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Time:
4:10-5p.m. Tuesday, 268 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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Jan 22, Tuesday |
Yaxiang Yuan, Chinese Academy of Sciences |
Subspace Methods for Large Scale Nonlinear Equations and Nonlinear Least Squares |
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Jan 22, Tuesday |
Leslie Hogben, Howard Levine, Justin Peters, etc. |
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Jan. 24, Thursday |
Alicia Labra, University of
Chile |
Semiprimality and Solvability Of Commutative Right-Nilagebras |
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Jan. 29, Tuesday |
Nikolaos Zygouras, Univ. of
South California |
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Feb. 5, Tuesday |
Alex Roitershtein, Iowa State University |
A random walk on Z with drift driven by its occupation time at zero |
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Feb. 7, Thursday |
Anastasios Matzavinos, Ohio State University |
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Feb. 12, Tuesday |
Howard Levine, Iowa State University |
A Mathematical Argument for Using Aptamers in Chemotherapy and Imaging |
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Feb. 22, Friday Carver 204, 11a.m.-11:50a.m. |
Marko Djordjevic, Ohio
State University |
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Mar. 7, Friday, Carver 202, 3:10p.m.-4p.m. |
Hemanshu Kaul, Illinois
Institute of Technology |
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Mar. 11, Tuesday |
Peter Olver, University of
Minnesota, Minneapolis |
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Mar. 25, Tuesday |
Alan Paterson, Univ. of Mississippi |
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April. 1, Tuesday |
Ae Ja Yee, Penn. State University |
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April. 3, Thursday |
Raffaele Romano, Max Planck Research Group, University of Erlangen-Nuernberg, Germany |
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April. 8, Tuesday |
Roger Lui, Worcester Polytechnic Institute |
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April. 10, Thursday |
Rakesh, University of Delaware |
The spherical mean value operator for functions supported in a ball |
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April. 15, Tuesday |
Isabel Darcy, University of Iowa |
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April. 17, Thursday |
Weizhu Bao, University of Singapore |
Mathematical Analysis and Numerical Simulation of Bose-Einstein Condensation |
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Apr. 22, Tuesday |
George Andrews, Penn. State University |
Miller Distinguished Lecture: The Indian Genius, Ramanujan: His Life and the Excitement of His Mathematics |
Abstracts:
January 22, Tuesday, Prof. Yaxiang Yuan, Institute of
Computational Mathematics, Chinese Academy of Sciences
Title: Subspace Methods for
Large Scale Nonlinear Equations and Nonlinear Least Squares
Abstract: In this talk, we consider large scale nonlinear systems of
equations and nonlinear least square problems. We present subspace methods for
solving these two special optimization problems. The subspace methods have the
characteristic to force the next iteration in a low dimensional subspace. The
main technique is to construct subproblems in low dimensions so that the
computation cost in each iteration can be reduced comparing to standard
approaches. The subspace approach offers a possible way to handle large scale
optimization problems which are now attracting more and more attentions.
Actually, quite a few known techniques can be viewed as subspace methods, such
as the conjugate gradient method, the limited memory quasi-Newton method, the
projected gradient method, and the null space method.
January 22, Tuesday, Prof. Leslie Hogben, Howard Levine,
Justin Peters etc. Iowa State University
Title: These are your NSF
Math Institutes - use them!
Abstract: The seven NSF
Mathematical Sciences Institutes,
o American Institute of Mathematics (AIM),
o Institute for Advanced Study (IAS),
o Institute for Mathematics and its Applications (IMA),
o Institute for Pure and Applied Mathematics (IPAM),
o Mathematical Biosciences Institute (MBI),
o Mathematical Sciences Research Institute (MSRI),
o Statistical and Applied Mathematical Sciences Institute (SAMSI),
as well as
o Banff International Research Station (BIRS) (supported by Canada, the
US, and Mexico),
o Mathematisches Forschungsinstitut Oberwolfach (MFO) (supported by
Germany, the US, etc.) represent
a wonderful resource for the mathematics community.
In this colloquium, programs for
faculty and graduate students offered by each institute will be described
briefly by a faculty member with experience at that institute. Links to the
pages of all the institutes can be found at http://mathinstitutes.org/.
Jan 24,
Thursday, Prof. Alicia Labra, University of Chile
Title: Semiprimality
and Solvability of Commutative Right-Nilagebras
Abstract: We study commutative right-nilalgebras of rigth-nilindex four
satisfying the identity (b,aa,a)=0, that is commutative algebras
satisfying the identities ((aa)a)a = 0 and (b(aa))a-b((aa)a)= 0.
We prove that if such a algebra is finitely generated and semiprime then it is
a nilpotent Jordan algebra. Moreover, we prove that without the hypothesis of
semiprimality these algebras are solvable. Our results require characteristic
different from 2,3. This is a joint work with I. Correa and I. R. Hentzel.
Feb. 5, Tuesday. Prof. Alexander Roitershtein, Iowa State
University
Title: A random walk on Z with drift driven by its occupation time at
zero
Abstract: We consider a one-dimensional nearest neighbor random walk on the
integer lattice with time-dependent drift towards the origin, given by an
asymptotically vanishing function of the number of visits to zero. We obtain
limit theorems for this random walk. In particular, we show the existence of
three regimes according to the rate of decay of the drift. When the rate is
sufficiently fast, the random walk satisfies the invariance principle. When the
rate is sufficiently slow, the position of the random walk, properly scaled,
converges to a symmetric exponential law.
This is a joint work with Iddo Ben-Ari (UC Irvine) and Mathieu Merle (UBC). If time allows, I will also discuss the critical case, which is a work in progress.
Feb. 7, Thursday, Prof. Anastasios Matzavinos,
the Ohio State University
Title: Theoretical approaches to actin filament dynamics
Abstract: Dynamic control
of the actin network in eukaryotic cells plays an essential role in their
movement, but to date our understanding of how the network properties are
controlled in space and time is still rudimentary. For example, how the cell
maintains the pools of monomeric actin needed for a rapid response to signals,
how the filament length distribution is controlled, and how the actin network
properties are modulated by various bundling and severing proteins to produce
the mechanical response is not known. In this talk we focus on the development
and analysis of mathematical models which enable us to investigate the temporal
evolution of the filament length distribution and the effect of the nucleotide
composition on the dynamics of actin filaments in vitro. We discuss recent
results on the relevant time scales for establishment of a time-invariant
length distribution. We find that there are very long-lived intermediate length
distributions that are not exponential. Also, we set up a master equation for
the biochemical processes appearing at the actin-filament level and simulate
the corresponding dynamics by generating numerical realizations through a Monte
Carlo scheme. Statistical analysis of ensembles of generated realizations
provides the moments of the various distributions of interest. Various
challenges in this direction concerning the complexity of the Monte Carlo
scheme are addressed and an analysis of the statistically-derived moments in
the framework of simplified analytic models and correlated random walks is
discussed.
Feb. 12, Tuesday Prof. Howard Levine, Iowa State
University
Title: A Mathematical Argument for Using Aptamers in Chemotherapy and Imaging
Abstract: A central challenge for drug design is to create molecules with
optimal function that also partition efficiently into the appropriate in vivo
compartment(s). This is particularly true in cancer treatments because cancer
cells upregulate their expression of multidrug resistant trans- porters, which
necessitates application of higher concentrations of extracellular drugs to
enable cell killing. Here we give proof in principle with a mathematical model
based on chemical kinetic considerations that intracellular RNA aptamers can
increase the effective intracellular concentration of a drug is by
"pulling" the drug in. We evaluate the use of cell-expressed aptamers
with affinity for the drug to increase the efficiency of drug transport across
the cell membrane and to increase the intracellular concentration of drug. We
show that this outcome will occur if the aptamer diffuses throughout the
cytoplasm. The ability of the aptamer to increase the intracellular
concentration of its target molecule could also be used for imaging cells. We
show by simulation that an intracellular aptamer can be enlisted for an
integrated approach to both increase drug effectiveness and image
aptamer-expressing cells.
An important finding from this study is the identification of the role of receptor diffusion in moving a drug from the membrane into the cell interior. The study predicts that the efficiency of drug action will be higher if the drug target molecule diffuses rather than being sequestered in an intracellular location such as is true for many enzymes.
Feb. 22,
Friday, Prof. Marko Djordjevic, Ohio State University
Title: Modeling and bioinformatics of gene regulation
Abstract: The talk will
address both mathematical modeling of biological systems and biophysics
approach to bioinformatic problems, through research examples arising in gene
transcription. The first part of the talk will address how RNA polymerase is
initiating gene transcription. The first quantitative model for the open
complex formation (the first step in transcription initiation) will be
presented, and shown to be in a good correspondence with the experimental data.
In the second part of the talk, the problem of determining protein-DNA
interaction parameters will be addressed. It will be shown how modeling of
in-vitro selection experiments can significantly improve both the experimental
design and bioinformatic procedure for inferring the interaction energies.
March 7, Friday
Prof. Hemanshu Kaul, Illinois Institute of Technology
Title: Graph Packing - Conjectures and Results
Abstract: A number of
basic problems in graph theory can be stated as packing problems. Let G1 and G2
be graphs of order at most n. We say that G1 and G2 pack if their vertex sets
map injectively into {1,...,n} so that the images of the edge sets are
disjoint. The concept of graph packing generalizes various extremal graph
problems, including problems on fixed subgraphs (such as the Hamiltonian Cycle
problem), forbidden subgraphs (Turan-type problems), and equitable coloring.
