Spring 2010
Colloquium Schedule
Department of Mathematics
Spring 2010
Colloquia
(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.
Here is a discussion of
what to expect at Colloquium talks and here
is a discussion of what might make a good colloquium talk.
Go here for tentative scheduling
for colloquia next semester.
Mon Jan 11:
(Expected)
First Day of classes
Jan 15:
Speaker: Martin Kassabov
Affiliation: Cornell University
Local host: Collin Bleak
Title: Subspace arrangements and property T
Abstract:
I will talk about my viewpoint regarding a method for proving property T developed by Dymara and
Januszkiewicz. A group G has Property T if every continuous affine isometric action of G on a real
Hilbert
space has a fixed point.
The original motivation of Dymara and Januszkiewicz came from groups acting on buildings, but the idea
does not use anything more than angles between subspaces in a finite-dimensional Euclidean space.
Their main result says that if a group G is generated by finite subgroups G_i and each pair generates a
group with property T and sufficiently large Kazhdan constant then the whole group also has property T.
One can use this result to show that some groups like SL_n(F_p[t_1,...,t_k]) have property T, almost
without using any representation theory. Another application allows us to compute the exact
values of the Kazhdan constant and the spectral gap for the Laplacian for any finite Coxeter group
with respect to its standard generating set.
Parts of the talk are based on work of M. Ershov and A. Jaikin.
Mon Jan 18:
Martin Luther King
Day/no colloq
Jan 22:
Jan 29:
In Nebraska Union auditorium at 4pm
Speaker:
Karen Vogtmann (NCUWM speaker)
Affiliation: Cornell University
Local host: Allan Donsig
Title:
Symmetries, ping-pong and outer space
Abstract:
Groups are very basic algebraic objects in mathematics, but one
can often find an
alternate description as symmetries of a geometric object. In fact it
turns out that
there is a
natural way to think of any algebraically-described group as
symmetries of
something
geometric, and the geometric properties of this object can reveal
characteristics of
the group which were not obvious from the original
algebraic
description.
One of the simplest of all types of groups are free groups. I will
discuss the geometry
of free groups, and use it to show how to recognize when a group
which looks like it
might be very complicated is in fact just a free group. The method
is to use the geometric
object as a ping-pong table; the reason for this terminology will be
clear when the
method is described.
The symmetries of free groups themselves form a group; the ping-pong
table for this
group is known as Outer space, and I will show how to
play ping-pong in Outer space.
Jan 29-31:
NCUWM
(Nebraska Conference for Undergraduate Women)
Feb 5: No Colloquium
Wednesday Feb 10: SPECIAL LECTURE in ROOM 106 Avery, 3:30pm
(in
addition to Friday's Colloquium) Refreshments at 4:30pm in 348 Avery
Speaker: Greg Smith
Affiliation: Queen's University
Local hosts: Susan Cooper & Srikanth Iyengar
Title:
Old and new perspectives on Hilbert functions
Abstract:
Hilbert functions are fundamental invariants in commutative algebra and algebraic
geometry.
After recalling the basic definitions and motivating examples, we will discuss
Macaulay's
characterization for the collection of all Hilbert functions. We'll then contrast
this
with a newer viewpoint and look at potential applications.
Friday Feb 12: COLLOQUIUM
(in addition to Wednesday's Special Lecture)
Speaker: Anda Degeratu
Affiliation: Max Plank Institute
Local host: Vladimir Itskov
Title:
Crepant resolutions of Calabi-Yau orbifolds
Abstract:
A Calabi-Yau orbifold is locally modeled on C^n/G with G a finite subgroup of SU(n).
A crepant
resolution of such a singularity is a resolution of singularities that keeps us in the
class of
Calabi-Yau manifolds. In this talk I will present an index theoretical approach for
studying the
geometry and topology of this type of resolutions.
Feb 19:
Speaker: Hemanshu Kaul
Affiliation: Illinois Institute of Technology
Local host: Stephen Hartke
Title: Finding Large Subgraphs
Abstract:
The maximum subgraph problem for a fixed graph property P asks: Given a
graph,
find a subgraph satisfying property P that has the maximum number
of edges.
Similarly, we can talk about maximum induced subgraph problem.
The property P
can be planarity, acyclicity, bipartiteness, etc.
