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Eberly College of Science Mathematics Department

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November 3rd, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Aerodynamic Design Optimization by A Continuous Adjoint Method
Speaker: Feng Liu, University of California, Irvine (Host: J Xu)
Location: MB114
Abstract: http://fliu.eng.uci.edu

I will present our latest research progress on the development of a continuous adjoint method to perform aerodynamic design optimization of wings and turbomachinery blade rows. This method requires only about twice the computational effort of flow calculation to obtain the complete gradient information at each operating condition, regardless of the number of design parameters. Therefore, it is orders-of-magnitude more efficient than a conventional finite-difference method for obtaining the gradient information in a optimization procedure when the design parameters are in the hundreds and more. Examples of single and multiple-point design of transonic wings and turbomachinery blade rows will be presented.

November 3rd, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Multiple Numerical Solutions and Stability of Transonic Flows over Airfoils
Speaker: Feng Liu, University of California, Irvine (Host: J Xu)
Location: MB106
Abstract: http://fliu.eng.uci.edu

Following a general presentation on the numerical simulation of steady and unsteady transonic flows over wings and turbomachinery blade rows by using computational fluid dynamics, I will focus on the findings of multiple numerical solutions for the Transonic Small-Disturbance equation and the Euler equations. Both symmetric and asymmetric solutions are possible for a symmetric airfoil at zero angle of attack within a certain free-stream Mach number range. The stability of the multiple solutions is analyzed using numerical methods. It is found, the symmetric solutions tend to be unstable, while the asymmetric solutions are stable. I will discuss the relevance of such stability analysis to the intrinsic unsteady behavior of transonic buffet over airfoils and wings.

November 3rd, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Krieger's finite generator theorem for ergodic actions of countable groups
Speaker: Brandon Seward, University of Michigan
Location: MB114

The classical Krieger finite generator theorem states that if a free ergodic probability-measure-preserving action of Z has entropy less than log(k), then the action admits a generating partition consisting of k sets. This was extended to actions of amenable groups independently by Rosenthal and Danilenko-Park. We introduce the notion of Rokhlin entropy which is defined for actions of arbitrary countable groups. In the case of actions of amenable groups, Rokhlin entropy coincides with classical entropy and can thus be viewed as a natural extension of classical entropy. Using this notion of entropy, we prove Krieger's finite generator theorem for actions of arbitrary countable groups.

November 4th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Double-Feature: The Geometry of Restricted Partitions and A Supercrank for P(n,3) modulo Primes of the form 6j - 1.
Speaker: Brandt Kronholm and Felix Breuer
Location: MB106
November 4th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: The compactness theorem for continuous model theory
Speaker: Jake Pardo, Penn State
Location: MB315

The talk will present a proof of the compactness theorem for continuous logic, using ultraproducts of metric spaces.

November 4th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Cocycle Reduction and Exponential Drift
Speaker: Alex Eskin, University of Chicago
Location: MB114

I will be discussing how some cocycle reduction results can be combined with the exponential drift technique of Benoist-Quint to prove some measure rigidity results, in particular for the SL(2,R) action on moduli space. This is joint work with Maryam Mirzakhani. Note: this talk will be self-contained, and no knowledge of Teichmuller theory will be assumed (or needed).

November 4th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Pointwise convergence of multiple ergodic averages and strictly ergodic models
Speaker: Xiangdong Ye, University of Science and Technology of China
Location: MB216

