**Seminars and Colloquiums**

for the week of March 21, 2016

for the week of March 21, 2016

*SPEAKER:*

Brian Allen, UTK, Monday

Michael Holloway, UTK, Monday

Paul Laiu, UMD, Wednesday

Kevin Sonnanburg, UTK, Thursday

**Monday, March 21st **

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: The Topology of Two-Convex Hypersurfaces in Euclidean Space

SPEAKER: Brian Allen (UTK)

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

In this talk we will discuss how to use Mean Curvature Flow (MCF) with surgery in order to classify the topology of two-convex hypersurfaces in Euclidean space. MCF will be introduced, examples explained, important prior results stated and the big ideas of the proof will be discussed.

DOCTORAL DEFENSE

TITLE: Duality of Scales

SPEAKER: Michael Holloway

TIME: 3:30pm – 4:30pm

ROOM: Ayres 121

His committee consists of Professors: Dydak (Chair), Brodskiy, Thistlethwaite, and Berry (EECS).

**Wednesday, March 23rd **

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Positive Filtered P_N method for linear transport equations

SPEAKER: Paul Laiu, UMD

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

We propose a positive-preserving approximation method for solving linear kinetic transport equations based on a filtered spherical harmonic (FPN) expansion in the

occurrence of (unphysical) negative particle concentrations. The origin of this problem is that the FPN approximation is not always positive at the kinetic level; the new FPN+ closure is developed to address this issue. A new spherical harmonic expansion is computed via the solution of an optimization problem, with constraints that enforce positivity, but only on a finite set of pre-selected points. Combined with an appropriate PDE solver, this ensures positivity of the particle concentration at each step in the time integration. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FPN+ approximation converges, in the L^2 sense, at the same rate as the FPN approximation; numerical tests suggest that this assumption may not be necessary. We simulate the challenging line source benchmark problem with several different approximating methods. The line source results indicate that, when compared to other positive-preserving methods, the accuracy of the FPN+ method makes up for the overhead incurred by the optimization problem.

**Thursday, March 24th**

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Ancient Solutions of Rotationally Symmetric Mean Curvature Flow

SPEAKER: Kevin Sonnanburg, UTK

TIME: 2:00pm - 3:00pm

ROOM: Ayres 113

As with many parabolic PDE, a common technique to study singularities of mean curvature flow is the use of rescaled variables. Through this blow up procedure, under certain conditions, the solutions tend toward contracting solitons, leading to an interest in ancient solutions (defined for all negative time). I will show that, given minimal hypotheses, ancient solutions to mean curvature flow, which are rotationally symmetric graphs over the cylinder, must be cylinders themselves.

*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:**

3/14/2016 - spring break