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Eberly College of Science Mathematics Department

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August 5th, 2014 (11:00am - 12:50pm)
Seminar: Ph.D. Thesis Defense
Title: "The auxiliary space technique for linear solvers"
Speaker: Lu Wang, Adviser: Jinchao Xu, Penn State
Location: MB106

Developing efficient iterative methods and parallel algorithms for solving sparse linear systems discretized partial differential equations (PDEs) is still a challenging tasks in scientific computing and practical applications. Though many mathematically optimal solvers such as the multigrid method have been developed, the unfortunate reality is that multigrid methods have not been much used in practical applications. Based on the methodology of Fast Auxiliary Space Preconditioning (FASP), we develop formulate and analyze preconditioning techniques that will narrow the gap between theory and practice, specifically by developing mathematically optimal solvers that are robust and easy to use in practice. A new parallel unsmoothed aggregation algebraic multigrid (UA-AMG) method for a PDE defined on an unstructured from the hierarchical structured coarse grid. It provides (nearly) optimal load balance and predictable communication patterns factors that make our new algorithm suitable for parallel computing. We will also try to extend the FASP techniques to saddle point and indefinite problems. Finally we present applications and show results from several application areas.

August 15th, 2014 (10:00am - 11:30am)
Seminar: Complex Fluids Seminar
Title: Cavity Computation in Nonlinear Elasticity
Speaker: Zhiping Li, Peking University
Location: MB106
August 18th, 2014 (10:00am - 11:30am)
Seminar: Complex Fluids Seminar
Title: : Large time blow up for a perturbation of the cubic Szegő equation
Speaker: Haiyan Xu, University Paris-Sud 11
Location: MB106

I am going to discuss a pertubed cubic Szegő equation i u_t = Pi (|u|^2u) + α (u|1) on the circle, where Pi is the Szegő projector on non-negative frequencies. This equation with α=0 was recently introduced as a toy model for totally non dispersive evolution equations by P. Gerard (Paris-Sud University, Orsay, France) and S. Grellier (University of Orleans, France). It is globally well-posed with a Lax pair structure for any real number α. Given initial data in a special subset of rational functions, the solutions stay in a relatively compact subset of trajectories for α<0. While for α> 0, there exist trajectories on which high Sobolev norms exponentially grow with time.

August 25th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Introduction to the CCMA Luncheon Seminar
Speaker: Various Speakers, Penn State University
Location: MB114
August 25th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Transport of Charged Particles in Physical and Biological Environments: An Energetic Variational Approach
Speaker: Chun Liu, Penn State University
Location: MB106

I will present a thermodynamics-consistent framework for studying the transport of charged particles in various environments. We will explore various physical and mathematical descriptions for 1) the free energy corresponding to the local and nonlocal interactions between particles as well as 2) dissipation mechanisms. For this talk, I will just focus on various classical and popular general diffusion problems, such as fractional Laplacian, porous media, nonlocal diffusion as well as various stochastic interpretations.

August 26th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Rozansky--Witten-type invariants from symplectic Lie pairs
Speaker: Yannick Voglaire, University of Luxembourg
Location: MB106

In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be built from only two objects: the Atiyah class of the underlying complex manifold, and the holomorphic symplectic form. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds and knots, given respectively by weight systems on trivalent and chord diagrams. In this talk, I will review the necessary notions to state the result and explain the construction of the weight systems.

August 26th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: An introduction to the use of algebraic geometry I ATTENTION: the second lecture in this series will take place on THURSDAY AUGUST 28 3:30-6pm n Teichmuller dynamics,I
Speaker: Alex Wright, Stanford University
Location: MB216
August 27th, 2014 (03:00pm - 04:30pm)
Seminar: Complex Fluids Seminar
Title: Navier-Stokes Equations with Density-dependentViscosity and Vacuum
Speaker: Yachun Li, Shanghai Jiao Tong University
Location: MB315

In this talk I will present some new results on isentropic Navier-Stokes equations for compressible fluids with density-dependent viscosity coefficients. These equations are degenerate when vacuum appears. The local existence of classical solutions is established when the shear viscosity coefficient and bulk viscosity coefficient are both proportional to the density and the initial data are arbitrarily large with vacuum appearing in the far field. Besides, we study the Cauchy problem for multi-dimensional compressible isentropic Navier-Stokes equations with radiation (Navier-Stokes-Boltzmann equations). I will prove that radiation effect cannot prevent the formation of singularities provided that the initial mass density is compactly supported.

August 27th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: When Group Work Fails
Speaker: Attendees, Penn State
Location: MB102

Group projects are lauded for their ability to teach students various skills important to professional work, including communication, management, and planning. But not all group work is successful. In some cases, members of a group may put in less work or no work at all. This week, we read a summary of literature from social psychology on this topic and discuss strategies to combat this phenomenon.
Myers, David G. "Many Hands Make Diminished Responsibility." Exploring Social Psychology. 6th ed. New York: McGraw-Hill, 1994. 203-08. Print.

August 28th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Lunch
Speaker: ANT group, PSU
Location: MB106

Meet at 11:30 by Octacube

August 28th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Diversity Workshop
Speaker: Diversity Workshop
Location: MB114
August 29th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: The A Posteriori Error Estimation for Finite Element Method of the H(curl)-elliptic Problem
Speaker: Shuhao Cao, Pennsylvania State University
Location: MB315

The coercive H(curl) problem, sometimes named as H(curl)-elliptic problem, arises from the implicit time discretization of the second-order hyperbolic initial boundary value problem for the electric field. Both the finite element discretization and its a posteriori error estimation are discussed. The residual-based error estimator, and several recovery-based error estimators are constructed and analyzed.