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Location: 232 Carver Hall
Time: 4:10-5p.m.
Tuesday
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Date |
Speaker |
Title (Click on the title of a talk for the abstract if available). |
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Jan 9,Tuesday |
Sang-Gu Lee, Sungkyunkwan
University |
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Jan. 16, Tuesday |
Luiz Antonio Peresi, University of Sao Paulo, Brazil |
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Jan. 23, Tuesday |
Jason Boggess, Abir Qamhiyah, Heather Thompson, Wolfgang Kliemann, Iowa State University |
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Feb. 1, Thursday |
Jonathan Farley, University of the West Indies |
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Feb. 2, Friday, 2:10-3p.m. 202 Carver Hall |
Kira Adaricheva, Harold Washington College, Chicago |
Realization of abstract convex geometries by point configurations |
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Feb. 6, Tuesday |
Santiago Schnell, Indiana University (Cancelled) |
A new model for the specification of the
vertebral precursors |
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Feb. 8, Thursday, 4:10-5p.m. |
Alexander Roitershtein, UBC Canada |
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Feb. 12, Monday, 4:10-5p.m. at 204 Carver |
Jason Swanson, University of Wisconsin-Madison |
Stochastic integration with respect to
a quartic variation process |
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Feb. 20, Tuesday |
Jing Shi, University of North Carolina, Charlotte |
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Feb. 21, Wednesday, 4:10-5p.m. |
Steven M. Wise, UC, Irvine (Cancelled) |
Modeling Solid Tumor Growth and
Angiogenesis: The Effect of the Microenvironment |
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Feb. 23, Friday, 3:10-4p.m. |
Christoph Walker, Vanderbilt University |
Global well-posedness of a haptotaxis
model with spatial and age structure |
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Feb. 27, Tuesday |
Ales Drapal, Charles University/University of Wisconsin |
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Mar. 6, Tuesday |
Bin Zhang, Sichuan University, China |
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Mar. 13, Tuesday |
Spring break |
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Mar. 20, Tuesday |
Yevgenia
Kashina, De Paul University |
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Mar. 27, Tuesday |
Neal Koblitz, University of Washington (LAS distinguished Miller lecture series) |
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Apr. 2, Monday |
Shili Lin, Ohio State University |
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Apr. 3, Tuesday |
Matt Papanikolas, Texas A&M |
Hypergeometric functions over finite fields, counting points, and modular forms |
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April 10, Tuesday |
Rob Lipton, Louisiana State
University |
Homogenization and field concentrations in heterogeneous media |
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April 12, Thursday |
Yang Kuang, Arizona State
University |
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Apr. 17, Tuesday |
Paul-Hermann Zieschang, University of Texas, Brownsville |
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Apr. 24, Tuesday |
Yu
Chen, New York University |
January 9, Tuesday, Sang-Gu Lee, Sungkyunkwan Univ., Korea
Title: On a three color sigma+ game
Abstract: After we cover some recent linear preserver problems that has
been solved. We will start to introduce a linear algebraic solution of the 3 by
3 Blackout game. Then we introduce a concept of sigma+ game which is a
generalization of the Blackout game, and show its relationship with automata
theory. Finally we will generalize the game on n by n board with 3 colors and
will show our tools in and JAVA that shows the optimal strategy to win the
game.
February 2, Friday, 2:10-3p.m. at 202 Carver Hall Kira Adaricheva, Harold Washington
College
Title: Realization of abstract convex geometries by point configurations (joint
work with Marcel Wild, University of Stellenbosch, South Africa)
Abstract: Convex geometries are closure systems with the anti-exchange
axiom. The Edelman-Jamison Problem asks to characterize finite convex
geometries which are representable by relatively convex sets of finite point
configurations on a plane.
Our work in progress gives a solution to the problem for those
convex geometries that are representable by either configurations of 2 points
in n-gon, or by at most 6-point configurations.
We also investigate the complexity of the problem by relating it
to the problem of realization of an order-type, which is known to be NP-hard.
