The Back-and-Forth Error Compensation and Correction Method for Linear Hyperbolic Systems and a Conservative BFECC LimiterFriday, June 22, 2018 - 11:00 , Location: Skiles Building 114 (Conference Room 114) , Xin Wang , School of Mathematics, Georgia Institute of Technology , firstname.lastname@example.org , Organizer: Xin Wang
In this dissertation, we studied the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems and nonlinear scalar conservation laws. We extend the BFECC method from scalar hyperbolic PDEs to linear hyperbolic PDE systems, and showed similar stability and accuracy improvement are still valid under modest assumptions on the systems. Motivated by this theoretical result, we propose BFECC schemes for the Maxwell's equations. On uniform orthogonal grids, the BFECC schemes are guaranteed to be second order accurate and have larger CFL numbers than that of the classical Yee scheme. On non-orthogonal and unstructured grids, we propose to use a simple least square local linear approximation scheme as the underlying scheme for the BFECC method. Numerical results showed the proposed schemes are stable and are second order accurate on non-orthogonal grids and for systems with variable coefficients. We also studied a conservative BFECC limiter that reduces spurious oscillations for numerical solutions of nonlinear scalar conservation laws. Numerical examples with the Burgers' equation and KdV equations are studied to demonstrate effectiveness of this limiter.
Series: AMS Club Seminar
Inkscape is an powerful open-source drawing program suitable for making figures for your math papers and lectures. In this talk I will discuss some of the useful tricks and features that you can take advantage of in this software, as well as some things to avoid. This will be a live demonstration talk, please bring a laptop if you can.
Tuesday, June 19, 2018 - 10:00 , Location: Skiles 005 , Shane Scott , Georgia Tech , email@example.com , Organizer: Shane Scott
The curve complex of Harvey allows combinatorial representation of a surface mappingclass group by describing its action on simple closed curves. Similar complexes of spheres,free factors, and free splittings allow combinatorial representation of the automorphisms ofa free group. We consider a Birman exact sequence for combinatorial models of mappingclass groups and free group automorphisms. We apply this and other extension techniquesto compute the automorphism groups of several simplicial complexes associated with map-ping class groups and automorphisms of free groups.
Series: Stochastics Seminar
Random balls models are collections of Euclidean balls whose centers and radii are generated by a Poisson point process. Such collections model various contexts ranging from imaging to communication network. When the distributions driving the centers and the radii are heavy-tailed, interesting interference phenomena occurs when the model is properly zoomed-out. The talk aims to illustrate such phenomena and to give an overview of the asymptotic behavior of functionals of interest. The limits obtained include in particular stable fields, (fractional) Gaussian fields and Poissonian bridges. Related questions will also be discussed.
Series: School of Mathematics Colloquium
Given two complex polynomials, we can try to mathematically paste them together to obtain a rational function through a procedure known as mating the polynomials. In this talk, we will begin by trying to understand the "shape" of complex polynomials in general. We will then discuss the mating of two quadratic polynomials: we explore examples where the mating does exist, and examples where it does not. There will be lots of movies and exploration in this talk.
Wednesday, May 30, 2018 - 14:00 , Location: Skiles 006 , Tongzhou Chen , GT Math , Organizer: Jiaqi Yang
We model and analyze the dynamics of religious group membership and size. A groups is distinguished by its strictness, which determines how much time group members are expected to spend contributing to the group. Individuals differ in their rate of return for time spent outside of their religious group. We construct a utility function that individ- uals attempt to maximize, then find a Nash Equilibrium for religious group participation with a heterogeneous population. We then model dynamics of group size by including birth, death, and switching of individuals between groups. Group switching depends on the strictness preferences of individuals and their probability of encountering members of other groups.
Series: Geometry Topology Seminar
This will be a 90 minute seminar
It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties are preserved under various types of contact surgeries. The case for the negative contact surgeries is fairly well understood. In this talk, we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically/Stein fillable when r is in (0,1]. This is joint work with James Conway and John Etnyre.
Series: PDE Seminar
The ground state solution to the nonlinear Schrödinger equation (NLS) is a global, non-scattering solution that often provides a threshold between scattering and blowup. In this talk, we will discuss new, simplified proofs of scattering below the ground state threshold (joint with B. Dodson) in both the radial and non-radial settings.
Wednesday, May 2, 2018 - 14:00 , Location: Skiles 006 , Hyunki Min , Georgia Tech , firstname.lastname@example.org , Organizer: Hyun Ki Min
Understanding contact structures on hyperbolic 3-manifolds is one of the major open problems in the area of contact topology. As a first step, we try to classify tight contact structures on a specific hyperbolic 3-manifold. In this talk, we will review the previous classification results and classify tight contact structures on the Weeks manifold, which has the smallest hyperbolic volume. Finally, we will discuss how to generalize this method to classify tight contact structures on some other hyperbolic 3-manifolds.
Monday, April 30, 2018 - 15:05 , Location: Skiles 006 , John Dever , Georgia Tech , Organizer: John Dever
We provide a new definition of a local walk dimension beta that depends only on the metric. Moreover, we study the local Hausdorff dimension and prove that any variable Ahlfors regular measure of variable dimension Q is strongly equivalent to the local Hausdorff measure with Q the local Hausdorff dimension, generalizing the constant dimensional case. Additionally, we provide constructions of several variable dimensional spaces, including a new example of a variable dimensional Sierpinski carpet. We use the local exponent beta in time-scale renormalization of discrete time random walks, that are approximate at a given scale in the sense that the expected jump size is the order of the space scale. We consider the condition that the expected time to leave a ball scales like the radius of the ball to the power beta of the center. We then study the Gamma and Mosco convergence of the resulting continuous time approximate walks as the space scale goes to zero. We prove that a non-trivial Dirichlet form with Dirichlet boundary conditions on a ball exists as a Mosco limit of approximate forms. We also prove tightness of the associated continuous time processes.