In this talk we discuss the pointwise convergence. By building some suitable strictly ergodic models, we prove that for an ergodic system $(X,\mathcal{X},\mu, T)$, $d\in\N$, $f_1, \ldots, f_d \in L^{\infty}(\mu)$, the averages $$\frac{1}{N^2} \sum_{(n,m)\in [0,N-1]^2} f_1(T^nx)f_2(T^{n+m}x)\ldots f_d(T^{n+(d-1)m}x)$$ converge $\mu$ a.e. Deriving some results from the construction, for distal systems we answer positively the question if the multiple ergodic averages converge a.e. That is, we show that if $(X,\mathcal{X},\mu, T)$ is an ergodic distal system, and $f_1, \ldots, f_d \in L^{\infty}(\mu)$, then the multiple ergodic averages $$\frac 1 N\sum_{n=0}^{N-1}f_1(T^nx)\ldots f_d(T^{dn}x)$$ converge $\mu$ a.e.. The two talks are mainly based on the following papers. a. S. Shao and X.Ye, Regionally proximal relation of order d is an equivalence one for minimal systems and a combinatorial consequence,Adv. in Math.,231(2012), 1786-1817. b. W. Huang, S. Shao and X. Ye,Nil Bohr-sets and almost automorphy of higher order, arXiv:1407.1179v1[math.DS], Memoirs of Amer. Math. Soc., to appear. c. W. Huang, S. Shao and X Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models, arXiv:1406.5930v1[math.DS], submitted.

November 4th, 2014 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Extremality, uniqueness and optimality of transference plans.
Speaker: Stefano Bianchini, SISSA, Italy
Location: MB106

For the transportation problem \[ \inf \int c(x,y) \pi \] where $\pi$ (the transference plan) is a probability measure with given marginals, and $c$ is a Borel cost, we are interested in the characterization of the minimizers (optimal plans). Analogous problems are the characterization of extremal points of the set of transference plans and its uniqueness. Even if the result is measure theoretic, it has applications to the solution of the Monge problem (existence of an optimal map) for convex l.s.c. costs.

November 5th, 2014 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Inference using noisy degrees: Differentially Private beta-model and synthetic graphs
Speaker: Sesa Slavkovic, Penn State
Location: MB106

The β-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. Motivated by data privacy problems with network data, we present a differentially private estimator of the parameters of β-model. We show that the estimator is asymptotically consistent and achieves the same rate as the non private estimator. Our techniques involve releasing the degree sequence using Laplace mechanism and constructing a maximum likelihood estimate of the degree sequence, which is equivalent to projecting the noisy degree sequence on the set of all graphical degree sequences. We present an efficient algorithm for the projection which also outputs a synthetic graph. Our techniques can also be used to release degree distributions accurately and privately, and to estimate noisy degrees arising from contexts other than the privacy. We evaluate the proposed estimator on real graphs and compare it with a current algorithm for releasing degree distributions and find that it does significantly better.

November 5th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Some results on the compressible Navier-Stokes equations with density-dependendt viscosity (part II)
Speaker: Mingjie Li, Minzu University of China
Location: MB106

We talk about some a priori estimations on the 1D compressible Navier-Stokes equations with density-dependendt viscosity which based on the special structure of equations. From these estimations we can study the behavior of vacuum state and blow up phenomena of the flow. Then we extend these a priori estimations into Multi-Dimensional case.

November 5th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Proficiency to Mastery (Week 1 of 3)
Speaker: Attendees, Penn State
Location: MB102

For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read the description of proficiency from Adding It Up.
Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy, 2001. 115-35. Print.

November 5th, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Around basics of h-principle and iots applications to symplectic topology II
Speaker: Alena Erchenko, Penn State
Location: MB114

his is the second talk on the subjet. Even though h-principle originated from Nash's embedding theorems and Gromov's book "Partial Differential Relations",the easiest applications are to symplectic topology. We follow books by Eliashberg and McDuff et al. Our goal is not to nearly cover the subject but to spark interest towards this very impressive set of ideas and techniques in (geometric) PDE and PD inequalitiues.

November 5th, 2014 (05:01pm - 06:01pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: moment map and representation theory II
Speaker: Ehssan Khanmohammadi
Location: MB216

Dear all, Tomorrow I will continue with the second part of my talk on the momentum map. Best wishes, Ehssan

November 6th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Portraits of rational functions modulo primes
Speaker: Tom Tucker, University of Rochester
Location: MB106

Let F be a rational function of degree > 1 over a number field or function field K and let z be a point that is not preperiodic. Ingram and Silverman conjecture that for all but finitely many positive integers (m,n), there is a prime p such that z has exact preperiodic m and exact period n (we call this pair (m,n) the portrait of z modulo p). We present some counterexamples to this conjecture and show that a generalized form of abc implies -- one that is true for function fields -- implies that these are the only counterexamples. One may also ask a similar question for tuples of portraits for several point in a number field or function field. This work is still in progress. The talk represents joint work with several other authors.

November 6th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Solutions to polynomials in two variables
Speaker: Thomas Tucker, University of Rochester
Location: MB114

You may remember the quadratic formula for finding solutions to quadratic polynomials in one variable. It is natural to ask: are there formulas like this for polynomials of higher degree? The answer, roughly speaking, is yes. Going further, one might ask: what about polynomials in more than one variable? Here, the answer is far more complicated, and involves geometry in what may seem a surprising way. One famous example of this type of polynomial equation is the Fermat equation x^n + y^n = z^n.

November 7th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Some error bounds for the finite element approximation to the steady-state Poisson-Nernst-Planck equations
Speaker: Ying Yang, Guilin University of Electronic Technology
Location: MB315

In this talk, we first discuss a two-grid method for the steady-state Poisson-Nernst-Planck (PNP) equations in the biomolecular modeling area. It is a coupled, nonlinear and singular system. We can decouple this system by the two-grid method which can avoid the divergence of coupled iterations for the original system. Secondly we will present some finite element error bounds for PNP equations including the local and global L2 norm and H1 norm error bounds.

November 7th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Limit distribution of return times to shrinking targets
Speaker: Xuan Zhang, PSU
Location: MB106

We revisit the problem of finding limit exponential laws for return times to shrinking targets and study a more general problem of finding limit distribution for stopping times when partial sums of bounded positive functions exceed a threshold. We give a sufficient condition for the limit distribution of these stopping times to exist and discuss some examples.

November 10th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Block Preconditioning for Multi-physics: From Jacobi to Schur Complements
Speaker: Eric Cyr, Sandia National Laboratory (Host: J Xu)
Location: MB114

Developing scalable solvers for fully-coupled multi-physics is challenging. One approach is to use advanced multigrid algorithms to achieve scalability on these problems. However, this approach can suffer from stability issues, in particular the coarse grid operators used in AMG can become ill-conditioned. An alternative to fully-coupled multigrid is to use a block decomposition of the linear system. This segregates the linear system into physical fields. For instance separating Navier-Stokes into velocity and pressure components leads to a 2x2 Jacobian operator. These approaches are appealing because segregated operators are more amenable to multigrid, yet achieving good parallel scalability for the coupled system is still possible. The difficulty with these methods is efficiently and effectively handling the coupling between the different physics. In this talk I will overview a number of block preconditioners focusing on exploiting the structure of the operators. Furthermore, I will present a few techniques for approximating Schur-complement operators. To make this concrete, applications in fluid dynamics and magnetohydrodynamics will be discussed.

November 10th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Scalable Implicit Resistive MHD with Stabilized Finite Element Methods and Fully-Coupled Newton-Krylov-AMG Solution Methods
Speaker: John Shadid, Sandia National Laboratory (Host: J Xu)
Location: MB106

