MONDAY, February 4, 2008
VIGRE – Algebraic Geometry
2:15pm, Room 222
Joint Algebra / Topology / Algebraic Geometry Seminar
2:30pm, Room 303
Speaker: Francois Loeser (Ecole Normale Superior, Paris)
Title of talk: Arcs and monodromy
Abstract : Given a function on an algebraic variety, a lot of information about its monodromy can be retrieved from the study of certain spaces of arcs. We plan to discuss some of these connections between arcs and monodromy; in particular we intend to explain how one can prove - and sometimes hope for - motivic analogues of some old results on the Hodge spectrum of singularities of functions.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, February 5, 2008
VIGRE - Graduate Student Seminar
2:00pm, Room 304
In this seminar, two speakers who are sponsoring math summer
internships for this coming summer will be discussing their research.
Their talks (about 25 minutes each) will be for a general audience.
Speaker: Christof Meile, Marine Sciences
Title of talk: Shades of Blue: Quantitative Methods in Marine Sciences
Abstract: Oceanography is an interdisciplinary field of study,
encompassing components from Biology, Chemistry, Physics and Geology.
Their integration and quantitative analysis often necessitates or is
facilitated by the use of numerical models. This presentation provides
a brief overview on some research efforts in the Department of Marine
Sciences using quantitative methods to unravel aspects related to
ocean carbon cycling: The quantification of export of carbon from the
photic surface waters to the deep ocean, modeling of carbon breakdown
in sediments and nutrient cycling associated with seagrasses and
numerical simulation of microbial dynamics in porous media at the
grain scale. Finally, specific areas for potential collaborative
endeavors are highlighted.
Speaker: Jim Prestegard, Complex Carbohydrate Research Center
Title of talk: TBA
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Colloquium – Note the Day
3:30pm, Room 304
Speaker: Simon Foucart, Vanderbilt University
Title of talk: From Approximation Theory to Compressive Sampling via Banach Spaces Geometry: a Computational Tour
Abstract: Starting with an issue on computation stability, I will introduce the notion of condition number for a system spanning a normed space $V$. I will show how optimization techniques can be used to calculate the minimum of these condition numbers. The latter is an intrinsic constant of the space $V$, and I will examine its connections with the projection constant of $V$. In particular, I will raise a question --- formulated only in terms of projections --- related to the $P_\lambda$-problem. The arguments will lead me to the new and exciting field of Compressive Sampling. The paradigm that only few information on a signal is necessary for its reconstruction will be illustrated by some striking yet simple results, including a proof of Kashin's theorem on widths as a byproduct. All along, an eye will be kept on the computational aspect of the theory.
Mathematical Physics
3:30pm, Room 303
Speaker: David Finkelstein, Georgia Tech (emeritus)
Title of talk: Generational quantum theory
WEDNESDAY, February 6, 2008
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Number Theory/Arithmetic Geometry
3:30pm, Room 304
No meeting this week
THURSDAY, February 7, 2008
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
2:00pm, Room 326
VIGRE – Number Theory
3:30pm, Room 303
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Michael Ching, Johns Hopkins University
Title of talk: Derivatives of the identity and chain rules for calculus of functors
Abstract: Goodwillie's calculus of functors is a way to apply some of the concepts of ordinary real-variable calculus to study homotopy theory. The main tool is a "Taylor series" that consists of a sequence of approximations to a functor of topological spaces. The analogy goes deeper than you might expect with, for example, sensible (and useful) notions of the derivatives of a functor.
In this talk, I'll address the existence of "chain rules" in this context and point out the similarities with, and differences to, ordinary calculus. Underlying such chain rules are the derivatives of the identity functor (which are more interesting than you might expect). I'll try to explain how these derivatives explain to some extent the appearance of Lie algebras in, for example, rational homotopy theory.
FRIDAY, February 8, 2008
VIGRE-Algebra
2:30pm, Room 322
Applied Math
2:30pm, Room 302
Speaker: Sergiy Borodachov, Georgia Tech
Title of talk: Optimal cubature formulas related to computer tomography
Abstract: We consider the problem of optimal recovery of the integral of the function f defined on the cube C. A priori, we know that the function has a given majorant for the modulus of continuity (i.e. belongs to the corresponding class of functions). Assume also that we know or can easily compute mean values of f along intersections of C with n arbitrary planes or n arbitrary straight lines. The problem is to choose best positions of these n planes (lines) and the best way to assign to the n-tuple of sampled means the approximate value of the integral of f along the whole cube C in order to minimize the maximal error over this class of functions. This problem is a generalization of the classical Kolmogorov-Nikol'skii problem about optimal quadratures.
Geometry
2:30pm, Room 410
No meeting this week