Fall 2008
Colloquium Schedule
Department of Mathematics
Fall 2008 Colloquia (and other events)
Schedule: Here is a
discussion of
what to expect at Colloquium talks and
here
is a discussion of what might make a good colloquium talk.
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.
Go here
for tentative
scheduling for colloquia next semester.
Mon Aug 25: First
Day of classes
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.
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.
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.
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.
Speaker: Jim Lewis
Affiliation: UNL
Local host:
Title: To be announced
Abstract: Later.
Speaker: Susan Cooper
Affiliation: UNL
Local host:
Title: To be announced
Abstract: Later.
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)
Speaker: Osamu Iyama
Affiliation: Nagoya University
Local host: Sri Iyengar
Title: To be announced
Abstract: Later.
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.
Film and Discussion: Julia Robinson
Affiliation:
Local host:
Title: To be announced
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.
Speaker: Christine Kelly
Affiliation: UNL
Local host:
Title: To be announced
Abstract: Later.
Speaker: Collin Bleak
Affiliation: UNL
Local host:
Title: To be announced
Abstract: Later.
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: