale, Georgia Institute of Technology, differential equations, September 2004
Michael Harris, University of Paris VII, number theory
Pierre-Louis Lions, University of Paris IX Dauphine, analysis and partial differential equations, September 2004
Robert Pego, University of Maryland, College Park, partial differential equations, applied mathematics, January 2005
Yongbin Ruan, University of Wisconsin, Madison, geometry, topology, and mathematical physics, October 2004
Professor Sasha Voronov has kindly given us the following note about the April 2004 Ordway visit by the Fields’ Medalist Maxim Kontsevich.
Ordway Lectures visit by Maxim Kontsevich
By Sasha Voronov
In April 2004, Professor Maxim Kontsevich paid us a week-long visit with a series of three Ordway Lectures. He was the second distinguished mathematician (after Professor Hillel Furstenberg, who visited us in February 2003) and the first Fields’ Medalist to visit the School of Mathematics on the new Ordway Lectureship program. Since then Professor Pierre-Louis Lions, who also holds a Fields’ Medal, gave Ordway Lectures in September-October 2004.
Below is a short biographical reference, which was compiled from an entry in Encyclopaedia Britannica, the American Mathematical Society web site, and other online sources.
Maxim Kontsevich (born 25 August 1964) is professor at the Institute des Hautes Etudes Scientifiques (IHES) in France and visiting professor at Rutgers University in New Brunswick, New Jersey. After studying at the Moscow State University with I. M. Gelfand and beginning research at the “Institute for Problems of Information Processing,” he gained a doctorate at the Max-Planck-Institut, Bonn, Germany in 1992 with D. B. Zagier as his advisor. He then received invitations to Harvard, Princeton, and Berkeley.
In 1998 at the 23rd International Congress of Mathematicians in Berlin, Germany he received the Fields Medal together with R. E. Borcherds, W. T. Gowers, and C. T. McMullen.
Maxim Kontsevich has established a reputation in pure mathematics and theoretical physics, with influential ideas and deep insights. He has been influenced by the work of Richard Feynman and Edward Witten. Kontsevich is an expert in the so-called “string theory” and in quantum field theory. He made his name with contributions to several important problems of geometry. He was able to prove a conjecture of Witten and demonstrate the mathematical equivalence of two models of so-called quantum gravity. The quantum theory of gravity is an intermediate step towards a complete unified theory. It harmonizes physical theories of the macrocosm (mass attraction) and the microcosm (forces between elementary particles).
Another result of Kontsevich relates to knot theory. Knots mean exactly the same thing for mathematicians as for everyone else, except that the two ends of the rope are always joined together. A key question in knot theory is, which of the various knots are equivalent? Or in other words, which knots can be twisted and turned to produce another knot without the use of scissors? This question was raised at the beginning of the 20th century, but is still unanswered. It is not even clear which knots can be undone, that is, converted to a simple loop. Mathematicians are looking for ways of classifying all knots. They would be assigned a number or function, with equivalent knots having the same number. Knots which are not equivalent must have different numbers. However, such a characterization of knots has not yet been achieved. Kontsevich has found the best “knot invariant” so far, which is now generally called the Kontsevich integral. Although knot theory is part of pure mathematics, there seem to be scientific applications. Knot structures occur in cosmology, statistical mechanics, and genetics.
Kontsevich also proved a deformation quantization conjecture, which had been open for more than twenty years. To solve the problem, he came up with an ingenious formula motivated by the Feynman diagram expansion of a string theory model. Another noticeable contribution of Kontsevich is in the field of mirror symmetry, an important duality between two quantum field theory models from the physical point of view and between two types of geometry, complex and symplectic, from the mathematical perspective. Kontsevich’s “homological mirror symmetry” turned out to provide an adequate mathematical description of this physical phenomenon.
As Ordway Lecturer in the School of Mathematics, Kontsevich gave three lectures on Affine Structures and Non-Archimedean Geometry, in which he described his recent work on mirror symmetry. The lectures gathered a big crowd of people, packing the colloquium room, Vincent Hall 16. At times it seemed like even the experts were lost, but the excitement of novel, state-of-the-art mathematics grabbed the attention of the audience.