The study of packings of graphs was started in the 1970s by Sauer and Spencer,
and by Bollobas and Eldridge. Graph packing results have also been widely
applied to the study of computational complexity of graph properties.
We will discuss a few
longstanding conjectures in this area, and present some recent results. In
particular, we will present an extension (with A. Kostochka) of a classical
theorem of Sauer and Spencer (1975) that is obtained through the
characterization of its extremal graphs, and the best current result (with A.
Kostochka and G. Yu) towards the well known Bollobas-Eldridge graph packing
conjecture (1978), that further extends the Sauer-Spencer theorem.
March 11,
Tuesday, Prof. Peter J. Olver University of Minnesota
Title: Applications of Moving Frames
Abstract: In this talk, I
will describe a new approach to the theory of moving frames that is based on
equivariant maps. The method is completely algorithmic, and can be readily
applied to completely general finite-dimensional Lie group and even
infinite-dimensional pseudo-group actions. After introducing the basic ideas, I
will attempt to survey a wide variety of new applications, including
classification of differential invariants, invariant variational problems and
differential equations, symmetries and object recognition in computer vision,
and the design of symmetry-preserving numerical approximations.
April 1,
Tuesday, Prof. Ae Ja Yee, Pennsylvania State University
Title: Rogers-Ramanujan identities and related partition theorems
Abstract: In the theory
of partitions, the most celebrated are the Rogers-Ramanujan identities in the
sense that not only they have motivated partitionists to search for further
identities in the partition theory but also they have become crucial bridges to
connect the theory to other fields.
Within the partition theory, the
discovery of the Rogers-Ramanujan identities raised two major questions: one is
relation between partitions with difference conditions and partitions into
parts satisfying certain arithmetic progressions, and the other is existence of
nice combinatorial proofs like the proof of Euler's identity. This talk will be
devoted to a survey of interesting partition theorems related to the
Rogers-Ramanujan identities.
April 3,
Thursday, Prof. Raffaele Romano Max Planck Research Group, University of
Erlangen-Nuernberg
Title: Introduction to Quantum Error Correction Codes
Abstract: The protection
against the environmental action is an important achievement for the
implementation of quantum technologies. In this talk, the main ideas founding
the theory of Quantum Error Correcting Codes are described by using simple
examples, and the general formalism is presented in a pedagogical way.
April 8,
Tuesday, Prof. Roger Lui, Worcester Polytechnic Institute
Title: Mathematics of Molecular and Cellular Biology
Abstract: The study of
molecular and cellular biology includes topics from nucleic acids (DNA and RNA)
all the way to cell motility and chemotaxis. Currently, this is a very active
area of mathematical biology and many papers are written in this area in
scientific and math journals every month. So far, there have not been a lot of
significant advances either because the mathematical problems are extremely
challenging or because people just don't know how to model them. In this talk,
I shall illustrate these two points by discussing three examples: protein
folding, biochemical network (cell signaling), and cell motility. I am an
analyst by training so you will see a lot of equations in my talk but I will
try to keep the technicalities to a minimum till the end.
April 15,
Tuesday Prof. Isabel Darcy,
Title: Modeling protein-DNA complexes using tangles.
Abstract: Protein-DNA
complexes were first mathematically modeled using tangles in Ernst and Sumners
seminal paper, "A calculus for rational tangles: applications to DNA
recombination" (Math Proc Camb Phil Soc, 1990). A tangle consists of arcs
properly embedded in a 3-dimensional ball. The protein is modeled by the 3D ball
while the segments of DNA bound by the protein can be thought of as arcs
embedded within the protein ball. This is a very simple model of protein-DNA
binding, but from this simple model, much information can be gained. The main
idea is that when modeling protein-DNA reactions, one would like to know how to
draw the DNA. For example, are there any crossings trapped by the protein
complex? How do the DNA strands exit the complex? Is there significant
bending? Tangle analysis cannot determine the exact geometry of the protein-bound
DNA, but it can determine the overall entanglement of this DNA, after which
other techniques may be used to more precisely determine the geometry.
April 17,
Thursday, Prof. Weizhu Bao, National University of Singapore
Title: Mathematical Analysis and Numerical Simulation of Bose-Einstein
Condensation
Abstract: In this talk, I
review the mathematical results of the dynamcis of Bose-Einstein condensate
(BEC) and present some efficient and stable numerical methods to compute ground
states and dynamics of BEC. As preparatory steps, we take the 3D
Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale it to
obtain a four-parameter model and show how to reduce it to 2D GPE in certain
limiting regimes. Then we study numerically and asymptotically the ground
states, excited states and quantized vortex states as well as their energy and
chemical potential diagram in rotating BEC. Some very interesting numerical
results are observed. Finally, we study numerically stability and interaction
of quantized vortices in rotating BEC. Some interesting interaction patterns
will be reported.