**Upcoming Events**

Wednesday, September 24, 2014 at 3:00 PM in SAS 4201

Xiao-Biao Lin, NC StateCodiagonalization of Matrices and Existence of Multiple Homoclinic Solutions

Consider an autonomous ordinary differential equation in R^n that has a homoclinic solution asymptotic to a hyperbolic equilibrium. The homoclinic solution is degenerate in the sense that the linear variational equation has 2 bounded, linearly independent solutions. We study bifurcation of the homoclinic solution under periodic perturbations. Using matrices codiagonalization, exponential dichotomies and Lyapunov-Schmidt reduction, we obtain general conditions under which the perturbed system can have transverse homoclinic solutions and nearby periodic or chaotic solutions.

Monday, October 6, 2014 at 3:00 PM in SAS 2102

Colin Grudzien, University of North Carolina at Chapel HIllGeometric phase in the Hopf bundle and the stability of nonlinear waves

Evans function analysis has become a standard method of calculating the stability of nonlinear waves for PDEs. Building on the machinery of the Evans function, we have proven the validity of a related, alternative form of analysis that uses the Hopf bundle, whose total space is S^{2n-1}. This bundle is naturally imbedded in complex n-space and is locally the product of a circle and a neighborhood in CP^{n-1}. The dynamical system associated with the linearized operator for a PDE induces a winding number through parallel transport in the fibre. Our method uses parallel transport to count the multiplicity of eigenvalues contained within a loop in the spectral plane.

Wednesday, October 15, 2014 at 3:00 PM in SAS 4201

Jianfeng Lu, Duke Universitytba

Wednesday, October 22, 2014 at 3:00 PM in SAS 4201

Justin Webster, NC Statetba

Monday, October 27, 2014 at 3:00 PM in SAS 2102

Matt Holzer, George Mason Universitytba

Monday, March 30, 2015 at 3:00 PM in tba

Jeff Humpherys, Brigham Young Universitytba

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Seminar Organizer: Lorena Bociu and Mark Hoefer