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April 1st, 2014 (01:15am - 02:15am)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: TBA
Speaker: Gung-Min gie, Indiana University
Location: MB106
Abstract: http://
April 1st, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Analysis of mixed elliptic and parabolic boundary layers with corners
Speaker: Gung-Min Gie, University of Indiana
Location: MB216

We study the asymptotic behavier at small diffusivity of the solutions to a convection-diffusion equation in a rectangular domain. The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along each edge, but only continuous at the corners. To resolve the discrepancy between the diffusive and corresponding limit solutions, we construct an asymptotic expansion of the diffusive solution at any arbitrary, but fixed, order with respect to the small diffusivity parameter. Here, to manage some singular effects near the corners, the so-called elliptic and ordinary corner correctors are added in the asymptotic expansions as well as the parabolic and classical boundary layer functions. The validity of our asymptotic expansions is established in suitable Sobolev spaces.

April 1st, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Variation of stability and derived categories
Speaker: Matt Ballard, University of South Carolina
Location: MB106

There is a long and fruitful interplay between moduli spaces and derived categories of coherent sheaves dating back to Mukai. In this talk I will discuss how Geometric Invariant Theory can mediate this interaction even in situations not necessarily coming from VGIT. The talk in based on joint works with A. Bayer, D. Favero, and L. Katzarkov.

April 1st, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Degrees of unsolvability: a survey.
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315

In 1936 Turing produced the first example of a mathematical problem which is algorithmically unsolvable. This was followed by various attempts to classify such problems according to their degrees of unsolvability, i.e., the amount of algorithmic unsolvability which is inherent in them. The theory of Turing degrees applies to decision problems and is very rich, but unfortunately not very useful for the original purpose. The more recent theory of Muchnik degrees applies to a more general class of problems known as mass problems, and is therefore much more relevant in this respect. Recent investigations have revealed many examples of natural, specific, Muchnik degrees which can be used to classify unsolvable problems arising in various contexts, especially algorithmic randomness and reverse mathematics. I will survey various results of this type. I will also announce a structural result, to the effect that the lattice of Muchnik degrees of effectively closed sets is dense. This new result will appear in a joint paper by Binns, Shore, and myself.

April 1st, 2014 (03:50pm - 04:50pm)
Seminar: Tensor Networks and Applications Seminar
Title: Rényi entropy
Speaker: Jason Morton, Penn State University
Location: MB315
April 2nd, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Continuation: lower bounds fr the injectivity radius
Speaker: Jinpeng Lu. PSU
Location: MB114
April 3rd, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Viscosity vanishing method for transonic flows (continued)
Speaker: Jiequan Li, Beijing normal University
Location: MB216
April 3rd, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The relative Langlands program
Speaker: Yiannis Sakellaridis, Rutgers (Newark)
Location: MB106

I will give an overview of what could now be termed the "relative Langlands program". This program, which is still under development, builds on the work of many experts in order to provide a conjectural description of the "local" and the "automorphic" spectra of spherical (e.g. symmetric) varieties in terms of a Langlands dual group attached to them. This has applications to functoriality, and to relations between periods and L-functions such as the ones suggested by the Gan-Gross-Prasad conjectures. The special case where a reductive group is considered as a symmetric variety should recover the usual Langlands conjectures.

April 3rd, 2014 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Three-dimensional gravity, state sum models, and black hole entropy
Speaker: Marc Geiller, Penn State, Department of Physics
Location: MB106

After recalling some properties and features of three-dimensional gravity, I will explain how its quantization can be achieved through the use of state sum models and the computation of topological invariants. Then, I will present an application to the computation of black hole entropy, and explain the relationship with recent developments in four-dimensional quantum gravity.

April 3rd, 2014 (02:30pm - 03:20pm)
Seminar: PMASS Colloquium
Title: Grouping and rearranging terms in infinite series
Speaker: Joe Roberts, Penn State
Location: MB113

When studying infinite series of real numbers, it is tempting to expect the familiar properties of addition to hold, and in some cases they do. Series that converge absolutely are as well behaved as finite series --- they are associative and commutative. However, series that are not absolutely convergent have very different properties. The Riemann Rearrangement Theorem states that any conditionally convergent series can be reordered to sum to any real number or to diverge (illustrating a failure of commutativity), and there are divergent series for which one can choose a subsequence of partial sums that converge to any arbitrary real number (a failure of associativity). I will give examples of these kinds of unexpected outcomes, eventually building to a construction due to Sierpinski of a single power series whose terms can be grouped to converge uniformly to any continuous function on [0,1] vanishing at 0 --- a "universal Taylor series".

April 3rd, 2014 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Localized representation of low lying eigenspaces with applications in electronic structure analysis
Speaker: Jianfeng Lu, Duke University
Location: MB114

Localized representation of eigenspaces play an important role in electronic structure theory. They give nice physical understanding of the electronic structure and are fundamental building blocks of fast algorithms. In this talk, we will present some mathematical results and efficient algorithms for the localized representations. In particular, we will discuss a convex variational principle that gives us these representations.

April 4th, 2014 (12:00pm - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Stochastic modeling of biochemical networks
Speaker: Hye-Won Kang, Department of Mathematics and Statistics, University of Maryland Baltimore County
Location: MB114

This talk will introduce stochastic modeling and simulation of biochemical processes. Stochasticity may play an important role in case the copy number of some component involved in the biochemical processes is small. A stochastic model for biochemical processes using continuous-time Markov jump processes is considered. In this talk, I will show several examples in biology and their stochastic models. The first part of the talk is about stochastic models in the spatially-homogeneous biological systems. In this part, multiscale approximations of chemical reaction networks will be suggested which help to reduce the network complexity using various scales in species numbers and reaction rates. The second part of the talk is about stochastic models in the spatially-distributed biological systems. Two examples in biology and the models will be introduced: the glycolytic pathway in the distributed system and pattern formation in developmental biology. These examples will show how stochasticity will change the biological systems in different ways.

April 4th, 2014 (12:20pm - 01:10pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Creativity and Mathematics
Speaker: Attendees, Penn State
Location: MB101

Many of us would argue that math classes do not contain creative elements despite the fact that mathematics is a subject requiring a great deal of creativity. This week, we will read "Creativity: The Essence of Mathematics," available through the library. Copies will be provided at the meeting. If you would like to receive regular emails containing the weekly readings, please email me at jamshidi@math.psu.edu.

April 4th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Perfection cocycles through stochastic differential equations
Speaker: Xiaofei Zheng, Penn State University
Location: MB106

This talk is mainly about L. Arnold and M. Scheutzow's work in 1995 on how to perfect crude cocycles. It is a technique problem of great importance, which was open for more than ten years. Since its significance depends partly on the existence of crude cocycles, one example "the semimartingale cocycle generated by a stochastic differential equation driven by a semimartingale with stationary increments: dX=F(X,。dt)" is given in their work. To make the definition of cocycle to be consistent with dynamic system, they extended the traditional SDE to two sided time T=R. From Kunita's work, it turns out that the regularity of this cocycle is the same as the generator F, which is the same as the ODE case.

April 6th, 2014 (10:00am - 12:00pm)
Seminar: Complex Fluids Seminar
Title: Lorentz Spaces and Applications in Navier-Stokes equations
Speaker: Jingchi Huang, Penn State
Location: MB315
Abstract: http://
April 7th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Functionalization, Perturbation, and Spectrum
Speaker: Keith Promislow, Michigan State University
Location: MB114
Abstract: http://www.math.msu.edu/~kpromisl/

We will present a simple overview of why functionalized free energies are relevant to network formation, and how it interacts with the functional calculus to control the spectra of the resulting linearized operators.

April 7th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Network formation in Ionomer Membranes
Speaker: Keith Promislow, Michigan State University
Location: MB106
Abstract: http://www.math.msu.edu/~kpromisl/

Functionalized polymer membranes have a strong affinity for solvent, imbibing it to form charge-lined networks which serve as charge-selective ion conductions in a host of energy conversion applications. We present a continuum model, based upon a reformulation of the Cahn-Hilliard free energy, which incorporates solvation energy and counter-ion entropy to stabilize a host of network morphologies. We derive geometric evolution for co-dimension 1 bilayers and co-dimension two pore morphologies and show that the system possesses a simple mechanism for competitive evolution of co-existing networks through the common far-field chemical potential.

April 7th, 2014 (03:35pm - 05:35pm)
Seminar: Dynamical systems seminar
Title: Ricci flow through singularities. Attention: this is "Geometry" talk....
Speaker: Bruce Kleiner, NYU
Location: MB114

It has been a long-standing problem in geometric analysis to find a good definition of generalized solutions to the Ricci flow equation that would formalize the heuristic idea of flowing through singularities. I will discuss a notion in the 3-d case that has good analytical properties, enabling one to prove existence and compactness of solutions, as well as a number of structural results. It may also be used to partly address a question of Perelman concerning the convergence of Ricci flow with surgery to a canonical flow through singularities. This is joint work with John Lott.

