Spring 2009 Department Colloquia
Tuesdays at 4:10 p.m. in 232 Carver Hall unless otherwise noted
For more information contact Anastasios Matzavinos or Alexander Roitershtein
January 20 - Huntington Tracy Hall (Brigham Young University) on Tunnel number and zero forcing. Hosts: Jason Grout and Leslie Hogben.
Wednesday, January 28 in 305 Carver- Tathagata Basak (Dickson Instructor, University of Chicago) A complex hyperbolic reflection group and the bimonster; host Jonathan Smith poster
Friday, January 30 in 202 Carver at 3:10 - Ameya Pitale (University of Oklahoma) L-functions and special value results xposter
Monday, February 2 (Carver 294) - Alexandr Labovschii (University of Missouri) Architecture for models of fluid flow phenomena Poster
February 3 in Carver 232 - Marta Lewicka (University of Minnesota) The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells. Host: Tasos Matzavinos. Poster
Friday, February 6 (Carver 202)- Nayantara Bhatnagar (Visiting Neyman Assistant Professor at Berkeley) Reconstruction for colorings on trees and scaling limits of random width-2 posets Poster
February 10 - Gary M. Lieberman (ISU) Oblique derivative boundary conditions. Poster
Monday, February 16 at 4:10 in Carver 202. Don Saari (UCI Distinguished Professor) The evolution of the universe Host: Bo Su
February 17 - Miller Lecture: 305 Carver. Don Saari (UC Irvine) We vote, we decide; but why can we get bad outcomes? Host: Bo Su
Friday, March 6 - Markus Mobius (Economics, Harvard) Consumption risk-sharing in social networks. 4:10 - 5:00 p.m.
March 10 - In-Jae Kim (Minnesota State Mankato) On potentially nilpotent sign patterns. Hosts: Leslie Hogben and Jason Grout
Thursday, March 12 in 305 Carver - Irina Mitrea, Boundary value problems for higher order elliptic operators
Thursday, March 26 - Erik Kostelich (Arizona State University) on Data assimilation: finding the initial conditions in complex
dynamical systems in Carver 305
Tuesday, March 31 - Alex Iosevich, Geometric configurations in discrete, continuous and arithmetic settings
April 2 in Carver 305 - Henri Darmon (McGill University) Diophantine equations and periods. Host: Ling Long. Sponsored by the ISU ADVANCE program. POSTER
April 7 - Harm Derksen (University of Michigan) Invariant theory and Hilbert's fourteenth problem. Host: James Murdock.
Thursday, April 16 in Carver 305 - William Yslas Vélez (University of Arizona) Increasing the number of mathematics majors
POSTER
Monday, April 20 at 4:10 p.m. in 3 Physics - we are co-sponsoring: Thomas F. Mayer (Augustana College) Trying Galileo
April 21 - Susana Serna (UCLA) Analysis and numerics of the nonconvex hyperbolic system of magnetohydrodynamics. Host: Howard Levine.
April 28 - Codina Cotar, Technical University of Munich, title TBA; Host: Alexander Roitershtein TO BE RESCHEDULED
Susana Serna (UCLA) Analysis and numerics of the nonconvex hyperbolic system of magnetohydrodynamics
We explore the structure of the solution of nonlinear hyperbolic systems of conservation laws in terms of the qualitative properties of the Jacobian of their fluxes. In particular we will focus on the equations of the compressible magnetohydrodynamics (MHD) and their wave structure. The ideal MHD equations form a non-strictly hyperbolic system of conservation laws. The complexity of this system of equations lies on the presence of the magnetic field that generates nonconvex waves. The rotation of the magnetic field induces the non-strict hyperbolicity of the MHD system and non-genuinely nonlinearity (non-convexity) of some of the local wavefields.
We present an analytical study of the wave structure of the ideal MHD system of equations based on the local decomposition in characteristic fields. We propose an appropriate spectral decomposition of the fluxes that allows to establish an explicit criteria to detect non-convexity points. We then formulate a general purpose shock capturing numerical scheme based on the proposed local characteristic field decomposition and we present some computational tests.