The resistive magnetohydrodynamics (MHD) model describes the dynamics of charged fluids in the presence of electromagnetic fields. MHD models are used to describe important phenomena in the natural physical world and in technological applications. This model is non-self adjoint, strongly coupled, highly nonlinear and characterized by multiple physical phenomena that span a very large range of length- and time-scales. These interacting, nonlinear multiple time-scale physical mechanisms can balance to produce steady-state behavior, nearly balance to evolve a solution on a dynamical time-scale that is long relative to the component time-scales, or can be dominated by just a few fast modes. These characteristics make the scalable, robust, accurate, and efficient computational solution of these systems extremely challenging. For multiple-time-scale systems, fully-implicit methods can be an attractive choice that can often provide unconditionally-stable time integration techniques. The stability of these methods, however, comes at a very significant cost, as these techniques generate large and highly nonlinear sparse algebraic systems of equations that must be solved at each time step. This talk describes the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for 3D resistive MHD. The brief discussion considers the development of the stabilized / variational multiscale (VMS) FE formulation and the underlying fully-coupled preconditioned Newton-Krylov (NK) nonlinear iterative solver. The VMS formulation and the fully- coupled NK solution methods allow the simulation of flow systems that range from incompressible to low Mach number compressible flows, as well as the development of a number of solution methods beyond forward simulation. The solution methods include parameter continuation, bifurcation, optimization, and adjoint-based methods for sensitivity analysis, error-estimation and UQ. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled multilevel preconditioners are developed. The multilevel preconditioners are based on two differing approaches. The first technique employs a graph-based aggregation method applied to the nonzero block structure of the Jacobian matrix. The second approach utilizes approximate block decomposition methods and physics-based preconditioning approaches that reduce the coupled systems into a set of simplified systems to which multilevel methods are applied. To demonstrate the capability of these approaches representative results are presented for the solution of challenging prototype MHD problems. These include duct flows, an unstable hydromagnetic Kelvin-Helmholtz shear layer, and an island coalescence problem used to model magnetic reconnection. In this context robustness, efficiency, and the parallel and algorithmic scaling of solution methods are discussed. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.

November 10th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Orbits closures for the action of SL(2,R) on moduli spaces.
Speaker: Amir Mohammadi, University of Texas, Austin
Location: MB114

There is an action of SL(2,R) on the moduli space of a compact Riemann surface which is expected to have similar rigidity properties as in the theory of unipotent flows on homogeneous spaces. In this talk we will discuss a joint work with Eskin and Mirzakhani in which orbits closures of this action are studied. The main ingredients are a measure rigidity theorem of Eskin and Mirzakhani, and a certain avoidance principle which we develop using ideas of Margulis.

November 11th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: A variational time discretization for Euler equations
Speaker: Fabio Cavalletti, Scuola Normale Superiore, Pisa
Location: MB216

I will present a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the acceleration of fluid elements, over the cone of monotone transport maps. We prove convergence to measure-valued solutions for the pressureless gas dynamics and the compressible Euler equations. This is a joint work with Marc Sedjro and Michael Westdickenberg.

November 11th, 2014 (01:00pm - 01:50pm)
Seminar: Mathematical Biology Colloquium
Title: Cell motility as a free boundary problem
Speaker: Alex Mogilner, Courant Institute, NYU
(Host: Leonid Berlyand)
Location: MB106

Cells migrate on surfaces by protruding their front through growth of actin networks, retracting the rear by myosin-driven contraction and adhering to the substrate. Recent experimental and modeling efforts elucidated molecular and mechanical processes that allow motile cells to maintain steady shape and speed. These processes are multiple and redundant, and the challenge is to understand how molecular machines operating on multiple scales synergize to initiate motility and allow the cell to move steadily or to turn. Mathematically and mechanically, the cell is a contractile and viscous actomyosin gel with free boundary. I will describe modeling of the simplest motile cell, fish keratocyte, and discuss future challenges in simulating more complex cells.

November 11th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Integration of singular foliations and usage
Speaker: Iakovos Androulidakis, University of Athens
Location: MB106

We discuss two aspects of integration, one in the (classical) spirit of Sophus Lie and the other in the framework of operator algebras. Starting from the context of regular foliations, we explain the evolution of these processes first to the almost regular case by C. Debord, and finally to singular foliations in full generality (joint work with G. Skandalis). We also give the use of these integration processes; the first integration provides a normal form of the foliation around a (singular) leaf, and the second leads to calculations of the spectrum for longitudinal Laplace operators.

