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Friday, October 23, 2009 - 15:00 ,
Location: Skiles 269 ,
Amey Kaloti ,
Georgia Tech ,
Organizer:

This is a 2 hour talk.

Abstract: Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter
Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with
connections to contact topology. In these talks we will try to define the Heegaard Floer
homology without assuming much background in low dimensional topology. One more goal is
to present the combinatorial description for this theory.

Series: Analysis Seminar

I will review recent and classical results concerning the
asymptotic properties (as N --> \infty) of 'ground state' configurations
of N particles restricted to a d-dimensional compact set A\subset {\bf R}^p
that minimize the Riesz s-energy functional
\sum_{i\neq j}\frac{1}{|x_{i}-x_{j}|^{s}}
for s>0.
Specifically, we will discuss the following
(1) For s < d, the ground state configurations have limit distribution as
N --> \infty given by the equilibrium measure \mu_s, while the first
order asymptotic growth of the energy of these configurations is given by
the 'transfinite diameter' of A.
(2) We study the behavior of \mu_s as s approaches the critical
value d (for s\ge d, there is no equilibrium measure). In the case that
A is a fractal, the notion of 'order two density' introduced by Bedford
and Fisher naturally arises. This is joint work with M. Calef.
(3) As s --> \infty, ground state configurations approach best-packing
configurations on A. In work with S. Borodachov and E. Saff we show that
such configurations are asymptotically uniformly distributed on A.

Series: Stochastics Seminar

In this talk, we study an interacting particle system arising in the
context of series Jackson queueing networks. Using effectively nothing
more than the Cauchy-Binet identity, which is a standard tool in
random-matrix theory, we show that its transition probabilities can be
written as a signed sum of non-crossing probabilities. Thus, questions
on time-dependent queueing behavior are translated to questions on
non-crossing probabilities. To illustrate the use of this connection,
we prove that the relaxation time (i.e., the reciprocal of the
’spectral gap’) of a positive recurrent system equals the relaxation
time of a single M/M/1 queue with the same arrival and service rates as
the network’s bottleneck station. This resolves a 1985 conjecture from
Blanc on series Jackson networks.
Joint work with Jon Warren, University of Warwick.

Series: Graph Theory Seminar

The Jacobian of a graph, also known as the Picard Group, Sandpile Group, or Critical Group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this talk I will present a combinatorial method of approaching the Jacobian of graphs by way of a chip-firing game played on its vertices. We then apply this chip-firing game to explicitly characterize the Jacobian of nearly complete graphs, those obtained from the complete graph by deleting either a cycle or two vertex-disjoint paths incident with all but one vertex. This is joint work with Sergey Norin.

Series: School of Mathematics Colloquium

After a brief account of some of
the history of this classical subject,
we indicate how such models are derived.
Rigorous theory justifying the models
will be discussed and the conversation
will then turn to some applications.
These will be drawn from questions
arising in geophysics and coastal
engineering, as time permits.

Series: Other Talks

Tea and light refreshments 1:30 in Room 2222. Organizer: Santosh Vempala

Concentration results for the TSP, MWST and many other problems with random inputs show the answer is concentrated tightly around the mean. But most results assume uniform density of the input. We will generalize these to heavy-tailed inputs which seem to be ubiquitous in modern applications. To accomplish this, we prove two new general probability inequalities. The simpler first inequality weakens both hypotheses in Hoffding-Azuma inequality and is enough to tackle TSP, MWST and Random Projections. The second inequality further weakens the moment requirements and using it, we prove the best possible concentration for the long-studied bin packing problem as well as some others. Many other applications seem possible..

Series: Analysis Seminar

In this talk we will discuss Kolmogorov and Landau type inequalities for the derivatives. These are the inequalities which estimate the norm of the intermediate
derivative of a function (defined on an interval, R_+, R, or
their multivariate analogs) from some class in terms of the norm of the
function itself and norm of its highest derivative.
We shall present several new results on sharp inequalities of this type
for special classes of functions (multiply monotone and absolutely
monotone) and sequences. We will also highlight some of the techniques
involved in the proofs (comparison theorems) and discuss several
applications.

Series: Other Talks

As we have seen already, the global section functor is left exact. To get a long exact sequence, I will first give the construction of derived functors in the more general setting of abelian categories withenough injectives. If time permits, I will then show that for any ringed space the category of all sheaves of Modules is an abelian category with enough injectives, and so we can construct sheaf cohomology as the right derived functors of the global section functor. The relation with Cech cohomology will be studied in a subsequent talk.

Series: Research Horizons Seminar

Orthogonal polynomials are an important tool in many areas of pure and
applied mathematics. We outline one application in random matrix
theory. We discuss generalizations of orthogonal polynomials such as
the Muntz orthogonal polynomials investigated by Ulfar Stefansson.
Finally, we present some conjectures about biorthogonal polynomials,
which would be a great Ph.D. project for any interested student.

Wednesday, October 21, 2009 - 11:00 ,
Location: Skiles 269 ,
Klas Udekwu ,
Biology, Emory University ,
ikeche@gmail.com ,
Organizer:

Treatment of bacterial
infections with antibiotics is universally accepted as one of (if not THE) most
significant contributions of medical intervention to reducing mortality and
morbidity during last century. Surprisingly, basic knowledge about how
antibiotics kill or prevent the growth of bacteria is only just beginning to
emerge and the dose and term of antibiotic treatment has long been determined
by clinicians empirically and intuitively.
There is a recent drive to
theoretically and experimentally rationalize antibiotic treatment protocols with
the aim to them and to design protocols which maximize antibiotics’ efficacy
while preventing resistance emergence. Central to these endeavors are the
pharmacodynamics of the antibiotic(s) and bacteria, PD (the relationship
between the concentration of the antibiotic and the rate of growth/death of
bacteria), and the pharmacokinetics of the antibiotic, PK (the distribution and
change in concentration of the antibiotics in a treated host) of each
bacteria. The procedures for
estimating of PD and PK parameters are well established and standardized
worldwide. Although different PK
parameters are commonly employed for the design of antibiotic treatment
protocols most of these considerations, a single PD parameter is usually used,
the minimum inhibitory concentration (MIC). The Clinical and Laboratory
Standards Institute (CLSI)
approved method for estimating MICs defines testing conditions that are optimal
for the antibiotic, like low densities and exponential growth, rarely obtain
outside of the laboratory and virtually never in the bacteria infecting
mammalian hosts. Real
infections with clinical symptoms commonly involve very high densities of
bacteria, most of which are not replicating, and these bacteria are rarely
planktonic, rather residing as colonies or within matrices called biofilms
which sometimes include other species of bacteria. Refractoriness (non-inherited resistance) is the term used to
describe an observed inefficacy of antibiotics on otherwise
antibiotic-susceptible bacterial populations. This talk will focus on our
efforts to describe the pharmacodynamic relationship between Staphylococcus
aureus and antibiotics of six
classes in the light of antibiotic refractoriness.
I will begin by addressing
the effects of cell density on the MIC index, after which I intend to present
unpublished data descriptive of physiology-related effects on antibiotic
efficacy. Additionally, we will explore
the potential contribution of such in vitro results, to observed/predicted clinical
outcomes using standard mathematical models of antibiotic treatment which also
serve to generate testable hypotheses.