We will discuss some old and new problems of this flavor, focusing on the
algorithmic
aspects of these problems. In particular, we will describe
some old
results on the
maximum bipartite subgraph problem and some new
results on
the maximum
series-parallel subgraph problem.
This colloquium is funded in part by the UNL Research Council.
Feb 26:
Speaker: Russell Johnson
Affiliation: University of Florence
Local host: Lynn Erbe and Allan Peterson
Title: Nonautonomous Dynamics
Abstract: We will discuss the relationship between the Sturm-Liouville
spectral problem
and the Camassa-Holm hierarchy.
March 5:
Speaker: Ananth Hariharan
Affiliation: UNL
Local host:Srikanth Iyengar
Title: Tales of a Local Algebraist
Abstract:
This talk will begin with examples of Artinian rings (mainly
quotients of polynomial rings) and
some structures defined over them. We will then explore
(through examples) a special sub-class called
Gorenstein Artin rings. Finally, I will talk
about Gorenstein colength, a number that shows how close an
Artinian ring is to being
Gorenstein Artin.
This will be a non-rigourous and self-contained (as far as possible) talk. Prereqs include
the knowledge
of polynomials and computing partial derivatives of polynomials.
March 9: SPECIAL LECTURE in ROOM 106 Avery, 3:30pm
Refreshments at 4:30pm in 348 Avery
Speaker: Roger Howe
Affiliation: Yale University
Local host: Jim Lewis
Title: Hibi Rings in Representation Theory
Abstract:
This talk will attempt to sketch some uses of Hibi rings in representation theory. A Hibi ring is a
semigroup ring associated to a partially ordered set. Recently, it has been found that several
algebras arising in representation theory can be described using Hibi rings. Moreover, the Hibi
ring perspective has shed new light on other basic questions, such as the Littlewood-Richardson
coefficients for decompositions of tensor products of representations of the general linear group.
(To see a more complete description of the talk,
click here where the abstract is in pdf form with
math symbols:
http://www.math.unl.edu/research/colloquia/spring/2010/Roger_Howe.pdf)
March 13-21
Spring break/no colloq
March 26: Colloquium in ROOM 115 Avery, 3:30pm
Refreshments at 4:30pm in 348 Avery
Speaker: Michael Hopkins
Affiliation: Harvard University
Local host: John Meakin
Title:
On the Kervaire invariant one problem
Abstract: I'll discuss the long history of this problem and the
recent solution by Mike Hill,
Michael Hopkins and Doug Ravenel.
April 2:
Speaker: Amy Cohen
Affiliation: Rutgers University
Local host: John Meakin
Title:
Solitons and what is odd about odd multiples of pi/2
Abstract: The Korteweg-deVries (KdV) equation and the nonlinear Schrodinger equation
in one space
dimension and with cubic non-linearity (NLS) both display soliton solutions and both
are amenable to a
so-called inverse scattering analysis. The story for KdV is more accessible and
will be described
qualitatively. The story for NLS is more complicated and will be described more
sketchily. If the initial
data for NLS is the characteristic function of an interval of width W,
then the inverse scattering analysis
produces an existence proof -- but only when W is not an odd
multiple of pi/2. The exceptional
values
of W mark the phase transitions where the number
of solitons in the solution jumps. This may be
the
reason that the inverse scattering method breaks
down.
April 9:
Speaker: Dan Katz
Affiliation:University of Kansas
Local host: Tom Marley
Title:
Limits and
asymptotic invariants in Commutative Algebra
Abstract: Let R be a Noetherian commutative ring. The ascending chain condition on ideals often
guarantees that certain properties associated to large powers of an ideal either stabilize or take a
particularly nice form. In this talk we will discuss a few limits from classical commutative algebra
derived from powers of an ideal and some of the asymptotic invariants they give rise to. If time permits,
we will discuss some open questions regarding sequences derived from powers of an ideal that
potentially have unexpected limits.
April 9-10
Spring Meeting of the
Nebraska-Southeastern
South Dakota Section of the MAA,
to be held at the University of South Dakota in Vermillion South Dakota
April 16: Mathematics Department 2010 Rowlee Lecture Avery 115,
Reception, 3:15 p.m. in Avery 348
Speaker: Carlos Kenig
Affiliation: University of Chicago,
Louis Block Distinguished Service
Professor of Mathematics
Local Host: Mohammad Rammaha
Title:
The Global Behavior of Solutions to
Critical Nonlinear Dispersive and Wave Equations
Abstract: We describe a method (which I call the concentration-compactness/rigidity theorem method)
that Frank Merle and I have developed to study global well-posedness and scattering for critical non-
linear elliptic problems which were studied earlier, for instance in the context of the Yamabe problem
and of harmonic maps. We illustrate the method with some concrete examples and also mention other
applications of these ideas.