April 8th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Mixed type problems in transonic flow and isometric embedding
Speaker: Dehua Wang, University of Pittsburgh
Location: MB216

Some mixed-type PDE problems for transonic flow and isometric embedding will be discussed. Recent results on the solutions to the hyperbolic-elliptic mixed-type equations and related systems of PDEs will be presented.

April 8th, 2014 (01:00pm - 02:15pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "On local structure of Finsler torus without conjugate points"
Speaker: Dong Chen, Adviser: Dima Burago, Penn State
Location: 167 Willard Building
Abstract: http://

In 1994 Burago and Ivanov proved Hopf’s conjecture, that is, Riemannian tori without conjugate points are flat. However, this conjecture does not hold in Finsler cases. 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. In order to prove this we need to extend the notion of Busemann functions and make some perturbation and extension of such functions. And we offer some future open problems to work on.

April 8th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Topological contact dynamics and two applications
Speaker: Peter Spaeth, Penn State Altoona
Location: MB106

The smooth dynamics of a contact structure admits a non-trivial extension to topological dynamics. We will discuss a key result in the subject, namely the 1-1 correspondence between topological contact isotopies (and their conformal factors) and their generating topological contact Hamiltonians, and two applications: topological rigidity of the geodesic flow on riemannian manifolds and the extension of the helicity invariant to topological dynamics.

April 8th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Invariant measures on Triangle-free graphs
Speaker: Jan Reimann, Penn State
Location: MB315

We present the construction, due to Petrov and Vershik (2010), of a measure on the set of all countable infinite graphs that concentrates on the triangle free graphs and is invariant under the canonical action of the symmetric group of the natural numbers.

April 8th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: New progress in the study of smooth actions of lattices in semisimple Lie groups, I
Speaker: Aaron Brown or Federico Rodriguez Hertz, Penn State
Location: MB216
April 8th, 2014 (03:50pm - 04:50pm)
Seminar: Tensor Networks and Applications Seminar
Title: The Hilbert-Mumford Criterion
Speaker: Jacob Turner, Penn State University
Location: MB315

In Invariant theory, understanding the Zariski closure of orbits is very important. However, since the Zariski topology is not Hausdorff, the usual notion of limits of sequences fails. We instead focus on a tool that allows us to still consider limit points, namely the Hilbert-Mumford criterion. We look at alternate formulations of this criterion as well as some motivating examples.

April 9th, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Injectivity radius estimates
Speaker: Jinpeng Lu, PSU
Location: MB114
April 10th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Conservation Laws with no Classical Riemann Solutions: Existence of Singular Shocks
Speaker: Charis Tsikkou, West Virginia University
Location: MB216

The basic tool in the construction of solutions to the Cauchy problem for conservation laws with smooth initial data is the Riemann problem. We review the results obtained for the solutions to the Riemann problem and present systems of two equations with no classical solutions. We then use the blowing-up approach to geometric singular perturbation problems to show that the systems exhibit unbounded solutions (singular shocks) with Dafermos pro files.

April 10th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No seminar this week
Speaker: No seminar this week
Location: MB106
April 10th, 2014 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Regularity properties for nuclear C*-algebras
Speaker: Stuart White, University of Glasgow
Location: MB106

In the past few years a number of properties of nuclear C*-algebras have been identified which are all seen to be satisfied by those algebras which have been classified by the Elliott programme, and fail drastically for the exotic counter examples to classification produced in the 2000's. These `regularity' properties have various different flavours: topological, functional analytic, algebraic, and all correspond naturally to features of injective von Neumann algebras used by Connes in his work on injectivity and hyperfiniteness. In this talk, I'll discuss these properties and the connections between them, focusing on obtaining finite non-commutative covering dimension from tensorial stability. All necessary terminology will be introduced in the talk.

April 10th, 2014 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: The evolution of networks
Speaker: David Kinderlehrer, Carnegie Mellon University
Location: MB114

Cellular networks are ubiquitous in nature. Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, the grains, separated by interfaces, the grain boundaries. The energetics and connectivity of the network of boundaries are implicated in many properties across all scales of use. The evolution of such networks, coarsening, is governed primarily by the attempt of the system to decrease interfacial energy subject to spatial constraints. The recently discovered grain boundary character distribution (GBCD) characterizes texture and its existence illustrates that the boundary network is ordered. We discuss a theory for the evolution of this statistic which bridges mesoscopic scales. It gives rise to many interesting questions and challenges: we still have much to learn about these very ancient questions.

