Department of Mathematics - University of Utah

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Graduate Student Colloquium

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 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 Thursdays at 3:05 PM in 104 Stewart, unless otherwise noted.


  • 13 January, Stefan Folias will present "Looking inside the Brain from the Outside: An Inverse Problem"

    ABSTRACT: Is it possible to reconstruct the electrical activity inside the brain by measuring the electric and magnetic fields on the scalp? The answer is yes, in a way. This is a good and terribly difficult example of an inverse problem. I will discuss some of the basic physics and mathematics in conjunction with some of the relevant neurophysiology and neurobiology. Also I will illustrate the problems and difficulties associated with this problem known as EEG and MEG Source Localization.

  • 20 January, Brad Peercy will present "Excitable Media: Qualitative Behavior"

    Abstract. The goal of this talk is to introduce the idea of excitability through common examples as well as examples in biology. Ordinary differential equations can be used to describe excitability, and I will use phase plane analysis to understand these ODE's. The biology of the nerve and the mathematical description, again using ODE's, developed by Hodgkin and Huxley will be described. Spatial considerations, in the form of diffusion, will be added into the ODE's. I will briefly discuss concerns in cardiology such as defibrillation and atrial arrhythmias. A short video will allow visualization of numerics describing some cardiac arrhythmias.

  • 27 January, Sean Sather-Wagstaff will present "Hilbert Polynomials".

  • 3 February, Kai-Uwe Bux will present "Geometry and Presentations of Groups".

    ABSTRACT: A group G can be described by means means of generators and relations as follows: Fix a set X:={g_1, ..., g_i, ...} of elements in G, called "generators", closed with respect to taking inverses; and fix a set R:={R_1=1, ..., R_j=1, ...} of identities where each R_j is a product of generators that evaluates to the trivial element 1 in G . The pair of these two sets determines the group G up to isomorphism provided that
    a) every element of G can be written as a product of generators, and
    b) whenever a product of generators evaluates to 1 in G , this is a formal consequence of the identities collected in R.
    In this case, the pair is called a "presentation of the group G". The group Z for instance has the presentation < x,y | xy=1 >.

    Not every group admits a presentations where X is finite, and among those that do, only a few admit a presentation where R is finite as well. To find those finite presentations, one can make use of geometric spaces upon which groups act nicely.

  • 10 February, Elizabeth Jones will present "More on Hilbert Polynomials".

  • 17 February, 2:45-3:55 Kenneth Golden will present "Mathematics of Sea Ice".

  • 24 February, Nathan Jones will present "Questions in Graph Theory".

  • 2 March, James Keener will present "Quorum Sensing in Biofilms -- How Do They Know?".

  • 9 March, Aaron Bertram will present "Riemann Surfaces and L\"uroth's Theorem".

    ABSTRACT: The Riemann sphere (the one-point compactificaton of C) is the natural geometric "model" for the field of rational functions C(t). Similarly, any finite extension K of C(t) has a geometric model, which is a compact (Riemann) surface. The genus (number of holes) of the surface is therefore a number we can assign to K. We will use these surfaces and a little topology to prove L\"uroth's theorem, that any subfield S of finite index in C(t) is of the form C(f(t)). If there is time, we will also discuss some of the considerable difficulties which arise when we try to push this circle of ideas out to fields C(t_1,...,t_d) of rational functions of several variables.

  • 16 March, Semester Break

  • 23 March, Renate Caspers will present "ARCH Processes".

  • Monday, 27 March, 11:45-12:35, in the INSCC Auditorium, Peter Brinkmann will present "Free groups, graphs, and folding". (This is a special colloquium for visiting prospective graduate students. Everyone is welcome and invited.)

  • 30 March, Nick Cogan will present "The Cahn-Hilliard Model of Phase Separation".

    ABSTRACT: Some binary alloys exhibit a property called phase transition, which describes the spatial and temporal distribution of components of the alloy. In particular, for certain parameters, striking patterns result in short time. These patterns are dynamic on a longer time scale. The Cahn-Hilliard model of phase separation will be derived using energy methods, and several physical assumptions. Some numerical simulations will be presented as well as some typical analytic results.

  • 6 April, Sung Yoon will present "Embedding Problems".

  • 13 April, Ismail Kucuk will present "Structural Optimization".

  • 20 April, Brian Briscoe will present "A Territorial Model for Wolves due to Scent Marking".

  • 27 April, Anca Mustata will present "Lines on a Quintic Family and Mirror Symmetry".

    For the schedule of last semester's talks, click here.

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    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

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