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Series: PDE Seminar

In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the free boundary compressible Euler equations satisfying the physical vacuum condition. The support of these solutions expands at a linear rate in time. We show that if the adiabatic exponent gamma belongs to the interval(1, 5/3] then these affine motions are globally-in-time nonlinearly stable. If time permits we shall also discuss several classes of global solutions to the compressible Euler-Poisson system. This is a joint work with Juhi Jang.

Series: Combinatorics Seminar

Series: Research Horizons Seminar

Series: CDSNS Colloquium

Series: Job Candidate Talk

Series: Geometry Topology Seminar

Monday, December 4, 2017 - 13:55 ,
Location: Skiles 005 ,
Prof. Tao Pang ,
Department of Mathematics, North Carolina State University ,
tpang@ncsu.edu ,
Organizer: Molei Tao

In the real world, the historical performance of a stock may
have impacts on its dynamics and this suggests us to consider models with
delays. We consider a portfolio optimization problem of Merton’s type in which
the risky asset is described by a stochastic delay model. We derive the
Hamilton-Jacobi-Bellman (HJB) equation, which turns out to be a nonlinear
degenerate partial differential equation of the elliptic type. Despite the
challenge caused by the nonlinearity and the degeneration, we establish the
existence result and the verification results.

Series: Combinatorics Seminar

Suppose we want to find the largest independent set or maximal cut in a sparse Erdos-Renyi graph, where the average degree is constant. Many algorithms proceed by way of local decision rules, for instance, the "nibbling" procedure. I will explain a form of local algorithms that captures many of these. I will then explain how these fail to find optimal independent sets or cuts once the average degree of the graph gets large. There are some nice connections to entropy and spin glasses.

Series: GT-MAP Seminars

TBA

Series: Stochastics Seminar

Cars are placed with density p on the lattice. The remaining vertices are parking spots that can fit one car. Cars then drive around at random until finding a parking spot. We study the effect of p on the availability of parking spots and observe some intriguing behavior at criticality. Joint work with Michael Damron, Janko Gravner, Hanbeck Lyu, and David Sivakoff. arXiv id: 1710.10529.