April 11th, 2014 (12:00pm - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Divots in Extracellular Geometry Direct Intracellular Signaling
Speaker: Bradford E. Peercy, Department of Mathematics and Statistics, University of Maryland Baltimore County
Location: MB114

The cellular decision to migrate depends on cascades of intracellular signals initiated by extracellular stimuli. In the biological model system of Drosophila melanogaster, border cells in the epithelium of the developing egg chamber are triggered to migrate or not depending on a secreted morphogen Unpaired. We will describe and discuss our modeling work in three steps of this process: 1) Secretion-diffusion-uptake of Unpaired into-through-from a heterogeneous extracellular domain, 2) Intracellular signaling involving chemical competition and bistability to induce motility, and 3) Force generation between activated cells and their environment to create clustered cell migration. We can address questions such as what is the effect of microRNAs on the intracellular signaling? Can we explain clustered cell migration with basic force balance dynamics? Are divots creating additional extracellular space sufficient to explain the variety of asymmetric activation patterns seen in prior to migration? This last question will be the main focus of the talk. This work was conducted as part of the NSF UBM grant to UMBC with undergraduates Xuan Ge, David Stonko, Ann Marie Weideman, and Bilal Moiz, graduate student Lathiena Manning, and faculty co-mentor Dr. Michelle Starz-Gaiano

April 11th, 2014 (02:30pm - 03:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Instability theory of gaseous stars
Speaker: Ian Tice, Carnegie Mellon University
Location: MB106
Abstract: http://www.math.cmu.edu/math/faculty/Tice

A simple astrophysical model of stars considers them to be a compact mass of self-gravitating compressible fluid. Such a fluid obeys the compressible Navier-Stokes-Poisson equations. In the case of "polytropic gases," in which the pressure behaves like $P = K \rho^\gamma$ for $K>0$ an entropy constant and $\gamma >1$ an adiabatic constant, one may construct compactly supported, finite mass, radially symmetric equilibrium solutions by reducing to the Lane-Emden ODE (at least when $6/5 < \gamma < 2$). A fundamental question in astrophysics is the stability of such equilibria, and it was believed that they should be unstable for $6/5 < \gamma < 4/3$ and stable for $4/3 \le \gamma < 2$. In this talk we will prove that the Navier-Stokes-Poisson system, perturbed around a Lane-Emden equilibrium configuration, is nonlinearly unstable when $6/5 < \gamma < 4/3$. This is joint work with Juhi Jang.

April 14th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Overview of Research Computing and Cyberinfrastructure (RCC @ PSU) resources
Speaker: William Brouwer, RCC Penn State
Location: MB114

This presentation will give a resource overview of the Research Computing and Cyberinfrastructure (RCC) unit at PSU, formerly a unit of ITS, now transitioning to the Office of the Vice President for Research. Several consultation examples will be given, encompassing research applications from physics, chemical and electrical engineering. This will be followed by aspects of important parallel computing models including shared and distributed memory parallelism, and general purpose computation using Graphics Processing Units (GPUs). This seminar will conclude with a hands on portion targeting scientists interested in numerically intensive computing. RCC is a CUDA research center: https://research.nvidia.com/content/penn-state-crc-summary and thus GPUs will feature prominently in the seminar overall.

April 14th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: From 0 to High Performance Computing in one hour or five ways to do kriging
Speaker: William Brouwer, RCC Penn State
Location: MB106

This presentation will give a resource overview of the Research Computing and Cyberinfrastructure (RCC) unit at PSU, formerly a unit of ITS, now transitioning to the Office of the Vice President for Research. Several consultation examples will be given, encompassing research applications from physics, chemical and electrical engineering. This will be followed by aspects of important parallel computing models including shared and distributed memory parallelism, and general purpose computation using Graphics Processing Units (GPUs). This seminar will conclude with a hands on portion targeting scientists interested in numerically intensive computing. RCC is a CUDA research center: https://research.nvidia.com/content/penn-state-crc-summary and thus GPUs will feature prominently in the seminar overall.

