Fall 2008
Colloquium Schedule
Department of Mathematics
Fall 2008 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 Aug 25:
First
Day of classes
Aug 29:
No colloquium
Mon
Sep 1: Labor Day/no colloq
Sept 5:
Speaker: Jim Rogers
Affiliation:
UNO
Local host: Richard Rebarber
Title:
Mathematical Analysis of Complex Biochemical Networks
Abstract:
As our understanding of biochemical pathway structures
increases, it is clear that these pathways form
networks of astonishing
complexity. This creates an immediate challenge in trying to make sense
of the
enormous amount of data that studies of these systems generate. The
field of bioinformatics has arisen
in recent years to meet this challenge,
and has been very successful in helping laboratory biochemists
interpret
their vast data, allowing them to understand the complex structures of the
chemical networks
they study. However, even when these chemical network
structures are worked out, it is often times
still not clear how these
structures actually function or why they are so complex. This has led
to
the need for another level of quantitative analysis of biochemical
systems. In this talk, new,
higher-level mathematical analysis of
biochemical networks will be presented, and there will be
a brief
discussion of a new role for mathematics in modern biological research.
Sept 12:
No colloquium
(faculty meeting)
Sept 19:
Speaker: Graham Leuschke
Affiliation: Syracuse University
Local host:
Roger Wiegand
Title: What is a non-commutative desingularization?
Abstract:
In algebraic geometry,
a resolution of singularities of an algebraic
variety is a smooth variety (manifold) sharing the
same field of
functions.
Also called a non-singular model or desingularization, resolutions of
singularities are fundamental tools for working with singular spaces.
They are known by Hironaka
to exist for varieties defined over the
complex numbers, but the question of existence is still open
in general.
One approach to the annoyance is to give a purely algebraic definition
of desingularization
in terms of ring theory. The world of
commutative rings turns out to be too small for this purpose, so
we are
led to the possibility of ``non-commutative desingularizations.''
I will briefly describe what's
known about commutative desingularizations,
and what they're good for, then some progress and results
on
what non-commutative desingularizations are, or at least should be.
This colloquium is funded by the
UNL Research Council.
Sept.20-21: KUMUNU (Kansas-Missouri-Nebraska Commutative Algebra
Conference)
Sept. 26:
Speaker: Lorena Bociu
Affiliation: UNL
Local host:
Title:
On Wave Equations with Interior and Boundary Interactions between
Supercritical Sources and Dampings
Abstract:
The model under consideration is the semilinear wave equation with
supercritical nonlinear sources and dampings and our aim is to
discuss the wellposedness of the system on finite energy space. A
distinct feature of the equation is the presence of the double
interaction of source and damping, both in the interior of the
domain and on the boundary. Moreover, the nonlinear boundary sources
are driven by Neumann boundary conditions. Since Lopatinski
condition fails to hold for dimension of the domain greater or equal to two, the
analysis of the nonlinearities supported on the boundary, within the
framework of weak solutions, is a rather subtle issue and involves
strong interaction between the source and the damping. I will
provide positive answers to the questions of local existence and
uniqueness of weak solutions and moreover give complete and sharp
description of parameters corresponding to global existence and
blow-up of solutions in finite time.
Oct. 3:
Speaker: Mike Ferrara
Affiliation: University of Akron
Local host: Steve Hartke
Title: Some Problems on Graph Subdivisions
Abstract:
Broadly, structural graph theory is concerned with ensuring or prohibiting the
presence of certain substructures within a graph. The most prevalent results
of this type in the literature deal with the existence of paths and cycles
having a wide variety of properties.
A "subdivision" of a graph H is any graph obtained by replacing the
edges of H with paths of arbitrary length. It is not difficult to see that
if H is a path or a cycle, then so too is any subdivision of H. With this
observation in mind, it is not surprising that many results that ensure the
existence of an arbitrary H-subdivision extend known results pertaining to
paths and cycles.
