Seminars and Colloquiums
for the week of September 18, 2017
Yu-Ting Chen, UTK, Tuesday
Thomas Weighill,UTK, Wednesday
Tricia Phillips and Cara Sulyok, UTK, Wednesday
Horst Behncke, Universität Osnabrück, Thursday
Carl Wagner, UTK, Thursday
Theodora Bourni, UTK, Thursday
3:00 pm – 3:30 pm
Monday, Tuesday, Ayres 406
Wednesday, Ayres 401
Hosted By: Jacob Dennerlein and Justin Groves
Tuesday, September 19th
STOCHASTICS/ PROBABILITY SEMINAR
TITLE: The Sherrington-Kirkpatrick model for mean-field spin glasses: an introduction; Part 2
SPEAKER: Yu-Ting Chen, UTK
TIME: 2:10pm – 3:25pm
ROOM: Ayres 113
One of the most important topics in solid state physics studies certain alloys of ferromagnets and conductors known as spin glasses. The major mathematical models are Gaussian models and include the Edwards-Anderson model (1975) and the mean-field extension introduced by Sherrington and Kirkpatrick (1975). In particular, the latter model has proven to represent an amazingly rich structure that is known to be mathematically hard to grasp.
In this talk, I will introduce the Sherrington-Kirkpatrick model and discuss some basic calculus. Then I will move on to an explanation of the identities of Ghirlanda and Guerra, which are known to play a fundamental role for mathematical investigations of the model.
Wednesday, September 20th
TITLE: Group actions and the maximal Roe algebra
SPEAKER: Thomas Weighill, UTK
TIME: 3:35pm – 4:25pm
ROOM: Ayres 405
The (maximal) Roe algebra is an important C*-algebra which appears in the index theory of non-compact complete Riemannian manifolds. It is also a coarse invariant, and so is naturally an object of study in coarse geometry. In a previous talk, we saw what it means for a group to act on a metric space by coarse equivalences and introduced a kind of "coarse quotient" which we call X_G. In this talk, we will begin to establish a relationship between the maximal Roe algebras of X and X_G for certain kinds of group action. This correspondence will involve the (full) crossed product of the Roe algebra with the group G. We will introduce all the necessary concepts from the theory of C* algebras, and recall the definition of the Roe algebra and its maximal version. This is joint work with Logan Higginbotham.
TITLE: Numerical Solution of Optimal Control Problems by Direct Collocation
SPEAKER: Tricia Phillips and Cara Sulyok, UTK
ROOM: Ayres 113
This talk is based upon findings from the paper with the same title written by Oskar von Stryk.
By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard methods. Convergence properties of the discretization are derived and shown to match convergence properties for the original continuous problem. Using a method known as direct collocation, these properties are used to obtain accurate and reliable estimates of adjoint variables. The talk will conclude with a numerical application.
Thursday, September 21st
PARTIAL DIFFERENTIAL EQUATIONS SEMINAR
TITLE: Optimal Control of Epidemics with a Core Group
SPEAKER: Horst Behncke, Universität Osnabrück
TIME: 2:10pm - 3:10pm
ROOM: Ayres 114
Epidemics are causing serious health problems in modern societies caused among others by increasing mobility. For sexually transmitted diseases, one finds often a group of highly active persons or people with risky behavior. Such a group will be called a core group. The core group may also consist of particularly exposed people, e.g. workers in health services.
It turns out that the epidemic is particularly relevant in the core group and that in many cases the core group is responsible for the spreading of the disease.
Epidemics can be controlled by vaccination, quarantine, screening, backtracking, and educational campaigns.
Limited resources require an optimal use of the means to control the epidemic. To as much as one describes the epidemic by a system of differential equations, this leads directly to a problem of optimal control. The formulation and solution of such systems will be the aim of this talk.
SPEAKER: Carl Wagner, UTK
TIME: 3:40pm - 4:30pm; 3:20pm for pizza
ROOM: Ayres 405
We’ll see how multiplying various power series leads to the solution of many interesting problems in enumerative combinatorics.
GEOMETRIC ANALYSIS SEMINAR
TITLE: Ancient Pancakes
SPEAKER: Theodora Bourni, UTK
TIME: 5:00pm - 6:00pm
ROOM: Ayres 405
We show that, up to rigid motions, there is a unique compact, convex, rotationally symmetric, ancient solution of mean curvature flow that lies in a slab of width $\pi$ and in no smaller slab. This is joint work with Mat Langford and Giuseppe Tinaglia.
Friday, September 22nd
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu