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Updated every Monday with upcoming seminars for the following week.
- May 1st, 2008 (11:15am - 12:05pm)
- Seminar: Algebra and Number Theory Seminar
Title: Algebraic hypergeometric functions
Speaker: Frits Beukers, Utrecht University
Location: MB106Hypergeometric functions (in one and several variables) are classical functions which occur at many places in mathematics and mathematical physics. We shall be interested in hypergeometric functions which are at the same time algebraic in their arguments. This subject started in 1873 with the work of H.A. Schwarz. In this lecture we discuss a number of examples, introduce a general class of several variable hypergeometric functions, the so-called GKZ-functions, and describe a combinatorial criterion for their alegebraicity.
- May 1st, 2008 (02:15pm - 03:45pm)
- Seminar: Symplectic Topology Seminar
Title: Length minimizing paths in the group of hamitonian diffeomorphismsdiffeomorphisms with applications to Ham(M,\omega).
Speaker: Peter Spaeth, PSU
Location: MB216On any closed symplectic manifold we construct a path-connected neighborhood of the identity within the Hamiltonian diffeomorphism group with the property that each Hamiltonian diffeomorphism in this neighborhood admits a Hofer and spectral length minimizing path to the identity. This neighborhood is open in the $C^1-$topology. The construction depends on a continuation argument in the spirit of the work of Y. Chekanov and a chain level result in the Floer theory of Lagrangian intersections. This generalizes results of Lalonde and McDuff, McDuff and Y.-G. Oh. While the proof is somewhat technical, effort will be made to present the argument from scratch. Of independent interest, Y.-G. Oh's spectral metric, which is a Floer theoretical refinement of the Hofer metric and Oh's homological area of will be presented in detail. Several open questions will also be addressed.
- May 1st, 2008 (05:00pm - 06:00pm)
- Seminar: Topology/Geometry Seminar
Title: Length minimizing paths in Ham(M,\omega).
Speaker: Peter Spaeth, Penn State
Location: MB106We will discuss the Hofer and spectral geometry of the Hamiltonian diffeomorphism group of any closed symplectic manifold. Many authors have worked in this area, and the goal of the lecture will be to discuss the scope of this problem and recent results. Attention will be paid to the Floer theoretical side of the story.
- May 2nd, 2008 (12:00pm - 02:00pm)
- Seminar: Ph.D. Oral Comprehensive Examination
Title: "Cocycles and cocycle rigidity"
Speaker: Zhenqi Wang
Location: 106 Osmond LabAdviser: Anatole Katok
- May 2nd, 2008 (12:15pm - 01:25pm)
- Seminar: CCMA Luncheon Seminar
Title: Freely Moving Structures Interacting with Thermal Convection
Speaker: Jun Zhang, Courant Institute of Mathematical Sciences, New York University
Location: MB114 - May 2nd, 2008 (02:00pm - 03:30pm)
- Seminar: Geometric Functional Analysis Seminar
Title: The Duflo isomorphism and classification of representations, III
Speaker: Nigel Higson, Penn State
Location: MB106Harish-Chandra computed the center of the enveloping algebra of a semisimple Lie algebra and so determined the possible infinitesimal characters for irreducible representations of semisimple groups. Kirillov proposed a reinterpretation Harish-Chandra's isomorphism that would determine the center of the enveloping algebra for any Lie algebra, and this was eventually proved by Duflo.
Quite recently Alekseev and Meinrenken gave a beautiful new proof the the Duflo isomorphism (for many although not all Lie algebras) by connecting the Kirillov-Duflo map to a non-commutative Chern-Weil homomorphism in equivariant cohomology. I shall present part of their work and consider its implications in representation theory. - May 2nd, 2008 (03:35pm - 04:25pm)
- Seminar: Computational and Applied Mathematics Colloquium
Title: Anomalous behavior of flexible, flapping bodies in fluid
Speaker: Jun Zhang, Courant Institute, New York University
Location: MB106 - May 5th, 2008 (10:00am - 12:00pm)
- Seminar: Ph.D. Oral Comprehensive Examination
Title: "Near Axisymmetric Configurations in Elastic Complex Fluids"
Speaker: Xiang Xu
Location: MB315Adviser: Chun Liu
- May 6th, 2008 (02:30am - 04:00am)
- Seminar: Mathematical Physics Seminar
Title: The Big Bracket in Poisson-Nijenhuis Theory
Speaker: Yvette Kosmann-Schwarzbach, Ecole Polytechnique, Palaiseau, France
Location: MB106We shall show how the supermanifold approach to the Poisson-Nijenhuis structures, using the big bracket, permits an easy formulation of the definition and properties of the quasi- and twisted structures that were introduced by Stienon and Xu in generalized complex geometry, and by Zucchini in the theory of sigma-models.
