Tuesdays, 4:35 - 5:35pm in JWB 335
Math 6960-001 (1 - 6 credit hours)
The goal of this Colloquium is to encourage interaction among graduate students, specifically between graduate students who are actively researching a problem and those who have not yet started their research. Speakers will discuss their research or a related introductory topic on a level which should be accessible to nonspecialists. The discussions will be geared toward graduate students in the beginning of their program, but all are invited to attend. This invitation explicitly includes undergraduate students.
Talks will be held on Tuesdays at 4:35pm in JWB 335, unless otherwise
Speaker: David Hartenstine
Title: Job Search Seminar
Speaker: Daniele Arcara
Title: Can't define a function? Just blow it up!
Abstract: After a quick review of polar coordinates, and a brief introduction to the basic objects and functions of algebraic geometry, we shall explore, through many examples, a process called blow-up (which generalizes polar coordinates). In particular, I shall explain how blow-ups are used to make sense of a function at the points where the function is not defined.
Speaker: Peter Trapa
Title: "Counting relative positions of flags"
Abstract: The famous local Langlands conjecture predicts that the infinite-dimensional representation theory of certain Lie groups (like the group of invertible n-by-n matrices with real or p-adic entries) should be controlled by complex algebraic geometry. This is a deep subject and it is not possible to even sketch an overview in just an hour. But fortunately it is possible to give the flavor of the geometry involved, and this is what I plan to do. The only background needed is a little group theory and some elementary linear algebra.
Speaker: Ian Renner
Title: "Evidence of Global Warming?"
Abstract: Global warming is a potentially catastrophic climatological problem, whose believers forecast imminent doom. However, is global warming truly evident in temperature data? This project analyzes the recorded temperature from Prague from 1775-1989 and utilizes various statistical methods to draw conclusions about the validity of global warming through the use of the random permutation method and the process of binary segmentation.
Speaker: Sandy Spiroff
Title: "The Divisor Class Group of a Noetherian Normal Domain."
Speaker: Gordan Savin
Title: "The Composition Law of Gauss and its Generalizations by Bhargava"
Abstract:TBA In 1801 Gauss defined a group law on the set of binary quadratic forms, which in modern language corresponds to multiplication of ideals in a quadratic filed.
In his remarkable 2001 thesis, Monjul Bhargava interprets the Gauss' law in terms of 2 x 2 x 2 cubes of integers, and shows that the Gauss' law is only one of about ten laws. Just as the Gauss law is related to quadratic fields, other laws are related to various number theoretic invariants, and all of them are related to exceptional Lie groups. For his work Bhargava was named one of the top ten Pop Science young researchers, and was recently given a full professorship at Princeton.
Speaker: Andre Cherkaev
Title: "Variational problems with unstable solutions"
Abstract: Equilibrium in optimal multiphase structures, breakable structures, or materials under phase transition is a solution to a nonconvex variational problem. The classical minimizer does not exist; minimizing sequences are characterized by infinitesimal spatial oscillations that correspond to media with microstructures. We outline formulations of such problem and corresponding variational techniques: Special necessary conditions and bounds.
Dynamics of such structures is marked by intensive waves that are excited when the system passes from one locally stable equilibrium to another. We discuss a model that describes nonlinear waves, including conditions of propagation of a transition wave ("house of cards" problem) and a homogenized state of the excited system.
Speaker: Robert Bell
Title: ``The geometry of Coxeter groups''
Abstract: The theory of Coxeter groups (i.e. abstract reflection groups) is important to many areas of mathematics. They arise naturally in the study of Lie groups, geometry, and topology. In particular, the most familiar Coxeter groups are the full symmetry groups of regular polyhedra or regular tilings of the plane. By way of example, we will explore the group of symmetries of a regular polytope, the Weyl group of a Lie group, the notion of a building, and the idea of a generalized braid group. If time permits, we will indicate how every Coxeter group admits a faithful geometric representation.
Speaker: Jim Keener
Title: "The Mathematics of Ranking - or - Should the Utes be Ranked in the Top 25?"
Abstract: The recent and surprising success of the Ute football team has brought to the forefront the longstanding question of how to rank teams when there are no playoffs and when the competition is not a round robin. In this talk I will give an overview of the ideas behind several different ranking schemes and then show that one important theorem - the Perron-Frobenius theorem - underlies them all. Finally, we will see how football team in the US are ranked at this, the end of the 9th week of the 2003 football season.
Speaker: Aaron McDonald
Title: "Evolutionary Game Theory"
Abstract: Over the past 30 years there has been much work in applying concepts of game theory to model various kinds of animal conflict. This talk introduces the history of evolutionary game theory where ideas from evolutionary biology and rationalistic economics meet - emphasizing the links between static and dynamic approaches to non-cooperative game theory.
Speaker: Renzo Cavalieri
Title: "A Cocktail Party Conversation About the Gopakumar-Vafa Conjecture."
Abstract: It has happened to all of us, and it's our biggest fear: Being asked the question "What do you do in your life?" by a non-mathematician. So I figured I better get prepared for whenever is going to happen next, and train to convey, in an informal and hopefully enjoyable manner, a flavor of what I am trying to do in my research.
Speaker: Aaron Bertram
Title: "How and why to apply for a grant"
Speaker: David Dobson
Title: "Optimization of photonic crystals"
Abstract: Photonic crystals are artificial materials constructed as a periodic arrangement of component materials. Light propagation (and propagation of electromagnetic waves in general) in such structures is often quite interesting, and difficult to predict in a straightforward way. Various applications require designing photonic crystals which have desirable wave behaviors. These problems can be approached mathematically, and solved numerically. This talk will outline some basic problems in the area and roughly describe some of the methods used in their solution.
Speaker: Robert D. Guy III
Title: "An introduction to non-Newtonian fluids and blood clotting"
Abstract: In this talk I will introduce the basic equations of Newtonian fluid mechanics, the Navier-Stokes equations. However the behavior of many fluids cannot be described by the NS equations, and I will give examples and demonstrations of some of these interesting behaviors. I will discuss some standard phenomenological models which account for both viscous and elastic behaviors of fluids. Such models can be derived by considering multiple spatial scales. I will present a multiple scale model of platelet aggregation, discuss some challenges these types of models present, and show some interesting results.
Department of Mathematics
University of Utah
155 South 1400 East, JWB 233
Salt Lake City, Utah 84112-0090
Tel: 801 581 6851, Fax: 801 581 4148