April 23:
Speaker: Raul Curto
Affiliation: University of Iowa
Local Host: Carina Curto
Title:
Cubic Column
Relations in Truncated Moment Problems
Abstract:
Inverse problems naturally occur in many branches of science and mathematics.
An inverse problem entails finding the values of one or more parameters
using the values obtained from
observed data. A typical example of an inverse problem
is the inversion of the Radon transform. Here a
function (for example of two
variables) is deduced from its integrals along all possible lines. This
problem
is intimately connected with image reconstruction for X-ray computerized
tomography.
Moment problems are a special class of inverse problems.
While the classical theory of moments dates
back to the beginning of the
20th century, the systematic study of truncated moment
problems began
only a few years ago. In this talk we first survey the
elementary theory of truncated moment problems,
and then focus on those
problems with cubic column relations.
For a degree 2n truncated moment problem to admit a representing measure, it is necessary for the
associated moment matrix M(n) to be positive semidefinite, and for the algebraic variety associated to
the problem, V, to satisfy the inequality rank M(n) < = card V, as well as a suitable consistency
condition involving the Riesz functional attached to the problem. In previous joint work with
L.Fialkow and M. Moeller, we proved that for the extremal case (rank M(n) = card V), positivity and
consistency are sufficient for the existence of a (unique, rank M(n)-atomic) representing measure.
In recent joint work with Seonguk Yoo we consider cubic column relations in M(3) related to harmonic
polynomials. Under appropriate conditions, we prove that the algebraic variety V consists of exactly
7 points, and we then apply the above mentioned solution of the extremal moment problem to obtain a
necessary and sufficient condition for the existence of a representing measure. This requires a new
representation theorem for sextic polynomials in z and Conjugate[z] which vanish in the 7-point set V.
Our proof of this representation theorem relies on two successive applications of the Fundamental
Theorem of Linear Algebra.
(To see a more complete description of the talk,
click here where the abstract is in pdf form:
http://www.math.unl.edu/research/colloquia/spring/2010/CurtoAbstractSpring2010.pdf)
April 30: Colloquium in ROOM 115 Avery at 3:30pm
Reception following: 4:30-5:30pm, Avery 348
Speaker: Carlos Castillo-Chavez
Affiliation: Arizona State University
Local host: John Meakin
Title:
Mathematical Epidemiology with
Applications: The Case of Influenza
Abstract: In a highly interconnected world, epidemic outbreaks become
instant potential health and economic
global threats. Increasing segments of the
population play active roles in the transmission patterns of infectious
diseases like
influenza. Individual or group actions, decisions and activities can enhance
or reduce the effectiveness
of intervention measures in the Information Era. Travel,
social distancing, the availability of medical supplies
(antiviral drugs and vaccine) and
timely diagnostic tools, and the access to quality medical care are but some of the
factors
that have been identified as significant during this ongoing influenza pandemic. Varying
levels of
participation in the implementation of policies aimed at reducing a population's
risk of infection are important
components not only of disease dynamics but also of their
evolutionary potential.
What can mathematics do to help understand disease dynamics and develop
effective control measures? What can
mathematics do to help develop resilient approaches
for the management of complex adaptive systems of this type?
Despite the myriad of
complexities associated with disease transmission dynamics, macroscopic epidemic patterns
emerge and ways of making use of this knowledge in real time can be critically important.
In this lecture some of the challenges in the study of the dynamics and evolution of
infectious diseases will be
addressed. This presentation
provides an overview of mathematical epidemiology in the context of influenza
(including the ongoing pandemic influenza) in order to highlight key questions
and approaches and the fundamental
role of mathematics in biology.
(To see a more complete description of the talk,
click
here
where the abstract is in pdf form:
http://www.math.unl.edu/~swiegand1/colloquia/CCCabs04-2010.pdf
The presentation will include material from various co-authored published manuscripts,
listed at
the link.)
Current
Schedule of Open Dates for Fall 2010