William Yslas Vélez (University of Arizona) Increasing the number of mathematics majors
In the late 1980's I began my efforts to increase the success rate of minorities in first semester calculus. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. These meetings with students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum.
I took over the position of Associate Head for Undergraduate Affairs in the department five years ago. I set a very modest goal for myself: to double the number of mathematics majors. With more than 500 mathematics majors I have reached that goal. I think the next doubling is going to be much harder to achieve. My work with minority students provided me with the tools to accept this new challenge of working with all students.
This talk will describe my own efforts to encourage ALL of our students that a mathematics major, or adding mathematics as a second major, is a great career choice.
Harm Derksen (University of Michigan) Invariant theory and Hilbert's fourteenth problem
If a group acts on an affine space, then it also acts on the ring of polynomial functions on that space. The ring of invariants is the set of all polynomial functions that are constant on orbits. Hilbert's fourteenth problem was inspired by the question whether the ring of invariants is finitely generated as an algebra.
Nagata showed that rings of invariants are not always finitely generated.
I will discuss how one can find generators of the invariant ring (if it is finitely generated), and what can still be done if the ring of invariants is not finitely generated.
Henri DarmonDiophantine equations and periods.
A period is the integral of a differential form along a closed cycle in an algebraic variety. Examples include the number $\pi$, elliptic integrals, and certain logarithms of algebraic numbers. I will explain how periods can be used to solve some of the classical equations of number theory such as Pell's equation or equations attached to elliptic curves.
Eric Kostelich. Data assimilation: finding the initial conditions in complex dynamical systems
Data assimilation refers to the question of how to
determine the initial conditions for a given dynamical model (such as
a weather forecast model) from a collection of measurements. This
talk will describe a novel approach that exploits the chaotic
dynamics of the weather to reduce the dimensionality of the problem
in a way that leads to a highly accurate, model-independent algorithm
with an efficient implementation on highly parallel computers.
Comparisons of this approach, called the Local Ensemble Transform
Kalman
Filter (LETKF), with the operational system of the National Weather
Service will be described. Other applications to ocean, climate, and
cancer models will be outlined.
Alex Iosevich, Geometric configurations in discrete, continuous and arithmetic settings
A classical problem that appears in a variety of forms in analysis, combinatorics and number theory is to determine how large a subset of a given vector space needs to be in order to be sure that it determines a suitable finite configuration up to a set of geometric invariances. In the discrete setting, a well-known example is the Erdos distance problem which asks for the minimal number of distances determined by a subset of ${\Bbb R}^d$, $d \ge 2$, consisting of $N$ points. In the continuous setting, the Falconer distance problems asks for how large the Hausdorff dimension needs to be to assure that the set of distances determined by a set has positive Lebesgue measure. In the setting of finite fields, the features of both of these problems interact with a set of interesting arithmetic obstructions.
We shall discuss these problems, some recent results and interplay of a variety of techniques from analysis, combinatorics and number theory.
Irina Mitrea, Boundary value problems for higher order elliptic operators
One of the most effective methods for solving boundary value problems for basic equations of Mathematical Physics in a domain is the method of layer potentials. Its essence is to reduce the entire problem to an integral equation on the boundary of the domain which is then solved using Fredholm theory.
Until now, this approach has been primarily used in connection with second order operators for which a sophisticated and far-reaching theory exists. This stands in sharp contrast with the case of higher order operators (arising for instance in plate elasticity) for which very little is known in this regard. In this talk I will survey recent results aimed at extending the method of singular integral operators (of layer potential type) to the higher order case.