April 14th, 2014 (03:35pm - 05:35pm)
Seminar: Dynamical systems seminar
Title: Parametrizing Hitchin components
Speaker: Guillaume Dreyer, Notre-Dame University
Location: MB114

Let S be a closed, connected, oriented surface of genus g>1. Hitchin components Hit_n(R) are components of the PSL_n(R)--character variety R_{PSL_n(R)}(S) that generalize Teichmuller components in the case where n=2. Over the recent years, groundbreaking work has revealed great geometric, dynamical and algebraic properties for the representations in Hit_n(R). In particular, these Hitchin representations turn out to share many features with the classic Fuchsian representations. In a joint work with Francis Bonahon, we construct a geometric, real analytic parametrization of Hitchin components Hit_n(R) The construction of this parametrization strongly relies on two independent approaches to studying Hitchin representations: the dynamical approach of Anosov representation, introduced by F. Labourie; and the algebraic-combinatorial approach of Positive representation, developed by V. Fock and A. Goncharov. In essence, our parametrization is an extension of Thurston's shear coordinates on the Teichmuller space, combined with Fock-Goncharov's coordinates on the moduli space of positive framed local systems of a punctured surface.

April 15th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Viscosity vanishing method for transonic flows (continued)
Speaker: Jiequan Li, Beijing normal university
Location: MB216
April 15th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Odd dimensional generalized geometry
Speaker: Marco Aldi, Virginia Commonwealth University
Location: MB106

Generalized geometry is the study of the geometry of the generalized tangent bundle (direct sum of the tangent and cotangent bundle) of a manifold. Partly because of the connection with supersymmetric sigma-models, most of the literature on generalized geometry specializes to even-dimensional manifolds. The odd-dimensional case, pioneered by Wade and Poon, is much less understood. In this talk we report on some recent progress (joint work with Daniele Grandini) on odd-dimensional generalized geometry including a spinorial formulation and T-duality.

April 15th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Invariant measures on Triangle-free graphs (II)
Speaker: Jan Reimann, Penn State
Location: MB315

We finish the construction by Petrov and Vershik of an invariant measure on the countable triangle-free graphs and describe how this construction can be generalized to arbitrary structures with trivial definable closure (due to Ackerman-Freer-Patel).

April 15th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: New progress in the study of smooth actions of lattices in semisimple Lie groups, II
Speaker: Aaron Brown or Federico Rodriguez Hertz, Penn State
Location: MB216
April 15th, 2014 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Singularities in stability analysis: From robust stability to dissipation-induced instabilities
Speaker: Oleg Kirillov, Magneto-Hydrodynamics (FWDH) Helmholtz-Zentrum Dresden-Rossendorf
Location: MB106

Stability analysis of physical and engineering systems is complicated in the presence of multiple governing parameters. For example, stability boundary becomes a non-smooth manifold with singularities. Practical needs require further separation of the domains of stability (instability) in order to distinguish between the character of decay (amplification) of a perturbation. The boundary of the domain of overdamping that is situated inside the domain of asymptotic stability has its own singularities. Surprisingly, these singularities correspond to the solutions of the spectral abscissa minimization problem. I will show how such separate at the first glance problems as robust stabilization and dissipation-induced instabilities are connected via the language of singularity theory. A broad range of physical applications will illustrate the theory.

April 16th, 2014 (09:30am - 11:30am)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "A peridynamic Formulation for Phase Transformation"
Speaker: Liming Yuan, Adviser: Qiang Du, Penn State
Location: 113 Osmond Laboratory
Abstract: http://

Phase transformation in solids has drawn much attention since 1970s, which also contributes to the study of the system of conservation law. Recently a peridynamic formulation for elastic problems is proposed. In this ongoing project, we target to explore the phenomenon from peridynamic point of view, focusing on the similarities and distinctions to the classical theory.

April 16th, 2014 (02:30pm - 04:30pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Uniqueness of conservative weak solution to Camassa-Holm equation via characteristics"
Speaker: Qingtian Zhang, Adviser: Alberto Bressan, Penn State
Location: MB106

Camassa-Holm equation is an approximate model to describe water waves. In this talk, I will introduce some classical results of Camassa-Holm equation, and present our recent result concerning the uniqueness of conservative solution to Camassa-Holm equation. This is a joint work with Alberto Bressan and Geng Chen.