Kontsevich’s visit was short, barely one week, but quite full of activity. Between the lectures, he managed to engage himself in mathematical discussions with a number of faculty. Apart from organizing a reception and dinner in his honor at Bistro West, Humphrey Center, we took him for a stroll along the pedestrian bridge across the Mississippi next to the Mills District, facing St. Anthony Falls. He seemed to be excited to recognize flour brand names on tops of the surrounding grain mills and compared the mill ruins to the remains of the Roman Empire. He also was very interested to see downtown St. Paul from our 29th floor apartment, and to visit the Lowertown area where my wife’s art studio is located.
Perhaps, the most unusual event during Kontsevich’s visit took place on that Thursday afternoon in Vincent Hall. It was a Russian-style, secret seminar, announced strictly by word of mouth, exclusively to the members of the cult. The idea behind such “misorganization,” as it may appear to a side observer, is that the speaker may allow himself to be very informal and get straight to the point, without spending half an hour on initiation of the laymen. Perhaps, because of the time elapsed since then, we may feel safe to disclose the topic of that seminar, From an A_infty-Algebra To a Topological Conformal Field Theory. Kontsevich described the idea of a construction, which generalized a conjecture of Deligne on Hochschild cohomology and related algebra with physics in a mind-blowing shot. In a way it was a mathematical gift to the distinguished audience; there was still some work to be done, and we were free to go ahead and complete it. Unfortunately, Kontsevich had given a similar informal talk elsewhere, and the work is completed by now, also elsewhere, see a paper by K. Costello of Imperial College, London, on topological conformal field theories and Calabi-Yau categories, available on the web at http://front.math.ucdavis.edu/math.QA/0412149.
2004-05 Continuing Postdocs and Visiting Faculty
Assistant Professors:
Jesus Carrero (Ph.D. UCLA, numerical analysis of partial differential equations, scientific computation)
Jamylle Carter (Ph.D. UCLA, image processing, computer graphics)
Huiqiang Jiang (Ph.D. Courant Institute, partial differential equations)
Simon Morgan (Ph.D. Rice University, geometric measure theory, harmonic maps)
Chian-Jen Wang, Dunham Jackson Assistant Professor (Ph.D. Ohio State, automorphic forms and representation theory)
Jennifer Wagner (Ph.D. UCSD, algebraic combinatorics)
Stephen Watson (Ph.D. Carnegie Mellon University, dynamical systems)
Tobias Weth (University of Giessen, numerical analysis)
Associate Professors:
Victor Padron (Universidad de Los Andes, Merida, Venezuela, differential equations and applications)
Raja Sridharan (The Tata Institute of Fundamental Research, commutative algebra, algebraic geometry)
Professors:
Tepper Gill (Howard University, mathematical physics, nonlinear dynamical systems, probability theory)
Ernie Kalnins (University of Waikato, New Zealand, mathematical physics)
Alexander Tikhomirov (Bielefeld University and Syktyvkar University, probability theory)
Postdoctoral Associates and Postdoctoral Fellows, including IMA Postdoctoral Associates who participate in the teaching activities:
Yassine Boubendir (Universite Paris 13, acoustics and electromagnetics, applied mathematics, numerical methods)
Mihail Cocos (University of British Columbia, differential geometry, geometric analysis)
Marshall Hampton, NSF Postdoctoral Fellow (dynamical systems, celestial mechanics, image processing)
McKay Hyde, NSF Postdoctoral Fellow (numerical solutions of partial differential equations, fast algorithms, spectral methods)
Jeremy Martin, NSF Postdoctoral Fellow (Ph.D. UCSD, combinatorics and algebraic geometry)
Anastasios Matzavinos (Ph.D. University of Dundee, applied mathematics, mathematical biology, optimization)
Magdalena Stolarska (Ph.D. Northwestern University, applied mathematics, mathematical biology)
Thomas Wihler (ETH Zurich, numerical analysis)
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