DECEMBER 8 - 10, 2004 |
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| Discrete Mathematics Seminar | |
| Topic: | Parameters of codes on bipartite graphs |
| Presenter: | Alexander Barg, University of Maryland |
| Date: | Wednesday, December 8, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Department Colloquium | |
| Topic: | Universal Acyclic groups and the Morse landscape of certain distortion functionals |
| Presenter: | Shmuel Weinberger, University of Chicago |
| Date: | Wednesday, December 8, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | In this talk I will try to explain two tools that have been useful in the past few years: the first is the applications of finitely presented acyclic groups that contain all other finitely presented groups and the second is the use of ideas of logic to produce many critical points for certain functionals (pioneered by Nabutovsky). Ideally, I will get to apply both together the study of nonsimply connected hypersurfaces in Euclidean space. |
| Joint Analysis Seminar | |
| Topic: | Prescribing symmetric functions of the eigenvalues of the Ricci tensor |
| Presenter: | Matt Gursky, University of Notre Dame |
| Date: | Thursday, December 9, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Abstract: | In joint work with J. Viaclovsky, we studied the problem of prescribing symmetric functions of the eigenvalues of the Schouten tensor for a conformal metric on a compact manifold (often referred to as the "Sigma-k Yamabe problem"). This is equivalent to solving a fully nonlinear elliptic equation of second order. Assuming the function satisfies certain structural conditions, and the underlying manifold satisfies a natural 'admissibility' condition, we prove a priori estimates for solutions. The proof involves a blow-up analysis and classification of certain global singular solutions. |
| Topology Seminar | |
| Topic: | Symplectic Floer theories, Hilbert Schemes, and the Jones polynomial |
| Presenter: | Ciprian Manolescu, Princeton University |
| Date: | Thursday, December 9, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | We will explain how the Jones polynomial of links appears in symplectic geometry. Seidel and Smith have used Floer homology for two Lagrangians in an affine variety Y to define an invariant of links. Their variety can be identified with an open subset in the Hilbert scheme of points on a Milnor fiber. As a consequence, we describe a set of generators for the Seidel-Smith chain complex which can also be used to compute the Jones polynomial, or as a set of generators for the Heegaard Floer chain complex of the double branched cover. |
| Special Seminar | |
| Topic: | Prime numbers, Riemann, and Langlands |
| Presenter: | Stephen Gelbart, Weizmann Institute and Institute for Advanced Study |
| Date: | Friday, December 10, 2004, Time: 2:30 p.m., Location: Fine Hall 110 |
| Abstract: | We start with some elementary properties of prime numbers, and why they should satisfy the Prime Number Theorem. Next comes the pathbreaking work of Riemann, whose fundamental theory for the zeta-function essentially proves the Prime Number Theory, but leaves open the "Riemann Hypothesis". Finally, we summarize the amazing conjectures of Langlands, stating that all the L-functions of Number Theory are special cases of generalizations of Riemann's zeta-function. |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar *** Please note special time |
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| Topic: | Ricci curvature for metric-measure spaces |
| Presenter: | John Lott, University of Michigan |
| Date: | Friday, December 10, 2004, Time: 2:30 p.m., Location: Fine Hall 314 |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar *** Please note special time |
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| Topic: | The Calabi-Yau conjectures for embedded surfaces |
| Presenter: | William Minicozzi, Johns Hopkins University |
| Date: | Friday, December 10, 2004, Time: 4:00 p.m., Location: Fine Hall 314 |
DECEMBER 13 - 17, 2004 |
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| Analysis Seminar | |
| Topic: | A minimax scheme for the existence of conformal metrics with constant $Q$-curvature |
| Presenter: | Andrea Malchiodi, SISSA, Italy |
| Date: | Monday, December 13, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | Finding metrics with constant $Q$-curvature on a compact four manifold amounts to finding critical points of a suitable Euler-Lagrange functional. We describe how to construct critical points of saddle type under generic assumptions on the manifold $M$. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Subconvexity bound for triple L-function and representation theory |
| Presenter: | Andre Reznikov, Bar-Ilan University |
| Date: | Monday, December 13, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract | We present a new method of estimating trilinear period for automorphic representations of PGL(2,R). Such a period gives rise to a special value of the triple L-function. We prove a bound on the triple period which amounts to a subconvexity bound on the corresponding special value. Our method is based on the study of analytic structure of the corresponding unique trilinear functional on unitary representations of PGL(2,R). |