**Seminars and Colloquiums**

for the week of September 11, 2017

for the week of September 11, 2017

*SPEAKERS*

Yu-Ting Chen, UTK, Tuesday

Tadele Mengesha, UTK, Wednesday

Tadele Mengesha, UTK, Thursday

Luan Hoang, Texas Tech, Thursday

Mathew Langford, UTK, Thursday

Farrah Sadre-Marandi, The Ohio State University, Friday

*TEA TIME*

3:00 pm – 3:30 pm

Monday, Tuesday & Wednesday

Room: Ayres 401

Hosted By: Hannah Thompson

**Tuesday, September 12th**

**STOCHASTICS/ PROBABILITY SEMINAR**

TITLE: The Sherrington-Kirkpatrick model for mean-field spin glasses: an introduction

SPEAKER: Yu-Ting Chen, UTK

TIME: 2:10-3:25pm

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 13th**

**ANALYSIS SEMINAR
** Title: A fractional Hardy-type inequality over the half space with an application

Speaker: Tadele Mengesha, UTK

Time: 2:30p – 3:20p

Room: Ayres 113

This is a continuation of last week’s seminar where we will continue to discuss a new fractional Hardy-type inequality for vector fields that is based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact gives a smaller norm, in general. As such, the new inequality improves the classical fractional Hardy’s inequality for vector fields.

Thursday, September 14th

**SACNAS CHAPTER OF SIAM**

TITLE: My Career Path from Ethiopia and My Research

SPEAKER: Tadele Mengesha, UTK

TIME: 11:50a – 12:30

ROOM: Ayres 401

**DIFFERENTIAL EQUATIONS SEMINAR**

TITLE: Foias-Saut asymptotic expansions for solutions of Navier-Stokes equations with time-dependent forces

SPEAKER: Luan Hoang, Texas Tech

TIME: 2:10p – 3:10p

ROOM: Ayres 114

We study the long-time behavior of solutions to the three-dimensional incompressible Navier-Stokes equations with periodic boundary conditions. The body forces decay in time either exponentially or algebraically. We establish the asymptotic expansions of Foias-Saut-type for all Leray-Hopf weak solutions. If the force has an asymptotic expansion, as time tends to infinity, in terms of exponential functions or negative-power functions, then any weak solution admits an asymptotic expansion of the same type. Moreover, when the force's expansion holds in Gevrey spaces, which have much stronger norms than the Sobolev spaces, then so does the solution's expansion. This extends the previous results of Foias and Saut for the case of potential forces in Sobolev spaces.

This talk is based on joint research projects with Dat Cao (Texas tech University) and Vincent Martinez (Tulane University).

G**EOMETRIC ANALYSIS SEMINAR**

TITLE: Ancient solutions of the mean curvature flow

SPEAKER: Mathew Langford

TIME: 5:00p - 6:00p

ROOM: Ayres 404

I will present a survey of some recent existence and rigidity results for ancient solutions of mean curvature flow. In particular, I will describe some recent work (with Giuseppe Tinaglia and Theodora Bourni) on the existence and uniqueness of rotationally symmetric ancient solutions which lie in a slab. We will finish with some interesting open problems

**Friday, September 15th **

**SPECIAL COLLOQUIUM**

TITLE: Gender differences in hepatic one-carbon metabolism

SPEAKER: Farrah Sadre-Marandi, The Ohio State University

TIME: 3:30-4:30pm

ROOM: Ayres 405

It is known that there are gender differences in one-carbon metabolism (OCM) and these differences are accentuated in pregnancy. Women in the child-bearing years exhibit lower plasma homocysteine, higher betaine and choline, and lower S-andenosylmethionine. Various enzymes in OCM are up-regulated or down-regulated in women due to estrogen. Furthermore, insulin and glucose affect some enzymes of OCM and change during pregnancy. All of these results suggest that a mechanistic understanding of how enzymatic differences in women affect OCM is important for precision medicine.

The reaction diagram for the folate and methionine cycles in OCM is very complicated consisting of loops within loops. Furthermore, many substrates in the network influence, through allosteric binding, the activity level of enzymes at distant locations in the network. These are systems properties of the whole network and to understand them one needs a mathematical model of OCM, based on the real underlying biochemistry and biology, and machine computation.

A mathematical model of folate and methionine metabolism is used to study the enzymatic changes in women of child-bearing age and the resulting concentrations of metabolites. In each case the results are compared to clinical and experimental studies. The causal mechanisms by which the gene expression or enzyme activity changes in women that lead to the metabolite changes will be discussed.

*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 *

**Past notices:**