We show that, under some additional assumptions on convex geometry and order
type, these two problems are polynomial-time equivalent.
Title: A new model for the specification of the vertebral precursors
Abstract: Somites are transient blocks of cells that form sequentially
along the antero-posterior axis of vertebrate embryos. They give rise to the
vertebrae, ribs and other associated features of the trunk. In this seminar we
show and analyse a mathematical formulation of a version of the Clock and
Wavefront model for somite formation, where the clock controls when the
boundaries of the somites form and the wavefront determines where they form.
Our analysis indicates that this interaction between a segmentation clock and a
wavefront can explain the periodic pattern of somites observed in normal
embryos.We can also show that a simplification of the model provides a
mechanism for predicting the anomalies resulting from perturbation of the
wavefront.
February 8,
Thursday, Alexander Roitershtein, University of British Columbia
Titlte: Transient random walks on a strip in a random environment.
Abstract: We will discuss a strong law of large numbers, an annealed
CLT, and the limit law of the ``environment viewed from the particle" for
transient random walks on a strip (product of Z with a finite set) in a random
environment. The model was introduced by Bolthausen and Goldsheid and includes
in particular RWRE with bounded jumps on the line as well as some
one-dimensional RWRE with a memory
Title: Stochastic integration with respect to a quartic variation process
Abstract: Brownian motion (BM) is used to model a wide array of stochastic
phenomena in a variety of scientific disciplines. Typically, this is done by
using BM as a driving term in a stochastic differential equation (SDE). We are
able to define and study these SDEs using Ito's stochastic calculus. Similarly,
stochastic partial differential equations (SPDEs) are often used to model
stochastic phenomena. In this talk, we consider a very simple example of a
stochastic heat equation. The solution to this SPDE, when regarded as a process
indexed by time, has a nontrivial 4-variation. It follows that we cannot use
the traditional methods of the Ito calculus to define an SDE driven by this
process.
In this talk, I will describe work in progress toward
constructing a stochastic integral with respect to this process and a
corresponding Ito-like change-of-variables formula. The integral being
constructed is a limit of discrete Riemann sums. It turns out that the process
we are considering has a very close relationship to a certain
"flavor" of fractional Brownian motion (FBM). The quest for a
calculus for FBM has led researchers in several different directions and there
is a large body of literature on the topic. I will discuss some of the connections
between our integral and an analogous approach for FBM.Part of this project is
joint work with Chris Burdzy.
Title: Multidimensional quantum tunneling: numerical instanton method with application
to polyatomic molecules
Abstract: Quantum tunneling plays a crucial role at the nano scale.
Multidimensional tunneling appears in the study of many problems ranging from
quantum field to enzyme catalysis. The high dimensionality of the potential
energy surface (e.g. many degrees of freedom) poses a great challenge in both
theoretical and numerical description of tunneling.
Numerical simulation based on Schrodinger equation is often
prohibitvely expensive. We propose an efficient and accurate numerical method
to calculate the tunneling splitting and decay rate. The method is based on
path integral formalism ('instanton' and 'bounce' approach) and free from any
further ad hoc assumptions on potential energy surface. The application to
proton tunneling between isomers of polyatomic molecule is demonstrated.
February 21, Wednesday, Steven Wise, University of
California-Irvine
Title: Modeling Solid Tumor Growth and Angiogenesis: The Effect of
the Microenvironment.
Abstract: I present and investigate models for solid tumor
growth that incorporate features of the tumor microenvironment, including
coupled, tumor-induced angiogenesis. Tumor growth is formulated as a free
boundary problem, and I compare sharp and diffuse interface descriptions. Using
analysis and efficient 2D and 3D nonlinear simulations, I explore the effects
of the interaction between the genetic characteristics of the tumor and the
tumor microenvironment on the resulting tumor progression. It is found that
tumor morphological evolution is qualitatively similar across a broad range of
parameters that govern the tumor genetic characteristics. Our findings
demonstrate the importance of the impact of microenvironment on tumor growth
and morphology and are consistent with recent experiments. I discuss possible
implications for some cancer therapy protocols.
