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October 2005
November 2005
January 2006
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January 10, 2006 (Please
note this is a Tuesday.) January 12, 2006
3:30pm, Room 302 Speaker: Xiang, Tang, UC Davis Title of talk: Foliations, Hopf algebras and modular forms Abstract: Recently Hopf algebras have played a role in several areas of mathematics and physics. The fact that the same Hopf algebra was useful in the study of foliations, renormalization in quantum field theory, and number theory has led to interesting discoveries. Inspired by the Rankin-Cohen brackets on modular forms, Connes and Moscovici constructed a universal deformation formula for the Hopf algebra associated to a codimension one foliation. In this talk, we will explain how to use differential geometry to understand their deformation and various structures involved. In particular, we will show that the Rankin-Cohen deformation is closely related to the Weyl-Moyal product. January 17, 2006
(Please note this is a Tuesday.)
3:30pm, Room 302 Speaker: Evgueni Tevelev, Univ. of Texas at Austin Title of talk: Equations of the moduli space of stable rational curves Abstract: At the most basic level, algebraic geometry studies (systems of) polynomial equations and the geometry of their solutions. Nowadays algebraic varieties are usually defined in an abstract functorial way and their equations (if one can find them!) provide an important information about their geometry, deformations, degenerations, etc. I will explain when equations are considered nice (Green-Lazarsfeld properties and Koszul algebras). I'll describe joint work with Sean Keel where we find equations in the Lie operad of the moduli space of stable rational curves . January 19, 2006 January 24, 2006 3:30pm, Room 302 Speaker: Ambrus Pal (IHES, France) Title of talk: K_2 of elliptic surfaces and the rigid analytic regulator Abstract: Milnor K-groups of algebraic varieties play a significant role in algebra, geometry, number theory and even in mathematical logic. In spite of some spectacular results, such as the work of Voevodsky on the Bloch-Kato conjecture, some fundamental finiteness conjectures remain open about these objects. In this talk I will explain how a refined form of the Langlands correspondence over function fields were used to make progress in this problem. January 26, 2006
3:30pm, Room 302 Speaker: Alexander Iosevich, Univ. of Missouri-Columbia Title of talk: "Analysis, combinatorics and number theory of distance sets". Abstract: The Erdos distance conjecture says that $N$ points in "d"-dimensional Euclidean space determine at least $CN^{\frac{2}{d}}$ distinct distances. The continuous analog of this conjecture, introduced by Falconer says that if the Hausdorff dimension of a set in Euclian space exceeds $d/2$ than the Lebesgue measure of the set of distances is positive. We shall discuss these conjectures and connections between them. We shall also describe the finite field analog of these problems where Gauss and Kloosterman sums play a crucial role. January 30, 2006
(Please note this is a Monday.)
3:30pm, Room 302 Speaker: Paul Balmer, ETH Zurich Title of talk: Triangular geometry and applications Abstract: We shall start with the concept of triangulated category, reviewing examples from Algebraic Geometry, Homotopy Theory, Modular Representation Theory, Motivic Theory and more. We will then introduce the basic ideas of how to do "geometry of triangulated categories". Finally, we will see how these techniques can be useful in some of the above examples. |
| February 7, 2006 3:30pm, Room 302 Speaker: Xiaoqiang Wang, University of Minnesota Title of talk: Phase Field Models and Simulations of Vesicle Bio-Membranes Abstract: Recently, we began to systematically model and simulate the shape deformation of vesicle membranes using a unified energetic variational phase field method based on the minimization of elastic bending energy with volume and surface area constraints. Mathematical theory and numerical algorithms are developed to for the phase field models. Rigorous convergence theories of the numerical methods are investigated. Many simulations are carried out in static and dynamic, axis-symmetric and full 3D, one component and multi-component cases. The new phase field modeling approach has the advantage of avoiding tracking the free interfaces, and it can easily handle topological changes. Meanwhile, a series of formulae for retrieving the Euler number of the vesicles have been given and discussed which may be useful for detection and control purposes. The 3D codes developed for the equilibrium shape deformations and the deformations and interactions with fluid fields allow us to conduct extensive computational studies. Both known and new equilibrium configurations have been discovered in our numerical simulations. A detailed examination of the energetic bifurcation landscape has been carried out. We have further studied the effect of the spontaneous curvature and have conducted simulations of vesicle transformations in fluids. The further development of the phase field approach for multicomponent vesicles gives us more tools to understand new and complex phenomena recently being experimentally studied by biologists. February 15, 2006 3:30pm, Room 302 Speaker: Olga Plamenevskaya, MIT Title of talk: Heegaard Floer theory, knots, and contact structures Abstract: Heegaard Floer theory is one of the most significant recent developments in low-dimensional topology. Reminiscent of gauge theory, it provides powerful invariants for 3-manifolds. Although defined via holomorphic disks, these 3-manifold invariants have an unexpected connection to combinatorial knot invariants developed by Khovanov. I will outline the construction of Heegaard Floer and Khovanov theories, as well as their relation (due to Ozsvath and Szabo). Then, I will expand these results to the world of contact topology, providing a new invariant for transversal knots, and bringing the correspondence between the two theories to a new level. |
April 12, 2006 -Please note
this is a Wednesday April 27, 2006 |
For abstracts and titles of previous years' colloquia click here:
1998-1999,
1999-2000,
2000-2001,
2001-2002,
2002-2003,
2003-2004,
2004-2005
For weekly seminar schedule click here.
For the Annual Distinguished Cantrell Lectures, click here.
Maps of Campus.
Your comments and suggestions for future
speakers are welcome. Please contact
Valery Alexeev,
valery @ math dot uga
dot edu