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Time:
4:10-5p.m. 204
Carver Hall
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Date |
Speaker |
Title (Click on the title of a talk for the abstract if available) |
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Sep. 5 |
Umesh Vaidya, ECE department |
Stability analysis of non-equilibrium behavior in nonlinear dynamical systems |
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Sep. 12 |
Alexander Kostochka, UIUC |
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Sep. 19 |
Torben Stender University of Augsburg in Germany |
Generalization of imaginary parts of eigenvalues: chain rotation numbers. |
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Sep. 26 |
Krishna Athreya Iowa State University |
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Oct. 10 |
Muthu Krishnamurthy, |
Harmonic Analysis and Number Theory: The principle of functoriality |
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Oct. 17 |
Bei Hu Notre Dame |
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Oct. 19 (1:10p.m. at 204 Carver) |
Jayadev Athreya Yale University |
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Oct. 24 |
Sung Y. Song |
Character tables of group-case commutative association schemes |
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Oct. 31 |
Markos Katsoulakis |
Mathematical strategies and error quantification in coarse-graining of extended microscopic systems |
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Nov. 7 |
Hailiang Liu |
Multi-valued Solution and Level Set Methods In Computational High Frequency Wave Propagation |
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Nov. 9, Thursday |
Bo Li UC, |
Surface Relaxation versus the Ehrlich-Schwoebel Effect in Thinfilm Growth |
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Nov. 14 (305 Carver) |
Sunil Kumar |
Dynamic Control of Queueing Systems via Diffusion Approximations |
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Nov. 21 |
Thanksgiving break |
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Nov. 28 |
Ivan Correa Metropolitan university of CS of the Education |
Oct. 10, Tuesday Prof. Muthu
Krishnamurthy,
Title:
Abstract: The principal of functoriality is one of the
central questions in number theory. It is a conjecture of Langlands that
emerged out of his attempt to classify number fields. The conjecture describes
deep relationships among the spectral data on different groups. The spectral
data arises from the theory of differential operators and group representations
which also carries arithmetic information of fundamental importance. In this
talk I will explain the conjecture and mention some known cases of
functoriality.
Oct. 17, Tuesday, Prof. Bei Hu, University of Notre Dame
Title: Stability analysis for tumor models
Abstract: We consider time-dependent free boundary problems modeling
tumor growth. We prove that there exists a critical number L such that if some
parameter is less than L, then the stationary solution is asymptotically
stable, whereas if the parameter is bigger than L, then the stationary solution
is unstable. This has implications on the aggressiveness of the tumor.
Oct. 19, Thursday, Prof. Jayadev Athreya, Yale
University,
Title: Counting problems for billiards and lattices.
Abstract: We discuss the problem of asymptotics of counting closed
trajectories for billiards in Euclidean polygons. We will be motivated by the
case of the torus, which we will discuss in detail.
Oct. 24,
Tuesday, Prof. Sung Y. Song, Iowa State University
Title: Character tables of group-case commutative association schemes
Abstract. The
condition that a group-case association scheme is (primitive) commutative
is equivalent to the fact that a permutation group acts on the cosets of a
(maximal) subgroup with multiplicity-free permutation representation. The works
by many group theorists on the classification of maximal subgroups of finite
simple groups (by using the classification of finite simple groups) provide us
with many such group-case association schemes. The construction of character
tables of known association schemes of this kind are important first step
towards the classification of commutative association schemes. The progress
which has been made in this research direction points out interesting
connections between association schemes, groups, and classical
geometries. In this talk we will discuss some of these connections.
Oct. 31 Tuesday Prof. Markos Katsoulakis, University of
Massachusetts
Title: Mathematical strategies and error quantification in coarse-graining of
extended microscopic systems
Abstract: In this talk we discuss recent and on going work in obtaining
coarse-grained
stochastic approximations of extended microscopic systems. Examples of such
models include stochastic lattice dynamics, as well as more complex off-lattice
models of macromolecules (e.g. polymers) that have internal degrees of freedom.
Computational comparisons of coarse-grained and microscopic simulations along
with accompanying rigorous estimates on the loss of information between the
coarse-grained and microscopic probability distribution functions (pdf)
highlight the validity regimes and the limitations of the method. Furthermore
we discuss spatial adaptivity for microscopic simulations constructed using the
coarse-graining tools we have already developed. The adaptivity criterion is
based, in analogy to PDE finite element methods, on a posteriori estimates on
the loss of information between the coarse-grained and the microscopic pdf.
Nov. 9, Thursday Prof. Bo Li, UC San Diego
Title: Surface Relaxation versus the Ehrlich-Schwoebel Effect in Thinfilm
Growth
Abstract: The surface of an epitaxially growing thin film often exhibits a
mound-like structure with its characteristic lateral size increasing in time.
In this talk, we consider two competing mechanisms for such a coarsening
process: (1) surface relaxation described by high-order gradients
of the surface profile; and (2) the Ehrlich-Schwoebel (ES) effect which is the
upper-lower terrace asymmetry in the adatom attachment and detachment to and
from atomic steps.
We present a theory based on a class
of continuum models that are mathematically gradient-flows of some effective
free-energy functionals describing these mechanisms. This theory consists of
two parts: (1) variational properties of the energies, such as ``ground
states'' and their large-system-size asymptotics, showing the unboundedness of
surface slope and revealing the relation between some of the models; (2)
rigorous bounds for the scaling law of the roughness, the rate of increase of
surface slope, and the rate of energy dissipation, all of which characterize
the coarsening process. Predictions on scaling laws made by our theory agree
well with experiments.
Nov. 14, Tuesday Professor Sunil Kumar, Graduate
School of Business, Stanford University.
Title: Dynamic Control of Queueing Systems via Diffusion Approximations
Absttract: Queueing systems are natural models of congested systems in many
applications. One way to design control policies for queueing systems is as
follows. First, one obtains optimal control policies for a diffusion
approximation of the system. This usually involves solving a singular
stochastic control problem. Then the optimal control for the diffusion
approximation is used to construct a control for the queueing system, and this
control is shown to be asymptotically optimal in some suitable asymptotic
regime. This approach provides a tractable way to construct asymptotically
optimal admission control, routing and scheduling policies for queueing
systems.
In this talk
we study an application of this method to a problem of interest in services. We
study admission control into a queue handled by a single server that is
populated by impatient customers. We construct an approximating diffusion
control problem. We solve this singular control problem by iteratively
constructing a solution to the associated Hamilton-Jacobi-Bellman equation. We
use this solution to construct a simple threshold admission control for the
queueing system. In the regime where the arrival rates and service rates are
equal and increasing to infinity, the so-called heavy traffic regime, we
establish that our control is asymptotically optimal using weak convergence
methods.
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