Markus Mobius (Economics, Harvard) Consumption risk-sharing in social networks
We develop a model of informal risk-sharing in social networks, where relationships between individuals can be used as social collateral to enforce insurance payments. We characterize incentive compatible risk-sharing arrangements and obtain two results. (1) The degree of informal insurance is governed by the expansiveness of the network, measured by the number of connections that groups of agents have with the rest of the community, relative to group size. Two-dimensional networks, where people have connections in multiple directions, are sufficiently expansive to allow very good risk-sharing. Social networks in Peruvian villages are shown to satisfy this condition, suggesting that real-world village networks should generate good informal insurance. (2) In second-best arrangements, agents organize in endogenous "risk-sharing islands" in the network, where shocks are shared fully within, but imperfectly across islands. As a result, network based risk-sharing is local: socially closer agents insure each other more. These results can be used to study the spillover effects of development aid. The paper is joint with Attila Ambrus (Harvard) and Adam Szeidl (Berkeley).
In-Jae Kim (Minnesota State Mankato) On potentially nilpotent sign patterns
A sign pattern is a matrix with entries in {+,-,0}. If a sign pattern A has a nilpotent realization, then A is said to be potentially nilpotent. Potentially nilpotent sign patterns arise in the context of asymptotic stability of (continuous and discrete) dynamical systems. For sparse sign patterns there is much work of identifying potentially nilpotent sign patterns according to their graphical configurations (using Coates digraph of a sign pattern). However, this approach does not work efficiently for dense sign patterns. This talk will review results on potentially nilpotent sign patterns and present some recent development on potentially nilpotent sign patterns, including potentially nilpotent full sign patterns with no zero entries.
Don Saari (UC Irvine) The evolution of the universe
In this expository lecture, an outline of the evolution of all solutions of the Newtonian N-body problem as time goes to infinity will be described. Along with the evolution, unsolved problems along with the source of "chaos" will be described.
Don Saari (UC Irvine) We vote, we decide; but why can we get bad outcomes?
Voting, as well as decisions in science, engineering, business and on and on are central to almost all of what we do. But, overly frequently the outcome sure appears to differ from what we expect should happen. As I will show in this expository lecture, which will have several actual examples, the problem is caused by how we make decisions. A warning; expect to leave this lecture worrying whether a correct decision was made in a recent election (maybe for a new chair, or who to hire), or setting, that was of importance to you.
Nayantara Bhatnagar (Berkeley) Reconstruction for colorings on trees and scaling limits of random width-2 posets
Consider the following random assignment of colors to the vertices of a tree of height h where each vertex has D children. First the
root is colored with one of k colors uniformly at random. Each vertex thereafter independently chooses one of k-1 colors randomly, different from its parent. Conditioned on having started with two different colors at the root, if the variation distance between the distributions of colorings at the leaves of the tree goes to 0 as the height goes to infinity, reconstruction does not hold. Thresholds for reconstruction have been studied for many models in contexts including statistical physics, information theory and evolutionary biology. For k > D it is easy to show that reconstruction does not hold while for k < D/ ln(D), reconstruction is possible. We show that for k D/ ln(D), reconstruction does not hold. (joint work with Vera, Vigoda and Weitz)
In the second result, we study a model of random bounded width posets on n elements, first studied by Brightwell and Goodall. For such posets of width at most 2, we show that under the appropriate scaling, for a random element, the number of incomparable elements to it converges to the height of a one dimensional Brownian excursion at a uniformly chosen random time in the interval [0,1]. We prove this by constructing combinatorial maps between random posets and certain constrained pairs of random walks on Z. The analysis of the local structure of the posets can then be reduced to the asymptotic analysis of these random walks. (joint work with Crawford, Mossel and Sen)
Alexandr Labovschii (University of Missouri) Architecture for models of fluid flow phenomena
We present several high accuracy numerical methods for fluid flow problems and turbulence modeling.
First we consider a stabilized finite element method for the Navier-Stokes equations which has second order temporal accuracy.
The method requires only the solution of one linear system (arising from an Oseen problem) per time step.
We proceed by introducing a family of defect correction methods for the time dependent Navier-Stokes equations, aiming at higher Reynolds' number. The method presented is unconditionally stable, computationally cheap and gives an accurate approximation to the quantities sought.
Next, we present a defect correction method with increased time accuracy. The method is applied to the evolutionary transport problem, it is proven to be unconditionally stable, and the desired time accuracy is attained with no extra computational cost.
We then turn to the turbulence modeling in coupled Navier-Stokes systems - namely, MagnetoHydroDynamics. We consider the mathematical properties of a model for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove existence, uniqueness and convergence of solutions for the simplest closed MHD model.
Furthermore, we show that the model preserves the properties of the 3D MHD equations.
Lastly, we consider the family of approximate deconvolution models
(ADM) for turbulent MHD flows. We prove existence, uniqueness and convergence of solutions, and derive a bound on the modeling error.
We verify the physical properties of the models and provide the results of the computational tests.
Tathagata Basak (Dickson Instructor, University of Chicago) A complex hyperbolic reflection group and the bimonster
Let R be the reflection group of the complex Leech lattice plus a
hyperbolic cell. Let D be the incidence graph of the projective plane
with three elements. Let A(D) be the Artin group of D : generators of
A(D) correspond to the vertices of D. Two generators braid if there is
an edge between them, otherwise they commute.
It is surprising that both the bimonster and the reflection group R are
quotiends of A(D), when the generators are mapped to elements of order
2 and 3 respectively.
A conjecture by Daniel Allcock seeks to explain this connection between
R and the bimonster via complex hyperbolic geometry. We shall try to
explain some of the evidence for this conjecture so far. We shall see
that D behaves like the Coxeter-Dynkin diagram for the reflection group
R. This imprecise analogy with Weyl groups actually makes our proofs
work. There is a parallel story for a quaternionic hyperbolic
reflection group, where the analogies repeat.
Gary Lieberman (ISU) Oblique derivative boundary conditions
In mathematical models involving partial differential equations, a boundary condition is an important part of the model. Typically, this boundary condition is the Dirichlet condition, which prescribes the value of the unknown on the boundary, but there are many important situations in which a different boundary condition is physically relevant. In this talk, we shall consider one such condition: the oblique derivative condition, which prescribes some directional derivative on the boundary. The usual approach to this boundary value problem considers it as (at least, philosophically) a weak modification of the Dirichlet condition, and our goal is show that this problem has its own unique characteristics. There will also be several model problems from different sources.
Marta Lewicka (University of Minnesota) The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells.
A central problem in the mathematical theory of elasticity is to
predict theories of lower-dimensional objects (such as rods, plates or
shells) subject to mechanical deformations, starting from the 3d
nonlinear theory. For plates, a recent effort has lead to rigorous
justification of a hierarchy of such theories (membrane, Kirchhoff,
von Karman). For shells, despite extensive use of their ad-hoc
generalizations present in the engineering applications, much less is
known from the mathematical point of view.
In this talk, I will discuss the limiting behavior (using the notion
of
Gamma-limit) of the 3d nonlinear elasticity for thin elliptic shells,
as their thickness h converges to 0, under the assumption that the
elastic energy of deformations scales like h^\beta, with \beta>2.
The ellipticity condition is used in the two major ingredients of the
proofs (for constructing the recovery sequence), which are: the
density of smooth maps in the space of Sobolev first order isometries,
and a result on matching smooth infinitesimal isometries to exact isometric immersions.
This is joint work with Maria Giovanna Mora (SISSA) and Reza Pakzad
(University of Pittsburgh).
Ameya Pitale (University of Oklahoma) L-functions and special value results
I will give a brief introduction to L-functions by looking at some simple examples including the Riemann zeta function. I will try to explain the importance of L-functions in number theory and how they very naturally arise while considering interesting problems.
Several of the applications of L-functions are related to their behavior at certain special values. For example, the values of the Riemann zeta function at positive even integers are related to Bernouilli numbers and give interesting connection to combinatorics. There are many important open problems regarding special values of L-functions - the Birch and Swinnerton-Dyer conjecture, Deligne's conjecture to name a few.
