Spring 2009
Colloquium (and other events) Schedule
Department of Mathematics

Spring 2009 Colloquium (and other events) Schedule:
Except as noted, all talks are on Friday, from 4:00 to 4:50pm, in Avery Hall 115,
preceded by refreshments at 3:30 pm in Avery Hall 348.
Eventually you will be able to go here for tentative scheduling for colloquia next semester.

Here is a discussion of what to expect at Colloquium talks and
here is a discussion of what might make a good colloquium talk.

Mon Jan 12 2009: First Day of classes/no colloquium
Jan 16 2009:
Speaker: Charles Weibel
Affiliation: Rutgers University
Local Host: Mark Walker
Title: Non-Desarguesian Projective Planes
Abstract:
If F is a field, the projective plane over F is the set of 1-dimensional subspaces (lines) in a 3-dimensional vector space.
An architect named Desargues discovered a theorem about these planes which bears his name, 400 years later. However, the notion
of a projective plane can be (and was) axiomatized and Hilbert (and later Marshall Hall) observed that Desargues' theorem fails
for any other projective plane.

This talk will be a survey of what we know (and don't) about these other (non-Desarguesian) planes. Many are parametrized by
strangeand wonderful nonassociative algebras, which are still interesting to modern algebraists.
Mon Jan 19: Martin Luther King Day/no colloquium
Jan. 23: Meeting
Jan. 30 2009: In Nebraska Union auditorium at 4pm
Speaker: Mary Lou Zeeman>(NCUWM speaker)
Affiliation: Bowdoin College
Local Host: Judy Walker
Title: Feedback Loops in Biology and Climate
Abstract:
One of the most powerful features of mathematics is that it can unify ideas from a wide variety of disciplines. Understanding
this allows us to harness math to dive deeper into scientific mysteries. For example, we will look at how feedback loops lead to cyclic
behavior in population dynamics, our hormones and our global climate.
Jan 30-Feb 1: NCUWM (Nebraska Conference for Undergraduate Women)
Feb. 6:
Speaker: Markus Pflaum
Affiliation: University of Colorado, Boulder
Local Host: Srikanth Iyengar
Title: Deformation quantization and index theory
Abstract:
It has been noticed in the work by Fedosov and Nest-Tsygan that deformation quantization opens up a path to formulate and prove
so- called algebraic index theorems and that from these one can derive the Atiyah-Singer index theorem. In the talk I will explain the principle
idea underlying this observation and show how it even leads to index theorems on orbifolds and possibly on even more general singular spaces.
Feb. 13, at 3:30pm, followed by refreshments at 4:30pm:
Speaker: To be announced
Local Host: John Meakin
Feb. 20:
Speaker: Said Sidki
Affiliation: University of Brasillia, Brazil
Local Host: John Meakin
Title: Recursive algebras
Abstract:
Groups which act on trees and whose generators are defined recursively by finite automata have stimulated questions about similar
constructions for associative algebras. The algebras are seen as infinite dimensional matrix algebras partitioned regularly in a finite of blocks
each defined recursively. Such constructions have been introduced by a number of authors including the speaker, Grigorchuk, Bartholdi and
Bacher.

We will review this topic and discuss the structure of some specific recursive rings.
Feb. 27: (Graduate recruiting weekend)
Speaker: Oliver Collins
Affiliation: University of Notre Dame (Department of Electrical Engineering)
Local Host: Christine Kelley
Title: Full Diversity Spacial Modulators
Abstract:
This talk presents a new approach for achieving both full rate and full transmit diversity. The techniques in this talk work on a symbol by
symbol basis and so are called spatial modulators. When there is only a single receive antenna, the goal is to design the modulator at each
transmit antenna so that(even for the worst case realization of the channel coefficients) the scheme achieves the capacity of the single
transmitter multiple receiver system with the same channel coefficients. The talk presents two approaches to modulator design. The first
expands the constellation by using a set of random phase sequences to modulate the transmitted symbol at each antenna. The receiver thus
sees an equivalent single antenna system with an expanded and distorted constellation. The second approach does not increase the
constellation size and transmits different permutations of the same constellation from different antennas. The permutations can be designed
either algebraically or numerically and the receiver thus sees a distorted constellation that depends on the channel realization.

In addition to being full rate and full diversity (which is impossible for conventional space-time codes except in special cases) these schemes
are potentially very simple to implement.
March 6:
Speaker: Greg Norgard
Affiliation: University of Colorado, Boulder
Local Host: Allan Donsig
Title: Shock regularization of conservation laws by employing spatial averaging
Abstract:
In the last several years turbulence models that employ spatial averaging, specifically the LANS-\alpha equations, have shown promise
modeling incompressible turbulent flows. With work in this field making progress it is thought to be possible to employ an
averaging technique successfully into compressible flow, thus modeling turbulence and shocks simultaneously. We have begun this work by
using averaging to regularize shocks in a drastically simple model of compressible flow, the Burgers Equation. An averaged convective
velocity is applied to the nonlinear term. This reduces the cascade of energy into the high wave modes and provides a smooth solution that
we have proven converges to the entropy solution as the averaging decreases. This work has then been extend into Homentropic Eulers
equations where similar behavior has been displayed.
 Mar. 13:
Speaker: Anthony Iarrobino
Affiliation: Northeastern University
Local Host: Lucho Avramov
Title: When do two matrices commute?
Abstract:
When do two n by n matrices A,B with entries in a field commute? If A has n distinct eigenvalues, then B commutes with A
when they may be simultaneously diagonalized. More generally, if A has only one Jordan block for each eigenvalue, then B commutes with
A when it is a polynomial in A. What if A has several Jordan blocks with the same eigenvalue? Given A in Jordan block form, classical
matrix theorists as Turnbull-Aitken, Gantmacher write B in a standard format. However, surprisingly little is known about B!

