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WEEKLY CALENDAR |
| Mon 13 |
3:10-4:00 pm,
room 1404. Graph Theory and Combinatorics Seminar.
Sam
Stueckle,
Trevecca Nazarene University.
Conway's Thrackle Conjecture.
A drawing of a graph is a thrackle drawing if every edge crosses every
other legal edge exactly once. Conway has conjectured that the maximum
number of edges in any thracklable graph on n vertices is n. The
conjecture for connected graphs is then that a connected graph is
thracklable iff it is a tree or unicyclic graphs, where the cycle is
not a 4-cycle. It is has been shown that all trees or unicyclic graphs
without a 4-cycle are thracklable. We will survey results and
techniques on the current state of the converse.
4:10-5:30 pm, room 1431. All Algebra Seminar. Aldo Ursini, University of Siena, Italy. Semi-Abelian Categories and Ideal Theory in Universal Algebra. Semi-Abelian categories were introduced by Janelidze-Marki-Tholen (2002) as an appropriate notion to establish the basic categorical framework to extend the isomorphism and decomposition theorems of group theory, the general radical theory for rings, the basic statements of homological algebra in a general, non-Abelian setting, just like MacLane's notion of Abelian category did for Abelian groups and modules. We'll give a short survey of this approach. It turns out [Bourn-Janelidze (2003)] that a variety of universal algebras is a semi-Abelian category exactly when it "has an excellent ideal theory": namely, the correspondence between congruences and ideals is particularly well-behaved. To explain this, we will recall some basic notions of ideal theory for universal algebras [Gumm-Ursini (1984), Agliano-Ursini (1992)]. Once this connection has been established between the two approaches, many other interconnections appear. We will explore some of these: comparing how category theory distinguishes between regular and normal epimorphisms, and algebra distinguishes between congruences and ideals; how internal precrossed modules and internal reflexive graphs compare to semi-congruences and ideals; how the algebraic notion of "clot" is translated categorically [Janelidze-Marki-Ursini (2003)]. 4:30 pm, room 1206. Special lecture. Emmanuele DiBenedetto. Modeling the Dynamics of Second Messengers in Visual Transduction. The lecture is part of an ongoing activity directed toward graduate students and non-biology faculty, as a way of exposing them to signaling issues that lend themselves to mathematical modeling and analysis. We will use this lecture to introduce the Department.s faculty to the area of signal transduction. Several biologists will attend and will be able to present other aspects of signal transduction and/or answer questions about the field. Abstract: Signal Transduction is the process by which signals originating outside a living cell cause functional changes in the interior of the cell by activating receptors located on the plasma membrane. These in turn activate cytoplasmic signaling molecules, termed second messengers. A particular aspect of this class of phenomena is Visual Transduction in vertebrates. The outside signal is a photon hitting the rod outer segment. This causes a cascade of events by which light is transformed into a change in electrical current which in turn permits vision. After briefly describing such a phenomenon we pose some mathematical questions naturally originating from the geometry/anatomy of the rod outer segment and the diffusion of second messengers within the cytoplasm, during visual transduction. The mathematical theory of homogenization is relatively recent and originated from the need of understanding the physical properties of a medium with a fine periodic structure. We will connect the mathematical theory of homogenization to some aspects of visual transduction and indicate how homogenization can be of help in generating a "predictive" theory of some aspects of visual transduction. Flu shots available starting today. |
| Tue 14 |
12:20-1, room 1431. Lectures
about Latex.
Eric Schechter.
Interactive editing, continued.
Inverse search (extremely useful in editing). Cross-referencing (ref
and label). Automatic index and automatic table of
contents. Hyperlinks (also very useful in editing).
(The talk about graphics is postponed.)
3-4:30 pm in room 1420. Noncommutative Geometry & Operator Algebras Seminar. Dietmar Bisch, Vanderbilt University. Exotic subfactors II (continued from last week). |
| Wed 15 |
3:10-4 pm, room 1308.
Analysis
& Biomathematics Seminar.
Tim Schulze, of the
University of Tennessee.
The Many Facets of Thin Film Growth.
Thin layers of crystalline material are often deposited onto a
substrate to produce coating surfaces and micro-electronic
materials. These "epitaxial" thin films are studied and modeled over
an enormous range of length scales. I will review some of the common
approaches to modeling this problem and present a hybrid method for
simulating epitaxial growth that combines kinetic Monte-Carlo (KMC)
simulations with the Burton-Cabrera-Frank model for crystal
growth. This involves partitioning the computational domain into KMC
regions and regions where one time-steps a discretized diffusion
equation. Computational speed and accuracy are discussed. The method
is significantly faster than KMC while accounting for many effects due
to stochastic fluctuations. I will illustrate this approach with
simulations of a two-dimensional "step-flow" instability.
3 pm, room 1432. Computational Analysis Seminar. Akram Aldroubi. Wavelet frames on irregular grids, with arbitrary dilation matrices, and in multi-dimension. This talk will be introductory and should be understandable by all. We will first introduce the concepts of wavelet bases and wavelet frames. Then, using a one dimensional simple example, we will present the main ideas on how to construct wavelet frames on irregular lattices, and with arbitrary dilation matrices. 4-5 pm, room 1403. Topology & Group Theory Seminar. Mozhgan Mirani, Vanderbilt University. Trees and Ultrametric Spaces. Ghys and de la Harpe show that a quasi-isometry of trees induces a Holder continuous and quasi-conformal homeomorphism on end spaces. By elaborating on their results I will show that there is a full and faithful functor from the category of locally finite trees and classes of quasi-isometries to the category of compact ultrametric spaces and quasi-conformal Holder homeomorphisms. |
| Thu 16 |
2:15 pm, room 1425. Graduate student tea. All
math personnel are invited.
4:10-5 pm, room 1206. Colloquium. Maxim Olshansky, Moscow University. A multigrid method for singular-perturbed problems. The multigrid method is a powerful tool to solve algebraic systems of equations arising in many applications and it is known to be among a few methods to provide an optimal complexity in terms of arithmetic operations per unknown. Pioneered in the 70's, multigrid soon become a crucial ingredient in engineering software for numerical solution of PDEs and integral equations. A mathematical theory of multigrid methods is nowadays well established in application to such "nice" problems as elliptic equations with full regularity. However it is still in an infant stage for many other problems of interest, even for some of those where a long evidence of successful calculations exists in the engineering applications. In the talk we first recall how and why the multigrid methods work. Further convergence analysis for a model problem is outlined. Finally we present some recent results for multigrid methods for singular-perturbed problems. ... Tea at 3:30 pm in SC 1425. |
| Fri 17 | Deadline for VU Employee Benefits Open Enrollment |
| Sat 18 - Tues 21 | holiday |