In this talk, I will elaborate on L-functions associated to automorphic forms and automorphic representations. I will present my current research (joint with Ralf Schmidt) on L-functions associated to GSp(4)xGL(2) and Deligne's conjecture in this setting.
Fall 2008 Department Colloquia
September 2 - Susan Montgomery (USC) Orthogonal representations of Hopf algebras Host: Richard Ng
September 9 - Benjamin Sudakov, Department of Mathematics, UCLA. Turan theorem: generalizations and applications. Host: Ryan Martin. This is a joint colloquium with the Computer Science Department.
September 16 - Stephen Willson, ISU Reconstruction of phylogenetic networks from data at their leaves
September 23 - Arka Ghosh (ISU) Optimal prices and production rate in a closed loop supply chain with re-manufacturing under heavy traffic
September 30 - Eric Weber (ISU) A history of the Kadison-Singer problem
October 7 - Ling Long (ISU) Finite index subgroups of the modular group and their modular forms
October 14 - Bo Su (ISU) Gamma-limit of fold energy problem
Thursday, October 16 -IN CARVER 305 - Amy R. Ward, Marshall School of Business, USC Optimal control of a high-volume assemble-to-order system Jointly hosted by Statistics, Industiral and Manufacturing Systems Engineering and Mathematics; Host: Ananda Weerasinghe
October 21 - No colloquia
October 27 - Ryan Martin (ISU) The edit distance in graphs xx poster
October 28 - Khalid Boushaba (ISU) A mathematical model for cell signaling and endothelial migration in living zebra fish embryos
Thursday, October 30 - Zhijian Wang, Aerospace Engineering (ISU) on High order methods for the Navier-Stokes equations on unstructured grids. Host: Jue Yan
November 7 - Nathaniel Dean, Texas State University. Mathematical programming for network visualization . 3:10 p.m. Host: Leslie Hogben.
November 10 - Mahamadi Warma, University of Puerto Rico, on The heat equation with nonlinear generalized robin boundary conditions. Host: Wolfgang Kliemann.
November 11 - Peter Polacik (University of Minnesota) Parabolic Liouville theorems and their applications Host: Bo Su 4:20 p.m.
November 18 - Joan Hutchinson (Macalester College) on Extending precolorings of graphs, list colorings, and how these concepts are related Host: Maria Axenovich
November 21 (Friday 3:10 - 3:50 p.m. in Carver 294) - Joint colloquium and CAM seminar: Tong Li (Univeristy of Iowa) on Critical thresholds in hyperbolic relaxation systems. Host: Hailiang Liu.
November 21 (Friday 4:00 - 4:40 p.m. in Carver 294) - Joint colloquium and CAM seminar: Lihe Wang (Univeristy of Iowa) on Estimates on Quasi-convex domains. Host: Hailiang Liu.
December 2 - please attend faculty meeting
Friday, December 5 - Yannis Kevrekidis (Princeton) on Coarse graining and the acceleration of complex/multiscale computations in 202 Carver Hall Host: Tasos Matzavinos
December 9 - Iddo Ben-Ari (University of Connecticut) on Large deviations for a last passage model Host: Alex Roitershtein
Benjamin Sudakov, Department of Mathematics, UCLA. Turan theorem: generalizations and applications.
In typical extremal problem one wants to determine maximum cardinality of discrete structure with certain prescribed properties.
Probably the earliest such result was obtain 100 years ago by Mantel who computed the maximum number of edges in a triangle free graph on n vertices. This was generalized by Turan for all complete graphs and became a starting point of Extremal Graph Theory. In this talk we survey several classical problems and results in this area and present some interesting applications of Extremal Graph Theory to other areas of mathematics. We also describe a recent surprising generalization of Turan's theorem which was motivated by question in Computational Complexity.