November 11th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: The compactness theorem for continuous model theory (II)
Speaker: Jake Pardo, Penn State
Location: MB315

This talk continues the discussion of the compactness theorem for continuous model theory.

November 12th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: PDE models for Ferrofluids and their Numerical Analysis
Speaker: Ignacio Tomas, University of Maryland
Location: MB106

A ferrofluid is a liquid which becomes strongly magnetized in the presence of applied magnetic fields. In this talk we will survey some models for ferrofluids: their physical origins, PDE models, and related numerics. There are two generally accepted ferrofluid models which we will call by the name of their developers: the Rosensweig and Shliomis model. We will start by developing a numerical scheme for the Rosensweig model and carefully track the requirements to devise of an energy-stable scheme. Both the Rosensweig and Shliomis models deal with one-phase flows, which is the case of many technological applications. However, many applications arise naturally in the form of a two-phase flow: one of the phases has magnetic properties and the other one does not (e.g. magnetic manipulation of microchannel flows, microvalves, magnetically guided transport, etc). We have also developed a matching-density two-phase ferrofluid model starting from the simplified framework of the Shliomis model and the Cahn-Hilliard equation. This model satisfies an energy law, and with the lessons learned from the Rosensweig model, we were able to devise an energy-stable scheme. In addition, with some simplifications of the two-phase model, it is possible to prove convergence of the scheme, and as a by product, existence of solutions of the simplified PDE system. Finally, I will illustrate the capabilities of the numerical schemes with some numerical simulations.

November 12th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Proficiency to Mastery (Week 2 of 3)
Speaker: Attendees, Penn State
Location: MB102

For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we consider if students are proficient based on results summarized in Adding It Up.
Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy, 2001. 136-55. Print.

November 12th, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Odd Khovanov homology, its applications, and related knot invariants.
Speaker: Aleksander Shumakovitch, George Washington University\
Location: MB114

We start with describing an odd version of the Khovanov homology recently introduced by Ozsvath, Rasmussen and Szabo. We discuss its properties that, despite similar definitions, appear to be drastically different from those of the ordinary (even) Khovanov homology. We then present several applications of the odd Khovanov homology to geometry, such as finding upper bounds for the Thurston-Bennequin number, detecting quasi-alternating knots, and (conjecturally) detecting transversely non-simple knots. Finally, we consider several homological operations that can be defined between even and odd Khovanov homology theories using the unified even/odd Khovanov homology theory developed by Krzysztof Putyra. We show how these homological operations give rise to new knot invariants with interesting properties.

November 13th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Quadratic Glimm Functional for general hyperbolic systems of conservation laws
Speaker: Stefano Modena, SISSA, Trieste
Location: MB216

I will present the construction of a new quadratic Glimm functional Q for an approximate solution, obtained by the Glimm scheme [3], to the Cauchy problem associated to a general hyperbolic system of conservation laws u_t + f(u)_x = 0, without any additional assumption on f besides the strict hyperbolicity. The definition of Q is based on a wave tracing algorithm, which splits each wavefront in the approximate solution into infinitesimal waves and thus it turns out to be dissimilar from the other ones already present in the literature (see for example [4]). Differently from the other Glimm-type functionals already known (see [3], [1]), our functional bounds the total variation in time of the speed of each infinitesimal wave, thus providing, by well known arguments (see [2]), together with the fact that Q has bounded total variation in time, the key step to obtain a sharp convergence rate of the Glimm scheme. One of the main features of Q is its non-locality in time, which requires a deep analysis of the past history of each pair of infinitesimal waves present in the approximate solution. REFERENCES [1] S. Bianchini, Interaction Estimates and Glimm Functional for General Hyperbolic Systems, Discrete and Continuous Dynamical Systems (9) (2003), 133-166. [2] A. Bressan, A. Marson, Error Bounds for a Deterministic Version of the Glimm Scheme, Arch. Rational Mech. Anal. (142) (1998), 155-176. [3] J. Glimm, Solutions in the Large for Nonlinear Hyperbolic Systems of Equations, Comm. Pure Appl. Math. 18 (1965), 697-715. [4] T.P. Liu, The deterministic version of the Glimm Scheme, Comm. Math. Phys., (57) (1975) 135-148.

