**Seminars and Colloquiums**

for the week of April 17, 2017

for the week of April 17, 2017

*SPEAKER:*

Conrad Plaut, UTK, Monday

Jim Coykendall, Clemson, Monday

Cheng Wang, UMass, Dartmouth, Monday

Phil Bowers, Florida University, Wednesday

Cory Hauck, ORNL and UTK, Wednesday

Kevin Sonnanburg, UTK, Thursday

Dr. Hem Raj Joshi, Xavier University, Friday

Haya Kaspi, Technion, Friday

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, and Wednesday: Ayres 401
*

*Hosted by: Tricia Phillips*

**Monday, April 17th**

##### TOPOLOGY/GEOMETRY SEMINAR

Title: Discrete Homotopy Theory

Speaker: Conrad Plaut, UTK

Time: 2:30p - 3:20p

Room: Ayres 113

Discrete homotopy theory replaces continuous paths and homotopies with discrete versions, allowing one to understand the fundamental group at a given scale in a metric space. I’ll give the basic definitions and constructions, then state "curvature-free" generalizations of some well-known finiteness theorems for Riemannian manifolds. If I have time I’ll discuss some preliminary results concerning extending these ideas to be dependent only on the topology of the underlying space rather than the metric. This leads to some new topological invariants that are closely connected to the geometric complexity of geodesic metrics that a compact space may have. This work lies at the beautiful interface between geometry and topology, when constraints on one can lead to constraints on the other. The talk will mainly be about fundamentals and ideas, with few technical details.

##### ALGEBRA SEMINAR

Title: Ideals and Graphs

Speaker: Jim Coykendall, Clemson

Time: 3:35p - 4:25p

Room: Ayres 113

We define the zero-divisor graph of a commutative ring, R, to have its vertex set be the set of nonzero zero divisors of R and we declare that there is an edge between x and y in R if and only if xy=0. D. F. Anderson and P. S. Livingston wrote a (perhaps the) seminal paper on the subject in 1999 and proved (among other things) that the zero divisor graph of R is always connected and has diameter no more than 3. In this talk, we will discuss a related concept where the vertices are taken as ideals in a commutative ring and edges are defined in various ways in an attempt to "pictorially" understand some of the ideal theoretic properties of R. We will discuss different types of edge definitions and some of the graph-theoretic properties that result. We will also glean some information on the ideal structure of R via these graphs.

##### COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR

Title: Preconditioned Steepest Descent (PSD) solver for the Cahn-Hilliard equation coupled with fluid flow

Speaker: Cheng Wang, UMass, Dartmouth

Time: 3:35p - 4:35p

Room: Ayres 405

The preconditioned steepest descent (PSD) solvers are applied to Cahn-Hilliard equation, coupled with certain fluid flow, such as the Hele-Shaw or Stokes equation. With a careful temporal discretization, the numerical scheme corresponds to a generalized gradient flow, and the numerical solution is equivalent to a minimization of a purely convex energy. In particular, due to the semi-implicit treatment of the nonlinear convention term, a linear energy functional is involved associated with the convection part, and this subtle fact greatly simplifies the numerical effort. By using the energy dissipation property, we derive a discrete bound for the solution, as well as an upper-bound for the second derivative of the energy. Furthermore, a geometric convergence rate is shown for the nonlinear PSD iteration applied to the Cahn-Hillird-Flow models, which turns out to be e very sharp theoretical result. Some numerical results are also presented in the talk.

**Wednesday, April 19th**

##### ANALYSIS SEMINAR

Title: Cauchy rigidity of circle polyhedra (told in two stories and one question).

Speaker: Phil Bowers, Florida University

Time: 2:30p – 3:20p

Room: 112 Ayres

##### COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR

Title: TBA

Speaker: Cory Hauck, ORNL and UTK

Time: 3:35p - 4:35p

Room: Ayres 113

**Thursday, April 20th**

##### DIFFERENTIAL EQUATIONS SEMINARS

Title: TBA

Speaker: Kevin Sonnanburg, UTK

Time: 2:00p – 3:00p

Room: Ayres 113

**Friday, April 21st**

Title: Research and Teaching at a small university

Speaker: Dr. Hem Raj Joshi, Xavier University

Time: 11:15a - 12:00p

Room: A114

PIZZA will be served!

##### COLLOQUIUM

Title: Local Times of Markov Processes and Permanental Processes

Speaker: Haya Kaspi, Technion

Time: 3:30pm – 4:30pm

Room: 405 Ayres

Permanental Processes are a certain class of Gamma processes that generalize squared Gaussian processes. One class of Permanentals is connected with Markov processes, their defining parameters are the potential densities of a corresponding Markov process. Permanental processes thus associated with Markov processes are infinitely divisible. We analize the connections of those Permanentals with the local time process, indexed by the states, of the associated Markov process. We deduce sample path properties of one process from the other, using their infinite divisibility and a formula known as the Isomorphism Theorem. Joint work with Nathalie Eisenbaum from CNRS Paris VI

*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:**

3/13/17 - Spring Break

Winter Break