Listen to the podcast below to find out more about Pittard:

You are invited to join math faculty and graduate students for an afternoon of fun including various outdoor activities, delightful snacks and riveting conversation. We will have volleyball, croquet, Frisbee, and other activities. Families are encouraged to come join the fun.

Title:  Continuity of a Right Inverse of the Divergence Operator

Abstract:  The divergence of a vector field u = (u1, ... , un), often written as div u = L,j=1  or V · u, is·a well-known  quantity in vector  calculus, rneasuring  'sinks' and 'sources' Of u. In fluid dynamics, this quantity manifests  itself  in the compression  and rarefaction  of a fluid whose velocity is given by u. The incompressibility  condition on _such a fluid, formulated as div u = 0, is well-known. A more general case, div u = J, is naturally a PDE of interest.

Given J E L§(D), a right inverse of divergence can be constructed from a singular integral kernel and used to solve div u = f. In my talk, I present a proof (due to Ricardo G.Duran) that this right inverse is bounded from L§ (fl) to HJ (l1r using the Fourier transform and elementary techniques.

Join the UK Appalachian Center at RCARS in Jackson, KY for our 2nd annual Pickin' Time Event on Saturday, November 1, 2014!  This is a great event for learning about culture through various musical workshops, cutting board workshops, a local craft market, a visual arts showcase, farmer's market, and much more. UK Students, Faculy, and Staff are invited to go by bus.  Please, RSVP to Erin Norton by October 15th, 2014 via email at erin.norton @uky.edu.  Please email one RSVP per person.  We will accommodate as many requests as possible, and admission is free!

Title:  Chip-Firing and Tropical Independence, II

Abstract:  We continue discussing the basic theory of divisors  on graphs, with a primary focus  on concrete examples.   If time permits, we will describe how these tools are used to provide  new proofs of some  well-known  theorems  in algebraic  geometry.

Title:  Efficient Solutions of Large Saddle-Point Systems

Abstract:  Summer projects are great; here is one such project. Linear systems of saddle-point type arise in a range of applications including optimization, mixed finite-element methods for mechanics and fluid dynamics, economics, and finance (basically everywhere). Due to their indefiniteness and generally unfavorable spectral properties, such systems are difficult to solve, particularly when their dimension is very large. In some applications - for example, when simulating fluid flow over large periods of time - such systems have to be solved many times over the course of a single run, and the linear solver rapidly becomes a major bottleneck. For this reason, finding an efficient and scalable solver is of the utmost importance. In this project, we examined various solution strategies for saddle-point systems.

The UK Appalachian Center is hosting a SWAP (Sharing Work on Appalachia in Progress) Meeting with presentations on research by 3 Brown Awardees: Tammy Clemons, Mary Beth Schmid, and Jasper Waugh-Quasebarth.