February 23 Friday Christoph Walker, Vanderbilt
University.
Title: Global well-posedness of a haptotaxis model with spatial and age
structure
Abstract: A system of non-linear partial differential
equations modeling tumor invasion into surrounding healthy tissue is analyzed.
The model focuses on key components involved in tumor cell migration and takes
into account cell motility and haptotaxis, that is, the directed migratory
response of tumor cells to the extracellular environment. Individual cell
processes are modeled according to cell age. The equation for the tumor cell
density thus incorporates second-order (parabolic) terms representing diffusion
and taxis as well as a first-order (hyperbolic) part due to cell aging. Global
existence and uniqueness of non-negative solutions is shown.
February 27, Tuesday, Ales Drapal, Charles
University/University of Wisconsin
Title: Multilinear forms via polarization and conjugacy closedness
Abstract: Let V be a vector space over a field F, and let f
be a symmetric multilinear form of degree n on V.
If f vanishes whenever two arguments coincide, then
either f = 0, or char F = 2. We shall observe that a similar phenomenon
exists also when p = char F > 2 if one considers symmetric
multilinear forms f such that f vanishes whenever p
arguments coincide.
All such forms can be derived by a polarization process from
mappings of V to F that are analogues of quadratic forms. If n
= p = 3, then the forms f can be obtained as the associator mappings
of conjugacy closed loops. That is similar to the case n = p = 2 since
in that case one can get quadratic forms as commutators in groups.
March 6, Tuesday, Bin Zhang, Sichuan University, China
Title: Renormalization on Multiple Zeta Values
Abstract: This is joint work with Li Guo (Rutgers, Newark). In this talk,
we adapt a renormalization procedure in quantum field theory (QFT) to define the
values of multiple zeta functions ζ(s1,...,sk)
at (
March 20, Tuesday, Yevgenia Kashina, De Paul University
Title: From Groups to Semisimple Hopf Algebras.
Abstract: In this talk we will discuss how to generalize certain concepts
and notions, such as power, exponent, order of an element, normal subgroup,
from group theory to Hopf algebras. We will see what properties of these
generalized notions still hold for semisimple Hopf algebras, and what
properties are not true anymore. We will also discuss some classification
results for semisimple Hopf algebras.
March 27, Tuesday, (001 Carver Hall) Neal Koblitz, University of
Washington
Title: The Strange Relation of Mathematics to Cryptography
Abstract: Starting in 1984, when Hendrik Lenstra introduced his elliptic
curve factoring algorithm, the level of sophistication of the mathematics used
in cryptography has risen dramatically. Many concepts from number theory and
algebraic geometry have been applied to the study of elliptic and hyperelliptic
curve cryptosystems, the number field sieve method for factoring, and other
topics. More recently, though, mathematics has been used to give formal
assurances of security, and this has raised some difficult questions and some
suspicions that math is being misused. I will discuss the controversy surrounding
``provable security'' and give some examples that illustrate the need for
caution and skepticism.
Monday April 2, 2007 4:10pm at
Title: Modeling and Analysis of SAGE Cerebellum
Libraries
Abstract: A Serial Analysis of Gene Expression (SAGE) library is a
collection of thousands of small DNA "tags", each of which represents
a distinct mRNA transcript. Existing methods have been proposed for analyzing
single library data (i.e., one library per group) or one tag at a time. The
practice of lumping all libraries together (in a multi-library setting) to form
a "mega" library for each group is obviously unsatisfactory, but
nonetheless performed frequently due to the lack of alternative methods. Since
the tag counts within each library are inter-related as they are drawn from a
multinomial distribution, analyzing thousands of tags one at a time is
undoubtedly inadequate. Not only does such a practice ignore the dependency,
but it also faces with the multiple testing adjustment issue. In this talk, I
will describe a method that attempts to address both of these issues so that
all tags from multi-library groups can be analyzed together. The method
proposed also gears toward multi-group data.
