This is a proposal requesting partial funding for a series of the Current Developments in Mathematics conferences organized by Professor Shing-Tung Yau and other members of Harvard University and the Massachusetts Institute of Technology. The first of the three conference will be held at Harvard University in the Science Center building in November, 2009. This series of conferences is known for bringing together excellent speakers at the forefront of their field as well as attracting a large audience from all over the country.

Mathematicians in the Northeast part of America benefit from such activities. They come to participate and communicate with each other, and it is truly interdisciplinary activity. The topics are wide-ranging, from mathematical physics to computing to applied mathematics. People come to this conference all the way from Europe and Asia, and it has been very fruitful for all parties involved. The applications for funding are primarily for graduate students and postdoctoral fellows who travel from all over the country and many are female students and minorities. Some graduate students can get enough ideas from the talks to write their theses, and they can communicate with the speakers on their research topics.

Project Report

, jointly organized by MIT and Harvard, hosted mathematicians working at the forefront of their fields. The lectures were well-attended by students, postdocs, faculty, and visitors. Funding provided by the NSF helped cover travel and lodging costs for graduate students and recent PhDs. Young researchers were provided opportunities to meet and make connections with the speakers and one another. Brief summaries of talks are below: Ian Agol: proof of virtual Haken conjecture. The work enables us to understand hyperbolic 3-manifolds, and leads to algorithms concerning 3-manifolds. James Arthur: outline of classifiation of the automorphic representations of special orthogonal and symplectic groups, in terms of those of general linear groups. Applications for number theory. Camillo De Lellis: lectures on the famous Plateau problem in geometry, which seeks an area-minimizing surface spanning a given boundary in arbitrary dimensions. Laszlo Erdos: recent solutions to the Wigner-Dyson-Gaudin-Mehta conjecture. The work has applications to random matrix theory and to complicated quantum systems. Mark Gross: SYZ conjecture, and its algebraic-geometric version called the Gross-Siebert program, and explained how tropical geometry plays an important role in the program. The work helps to understand mirror symmetry and the fundamental physical principles that govern our universe. Martin Hairer: provided rigorous mathematical insight into many stochastic partial differential equations arising from physics. He provides solutions to problems that had been considered unsolvable. Jeremy Kahn: outlined ideas to prove the surface subgroup theorem and the Ehrenpreis conjecture in joint work with Markovic. These are important problems in low dimensional geometry and topology. Richard Kenyon: discussed the most basic operator, the Laplacian, on planar graphs which has many uses in mathematics. This work has applications for medical imaging and nondestructive materials testing. Thomas Lam: talked about his work on integrals in the space of matrices. He related this work to solutions of an ordinary differential equation (Whittaker functions) and discussed applications to physics and mirror symmetry. Maryam Mirzakhani: dynamics of Teichmuller space, a geometric object which parameterizes complex structures on a 2-D surface. She explained mixing behavior of certain flows on this space and demonstrated that geodesic paths in this space exhibit surprisingly regular properties. Fabian Morel: proof of cases of the Friedlander-Milnor conjecture using the A^1 homotopy theory of schemes. Morel's results reveal the relations between algebraic and arithmetic K groups. Andre Neves: reported the recent solution of the Willmore conjecture on the two-dimensional immersed torus. Dmitry Panchenko: the Sherrington-Kirkpatrick model, a spin glass model which was introduced with the goal of understanding the unusual magnetic properties of some metal alloys. Robin Pemantle: the development and uses of hyperbolicity and stability. Applications in combinatorics and probability. Jeremy Quastel: the default model for random interface growth in physics described by the Kardar-Parisi-Zhang equation, which is equivalent to a toy model for turbulence. The equations help to understand large-scale fluctuation. Peter Scholze: described his theory of perfectoid spaces and applications. The work leads to major advances in algebraic geometry, number theory, and representation theory. Thomas Spencer: the spectrum of random band matrices through study of dual statistical mechanics theory as a class of supersymmetric spin models on a lattice. The work gives new insight for dynamics of a quantum particle in a random environment. Dan Spielman: the recent solution to the Kadison-Singer conjecture and on the Ramanujan property of d-regular graphs. The work is related to combinatorics and computer science. Yu-Jong Tzeng: her breakthrough in the proof of the Yau-Zaslow conjecture in enumerative geometry, for counting nodal curves on a smooth algebraic K3 surface. Her work has applications for algebraic geometry and superstring theory. Akshay Venkatesh: conjectures concerning asymptotic behavior of counting number fields ordered by their natural invariant. The conjectures and results give evidence that torsion classes play an essential role in understanding the full scope of the Langlands correspondence. Jean-Loup Waldspurger: progress regarding automorphic representations of p-adic orthogonal groups, especially proof of Gross-Prasad conjecture. The results are important for number theory and algebraic geometry. Edward Witten: new work on the Jones polynomial of a knot. The work has applications for string theory, quantum field theory, and mathematical physics. Sijue Wu: water wave equations and their solutions in both 2- and 3-D cases. The work contributes to nautical navigation and safety. Zhiwei Yun: survey on rigidity in the Langlands correspondence and a new construction of local systems on open curves. The work has applications to classical problems in algebraic geometry and number theory. Wei Zhang : the arithmetic intersection theory of Shimura varieties and the relation with automorphic forms. The work has applications for algebraic number theory. Yitang Zhang: work on the first proof that gaps between prime numbers are finite. This problem has been open for centuries, and his result is considered a major breakthrough in number theory.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
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Tie Luo
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Harvard University
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