- May 6th, 2008 (03:00pm - 05:00pm)
- Seminar: Ph.D. Thesis Defense
Title: "Finite Element Approximations of High Order Partial Differential Equations"
Speaker: Bin Zheng
Location: MB106Advsier: Jinchao Xu
- May 7th, 2008 (10:30am - 12:30pm)
- Seminar: Ph.D. Thesis Defense
Title: "Growth rate of periodic orbits for geodesic flows on surfaces with regions of positive curvature"
Speaker: Bryce Weaver
Location: MB106Adviser: Anatole Katok
- May 12th, 2008 (03:30pm - 04:30pm)
- Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Mimetic finite difference method for PDEs (special date 5/19)
Speaker: Konstantin Lipnikov, Los Alamos National Laboratory
Location: MB315ABSTRACT. A successful discretization method inherits or mimics fundamental properties of the underlying PDEs such as conservation laws, symmetries, solution positivity and maximum principle. Construction of such a method is made more difficult when the mesh is distorted so that it can conform and adapt to the physical domain and problem solution. The talk is about one such method - the mimetic finite difference (MFD) method. The MFD method is used to solve problems with full tensor coefficients on unstructured polygonal and polyhedral meshes. Polyhedral meshes may include arbitrary elements: tetrahedrons, pyramids, hexahedrons, degenerated and non-convex polyhedrons, generalized polyhedrons, etc. Modeling with polyhedral meshes has a number of advantages that will be addressed in the talk. The MFD method has been applied successfully to several applications including diffusion, electromagnetics, acoustics, and gasdynamics. I present a general framework for building MFD methods, give examples of discretizations of the gradient, divergence and curl operators on polygonal and polyhedral meshes, and review existing theoretical results including convergence estimates, orthogonal decomposition theorems, etc. I'll present in more details the MFD methods for solving a linear diffusion problem. I'll show how the method produces a family of schemes with equivalent properties and establish connections with the mixed finite element, finite volume and multi-point flux approximation methods.
- May 14th, 2008 (03:00pm - 05:00pm)
- Seminar: Ph.D. Thesis Defense
Title: "Robust preconditioners for H(grad), H(curl) and H(div) systems with strongly discontinuous coefficients"
Speaker: Yunrong Zhu
Location: MB106Adviser: Jinhcao Xu
- May 15th, 2008 (11:00am - 12:00pm)
- Seminar: Applied Analysis Seminar
Title: Excellent swimmers
Speaker: A. De Simone, Trieste, Sissa, Italy
Location: MB106We will discuss swimming strategies for microscopic swimmers and recipes to optimize their stroke.
- May 16th, 2008 (10:30am - 12:30pm)
- Seminar: Ph.D. Oral Comprehensive Examination
Title: "Modeling of Bacterial Suspensions"
Speaker: Vitaliy Gyrya
Location: MB106Adviser: Leonid Berlyand
- May 19th, 2008 (03:35pm - 04:25pm)
- Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Mimetic finite difference method for PDEs
Speaker: Konstantin Lipnikov, Theoretical Division, Los Alamos National Laboratory
Location: MB315ABSTRACT. A successful discretization method inherits or mimics fundamental properties of the underlying PDEs such as conservation laws, symmetries, solution positivity and maximum principle. Construction of such a method is made more difficult when the mesh is distorted so that it can conform and adapt to the physical domain and problem solution. The talk is about one such method - the mimetic finite difference (MFD) method. The MFD method is used to solve problems with full tensor coefficients on unstructured polygonal and polyhedral meshes. Polyhedral meshes may include arbitrary elements: tetrahedrons, pyramids, hexahedrons, degenerated and non-convex polyhedrons, generalized polyhedrons, etc. Modeling with polyhedral meshes has a number of advantages that will be addressed in the talk. The MFD method has been applied successfully to several applications including diffusion, electromagnetics, acoustics, and gasdynamics. I present a general framework for building MFD methods, give examples of discretizations of the gradient, divergence and curl operators on polygonal and polyhedral meshes, and review existing theoretical results including convergence estimates, orthogonal decomposition theorems, etc. I'll present in more details the MFD methods for solving a linear diffusion problem. I'll show how the method produces a family of schemes with equivalent properties and establish connections with the mixed finite element, finite volume and multi-point flux approximation methods.