Focusing on the problem of identifying genes that are
differentially expressed, a Bayesian formulation is established. Under this
formulation, the problem of separating the differentially expressed genes from
the majority of similarly expressed ones is treated as a model selection
problem, and the reversible jump Markov chain Monte Carlo method is adapted for
this purpose. The method is applied to a set of mouse libraries to uncover
genes that are associated with the process of aging in the cerebellum. Our Gene
Ontology (GO) analysis of the genes selected classifies them into several GO
categories, which appear to be functionally relevant to aging. This is joint
work with Dr. Zailong Wang.
Tuesday
Title: Hypergeometric functions over finite fields,
counting points, and modular forms
Abstract: First studied by Greene and Stanton in the 1980's, finite field
hypergeometric functions are constructed as certain sums of products of Jacobi
sums. Work of Ahlgren, Koike, Ono, and others have shown in certain examples
that values of these hypergeometric functions are closely related to counting
points on some Calabi-Yau manifolds over finite fields as well as to Fourier
coefficients of modular forms. Our overall goal is to explain these phenomena,
and we consider additional examples of values of 4F3-hypergeometric functions
and investigate how they count points on families of varieties whose
Picard-Fuchs equations are essentially hypergeometric. Joint work with S.
Frechette.
April 10
Title: Homogenization and field concentrations in heterogeneous media
Abstract: A multi-scale characterization of the field concentrations inside
composite and polycrystalline media is developed. The talk focuses on gradient
fields associated with solutions of second order elliptic PDE with measurable
coefficients. A rigorous mathematical theory for assessing the $L^p$
integrability of gradient fields inside micro-structured media is developed. The
results are described in terms of the $p^{th}$ order moments of the solution of
two-scale corrector problems. Examples are provided that illustrate the theory
and its application.
Title: Resource quality dynamics and its ecological implications
Abstract: Mathematical biologists have built on variants of the
Lotka–Volterra equations and in almost all cases have adopted the pure physical
science's single-currency (energy) approach to understanding population
dynamics. However, biomass production requires more than just energy. It is
crucially dependent on the chemical compositions of both the consumer species
and food resources. In this talk, we explore how depicting organisms as built
of more than one thing (for example, C and an important nutrient, such as P) in
stoichiometrically explicit models results in qualitatively different and
realistic predictions about the resulting dynamics. Specifically,
stoichiometric models incorporate both food quantity and food quality effects
in a single framework, appear to stabilize predator–prey systems while
simultaneously producing rich dynamics with alternative domains of attraction
and occasionally counterintuitive outcomes, such as coexistence of more than one
predator species on a single-prey item and decreased herbivore performance in
response to increased plant growth rate. Stoichiometric theory has tremendous
potential for both quantitative and qualitative improvements in the predictive
power of mathematical population models in the study of both ecological and
evolutional dynamics.
Title: FM approach vs AM approach to sensing and imaging
Abstract: No large amount of information can be long continued in space without
being carried by waves. Representations and transformations with wave functions
$e^{ikx}$ or $e^{i\omega t}$ as the basis thus play an important part in
sensing and imaging. The first fundamental theorem and tool for imaging is
undoubtedly the Fourier transform, in all its forms. If Joseph Fourier(1768 -
1830) initiated the use of Fourier transform, his contemporary compatriot
Gaspard de Prony (1755-1839) discovered a method, the Prony's method for
spectral analysis. While the Fourier transform is a linear process, Prony's
method is a nonlinear Fourier analysis, both performed on the signal or
scattering data in which the image or information sought is encoded.
The Fourier transform is extremely powerful and desirable
for sensing and imaging due to its well known analytical and numerical
properties. This attractiveness of the Fourier transform is pervasive and
appears to have concealed a fundamental flaw or limitation to its universal
utility in imaging. It seems that the Fourier transform leads to the so-called
AM model of imaging, as opposed to the FM model of imaging supported by Prony's
method.
In telecommunication frequency modulation (FM) has several
major advantages over amplitude modulation (AM). In this talk we will
characterize the FM and AM approaches to sensing and imaging. We will
illustrate similar gains and new capabilities of the FM approach over the AM
approach.