We will discuss two classes of problems related to H-subdivisions. First,
we will introduce the notion of an H-linked graph, which extends several
concepts including k-linked, k-ordered and k-connected graphs. We will
then discuss conditions that assure the existence of H-subdivisions of many
different sizes in a graph, and use our results to draw several parallels to
pancyclicity and panconnectivity.
Oct. 10:
Speaker: Ruth Heaton & Jim Lewis
Affiliation: UNL
Local host:
Title: From Math Matters to NEBRASKA MATH
Abstract:
In 2001, the Conference Board of the Mathematical Sciences (CBMS) released their report,
"The Mathematical Education of Teachers". The MET report stresses the intellectual substance
in school mathematics and the special nature of the mathematical knowledge needed for teaching.
This report is one of a series of reports which argue that investing in good teachers is the key step
in improving K-12 education in America. In addition, the report advocates partnerships between
mathematicians and mathematics educators as key to strengthening the mathematical education of teachers.
At UNL, the speakers began such a partnership in 1999. Three NSF grants have supported their work.
Math Matters, which began in 2000, completely changed mathematics education for UNL students studying
to become elementary teachers. Math in the Middle, an institute for middle-level mathematics teachers is
strengthening mathematics instruction in middle schools across Nebraska. The recently announced
NEBRASKA MATH offers the opportunity for major initiatives that work with K-3 teachers and
Algebra teachers. We will report on lessons learned during this decade long journey.
Oct. 17:
Speaker: Susan Cooper
Affiliation: UNL
Local host: Brian Harbourne
Title: Generalizations and Consequences of Macaulay's Theorem
Abstract:
In this talk we consider homogeneous ideals I in a polynomial ring over a field. The Hilbert function of
I is a sequence of non-negative integers which gives the dimensions of the graded pieces of I degree-by-degree.
Hilbert functions have played a central role in many algebraic problems. Indeed, many people
have obtained methods to extract non-trivial information about an ideal from its Hilbert function.
A famous theorem due to Macaulay has characterized which sequences arise as Hilbert functions of
homogeneous ideals. There are many generalizations
of this theorem. In this talk we will survey some of these generalizations and related conjectures.
Oct. 20-21: October Break
Oct. 24:
Speaker: Irena Swanson
Affiliation: Reed College
Local host: Sylvia Wiegand
Title:
Computational aspects of integral closure
Abstract:
I will explain what integral closure is, how it is used, and some
history of its computation.
I will concentrate mostly on the algorithmic
aspects of the computation. The first algorithmic
consideration is
due to Stolzenberg 1968, and was improved by Seidenberg in 1970 and
1975. A more
effective method for computing the integral closure of
affine domains is due to Grauert, Remmert,
These algorithms successively approximate the integral closure
"from below", namely, by building
successively strictly larger rings
contained in the integral closure. Based on a specialized 2003
algorithm
of Leonard--Pellikaan, Anurag Singh and I prove a more general version of
the construction
of the integral closure in positive prime characteristic
that starts instead with a finitely generated
module over the ring that
contains the integral closure, and the successive steps produce strictly
smaller submodules, eventually terminating in the integral closure
"from above". We also prove a new
algorithm for computing the integral
closure of some ideals. We implemented our algorithm in Macaulay2.
The
talk will be accessible to graduate students.
Oct 31: No colloquium (meeting)
Nov 7
Speaker: Osamu Iyama
Affiliation: Nagoya University, Japan
Local host: Sri Iyengar
Title: Quiver mutation and cluster tilting
Abstract:
We will discuss a relationship between combinatorics on quivers
(=directed graph) and representation theory of finite dimensional
algebras. Quiver mutation is a combinatorial algorithm to create
a new quiver from an old one. This is a key ingredient in the
definition of cluster algebras introduced by Fomin-Zelevinsky,
which will be explained early in the talk.
The Fomin-Zelevinsky construction has inspired important developments
in representation theory. In 2004, Buan, Marsh, Reineke, Reiten and
Todorov introduced certain triangulated categories called cluster categories. This has started a "categorification project," which currently is one of the
most active areas in the field. Some major developments will be described
in the talk.