November 13th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The Entropy of Schur-Weyl measures
Speaker: Sevak Mkrtchyan, University of Rochester
Location: MB106

We will study local and global statistical properties of Young diagrams with respect to a Plancherel-type family of measures called Schur-Weyl measures and use the results to answer a question from asymptotic representation theory. ore precisely, we will solve a variational problem to prove a limit-shape result for random Young diagrams with respect to the Schur-Weyl measures and apply the results to obtain logarithmic, order-sharp bounds for the dimensions of certain representations of finite symmetric groups.

November 13th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Lengthening the edges of a tetrahedron
Speaker: Richard Schwartz, Brown University
Location: MB114

I'll describe what happens to the volume of a tetrahedron when one lengthens some or all of the edges of the tetrahedron. The analysis involves the Cayley-Menger determinant, a computer algorithm for certifying that a polynomial is positive on a simplex, and a very pretty triangulation of the moduli space of "tetrahedron-like" labelings of the complete graph on 4 vertices.

November 13th, 2014 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Singular subalgebroids
Speaker: Iakovos Androulidakis, University of Athens
Location: MB216

Recently Gualtieri and Li gave a symplectic realization for Log-symplectic manifolds by deploying the "blow-up" construction used by Melrose. In this talk we introduce singular subalgebroids and their integration. Log-symplectic manifolds are instances of singular subalgebroids, and we show that in this context the above symplectic realization is really a holonomy groupoid. The basic ingredient of our constructions is the notion of a bisubmersion. At the end of the talk we discuss how bisubmersions allow the construction of the C*-algebra of any Lie algebroid (possibly non-integrable). This is joint work with Marco Zambon (Leuven).

November 13th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: The projective heat map acting on pentagons
Speaker: Richard Schwartz, Brown University (Host: Mark Levi)
Location: MB114

I will describe a straight-line construction in which > one starts with an N-gon P and produces a new N-gon P'. The > operation is projectively natural - i.e. commutes with projective > transformations - and also has some resemblance to heat flow. I'll > give some computer demonstrations showing what this map appears to > do in general, and then sketch a proof of what happens for pentagons.

November 14th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: An Unfitted Hp-Interface Penalty Finite Element Method For Elliptic Interface Problems
Speaker: Yuanming Xiao, Nanjing University
Location: MB315

An hp version of interface penalty finite element method (hp-IPFEM) is proposed for elliptic interface problems in two and three dimensions on unfitted meshes. Error estimates in broken H1 norm, which are optimal with respect to h and suboptimal with respect to p by half an order of p, are derived. Both symmetric and non-symmetric IPFEM are considered. Error estimates in L2 norm are proved by the duality argument.

November 14th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Convergence of stochastic processes to Brownian local time
Speaker: Xiaofeng Zheng, PSU
Location: MB106

I will introduce some results about the convergence of various sequences of processes describing the behavior of Brownian trajectories near the level x at the instant t to Brownian local time. We are also interested in the question whether local time of random walks can be convergent to Brownian local time almost surely. Peter Morters and Yuval Peres gave a positive answer to the subsequence of local time of random walks case by embedding method, which will also be discussed.

November 17th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: An Unfitted hp-Interface Penalty Finite Element Method For Elliptic Interface Problems
Speaker: Yuanming Xiao, Nanjing University
Location: MB106

An hp version of interface penalty finite element method (hp-IPFEM) is proposed for elliptic interface problems in two and three dimensions on unfitted meshes. Error estimates in broken H1 norm, which are optimal with respect to h and suboptimal with respect to p by half an order of p, are derived. Both symmetric and non-symmetric IPFEM are considered. Error estimates in L2 norm are proved by the duality argument.

November 17th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Flat surfaces, Bratteli diagrams and adic transformations
Speaker: Rodrigo Treviño, Cornell University
Location: MB114

I will survey some recent developments in the theory of flat surfaces of finite area and translation flows, including both compact and (infinite genus) non-compact surfaces. In particular, I will concentrate on a new point of view based on a joint paper with K. Lindsey, where we develop a close connection of Bratteli diagrams and flat surfaces. I will also state a criterion for unique ergodicity in the spirit of Masur's criterion which holds in this very general setting and which implies Masur's criterion in moduli spaces of (compact) flat surfaces.

November 18th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Results on simultaneous core partitions
Speaker: Dr. Rishi Nath, York College, CUNY
Location: MB106

Simultaneous core partitions were first investigated in 1999 by J. Anderson. A recent conjecture by D. Armstrong on the average size of a simultaneous (s,t)-core; and subsequent work by R. Stanley and F. Zanello on the (s, s+1) (Catalan) case has renewed interest in this area. We will survey the main results in the field--highlighting connections with posets, actions of the affine symmetric group, and the GBG-rank--and offer new results on simultaneous (s, s+2)-cores.

November 18th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: TBA
Speaker: TBA
Location: MB106
November 18th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: The symplectic displacement energy
Speaker: Augustin Banyaga, Penn State
Location: MB106

We show that the symplectic displacement energy of a non-empty open subset of a compact symplectic manifold (i.e. the infimum of the Hofer-like norms of symplectic diffeomorphisms that displace the subset) is a strictly positive number. We apply this fact to prove a result that justifies the introduction of the notion of strong symplectic homeomorphisms. This is a joint work with David Hurtubise and Peter Spaeth.

November 18th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Connectives and Constructions in Model Theory for Metric Structures
Speaker: Jason Rute, PSU
Location: MB315

This is a continuation in the series on Model Theory for Metric Structures. This week we will talk about how to express certain types of properties in the language of metric structures, namely existential properties and implications between properties. In addressing this topic we will discuss logical connectives, Lowenheim-Skolem, saturated models, strong-homogeneous models, and equivalent ways to express implication.

November 18th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Free Products as Topological Groups in Dynamics,I
Speaker: Kurt Vinhage, Penn State
Location: MB216

In the study of partially hyperbolic homogeneous systems, the Lyapunov manifolds become cosets of unipotent subgroups and their free product appears as a natural object of study. At best, the natural topology of such a free product can be described as unpleasant, with key properties like local compactness and first countability failing. In these talks, we will see how dynamical and topological arguments can be used to tame these complexities, leading to a local rigidity result. In particular, we will see two powerful and classical theorems on topological groups appear (one of Montgomery-Zippin and another of Gleason-Palais), and prove one of them. Time-permitting, we will see how free products may also appear in a non-homogeneous setting.

November 18th, 2014 (03:35pm - 04:25pm)
Seminar: Center for Interdisciplinary Mathematics Seminar
Title: Motility at microscopic scales
Speaker: Antonio De Simone, International School for Advanced Studies, Trieste, Italy
Location: MB114
Abstract: http://

Motility of cells is at the root of many fundamental processes in biology: from sperm cells swimming to fertilize an egg cell, to leukocytes migrating towards newly opened wounds to activate the response of the immune, to metastatic tumor cells crawling to invade nearby tissues. We will discuss the mechanical bases of cellular motility by swimming and crawling. Special emphasis will be placed on the connections between low Reynolds number swimming and Geometric Control Theory, and on the geometric structure of the underlying equations of motion. We will then examine some concrete example, taken from the case studies that have been recently considered by our group and including: reverse engineering of the euglenoid movement, undulatory locomotion of snake-like robots, and one-dimensional models of slender crawlers. Finally, we will re-examine the lessons learned in the context of biological cell motility with the aim of building a dictionary of elementary motility mechanism to be used in prototypes of bio-inspired motile micro-robots.

