Seminars and Colloquiums
for the week of March 21, 2016
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.
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
3/14/2016 - spring break