Where:
When: Wednesday, Thursday, and Friday from 45 PM 

Current Schedule 
Thursday, April 3rd:
9:0010:00 AM  Zworski Lecture I in Peabody 008.
Talk Slides.
10:0011:00 AM  Coffee and Refreshments in 331 Phillips
11:00 AM  12:00 PM Zworski Lecture II in Wilson Library Pleasant's Room
Friday, April 4th:
1:002:00 PM  Zworski Lecture III in 332 Phillips
2:003:00 PM  Grad Lecture I  Jeffrey Galkowski
Talk Slides.
3:004:00 PM  Coffee and Refreshments in 331 Phillips
4:005:00 PM  Zworski Lecture IV in 381 Phillips
Current Schedule 
Thursday, November 21st:
3:00 PM  Coffee/Snacks in 330 Philips
3:304:30 PM  Lecture 1 from Professor Sogge in 381 Phillips
Talk I: Focal points and supnorms of eigenfunctions.
abstract: If (M,g) is a compact real analytic Riemannian manifold,
we give a necessary and sufficient condition for there to be a
sequence of quasimodes saturating supnorm estimates. The condition
is that there exists a selffocal point x_0 in M for the geodesic
flow at which the associated PerronFrobenius operator U: L^2
(S_{x_0}^* M ) > L^2 (S_{x_0}^* M )
has a nontrivial invariant function. The proof is based on von Neumann's ergodic theorem and stationary phase.
Talk Slides.
4:355:20 PM  1st 30 minute talk by Hongtan Sun in 381 Phillips 
Title: Strichartz type estimates for wave equations on hyperbolic trapped domain.
Abstract: We establish Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega,g)$,
for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is a positive odd integer.
As for the normally hyperbolic trapped obstacles, we will get some loss of derivatives for data in the local energy decay estimate. Hence the Strichartz estimate has a derivative loss,
and we need two different $L^p_tL^q_x$ norm of the forcing term to bound the solution of inhomogeneous equation.
Talk Slides.
Friday, November 22nd:
3:00 PM  Coffee/Snacks in 330 Philips
3:304:30 PM  Lecture 2 from Professor Sogge in 328 Phillips
Talk II: Focal points and supnorms of eigenfunctions.
abstract: If (M,g) is a compact real analytic Riemannian manifold,
we give a necessary and sufficient condition for there to be a
sequence of quasimodes saturating supnorm estimates. The condition
is that there exists a selffocal point x_0 in M for the geodesic
flow at which the associated PerronFrobenius operator U: L^2
(S_{x_0}^* M ) > L^2 (S_{x_0}^* M )
has a nontrivial invariant function. The proof is based on von Neumann's ergodic theorem and stationary phase.
Talk Slides.
4:355:20 PM  2nd 30 minute talk by Min Xue in 328 Phillips 
Title and Abstract.
Talk Slides.
Current Schedule 
Wednesday, October 2nd:
3:30 PM  Coffee/Snacks in 330 Philips
45 PM  Lecture 1 from Professor Zumbrun in 381 Phillips
Talk I: Periodic patterns with conservation laws: the Whitham
equations and rigorous longtime asymptotics.
abstract: Periodic patterns and traveling waves arise quite generally
in optics, biology, chemistry, and many other applications. A great
success story over the past couple decades for the dynamical systems
approach to PDE has been the rigorous treatment of modulation of
periodic patterns in reaction diffusion systems. However, the
techniques used were designed for modulations with a single degree
of freedom. For systems possessing one or more conservation laws,
hence one or more additional degrees of freedom, these methods do
not apply. Here, motivated by applications to thin film flow, we
present an approach applying also to this more general situation,
emphasizing connections to the hyperbolicparabolic ``Whitham
equations'' formally governing slow modulations, and through them an
analogy to viscous shock wave theory.
Talk Slides.
reading list:
arXiv:1105.5040 
Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability by Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, Kevin Zumbrun;
arXiv:1105.5044 
Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation by Mathew Johnson, Pascal Noble, L. Miguel Rodrigues, Kevin Zumbrun;
arXiv:1211.2156 
Behavior of periodic solutions of viscous conservation laws under
localized and nonlocalized perturbations by Mathew A. Johnson, Pascal Noble, L.Miguel Rodrigues, Kevin Zumbrun;
arXiv:1307.6957 
Nonlinear stability of source defects in the complex GinzburgLandau
equation by Margaret Beck, Toan T. Nguyen, Bjorn Sandstede, Kevin
Zumbrun;
PDF File 
Viscoelastic behaviour of cellular solutions to the
KuramotoSivashinsky model by U. Frisch, Z.S. She, O. Thual.
5:005:30 PM  1st 30 minute talk by Blake Barker in 381 Phillips 
"Numerical stability analysis for thin film flow: toward rigorous
verification"
Talk Slides.
Thursday, October 3rd:
3:30 PM  Coffee/Snacks in 330 Philips
45 PM  Lecture 2 from Professor Zumbrun in 332 Phillips
Talk II: Spectral stability analysis I: numerical methods and phenomena in thin film flow.
abstract: Having reduced the study of behavior to the study of
Floquet spectra, we discuss in various numerical methods for
approximating the spectra of general, possibly largeamplitude waves,
and give an overview of numerically observed phenomena in thin film
flow. These include``viscoelastic behavior'' in cellular
KuramotoSivashinsky behavior, ``dispersionenhanced stability,'' and
the ``homoclinic paradox'' in inclined thinfilm flow, the latter
concerning the puzzling phenomenon that asymptotic behavior appears to
consist of solitary waves, despite that solitary waves are readily
seen to be exponentially unstable.
Talk Slides.
reading list:
arXiv:1203.3795 
Nonlinear modulational stability of periodic travelingwave solutions
of the generalized KuramotoSivashinsky equation by Blake Barker, Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues, Kevin Zumbrun;
arXiv:1011.5695 
$2$modified characteristic Fredholm determinants, Hill's method, and
the periodic Evans function of Gardner by Kevin Zumbrun;
arXiv:1008.4729 
Whitham Averaged Equations and Modulational Stability of Periodic
Traveling Waves of a HyperbolicParabolic Balance Law by Blake Barker,
Mathew A. Johnson, Pascal Noble, L.Miguel Rodrigues, Kevin Zumbrun;
arXiv:1007.5262 
Metastability of solitary roll wave solutions of the St. Venant
equations with viscosity by Blake Barker, Mathew A. Johnson, L. Miguel Rodrigues, Kevin
Zumbrun.
5:005:30 PM  2nd 30 minute talk by Soyeun Jung in 332 Phillips 
"Pointwise asymptotic behavior of modulated periodic
reactiondiffusion waves"
Friday, October 4th:
2:303:30 PM  Lecture 3 from Professor Zumbrun in 224 Phillips
Talk III: Spectral stability analysis II: rigorous existence and stability in the weakly unstable regime.
abstract: Finally, we discuss rigorous existence and spectral
stability theory in the ``weakly unstable'' regime at the threshold of
instability of constant (e.g., laminar) solutions, comparing the
classical Turing scenario involving Ginzburg Landau equations and the
familiar Eckhaus stability boundaries to the much more complicated
scenario arising in inclined thin film flow, involving a singularly
perturbed KdV equation and physical wavelengths approaching
infinity.
Talk Slides.
reading list:
arXiv:0006002 
Pattern formation with a conservation law by P. C. Matthews, S. M. Cox;
arXiv:1202.6402 
Spectral stability of periodic wave trains of the Kortewegde
Vries/KuramotoSivashinsky equation in the Kortewegde Vries limit by Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues, Kevin
Zumbrun;
PDF File 
Stability of periodic waves govemed by the modified
Kawahara equation by D.E. Bar, A.A. Nepomnyashchy.
3:304:00 PM  3rd 30 minute talk by Fang Yu in 224 Phillips 
"Stability of supersonic contact discontinuities for three
dimensional compressible steady Euler flows"
4:004:30 PM  Coffee/Snacks in 330 Philips
4:305:30 PM  Tom Beale speaks in the Applied Math Seminar in 332 Phillips 
"Numerical methods for nearly singular integrals and moving interfaces in fluids"