April 16th, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: The Sphere Theorem; Ricci Curvature
Speaker: Jinpeng Lu; Nan Li, PSU
Location: MB114

Jinpeng Lu will quickly show how injectivity radius estimates are used to prove the Sphere Theorem. Then Nan Li will speak on basics in Ricci curvature (Meyer’s Theorem - a trivial generalization of Synge’s, Bishop-Gromov volume growth inequality and maybe he would have time to start U. Abresch distance estimates). We have a challenging goal to get to Colding-Minicozzi and Cheeger-Colding work on non-negative Ricci, but I guess that realistically this has to be put off to the next semester.

April 17th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Viscosity vanishing method for transonic flows (continued)
Speaker: Jiequan Li, Beijing Normal University
Location: MB216
April 17th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Derived equivalent rational threefolds
Speaker: John Lesieutre, MIT
Location: MB106

I will describe the construction of an infinite set of smooth projective threefolds that have equivalent derived categories but are not isomorphic, contrary to a conjecture of Kawamata. The example is quite elementary: the varieties arise as blow-ups of CP^3 at various configurations of 8 points, related by sequences of Cremona transformations. As time permits, I will discuss how related constructions give rise to some other counterexamples in birational geometry.

April 17th, 2014 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Is C_0(X) tensor O_2 AF-embeddable?
Speaker: Bhishan Jacelon, Purdue University
Location: MB106

We discuss this question for locally compact, Hausdorff spaces X that are connected but not locally connected (in particular, when X is a protorus). The primary motivation is to extend the result of Ozawa (the case X=(0,1]), in order to perhaps shed some light on the question of AF-embeddability of nuclear, quasidiagonal C*-algebras. This is work in progress with Marius Dadarlat.

April 17th, 2014 (02:30pm - 03:20pm)
Seminar: PMASS Colloquium
Title: What is a random number?
Speaker: Jason Rute, Penn State
Location: MB113

Suppose there was a new lottery, Power Coin. Once a week, the lotto agency flips a fare coin 50 times, converts the heads to ones and the tails to zeros, and publishes that as the winning lottery ticket. Consider these three lottery ticket numbers: 01010101010101010101010101010101010101010101010101, 11001001000011111101101010100010001000010110100011, 011000110 01001110100110110001011100110110000000111. Do any of these seem more random than the others? (What if I told you the second was the first 50 binary digits of pi?) Does it even make sense to say that a finite sequence of bits is more random than another? What about an infinite sequence of bits? In this talk, I am going to explore different definitions of random number. I will talk about the view that random numbers are a myth. I will talk about normal numbers. I will talk about Kolmogorov complexity, a way to measure randomness via computable compression. Last, I will introduce Martin-Löf randomness.

April 17th, 2014 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Department Meeting
Speaker: Department Meeting
Location: MB114
April 18th, 2014 (09:00am - 11:00am)
Seminar: Ph.D. Thesis Defense
Title: "Approximate solutions to second order parabolic equations, with application to finance"
Speaker: Chao Liang, Adviser: Xiantao Li and Victor Nistor
Location: 113 Osmond Laboratory
Abstract: http://

We further develop the Dyson-Taylor method, which aims to get a series expansion approximation to the solution of second parabolic equations, with variable coefficients. I will explain how to use a slightly different way to construct the approximate solution, and show algorithms to compute the approximation to arbitrarily high order. Time-dependent coefficients and higher order parabolic PDEs will also be considered. For the application, I will present the result for the implied volatility approximation for CEV/SABR/Heston models.

April 18th, 2014 (12:00pm - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Semi-mechanistic Modeling and its Application in Understanding Immune Cell Migration
Speaker: Hongyu Miao, Department of Biostatistics and Computational Biology, University of Rochester
Location: MB114

Semi-mechanistic modeling (SMM) is a flexible and powerful technique that allows one to quantitatively describe a dynamic system with unclear or undistinguishable interactions. However, the traditional SMM technique uses constant coefficients to represent unknown interactions and thus may fail to capture the essence of a dynamic process. In the past few years, we have developed the generalized semi-mechanistic modeling (GSMM) technique and paid particular attention to the identifiability analysis and parameter estimation problems associated with GSMM. We applied GSMM to our experiment data on three major immune cell types (CD4, CD8, and antibody-secreting cells) involved in adaptive responses against influenza virus infection in mice. The results suggest several interesting and novel characteristics of immune cell migration heterogeneity and the linkage between cell phenotype and proliferation.

