The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2014-04-20webmaster@math.psu.eduSymbolic dynamics for three dimensional flows with positive entropy (joint work with Y. Lima)
http://www.math.psu.edu/seminars/meeting.php?id=20910
Speaker(s): Omri Sarig
Suppose M is a smooth flow on a compact smooth three dimensional manifold M, and suppose \mu is an ergodic invariant measure with positive entropy. We find an invariant set of full measure on which the flow is a finite-to-one factor of a Holder suspension over a countable Markov shift.
This provides symbolic dynamics in the style of Bowen and Ratner for geodesic flows of surfaces, on the part which carries an ergodic measure with positive entropy. The new aspect of our work is that we do not assume negative curvature or uniform hyperbolicity. Applications to closed orbits will be discussed.
This is work in progress with Yuri Lima.2014-04-21T15:35:00Dynamical systems seminartab54@math.psu.eduroyer@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduburago@math.psu.eduViscosity vanishing method for transonic flows (continued)
http://www.math.psu.edu/seminars/meeting.php?id=19948
Speaker(s): Jiequan Li
2014-04-22T10:00:00Hyperbolic and Mixed Type PDEs Seminarzhang_t@math.psu.edu"On ergodicity of geodesic flows and nondense orbits of certain partially hyperbolic systems"
http://www.math.psu.edu/seminars/meeting.php?id=23245
Speaker(s): Weisheng Wu, Advisers: Federico Rodriguez-Herts and Anatole Katok
We present two results on two different dynamical systems with certain hyperbolic behavior. In the first one, we consider the geodesic flows in a rank one surface of nonpositive curvature. While the ergodicity of geodesic flow in surfaces of negative curvature is well known since 1940's by Hopf, the ergodicity in rank one case remains open. We will present a proof of ergodicity in rank one case under a condition. In the second part, we discuss a result on the full Hausdorff dimension of the set of points with nondense forword orbit in partially hyperbolic systems with conformal unstable manifolds. Particularly we will talk about Schmidt games and how to build measures with pointwise dimension converging to dim(M) from a result due to McMullen.2014-04-22T10:00:00Ph.D. Thesis Defensehalpenny@math.psu.eduAction Research Reports
http://www.math.psu.edu/seminars/meeting.php?id=22278
Speaker(s): Tim Slater
2014-04-22T11:30:00Teaching Seminarhager@math.psu.eduConstructions in shifted symplectic geometry
http://www.math.psu.edu/seminars/meeting.php?id=20109
Speaker(s): Tony Pantev
I will introduce a version of algebraic symplectic geometry
that is suitable for dealing with singular or stacky spaces. I will
explain how this generalization arises naturally in the study of
moduli spaces and will outline the connections to ordinary symplectic
geometry. I will also give interesting examples and will describe a
several non-trivial constructions of shifted symplectic structures.
This is a joint work with Toen, Vaquie, and Vezzosi.2014-04-22T14:30:00GAP Seminarping@math.psu.edustienon@math.psu.edudaenzer@math.psu.eduroyer@math.psu.eduhigson@math.psu.eduTBD
http://www.math.psu.edu/seminars/meeting.php?id=20110
Speaker(s): Sankha Basu
2014-04-22T14:30:00Logic Seminarjmr71@math.psu.edusimpson@math.psu.edureimann@math.psu.eduMarkov partitions for three-dimensional flows with positive entropy, I
http://www.math.psu.edu/seminars/meeting.php?id=19973
Speaker(s): Omri Sarig
2014-04-22T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduSpectral Curves of Constant Mean Curvature Tori
http://www.math.psu.edu/seminars/meeting.php?id=21401
Speaker(s): Emma Carberry
Constant mean curvature tori in S ^ 3, R ^ 3 or H ^ 3 are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes. I will address these periodicity questions for the spherical and Euclidean cases, using Whitham deformations, which I will explain.2014-04-23T12:05:00Geometry Luncheon Seminarroe@math.psu.eduburago@math.psu.edukatok_a@math.psu.edutab54@math.psu.eduViscosity vanishing method for transonic flows (continued)
http://www.math.psu.edu/seminars/meeting.php?id=19949
Speaker(s): Jiequan Li
2014-04-24T10:00:00Hyperbolic and Mixed Type PDEs Seminarzhang_t@math.psu.eduThe generator problem for C*-algebras
http://www.math.psu.edu/seminars/meeting.php?id=20111
Speaker(s): Hannes Thiel
The generator problem asks to determine for a given C*-algebra the minimal number of generators, i.e., elements that are not contained in a proper C*-subalgebra. It is conjectured that every separable, simple C*-algebra is generated by a single element. The generator problem was originally asked for von Neumann algebras, and Kadison included it as number 14 of his famous list of 20 “Problems on von Neumann algebras”. The general problem is still open, most notably for the free group factors.
With Wilhelm Winter, we proved that every a unital, separable C*-algebra is generated by a single element if it tensorially absorbs the Jiang-Su algebra. This generalized most previous results about the generator problem for C*-algebra.
In a different approach to the generator problem, we define a notion of `generator rank', in analogy to the real rank. Instead of asking if a certain C*-algebra A is generated by k elements, the generator rank records whether the generating k-tuples of A are dense. It turns out that this invariant has good permanence properties, for instance it passes to inductive limits. It follows that every AF-algebra is singly generated, and even more the set of generators is generic (a dense G_delta-set).2014-04-24T14:30:00Noncommutative Geometry Seminarhigson@math.psu.eduroyer@math.psu.eduroe@math.psu.eduString theory on elliptic curves: topology, algebraic geometry, and physics
http://www.math.psu.edu/seminars/meeting.php?id=20839
Speaker(s): Jonathan Rosenberg
Supersymmetric string theory in 10 dimensions is the leading candidate for a unified theory of all the fundamental forces of nature. For maximal supersymmetry, it is usually assumed that space-time is the product of flat Minkowski spacetime with a compact Calabi-Yau manifold (a complex manifold with trivial canonical bundle). The simplest Calabi-Yau manifold is an elliptic curve, and in joint work with Chuck Doran and Stefan Mendez-Diez of the University of Alberta, we have recently made a thorough study of all "orientifold" string theories on elliptic curves (crossed with flat spacetime). I will explain how our findings illustrate deep connections between algebraic topology, algebraic geometry, and physics.2014-04-24T15:35:00Department of Mathematics Colloquiumhigson@math.psu.eduroyer@math.psu.eduHydrodynamics and collective behavior of the tethered bacterium Thiovulum majus
http://www.math.psu.edu/seminars/meeting.php?id=21363
Speaker(s): Alexander Petroff
The ecology and dynamics of many microbial systems are shaped by how bacteria respond to evolving nutrient gradients and microenvironments. Here we show how the response of the sulfur-oxidizing bacterium Thiovulum majus to changing oxygen gradients cause cells to organize into large-scale fronts. We show that these dynamics occur in two steps. First, chemotactic cells moving up the oxygen gradient form a front that propagates with constant velocity. We then show, through observation and mathematical analysis, that this front becomes unstable to changes in cell density. Random perturbations in cell density create oxygen gradients, which lead to the formation of millimeter-scale fluid flows. We argue that this flow results from a nonlinear instability excited by stochastic fluctuations in the density of cells. These results provide a mathematically tractable example of how collective phenomena in ecological systems can arise from the individual response of cells to a shared resource.2014-04-25T12:00:00Mathematical Biology and Physiology Seminaryuy17@math.psu.edubelmonte@math.psu.edutreluga@math.psu.edusaz11@math.psu.eduliu@math.psu.educhenmx@math.psu.eduA Saddle-Point Formulation And Finite Element Method For The Stefan Problem With Surface Tension
http://www.math.psu.edu/seminars/meeting.php?id=22726
Speaker(s): Shawn Walker
A dual formulation is proposed for the Stefan problem with surface tension (Gibbs-Thomson law). The method uses a mixed form of the heat equation in the solid and liquid domains, and imposes the interface motion law (on the solid-liquid interface) as a constraint. Well-posedness of the time semi-discrete and fully discrete (finite element) formulations is proved in 3-D, as well as an a priori bound, conservation law, and error estimates with low regularity assumptions on the solution. Simulations of interface growth (in two dimensions) are presented to illustrate the method. This is joint work with Christopher Davis (LSU).2014-04-25T14:30:00Complex Fluids Seminartxh35@math.psu.edufuy3@math.psu.eduThe Smoluchowskii-Kramers approximation and the large deviation principle for SPDEs
http://www.math.psu.edu/seminars/meeting.php?id=20029
Speaker(s): Sandra Cerrai
We study the limiting behavior of the large deviation action functional and of the quasi-potential for a stochastic semi-linear wave equation in presence of a small mass. We show that the small noise asymptotic (large deviation) is consistent with the small mass asymptotic (Smoluchowskii-Kramers approximation).2014-04-25T15:35:00Probability and Financial Mathematics Seminarmazzucat@math.psu.eduroyer@math.psu.edunistor@math.psu.edudenker@math.psu.eduanovikov@math.psu.edu