Suppose that A is a nilpotent Jordan matrix -- eigenvalues all zero -- whose block sizes correspond to the partition P of n. What
are the Jordan block sizes for most nilpotent matrices B commuting with A? We illustrate this problem for P=-(3,1) and P=(3,1,1), and
mention some other cases where the answer is known. We also discuss a connection developed by H. Nakajima, V. Baranovsky, R. Basili and
others between pairs of commuting nilpotent matrices and Artinian algebras in two variables.
Mar. 15-22 Spring Break
Mar. 27:
Speaker: Paul Muhly
Affiliation: University of Iowa
Local Host: Allan Donsig
Title: When is a matrix of functions a function of matrices?
Abstract: This chiastic question, perhaps in a different form, has been around for a long time. However, I only recently stumbled upon it when
thinking about function theory that arose in work that I was doing on certain operator algebras. I will discuss the question and give two answers--
largely without proof. One comes from invariant theory. I will leave it as an exercise, accessible to students who know the Jordan canonical form. I
will give hints, and an outline, however. As for the other, I will describe how it arose in my work and how it is related to the Nevanlinna-Pick
interpolation theorem, which relates bounded analytic functions on the open unit disc to certain matrices constructed from their values.
April 3: 2009 Department Rowlee Lecture
Speaker: Michael Hopkins
Affiliation: Harvard University
Local Host: Mark Walker
Title: How topologists count things
Abstract:
The mathematical field of "Algebraic Topology" came into being largely in order to come to grips with a single question:
How can we count the number of solutions to an equation? In this talk I will describe some of the remarkable answers mathematicians have
found to this question, and how, in recent years, the fundamentals of algebraic topology have been re-thought in order to come to grips with
the demands of modern quantum field theory.
This lecture is partially supported by a grant from the UNL Research Council.
April 10: Speaker: Ira Papick
Affiliation: UNL
Local Host: Jim Lewis
Title: Developing a Graduate Credit Algebra Course for Teachers:
Building a Conceptual Understanding of Polynomial Algebra in the Secondary Curriculum
Abstract:
In this talk we will discuss the need for and nature of specialized graduate credit mathematics courses for practicing teachers. Our primary focus will
involve the description of an algebra course for algebra teachers. The main goal of this course is to help teachers better understand the conceptual
underpinnings of school algebra, and how to leverage that understanding into improved classroom practice. Specific course content and pedagogy
will be highlighted.
April 17:
Speaker: Irena Lasiecka
Affiliation: University of Virginia
Local Host: Lorena Bociu
Title: Analysis and control of dynamic fluid-structure interactions
Abstract:
Fluid and structure interacting on an interface between the two media is an established model used frequently in engineering and medical applications.
The response of the tissue due to radiation force penetrating body fluids or the movement of microbubbles used as dye contrast in ultrasound imaging
are just examples of a multitude of applications that motivate studying PDE structure of the underlying model. Fluid-structure interaction comprises
the Navier Stokes equation and the dynamic system of elasticity coupled on the interface between fluid and solid. The coupling is prescribed via matching
conditions imposed on Cauchy Polya stress tensors and on velocities. The popularity of the model and its strong link with fundamental applications has
generated in recent times a lot of interest in the area. In fact, there are many results pertaining to numerical and experimental treatment of the model.
Much less, however, is known with respect to PDE analysis of the system. Questions such as wellposedness of finite energy solutions, or stability and
controllability of solutions, still present vastly unknown territory.

The main aim of this talk is to report some of the recent developments in this area, which include topics such as:
This colloquium is funded by the UNL Research Council.
April 24:
Speaker: Lia Bronsard
Affiliation: McMaster University
Local Host: Petronela Radu
Title: Vortices in the Ginzburg-Landau model
Abstract:
The Ginzburg-Landau model is a widely used tool for describing the physical state of superconductors, superfluids, or Bose-Einstein condensates.
It is also a rich source of interesting results in the calculus of variations and in the study of singularities in solutions to partial differential equations.
In this talk, I will start with the basics of Ginzburg-Landau vortices, with the classical results of Bethuel-Brezis-Hélein. Then I will present some
3D results on vortex lines for the full Ginzburg-Landau model in the context of Gamma-convergence. Finally, I will present an overview of some
recent results on the effect of anisotropy in the mathematical study of superconductors. Anisotropy is very important in the understanding of high
temperature superconductors, and it presents very nice unexpected mathematical results.

This colloquium is funded by the UNL Research Council.
May 1: (Dead week)
Speaker: Jan Minac
Affiliation: University of Western Ontario, Canada
Local Host: Lucho Avramov
Title: The Bloch-Kato conjecture and small quotients of absolute Galois groups
Abstract:
Absolute Galois groups of fields play an important role in current mathematics, yet they are quite mysterious profinite groups. The Bloch-Kato conjecture
describes the cohomology ring of absolute Galois groups using generators and relations. The Bloch-Kato conjecture was recently established by M. Rost
and V. Voevodsky, with Ch. Weibel’s patch. I will discuss the consequences of the Bloch-Kato conjecture on the structure of small quotients of absolute
Galois groups. Some joint work with D. Benson, S. Chebolu, I. Efrat, A. Schultz, and J. Swallow will be described.
May 8: OPEN (Exam week)
The Fall 2009 schedule is wide open. The current schedule of open dates for Fall 09 is here .