April 18th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: An Analytic Approach to Quasirandom (Hyper)graphs
Speaker: Henry Towsner, University of Pennsylvania
Location: MB216

The many equivalent characterizations of quasirandomness for graphs have been extensively studied. When generalized to hypergraphs, these notions split into a partially ordered family of distinct notions, recently shown by Lenz and Mubayi to not even be linearly ordered. The ultraproduct setting, equipped with Loeb measure, turns out to be a natural place to examine these notions. We show that notions of hypergraph randomness have a natural analytic characterization---orthogonality to certain sigma algebras generated by definable sets---and that all the notions which have been previously studied can be considered examples of this phenomenon. We use this to generalize several results known about some notions to all these randomness notions.

April 18th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: A finite element method for the second order linear elliptic equation in non-divergence form
Speaker: Wujun Zhang, University of Maryland
Location: MB315
Abstract: http://www2.math.umd.edu/~wujun/

Fully nonlinear elliptic PDEs, including Monge-Ampere equation and Isaac's equation, arise naturally from differential geometry, optimal mass transport, stochastic games and the other fields of science and engineering. In contrast to an extensive PDE literature, the numerical approximation reduces to a few papers. One major difficulty is the notion of viscosity solution which hinges on the maximum principle, instead of a variational principle. In this talk, we consider linear uniformly elliptic equations in non-divergence form, which may be regarded as linearization of fully nonlinear equations. We discuss the design of convergent numerical methods for such equations. We introduce a novel finite element method which satisfies a discrete maximum principle. This property, together with operator consistency, guarantees convergence to the viscosity solution provided that the coefficient matrix and right-hand side are continuous. We also present a discrete version of the Alexandroff-Bakelman-Pucci estimate, and use it to derive convergence rates under suitable regularity assumptions of the coefficient matrix and viscosity solution.

April 18th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: CANCELED (RESERVED)
Speaker: Wen Cheng, JP Morgan
Location: MB106
April 18th, 2014 (04:00pm - 06:00pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Covering Dimension for Nuclear C*-algebras"
Speaker: Hung-Chang Liao, Adviser: Nate Brown, Penn State
Location: 115 Osmond Laboratory

The classical covering dimension of a topological space can be defined through a certain decomposability of open coverings. The noncommutative version (for nuclear C*-algebras) is defined in terms of uniformly decomposable completely positive approximations. In this talk, I will begin with some background in approximation properties related to nuclear C*-algebras, and then discuss the connection between nuclearity and dimension of topological spaces.

April 21st, 2014 (03:35pm - 05:35pm)
Seminar: Dynamical systems seminar
Title: Symbolic dynamics for three dimensional flows with positive entropy (joint work with Y. Lima)
Speaker: Omri Sarig, Weizmann Institute of Science
Location: MB114

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.

April 22nd, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Viscosity vanishing method for transonic flows (continued)
Speaker: Jiequan Li, beijing normal University
Location: MB216
April 22nd, 2014 (10:00am - 12:00pm)
Seminar: Ph.D. Thesis Defense
Title: "On ergodicity of geodesic flows and nondense orbits of certain partially hyperbolic systems"
Speaker: Weisheng Wu, Advisers: Federico Rodriguez-Herts and Anatole Katok, Penn State
Location: 144 Fenske Laboratory
Abstract: http://

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.

April 22nd, 2014 (11:30am - 01:30pm)
Seminar: Teaching Seminar
Title: Action Research Reports
Speaker: Tim Slater
Location: MB114
Abstract: http://
April 22nd, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Constructions in shifted symplectic geometry
Speaker: Tony Pantev, University of Pennsylvania
Location: MB106

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.

April 22nd, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: TBD
Speaker: Sankha Basu, Penn State
Location: MB315
April 22nd, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Markov partitions for three-dimensional flows with positive entropy, I
Speaker: Omri Sarig, Weizmann Institute of Science, Rehovot, Israel
Location: MB216
April 23rd, 2014 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Spectral Curves of Constant Mean Curvature Tori
Speaker: Emma Carberry, University of Sydney
Location: MB114

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.

April 24th, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Viscosity vanishing method for transonic flows (continued)
Speaker: Jiequan Li, Beijing Normal University
Location: MB216
April 24th, 2014 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: The generator problem for C*-algebras
Speaker: Hannes Thiel, University of Copenhagen
Location: MB106

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).

April 24th, 2014 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: String theory on elliptic curves: topology, algebraic geometry, and physics
Speaker: Jonathan Rosenberg, University of Maryland
Location: MB114

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.

April 25th, 2014 (12:00pm - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Hydrodynamics and collective behavior of the tethered bacterium Thiovulum majus
Speaker: Alexander Petroff, Center for Studies in Physics and Biology, Rockefeller University
Location: MB114

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.

April 25th, 2014 (02:30pm - 03:30pm)
Seminar: Complex Fluids Seminar
Title: A Saddle-Point Formulation And Finite Element Method For The Stefan Problem With Surface Tension
Speaker: Shawn Walker, Louisiana State University
Location: MB216

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).

April 25th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: The Smoluchowskii-Kramers approximation and the large deviation principle for SPDEs
Speaker: Sandra Cerrai, University of Maryland, College Park and University of Florence, Italy
Location: MB106

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).

April 28th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: An introduction to current problems in modeling cell motility
Speaker: Hans G Othmer, University of Minnesota
Location: MB114
Abstract: http://www.math.umn.edu/~othmer/

Cell motility is one of the most important processes in biology, yet it is poorly understood at the biological level and even more poorly modeled. In this introductory lecture I will describe some of the fundamental problems and suggest how mathematical modeling can contribute to solving these problems.

April 28th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: From Crawlers to Swimmers- Mathematical and Computational Problems in Cell Motility
Speaker: Hans G Othmer, University of Minnesota
Location: MB106
Abstract: http://www.math.umn.edu/~othmer/

Cell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the detection and transduction of extracellular chemical and mechanical signals, integration of the signals into an intracellular signal, and the spatio-temporal control of the intracellular biochemical and mechanical responses that lead to force generation, morphological changes and directed movement. While many single-celled organisms use flagella or cilia to swim, there are two basic modes of movement used by eukaryotic cells that lack such structures -- mesenchymal and amoeboid. The former, which can be characterized as `crawling' in fibroblasts or `gliding' in keratocytes, involves the extension of finger-like filopodia or pseudopodia and/or broad flat lamellipodia, whose protrusion is driven by actin polymerization at the leading edge. This mode dominates in cells such as fibroblasts when moving on a 2D substrate. In the amoeboid mode, which does not rely on strong adhesion, cells are more rounded and employ shape changes to move -- in effect 'jostling through the crowd' or `swimming'. Here force generation relies more heavily on actin bundles and on the control of myosin contractility. Leukocytes use this mode for movement through the extracellular matrix in the absence of adhesion sites, as does Dictyostelium discoideum when cells sort in the slug. However, recent experiments have shown that numerous cell types display enormous plasticity in locomotion in that they sense the mechanical properties of their environment and adjust the balance between the modes accordingly by altering the balance between parallel signal transduction pathways. Thus pure crawling and pure swimming are the extremes on a continuum of locomotion strategies, but many cells can sense their environment and use the most efficient strategy in a given context. We will discuss some of the mathematical and computational challenges that this diversity poses.

April 28th, 2014 (03:35pm - 05:35pm)
Seminar: Dynamical systems seminar
Title: Localized Pressure and Equilibrium States
Speaker: Christian Wolf, The City College of New York
Location: MB114

In this talk we discuss a notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose statistical sums with respect to an $m$-dimensional potential $\Phi$ are "close" to a given value $w\in \bR^m$. We then establish for several classes of systems and potentials $\varphi$ and $\Phi$ a local version of the variational principle. We also construct examples showing that the assumptions in the localized variational principle are fairly sharp. Next, we study localized equilibrium states and show that even in the case of subshifts of finite type and H\"older continuous potentials, there are several new phenomena that do not occur in the theory of classical equilibrium states. In particular, ergodic localized equilibrium states for H\"older continuous potentials are in general not unique.

April 29th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: TBA
Speaker: Camille Laurent-Gengux, Universite de Lorraine
Location: MB106
April 29th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Lebesgue density and \Pi^0_1 classes
Speaker: Mushfeq Khan, University of Wisconsin - Madison
Location: MB315

Analyzing the effective content of the Lebesgue density theorem was an important step towards the recent solutions of the ML-covering and ML-cupping problems. Two new classes of reals emerged from this analysis: the positive density points with respect to effectively closed (or \Pi^0_1) sets of reals, and a proper subclass, the density-one points. Bienvenu, Holzl, Miller, and Nies have shown that the ML-random positive density points are exactly the ones that do not compute the halting problem. Using this theorem as a starting point, I will discuss several new results on the interactions between density, domination properties, minimality, completeness, 1-genericity, and randomness.

April 29th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Markov partitions for three-dimensional flows with positive entropy, II
Speaker: Omri Sarig, Weizmann Institute of Science, Rehovot, Israel
Location: MB216