Stephen Willson, ISU, Reconstruction of phylogenetic networks from data at their leaves
A phylogenetic network is a directed graph in which the leaves correspond to extant species while interior vertices correspond to ancestral species. The network seeks to depict evolutionary history. Typically such a network is constructed using DNA data.
Most phylogenetic networks currently are trees. This talk concerns the construction of such networks which are not necessarily trees. A simple model of evolution is considered in which all characters are binary and in which back-mutations occur only at hybrid vertices. It is assumed that the genome is known for each leaf. If the network is known and is assumed to be "normal," then the genome of every vertex is uniquely determined and can be explicitly reconstructed. Under additional hypotheses involving separation of the hybrid vertices and temporal consistency, the network itself can also be reconstructed from the genomes of all leaves. A polynomial-time graph-theoretic procedure is outlined for performing the reconstruction.
Amy Ward , USC,Optimal control of a high-volume assemble-to-order system
For an assemble-to-order system with a high volume of prospective customers arriving per unit time, we show how to set nominal component production rates, quote prices and maximum leadtimes for products, and then, dynamically, sequence orders for assembly and expedite components. (Components must be expedited if necessary to fill an order within the maximum leadtime.) We allow for updating of the prices, maximum leadtimes, and nominal component production rates in response to periodic, random shifts in demand and supply conditions. Assuming expediting costs are large, we prove that our proposed policy maximizes infinite horizon expected discounted profit in the high volume limit. For a more general assemble-to-order system with arbitrary cost of expediting and the option to salvage excess components, we show how to solve an approximating Brownian control problem, and translate its solution into an effective control policy.
Eric Weber (ISU) A history of the Kadison-Singer problem
The Kadison-Singer Problem, dating from 1959 and still open, is a problem concerning pure states on C*-algebras. However, recent work has shown that this problem has implications in many branches of mathematics as well as science and engineering. We will present a history of the problem and describe our contributions to the story.
Ling Long (ISU) Finite index subgroups of the modular group and their modular forms
The modular group, the group of all 2-by-2 integral matrices with determinant 1, is one of the most important discrete groups. Given a finite index subgroup G of the modular group, it acts on the upper half complex plane by linear fractional transformations. The compactified orbit space is called the modular curve associated with G. By a theorem of Belyi, modular curves play an important role in the study of smooth indecomposable projective algebraic curves which are compact orientable Riemann surfaces. Modular forms for G are spectacular functions whose symmetries are essentially characterized by G. The theory of modular forms has been in the central focus of number theory for more than one century and it is one of the key ingredients in the celebrated proof of the Fermat's Last Theorem.
In this talk, we will consider the arithmetic properties of finite index subgroups of the modular group and their modular forms. Our goal is to characterize special modular forms called congruence modular forms. We will discuss some current results in this direction and their applications to other fields.
Peter Polacik (University of Minnesota) Parabolic Liouville theorems and their applications
Parabolic Liouville theorems state that if u is an entire solution of a very specific parabolic equation (semilinear heat equation with power nonlinearity) and u is contained in an admissible class of functions, then u is necessarily the trivial solution. In this talk I shall present Liouville theorems for nonnegative solutions as well as for some radial sign-changing solutions. Among applications of such theorems I shall discuss universal a priori estimates of solutions and a construction of infinitely many periodic solutions of periodic-parabolic boundary value problems.
Tong Li (University of Iowa) on Critical thresholds in hyperbolic relaxation systems
Critical threshold phenomena in one dimensional $2\times 2$ quasi-linear hyperbolic relaxation systems are investigated.
We prove global in time regularity and finite time singularity formation of solutions simultaneously by showing the critical threshold phenomena associated with the underlying relaxation systems. Our results apply to the well-known isentropic Euler system with damping.
This is a joint work with Hailiang Liu.
Lihe Wang (University of Iowa) on Estimates on Quasi-convex domains
Wang will review some techniques of analysis for proving integral estimates. The quasi-convex domains are those domains in R^n that can be locally, in all small scales, approximated by convex domains.