Nov. 13: 19th Annual Math Day
Nov. 14
Speaker: Roman Hilscher
Affiliation: Masaryk University, CZECH REPUBLIC
Local host: Al Peterson
Title: Optimality conditions for variational problems on time scales
Abstract:
The theory of dynamic equations on time scales unifies and extends the classical differential and
difference equations theories. Therefore, it is necessary to combine the analytical methods from the
continuous time and the algebraical methods from the discrete time to obtain new results covering both cases.
In this talk we focus on first and second order optimality conditions in variational problems on time scales.
We start with nonlinear calculus of variations problems on time scales. We show the role of the
Euler-Lagrange equation, the transversality condition, the appropriate (strengthened) Legendre condition,
and the definiteness of the associated accessory problem (second variation) in the necessary and sufficient
optimality conditions. These problems involve only the state variable and are naturally normal (or
controllable). Some recent sufficient conditions for problems with general jointly varying endpoints are
obtained through the positivity of the second variation and they are new even for the continuous time setting.
Then we proceed by studying more general variational problems, namely nonlinear optimal control problems
on time scales. These problems involve both state and control variables which are connected through
a nonlinear dynamic equation. For this setting we present the weak Pontryagin maximum principle, the
transversality condition, and the accessory problem as necessary optimality conditions. The presented proof
of the weak maximum principle is direct and rather simlple, and for the variable endpoints setting it is new
even for the continuous case. The study of the accessory problem then naturally leads to time scale Hamiltonian
and symplectic systems.
The presented results were obtained jointly with Vera Zeidan from the Michigan State University.
Nov. 21: Film at 3:30pm, Discussion and refreshments at 4:30pm in 348.
Film & Discussion topic:
Julia Robinson
Title of movie:
Julia Robinson and Hilbert's Tenth Problem
Abstract: At the discussion, people who knew her or her work are invited to
comment on the
film and their impressions of Julia or her work.
Nov. 26- 30 Thanksgiving Break
Dec. 5:
Speaker: Christine Kelley
Affiliation: UNL
Local host: Judy Walker
Title: Algebraic constructions of codes using voltage graphs
Abstract:
Graph-based codes, such as low-density parity-check (LDPC) codes and repeat-accumulate codes, are being widely studied due to
their efficient decoding algorithms and remarkable performance on several communication channels. One recent avenue of approach
is to construct these codes by first designing small graphs with suitable properties, and then using random lifts of
these “protographs”
to represent codes.
In this talk, we introduce an algebraic analog of this approach using voltage graphs.
After a brief background on LDPC codes, we present a code construction by giving an algebraic method of choosing the permutation
voltages so that the resulting codes have good properties. This construction illustrates how simple results from graph theory and algebra
may be used to get codes that outperform their random counterparts.
Dec. 12:
Speaker: Collin Bleak
Affiliation: UNL
Local host: Susan Hermiller
Title: Free products in R. Thompson's group V.
Abstract:
R. Thompson's group V is a finitely presented simple group of current research interest.
It can be thought of as a group of automorphisms of the standard deleted-middle-thirds
Cantor set or as the full group of automorphisms of a certain algebra. V is a big,
slightly mysterious group; it is writhe with embedded free groups, and it contains
copies of every finite group.
Recently, a question from language theory/algorithmic group theory percolated its
way into the theory of V. As a consequence, researchers began to investigate
whether the free product Z^2 * Z can be found embedded in V. In this talk, we
study the dynamics of V's action on the Cantor set, and begin an investigation
into the range of free products of groups that V may actually contain. We can
now answer the question above, and state other interesting facts and questions
about V.
(The talk will describe joint work with Olga Salazar-Diaz.)
Dec. 17: OPEN (Exam week )
Current Schedule of
Open Dates for Spring 09
April 3
2009: Rowlee Lecture
Speaker: Michael Hopkins
Affiliation: MIT
Local Host: Mark Walker
Title: To be announced
Abstract: