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Eberly College of Science Mathematics Department

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September 3rd, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Organizational meeting
Speaker: Yuxi Zheng, Penn State
Location: MB216
September 3rd, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Forcing for basis theorems
Speaker: John Pardo, Pennsylvania State University
Location: MB315

The technique of forcing, primarily known for its applications in set theory, has proven to be quite useful in computability theory as well. I will discuss how forcing is made effective in the computable sense, as well as use this technique to prove the Low Basis Theorem, the Hyperimmune Free Basis Theorem, and the Cone Avoidance Basis Theorem, all of which are due to Jockusch and Soare.

September 3rd, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: On subadditivity of Kodaira dimension in positive characteristic
Speaker: Zsolt Patakfalvi, Princeton University
Location: MB106

Kodaira dimension is a fundamental (if not the most fundamental) birational invariant of algebraic varieties. It assigns a number between 0 and the dimension or negative infinity to every birational equivalence class of varieties. The bigger this number is the more the variety is thought of as being "hyperbolic". Subadditivity of Kodaira dimension is a conjecture of Iitaka stating that for an algebraic fiber space f : X -> Y, the Kodaira dimension of the total space is at least as big as the sum of the Kodaira dimensions of the generic fiber and the base. I will present a positive answer to the above conjecture over a field of positive characterisitc, when Y is of general type, f is separable and the Hasse-Witt matrix of the generic fiber is not nilpotent.

September 3rd, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Ergodicity of irrational billiards, II
Speaker: Giovanni Forni, University of Maryland
Location: MB216
September 4th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Smooth conjugacy for Anosov automorphisms: a new bootstrap argument.
Speaker: Andrey Gogolev, SUNY- Binghamton
Location: MB114

Let L be an Anosov diffeomorphism of a 3-torus with real spectrum and let f be a small perturbation. Then the spectra of the differential at periodic points of f give obstructions to smooth conjugacy between f and L. We will present a new bootstrap scheme that yields a C^infinity smooth conjugacy between f and L, provided vanishing of obstructions and a mild spectral gap assumption on L. This builds upon and improves an earlier result of Guysinsky and myself.

September 5th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: A generic vanishing theorem in positive characteristic (joint work with Christopher Hacon)
Speaker: Zsolt Patakfalvi, Princeton University
Location: MB106

I will present a generic vanishing type theorem in positive characteristic. I will also introduce a new invariant the S-Kodaira dimension which can be thought of as the Frobenius stable Kodaira dimension. Example applications of the above mentioned generic vanishing type theorems, that I will present, are: 1.) if the S-Kodaira dimension of a smooth variety  X over an algebraically closed field of positive characteristic is zero then the Albanese morphism of X is surjective. In particular, the first Betti number of X is at most the dimension of X 2.) a characteriztaion of smooth projective varieties birational to ordinary abelian varieties. 

September 5th, 2013 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Mathematics through physics
Speaker: Mark Levi, Penn State University
Location: MB114

Physics often provides mathematics not only with a problem, but sometimes also with the idea of a solution. Some calculus problems can be solved by a physical argument more quickly and easily than by the "standard" approach used in college courses. This simplification can be quite striking in some cases. Quite a few theorems which may seem somewhat mysterious become completely obvious when interpreted physically (the trick is to find a suitable interpretation). This is the case for some “elementary” theorems (the Pythagorean Theorem, Pappus' theorems, some trig identities (e.g., cos(x+y)=..., Euler's famous formula V-E+F=2, and more) and for some less elementary ones (no familiarity with any of these is assumed): Green's theorem, the Riemann Mapping Theorem, the Gauss-Bonnet theorem, Noether's theorem on conserved quantities, Poincare integral invariance, and more. I will describe a miscellaneous sampling of problems according to the audience's preferences.

September 5th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Index functionals on uniform K-homology
Speaker: Alexander Engel, University of Augsburg
Location: MB106

In 1988 John Roe generalized the Atiyah-Singer index theorem to certain non-compact manifolds (concretely, to amenable ones). In this version of the index theorem the analytical index of a Dirac operator lives in the K-theory of the nowadays so called uniform Roe algebra and then functionals on this K-group are constructed to compare the analytical index to the topological one. In 2009 Jan Spakula constructed a uniform version of K-homology which admits an assembly map into the K-theory of the uniform Roe algebra (an analogue of the coarse Baum-Connes assembly map). The goal of this talk is to give a construction of index functionals on the uniform K-homology such that the diagram consisting of the uniform assembly map and the corresponding index functionals commutes.

September 5th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

September 6th, 2013 (12:00pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Space-Time Moving Finite Element Methods for Convection-Dominated Problems
Speaker: Maximilian Metti, Penn State University
Location: MB315

This is a study of certain moving finite element methods designed for convection-dominated, time-dependent partial differential equations. These methods can lead to significant savings in computation costs for problems having solutions that develop steep moving fronts or other localized time-dependent features. A symmetric error bound is proven for a particular class of time-integrators and numerical results are also presented.

September 9th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: A brief introduction to conservation law models
Speaker: Wen Shen, Penn State
Location: MB114

In this lecture I will give some basics on hyperbolic conservation laws and give several examples in traffic flow and granular flow.

September 9th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Modeling Traffic Flow on Networks
Speaker: Alberto Bressan, Penn State
Location: MB106
Abstract: http://www.math.psu.edu/bressan/

This talk will review some basic models describing traffic flow on a network of roads. Microscopic (ODE) and macroscopic (PDE) models of vehicle flow will be presented, together with boundary conditions to be imposed at road intersections. Here a key issue is to identify suitable Riemann solvers, which yield existence and uniqueness of solutions to the Cauchy problem, continuously depending on parameters. The existence and stability of Nash equilibria, where each driver chooses an optimal departure time and route to destination in order to minimize his own cost, will be also discussed. A large portion of the talk will be devoted to open problems and research directions.

September 9th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Laplacian and dynamics in Finsler geometry
Speaker: Thomas Barthelmé, Penn State
Location: MB114

In Riemannian geometry, there are a lot of links between the geometry and dynamics of a metric and the Laplace-Beltrami operator. In this talk, I will present Finsler geometry, a generalisation of Riemannian geometry, and introduce a well-suited Laplacian operator. I will then focus on negatively curve manifolds and give some results and questions on the relationships between geometry and Laplacian.

September 10th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Basics on mixed type PDEs
Speaker: Jiequan Li, Beijing normal university
Location: MB216
September 10th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: The reverse mathematics of Ramsey's Theorem: an overview
Speaker: John Pardo, Pennsylvania State University
Location: MB315

Combinatorial principles have proven to be of great interest in reverse mathematics, and Ramsey's Theorem is no exception. I will explain what reverse mathematics is, as well as give a survey of the reverse mathematical and computability-theoretic results surrounding Ramsey's Theorem.

September 10th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Relative Duflo Isomorphism and Representation Theory through Quantization
Speaker: Panagiotis Batakidis, Penn State
Location: MB106

After a review of the classical Duflo Theorem, we describe some results of deformation quantization towards the relative Dulfo Isomorphism and an application of deformation quantization into computing representations of $W-$ algebras, recovering Duflo's Theorem in the semisimple case.

September 10th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Ergodicity of irrational billiards, III
Speaker: Giovanni Forni, University of Maryland
Location: MB216
September 11th, 2013 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Answering a question of Le Roux on displacing a topological disc of significant area on S^2 by an area preserving homeomorphism.
Speaker: Andrew Hanlon, Penn State
Location: MB114

Answering a question of Le Roux on displacing a topological disc of significant area on S^2 by an area preserving homeomorphism.

September 11th, 2013 (07:00pm - 08:30pm)
Seminar: Complex Fluids Seminar
Title: Introduction of the General Diffusion
Speaker: Chun Liu, Penn State
Location: MB216
September 12th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Two dimensional Steady Euler equations
Speaker: Jiequan li, Beijing Normal University
Location: MB216
September 12th, 2013 (11:00am - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Mathematical modeling of bacterial communities: Swarming processes and mechanical behavior of biofilms.
Speaker: Giordano Tierra, University of Notre Dame
Location: MB216

Bacterial biofilms are structured cellular communities that represent the dominant bacterial growth state for both environmental and clinical scenarios. There is great interest to understand biofilm assembly, as infections resulting from biofilms are notoriously resistant to antibiotic treatments. Treatment of a broad spectrum of human health issues, ranging from lethal infections from opportunistic pathogens such as those in cystic fibrosis patients, to catastrophic failure of prosthetic implants, could improve with a greater understanding of biofilm formation. Among the biofilm development steps for which we lack understanding is the ability of bacteria to first colonize host surfaces. Bacterial swarming motility has been shown to be important to biofilm formation, where cells act not as individuals, but as coordinated groups to move across surfaces, often within a thin-liquid film. In this talk two models are presented. The first one focuses on simulating the swarming process for Pseudomonas aeruginosa bacterial communities, whose spread is aided by the production of a surfactant that lowers surface tension of the liquid film to improve bacterial motility. The second model simulates the mechanical behavior of biofilms. In particular, deformation and detachment produced by interaction with liquid flow is studied by using a multi-component complex fluid formulation.

September 12th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Branched covers and linear series
Speaker: Ryan Eberhart, Penn State
Location: MB106

I will discuss how considering linear series on a curve X suggests a natural equivalence relation on covers, different from the usual equivalence given on covers of a fixed base. In the usual equivalence, since the tame étale fundamental group is finitely generated, there are no non-trivial families of tame covers of fixed degree and branch locus. However, as noted by Osserman, under the equivalence suggested by linear series there do exist tame families of fixed degree and ramification locus. In the non-Galois case I will present some results towards classifying when such families can exist. In the Galois case, I will provide a complete classification.

September 12th, 2013 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Some applications of geometry to problems in biology
Speaker: Joel Hass, UC Davis
Location: MB114

Many problems arising in biology are geometric, since many biological properties are reflected in the shapes of biological objects.
We will explain recent developments in the use of conformal mappings and hyperbolic geometry to study several biological problems.
1. The study of cortical surfaces. In particular, the question of how similar are two brains.
2. The classification of proteins.
3. Deducing the evolutionary tree of old-world monkeys from fossilized skulls.

September 12th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: On the analytic solution of the quantization commutes with reduction problem, 1
Speaker: Nigel Higson, Penn State University
Location: MB106

The "quantization commutes with reduction" phenomenon was first explored by Guillemin and Sternberg within the context of Kahler geometry. A great deal has been written on the topic since then, often with the goal (successfully achieved) of broadening the context to symplectic geometry or beyond. But I want to return to the Kahler context and examine there the remarkable analytic proof of Tian and Zhang of the general quantization commutes with reduction theorem in symplectic geometry. The general argument simplifies considerably in the Kahler case. I hope this observation will help make clearer the power and elegance of the Tian-Zhang approach. It might also offer clues to help find analytic proofs quantization commutes with reduction theorems in other contexts.

September 12th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: The complexity of recognizing the 3-sphere
Speaker: Joel Hass, UC Davis
Location: MB114

An algorithm for determining whether a given 3-dimensional manifold is a 3-sphere was given by Rubinstein in 1992. This problem was shown to be in the complexity class NP by Schleimer, based on work of Casson. Recent joint work with Greg Kuperberg shows that this problem also lies in coNP, assuming the Generalized Riemann Hypothesis.

September 12th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

September 13th, 2013 (12:00pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Discrete Stoke complex on quadrilateral grid
Speaker: Shuo Zhang, Institute of Computational Mathematics, Chinese Academy of Sciences
Location: MB315

Note: the talk starts at 3:30 pm This talk is devoted to the stable discretization of 2D incompressible Stoke problem on quadrilateral grid. Particularly, a newly developed stable finite element pair and a related discrete Stoke complex will be introduced, where the finite element functions are kept piecewise polynomials on convex quadrilateral grids. Connection to and comparison with existing results are also talked about.

September 16th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Linear Scaling Methods for Density Functional Theory
Speaker: Carlos Garcia-Cervera, University of California, Santa Barbara
Location: MB114
Abstract: http://www.math.ucsb.edu/~cgarcia/

Abstract: Density Functional Theory (DFT) provides a way to carry out realistic computations of molecular systems at the quantum level. Typical approaches scale as N^3, where N is the number of electrons in the system. I will give an introduction to DFT, and describe some of the approaches developed for linear scaling algorithms. I will also describe our own approach, which is based on a subspace iteration, and takes advantage of the localization properties of nonorthogonal wave functions.

September 16th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Spin-polarized transport in ferromagnetic multilayers
Speaker: Carlos Garcia-Cervera, University of California, Santa Barbara
Location: MB106
Abstract: http://www.math.ucsb.edu/~cgarcia/

Magnetic storage devices rely on the fact that ferromagnetic materials are typically bistable, and that it is possible to switch between different states by applying a magnetic field. The discovery of the Giant Magneto-Resistance effect has enabled the use of layered ferromagnetic materials in magnetic devices, such as magnetic memories (MRAMs). Even in the absence of thermal effects, there are limitations in the storage capacity of such devices due to the fact that as the size is decreased, the magnitude of the switching field increases, due to an increase in shape anisotropy. Given that magnetic fields have long range interactions, the density of such devices is limited. A new mechanism for magnetization reversal in multilayers was proposed by Slonczweski and Berger. In this new mechanism, an electric current flows perpendicular to the layers. The current is polarized in the first layer, and the polarization travels with the current to the second layer, where it interacts with the underlying magnetization. Since currents are localized in each cell, long range effects can be reduced. In this talk we will discuss the connection between several models for the description of the spin transfer torque at different physical scales. Specifically, we connect the quantum and kinetic descriptions with the help of the Wigner transform, and the kinetic and diffusion models by a specific parabolic scaling. Numerical examples will presented to illustrate the applicability and limit of the different models. This is joint work with Jingrun Chen and Xu Yang at UCSB.

September 16th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Laplacian and dynamics in Finsler geometry II
Speaker: Thomas Barthelmé, Penn State
Location: MB114

In Riemannian geometry, there are a lot of links between the geometry and dynamics of a metric and the Laplace-Beltrami operator. In this talk, I will present Finsler geometry, a generalisation of Riemannian geometry, and introduce a well-suited Laplacian operator. I will then focus on negatively curve manifolds and give some results and questions on the relationships between geometry and Laplacian.

September 16th, 2013 (04:00pm - 05:30pm)
Seminar: Tensor Networks and Applications Seminar
Title: What are Tensor Networks?
Speaker: Sara Jamshidi, Penn State University
Location: MB315

Tensor Networks are mathematical structures that have proven to be quite useful in describing entangled states of quanta; therefore, it is used often in research related to quantum computing. This talk seeks to introduce these structures to a general audience. It will cover a little history, a little physics, a little computing, and some interesting algebra.

September 17th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: 2d Euler equations continued
Speaker: Jiequan li, Beijing normal University
Location: MB216
September 17th, 2013 (10:10am - 11:00am)
Seminar: Combinatorics/Partitions Seminar
Title: Refinements of overpartitions via restrictions on the overlined parts, part 2
Speaker: James Sellers, PSU
Location: MB106

Over the past several years, numerous authors have studied properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In this talk, we consider various classes of overpartitions where the overlined parts are restricted in specific ways which will be outlined in the talk. Once these new objects are defined, we will prove a number of Ramanujan-like congruences for many of these restricted overpartition functions using elementary generating function manipulations.

September 17th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Schnorr random pairs
Speaker: Jason Rute, Pennsylvania State University
Location: MB315

Algorithmic randomness uses computable techniques to robustly define a random real number. The most well know randomness notion is Martin-L"of randomness. In 1971 Schnorr criticized Martin-L"of randomness as being not effective enough. One of his suggested replacements was a notion of randomness now called Schnorr randomness. Schnorr randomness has many similar properties to Martin-L"of randomness. However, at first, it seems that van Lambalgen's theorem, an important theorem about the randomness of pairs, fails for Schnorr randomness. However, by using a more uniform notion of randomness relative to an oracle, we can recover van Lambalgen's theorem for Schnorr randomness. I will present a proof of van Lambalgen's theorem for Schnorr randomness, which can be found in these two papers: K. Miyabe, Truth-table Schnorr and truth-table reducible randomness; K. Miyabe, J. Rute, Van Lambalgen's theorem for uniformly relative Schnorr and computable randomness.

September 17th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: The curious properties of scattering amplitudes in certain quantum field theories
Speaker: Radu Roiban, Penn State Physics
Location: MB106

I will begin by briefly reviewing the perturbative construction of scattering amplitudes in general gauge theories and then discuss some of their unexpected properties: a relation between their momentum dependence and their group theory structure, a momentum space conformal symmetry. If time allows, I will also comment on the result of the evaluation of momentum integrals. An all-order proof and a fundamental understanding of these properties are currently open questions.

September 17th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Smooth and measure rigidity for actions of lattices in higher rank Lie groups, I
Speaker: Aaron Brown and Federico Rodriguez Hertz, Penn State
Location: MB216

In this series of talks we plan to show how to prove smooth rigidity of higher rank lattice Anosov actions on infranilmanifolds. The keynote is that existence of an invariant measure is not assumed. The main new technical ingredient here is the existence of a semiconjugacy for higher rank lattice actions with Anosov homotopy data. Also we will discuss the existence of invariant measures for general higher rank lattice actions on arbitrary manifolds. Of particular interest is the understanding of what distinguish the examples of the standard action of SL(n,\Z) on \T^n and the projective action of SL(n,\Z) in S^{n-1}. The first one preserves Haar measure, the second one has no-invariant measure at all. We shall give an explanation for this phenomenon relating weights and roots and then give a general criterion.

September 18th, 2013 (07:00pm - 08:30pm)
Seminar: Complex Fluids Seminar
Title: (1) Nonlocal Master Equations and Variational Approach (2) The Results of Wellposedness of the General Diffusion Equation
Speaker: Chun Liu (Penn State) and Chao Deng (Jiangsu Normal University)
Location: MB216
September 19th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Steady and self-similar solutions to systems of two-dimensional conservation laws.
Speaker: Joe Roberts, Penn State
Location: MB216

We consider solutions to systems of 2D conservation laws that are steady in time and constant along rays emanating from the origin. This reduction is inspired by problems in shock wave reflection for the compressible Euler equations, in which the flow is locally well described by solutions with these symmetry properties. For general systems with genuinely nonlinear or linearly degenerate characteristic fields of constant multiplicity, we prove any admissible $L^\infty$ solution that is a small perturbation of a constant state is necessarily a special function of bounded variation. In addition, we describe the possible configurations of different kinds of waves, and show that they are what we intuitively expect. How this answers some questions and improves known results regarding uniqueness (forward in time) and regularity (more interesting for backward in time) for one-dimensional Riemann problems will also be discussed.

September 19th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Dyadic Torsion of Elliptic Curves
Speaker: Jeffrey Yelton, Penn State
Location: MB106

The image of the action of Galois on \ell-adic Tate modules of abelian varieties has been a topic of considerable study. A particularly interesting case is that of hyperelliptic jacobians for \ell = 2. Certain results such as Serre's celebrated \open image theorem" have shown that, under certain conditions, the image of Galois in the symplectic group of automorphisms of the Tate module is open of finite index. However, little is known about exactly how the Galois group acts on the field of definition of dyadic torsion of a given hyperelliptic jacobian.  In this talk, I will give formulas for the field of definition of dyadic torsion of certain elliptic curves, as well as describe the structure of the Galois group of this fi eld extension and how it acts on certain generators.

September 19th, 2013 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Counting collisions in hard ball gas models and singular geometry of non-positive curvature
Speaker: Dmitri Burago, Penn State University
Location: MB114

We will discuss a solution to a long–standing problem. The problem itself can be explained to school kids. Basically, one asks if there exists an N that not more than N elastic collisions can occur between 10 identical balls before they fly away from each other (no gravity, no external forces). Of course, there is nothing special about 10, it could be any M and then N=N(M). The solution is also elementary modulo a few well–known facts. The problem was that the tools and facts lie in an area of math which was thought to be very far from the original problem. We will not get into any technicalities, so the talk should be easily accessible.

September 19th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: On the analytic solution of the quantization commutes with reduction problem, 2
Speaker: Nigel Higson, Penn State University
Location: MB106

The "quantization commutes with reduction" phenomenon was first explored by Guillemin and Sternberg within the context of Kahler geometry. A great deal has been written on the topic since then, often with the goal (successfully achieved) of broadening the context to symplectic geometry or beyond. But I want to return to the Kahler context and examine there the remarkable analytic proof of Tian and Zhang of the general quantization commutes with reduction theorem in symplectic geometry. The general argument simplifies considerably in the Kahler case. I hope this observation will help make clearer the power and elegance of the Tian-Zhang approach. It might also offer clues to help find analytic proofs quantization commutes with reduction theorems in other contexts.

September 19th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: Multilevel Solvers for Implicit SPH
Speaker: Kai Yang, Pennsylvania State University
Location: MB106

In this talk, I will first introduce some basics of SPH and how we use it to discretize Navier-Stokes equations. Since SPH is a non-variational method without any underlying geometric grids, multigrid methods can not be applied easily to solve the resulting algebraic systems. I will report some preliminary results on how multilevel methods can be designed for this type of problems and can still give good performance as shown by various numerical experiments.

September 20th, 2013 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Simulated annealing methods for improving particle filters
Speaker: Vasileios Maroulas, University of Tennessee, Statistics
Location: MB106

*This seminar is cross listed from the Department of Statistics, Colloquium. PLEASE NOTE DIFFERENT TIME AND DAY: OCTOBER 19TH, 4-5 PM, 201 THOMAS.* We present a novel approach for improving particle filters for multi-target tracking with a nonlinear observation model. The suggested approach is based on simulated annealing for stochastic differential equations. Simulated annealing is used to design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particle filter samples closer to the observations while at the same time respecting the dynamics. We employ a similar algorithm for non-Gaussian dynamics and data. The numerical results based on two tracking scenarios show that the suggested approach can improve significantly the performance of a particle filter. The talk is based on joint works with Kai Kang and Panos Stinis.

September 20th, 2013 (04:40pm - 05:30pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: The Art of Test Writing
Speaker: Aleksey Zelenberg, Penn State University
Location: MB106

What are your goals when writing a test? How do you achieve them? This week, we will discuss the many motivations behind testing students and how they are (and aren't) achieved. For more information about this discussion group, please visit http://bit.ly/19ySDan

September 23rd, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Nonlocal diffusions with applications to charge transport
Speaker: Chun Liu, Penn State
Location: MB114
Abstract: http://www.personal.psu.edu/cxl41/
September 23rd, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Equilibrium bidding in complementary auctions
Speaker: Ed Green, Penn State, Economics Department
Location: MB106
Abstract: http://www.personal.psu.edu/users/e/u/eug2/

You and someone else both want to purchase (1) a house, and (2) furniture. One house and one lot of furniture are being auctioned. To both you and your competitor, the house and furniture are complements -- you would be willing to pay more to acquire both of them than the sum of what you would pay for each of them, if you had to consume it alone. But the two auctions are entirely separate. You cannot place a joint bid for the furnished-house package. What will be the equilibrium bidding strategies in this competition? After reviewing the model of, and two solution methods for, a single (private-value, first-price) auction, one method based on formulating and solving an ordinary differential equation and the other taking a lattice-theoretic approach, I will outline the respective 2-dimensional generalizations to attack the complementary-auctions problem. Each of these attempts runs into a mathematical problem that needs to be solved. The focus of this talk is to introduce an active research area in economic theory that generates problems in applied mathematics, rather than to exposit completed results. The complementary-auction model is drawn from research in progress by my student, Wiroy Shin.

September 23rd, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Measure Rigidity for Random Surface Diffeomorphisms
Speaker: Aaron Brown, Penn State
Location: MB114

We consider stationary and invariant measure for actions by diffeomorphisms on surfaces. Assuming the "fibre entropy" for such an action and measure is non-zero, we deduce the following dichotomy: either the measure is SRB, or the stable distribution is "non-random." We deduce a number of corollaries for actions without common invariant measurable line fields.

September 23rd, 2013 (04:00pm - 05:30pm)
Title: Private
Location: MB315
September 24th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Regularizing properties of nonlinear flows
Speaker: Alberto Bressan, Penn State
Location: MB216

t is well known that some linear evolution equations, such as the heat equation, improve the regularity of solutions as time increases. Can this be extended to nonlinear equations ? How can one take advantage of this smoothing property ? The talk will survey some classical results, and discuss open problems and research directions.

September 24th, 2013 (11:30am - 01:00pm)
Seminar: Teaching Seminar
Title: ALEKS - An Open Discussion of the Math Department Diagnostic, Remediation, and Calibration Strategies in the Upcoming Year
Speaker: James Sellers, Penn State
Location: MB114
Abstract: http://
September 24th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Presburger arithmetic, rational generating functions, and quasi-polynomials
Speaker: Antonio Bonelli, University of Basilicata, Potenza, Italy
Location: MB315

A Presburger formula is a predicate calculus formula with variables ranging over N, the set of natural numbers, that can be written using +, <, Boolean operations (and, or, not), and quantifiers (for all, there exists). We characterize the subsets of N^d that can be defined by a Presburger formula as exactly the sets that can be represented by a rational generating function. A geometric characterization of such sets is also given. These characterizations are from a recent paper by Kevin Woods.

September 24th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: The structure of simple operator algebras
Speaker: Nate Brown, Penn State
Location: MB106

C*- and W*-algebras are closely related theories, in the same way that topology and measure theory are closely related. What? I know, that's nonsense. But I'll try to make sense of it and describe the surprising parallels that have emerged when we restrict attention to some of the most common and important examples: simple, amenable operator algebras.

September 24th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Smooth and measure rigidity for actions of lattices in higher rank Lie groups, II
Speaker: Aaron Brown and Federico Rodriguez Hertz, Penn State
Location: MB216

In this series of talks we plan to show how to prove smooth rigidity of higher rank lattice Anosov actions on infranilmanifolds. The keynote is that existence of an invariant measure is not assumed. The main new technical ingredient here is the existence of a semiconjugacy for higher rank lattice actions with Anosov homotopy data. Also we will discuss the existence of invariant measures for general higher rank lattice actions on arbitrary manifolds. Of particular interest is the understanding of what distinguish the examples of the standard action of SL(n,\Z) on \T^n and the projective action of SL(n,\Z) in S^{n-1}. The first one preserves Haar measure, the second one has no-invariant measure at all. We shall give an explanation for this phenomenon relating weights and roots and then give a general criterion.

September 25th, 2013 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: On local structure of Finsler torus without conjugate points
Speaker: Dong Chen, Penn State
Location: MB114

In this talk I will present a recent joint work with Dimitri Burago. We proved, given a point on a Finsler surface, one can always find a neighborhood of the point and isometrically embed this neighborhood into a Finsler torus without conjugate points. This result does not hold in Riemannian cases, due to Burago and Ivanov, who proved Hopf's conjecture, that is, Riemannian tori without conjugate points are flat. In order to prove this we need to extend the notion of Busemann functions and make some perturbation and extension of such functions.

September 25th, 2013 (04:00pm - 05:00pm)
Seminar: MASS Colloquium
Title: From flapping birds to space telescopes: the mathematics of origami
Speaker: Robert Lang, Alamo, CA
Location: MB114

The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami has enabled safer airbags, Brobdingnagian space telescopes, and more.

September 25th, 2013 (07:00pm - 08:30pm)
Seminar: Complex Fluids Seminar
Title: The well-posedness of Inhomogeneous Incompressible Navier-Stokes System
Speaker: Jingchi Huang, Penn State
Location: MB216
September 26th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Steady and self-similar solutions to systems of two-dimensional conservation laws continued
Speaker: Joe Roberts, penn State
Location: MB216

We consider solutions to systems of 2D conservation laws that are steady in time and constant along rays emanating from the origin. This reduction is inspired by problems in shock wave reflection for the compressible Euler equations, in which the flow is locally well described by solutions with these symmetry properties. For general systems with genuinely nonlinear or linearly degenerate characteristic fields of constant multiplicity, we prove any admissible $L^\infty$ solution that is a small perturbation of a constant state is necessarily a special function of bounded variation. In addition, we describe the possible configurations of different kinds of waves, and show that they are what we intuitively expect. How this answers some questions and improves known results regarding uniqueness (forward in time) and regularity (more interesting for backward in time) for one-dimensional Riemann problems will also be discussed.

September 26th, 2013 (11:00am - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Genes must predict biological traits, mustn't they? Then why is it so difficult to understand how? (a non-mathematical, philosophical view of biological causation and evolution)
Speaker: Ken Weiss, Penn State University
Location: MB216

It’s widely assumed that genes determine who we are. But the genetic basis of human traits often turns out to be perplexingly complicated. We face the same problem in trying to understand normal traits, disease, and even behavior—and their evolution. Genomic determinism is at the heart of some of the key problems in modern biology. Computer simulation may be useful here, if we do not build in what we want to learn.