November 19th, 2014 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Curvature constraints of a stressed pancake
Speaker: Marta Lewicka, U Pittsburgh
Location: MB114
November 19th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Proficiency to Mastery (Week 3 of 3)
Speaker: Attendees, Penn State
Location: MB102

For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read about Mastery from How Learning Works.
Ambrose, Susan A. "How Do Students Develop Mastery." How Learning Works: Seven Research-based Principles for Smart Teaching. San Francisco, CA: Jossey-Bass, 2010. 91-120. Print.

November 20th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Zagier polynomials and modified N\"{o}rlund polynomials
Speaker: Atul Dixit
Location: MB106

In 1998, Don Zagier studied the numbers B_{n}^{*} which he called the 'modified Bernoulli numbers'. They satisfy amusing variants of the properties of the ordinary Bernoulli numbers. Recently, Victor H. Moll, Christophe Vignat and I studied an obvious generalization of the modified Bernoulli numbers, which we call 'Zagier polynomials'. These polynomials are also rich in structure, and we have shown that a theory parallel to that of ordinary Bernoulli polynomials exists. Zagier showed that his asymptotic formula for B_{2n}^{*} can be replaced by an exact formula. In an ongoing joint work with M. L. Glasser and K. Mahlburg, we have shown that a similar thing is true for the Zagier polynomials. This exact formula involves Chebyshev polynomials and infinite series of Bessel function $Y_{n}(z)$. Through a motivation coming from diffraction theory, C. M. Linton has already proved this, but in a disguised form, and our proof is new and gives new results along the way. We also derive Zagier's formula as a limiting case of this general formula, which is interesting in itself. In the second part of my talk, I will discuss another generalization of the modified Bernoulli numbers that we recently studied along with A. Kabza, namely 'modified N\"{o}rlund polynomials' B_{n}^{(\alpha)*}, \alpha\in\mathbb{N}, and obtain their generating function along with applications.​ The talk will include an interesting mix of special functions, number theory, probability and umbral calculus.

November 20th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: PDE models of traffic flow
Speaker: Alberto Bressan, Penn State University
Location: MB114

Daily traffic patterns are the result of a large number of individual decisions, where each driver chooses an optimal departure time and an optimal route to reach destination. From a mathematical perspective, traffic flow can be modeled by a family of conservation laws, describing the density of cars along each road. In addition, one can introduce a cost functional, accounting for the time that each driver spends on the road and a penalty for late arrival. In this talk I shall explain how to construct solutions of these PDEs, and discuss the existence of (i) globally optimal solutions, minimizing the sum of the costs to all drivers, and (ii) Nash equilibria, where no driver can lower his individual cost by changing his own departure time, or the route taken to destination. An intriguing mathematical problem is to understand the dynamic stability of Nash equilibria. In this direction, some numerical experiments and conjectures will be presented.

November 21st, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Characterization of stationary distributions of reflected diffusions
Speaker: Weining Kang, University of Maryland
Location: MB106

In this talk I will focus on a characterization of stationary distributions of reflected diffusions that arise as approximations to stochastic systems commonly from telecommunications and manufacturing, etc. I will describe the extended Skorokhod problem formulation and the submartingale problem formulation of the class of reflected diffusions and explore their connections. Also I will discuss how their connections can be used to give a characterization of their stationary distributions and how this characterization can be used to compute those stationary distributions. Some additional applications of this characterization will also be discussed.

November 24th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Fall Break, No Seminar
Speaker: Fall Break, No Seminar
Location: MB114
November 24th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Fall Break, No Seminar
Speaker: Fall Break, No Seminar
Location: MB106
November 27th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No meeting
Speaker: Mr Turkey, Thanksgiving
Location: MB106
November 27th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Thanksgiving Break
Speaker: Thanksgiving Break
Location: MB114