September 26th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: On the constancy regions for mixed test ideals
Speaker: Felipe Perez, University of Michigan
Location: MB106

Given a regular ring R of characteristic zero and an elements  f_1,...,f_r in R the  mixed multiplier ideal encodes information about the singularities of mixed products of the f_i. In characteristic zero the constancy regions for mixed multiplier ideals consist of rational polytopes with non-overlapping interiors. In positive characteristic, the test ideals are the analogue of multiplier ideals. In this talk we study the situation for mixed test ideals and describe the constancy regions as p-fractals. 

September 26th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Free actions of compact quantum groups on unital C*-algebras
Speaker: Piotr Hajac, Polish Academy of Sciences
Location: MB106

Let F be a field, G a finite group, and Map(G,F) the Hopf algebra of all set-theoretic maps from G to F. If E is a finite field extension of F and G is its Galois group, the extension is Galois if and only if the canonical map resulting from viewing E as a Map(G,F)-comodule is an isomorphism. Similarly, a finite covering space is regular if and only if the analogous canonical map is an isomorphism. The main result to be presented in this talk is an extension of this point of view to arbitrary actions of compact quantum groups on unital C*-algebras. I will explain that such an action is free (in the sense of Ellwood) if and only if the canonical map (obtained using the underlying Hopf algebra of the compact quantum group) is an isomorphism. In particular, we are able to express the freeness of a compact Hausdorff topological group action on a compact Hausdorff topological space in algebraic terms. Also, we can apply the main result to noncommutative join constructions and coactions of discrete groups on unital C*-algebras. (Joint work with Paul F. Baum and Kenny De Commer.)

September 26th, 2013 (03:30pm - 06:30pm)
Seminar: Special Event
Title: Diversity Workshop
Speaker: Climate and Diversity Committee, Penn State University
Location: MB114

NOTE: This event will only be **90 minutes,** despite the end time listed. Policy makers in the US have made it a priority to encourage diversity in higher education, especially in the STEM fields (science, technology, engineering, and math). It is no surprise, either. Research has shown that students who work in more diverse group settings are influenced by the different perspectives of minority participants and demonstrate enhanced complex thought processes as a result. There is also evidence suggesting that diverse organizations are more productive, better equipped to solve problems, and tend to come up with more innovative solutions. Therefore, developing skills for navigating a diverse environment is crucial to our professional development. After all, mathematicians collaborate. This workshop will be a venue for graduate students to talk about their own experiences and opinions regarding diversity in their own lives. After the discussion, attendants will draft a collective "community contract," which will outline the expectations we have of ourselves and each other. The goal of this contact is to help us create a welcoming environment for everyone, regardless of who they are. In such an environment, graduate students will be better equipped to develop the skills needed to succeed in their future career.

September 26th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

September 27th, 2013 (04:40pm - 05:30pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Grading Philosophy
Speaker: Attendees, Penn State University
Location: MB106

What messages are we communicating through grading? This week, we will discuss what messages we want to communicate to students and consider what messages we are actually sending when we grade assignments. For more information about this group, visit http://bit.ly/19ySDan

September 30th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: PDEs and image processing
Speaker: Eitan Tadmor, University of Maryland
Location: MB114
Abstract: http://www.cscamm.umd.edu/tadmor/
September 30th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: CONSENSUS and FLOCKING in SELF-ALIGNMENT DYNAMICS
Speaker: Eitan Tadmor, University of Maryland
Location: MB106
Abstract: http://www.cscamm.umd.edu/tadmor/

Abstract. We discuss self-organized dynamics of agent-based models with focus on a prototype model driven by non-symmetric self-alignment introduced in [1]. Unconditional consensus and flocking emerge when the self-alignment is driven by global interactions with a sufficiently slow decay rate. In more realistic models, however, the interaction of self-alignment is compactly supported, and open questions arise regarding the emergence of clusters/flocks/consensus, which are related to the propagation of connectivity of the underlying graph. In particular, we discuss heterophilious self-alignment: here, the pairwise interaction between agents increases with the diversity of their positions and we assert that this diversity enhances flocking/consensus. The methodology carries over from agent-based to kinetic and hydrodynamic descriptions. [1] A new model for self-organized dynamics and its flocking behavior, J. Stat. Physics 144(5) (2011) 923-947.

September 30th, 2013 (04:00pm - 05:30pm)
Title: Private
Location: MB315