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Eberly College of Science Mathematics Department

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November 1st, 2012 (09:00am - 10:10am)
Seminar: Mathematical Biology & Physiology Seminar
Title: mathematical biology seminar
Speaker: TBA, TBA
Location: MB114
Abstract: http://www.math.psu.edu/treluga/mmbs.html
November 1st, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discuss session
Speaker: TBA
Location: MB216
November 1st, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Improvements and Extensons of Two Theorems of Sarkozy
Speaker: Alex Rice, Bucknell University
Location: MB106

In a series of papers in the late 1970s, Sarkozy employed the circle method to answer questions of Lovasz and Erdos, the qualitative versions of which state that any set of natural numbers of positive upper density necessarily contains two distinct elements which differ by a perfect square, as well as two elements which differ by one less than a prime number. Here we discuss quantitative improvements and extensions of these theorems, including my thesis work and joint work with Mariah Hamel and Neil Lyall.

November 1st, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Real group orbits on flag varieties and equivariant K-theory
Speaker: Zhaoting Wei, University of Pennsylvania
Location: MB106

Let G be a real semisimple Lie group and X be the complete (complex) flag variety. I will show how to study the orbits of G-action on X using Morse theory. This method is proposed by Mirković, Uzawa and Vilonen. Based on the G-orbit-decomposition, I will prove that the equivariant K-theory K^G(X) is isomorphic to K^U(X), after a shift of dimension, where U is the maximal compact subgroup of G. This gives a proof of the Connes-Kasparov conjecture "on flag variety". If time allows I will also talk about the relation between G-orbits on flag variety and representation theory.

November 1st, 2012 (02:30pm - 03:30pm)
Seminar: MASS Colloquium
Title: Some polynomial dynamics systems
Speaker: Alice Medvedev, UC Berkeley
Location: MB113

Consider a (discrete) dynamical system F(x, y, z) := ( f(x), g(y), h(z) ) for polynomials f, g, and h, acting on the three-dimensional space over complex numbers. What subsets S are invariant under F, in the sense that F(S) is a subset of S? In particular, what algebraic sets, that is solution sets of systems of polynomial equations, are invariant under F? I will describe the tools from modern model theory, a branch of mathematical logic, that reduce this question to understanding composition of one-variable polynomials, and an old theorem of Ritt that supplies this understanding.

November 1st, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: numerical modeling of multicomponent multiphase reactive flow in porous media
Speaker: Changhe Qiao, Dept. of Mathematics
Location: MB216
November 2nd, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Block Preconditioning for Multi-physics: From Jacobi to Schur Complements*
Speaker: Eric Cyr, Sandia Natl. Lab.
Location: MB114

Developing scalable solvers for fully-coupled multi-physics is challenging. One approach is to use advanced multigrid algorithms to achieve scalability on these problems. However, this approach can suffer from stability issues, in particular the coarse grid operators used in AMG can become ill-conditioned. An alternative to fully-coupled multigrid is to use a block decomposition of the linear system. This segregates the linear system into physical fields, for instance separating Navier-Stokes into velocity and pressure components leads to a 2x2 Jacobian operator. These approaches are appealing because segregated operators are more amenable to multigrid, yet achieving good parallel scalability for the coupled system is still possible. The difficulty with these methods is efficiently and effectively handling the coupling between the different physics. In this talk I will overview a number of block preconditioners focusing on exploiting the structure of the operators. Furthermore, I will present a few techniques for approximating Schur-complement operators. To make this concrete, applications in fluid dynamics and magnetohydrodynamics will be discussed. *This work was partially supported by the DOE office of Science Applied Math Program at Sandia National Laboratory. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DEM-AC04-94AL85000.

November 2nd, 2012 (02:20pm - 03:20pm)
Seminar: Seminar on Probability and its Application
Title: Nonlinear and Nonlocal Evolution Equations Driven by Levy Diffusions: Porous Media and Evolutionary Ecology
Speaker: W.A. Woyczynski, Case Western Reserve University
Location: MB106

Quasilinear evolution equations involving nonlocal generators can be often interpreted as hydrodynamic limits of interacting particle systems. However, for strongly nonlinear equations, such as the porous medium equation, the probabilistic interpretation is more complex and leads to the so-called nonlinear McKean-Vlasov equations. In cases of branching processes the limiting description may even preserve a random fluctuation term in the resulting evolution equation. Such is the case in certain evolutionary population dynamics models.

November 2nd, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Scalable Implicit Solution Methods for Multiple-time-scale Multiphysics Systems: Applications from CFD, Transport/Reaction, and MHD*
Speaker: J.N. Shadid, Sandia Natl. Lab.
Location: MB106

A current challenge before the computational science and numerical mathematics community is the efficient computational solution of multiphysics systems. These systems are strongly coupled, highly nonlinear and characterized by multiple physical phenomena that span a very large range of length- and time-scales. These interacting, nonlinear, multiple time-scale physical mechanisms can balance to produce steady-state behavior, nearly balance to evolve a solution on a dynamical time scale that is long relative to the component time-scales, or can be dominated by just a few fast modes. These characteristics make the scalable, robust, accurate, and efficient computational solution of these systems extremely challenging. This presentation will discuss issues related to the stable, accurate and efficient time integration, nonlinear, and linear solution of multiphysics systems. The discussion will begin with an illustrative example that compares operator-split to fully-implicit methods. The talk will then continue with an overview of a number of the important fully-coupled solution methods that our research group has applied to the solution of coupled multiple-time-scale multi-physics systems. These solution methods include, fully-implicit time integration, direct-to-steady-state solution methods, continuation, bifurcation, and optimization techniques that are based on Newton-Krylov iterative solvers. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled multilevel preconditioners are employed. The multilevel preconditioners are based on two differing approaches. The first technique employs a graph-based aggregation method applied to the nonzero block structure of the Jacobian matrix. The second approach utilizes approximate block decomposition methods and physics-based preconditioning approaches that reduce the coupled systems into a set of simplified systems to which multilevel methods are applied. The multilevel preconditioners are then compared to standard variable overlap additive one-level Schwarz domain decomposition type preconditioners. To demonstrate the capability of these methods representative results are presented for the solution of transport/reaction and resistive magnetohydrodynamic systems with stabilized finite element methods. In this context robustness, efficiency, and the parallel and algorithmic scaling of solution methods are discussed. These results will include the solution of systems with up to a billion unknows on 100K cores of current large-scale parallel architectures. *This work was partially supported by the DOE office of Science Applied Math Program at Sandia National Laboratory. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DEM-AC04-94AL85000.

November 2nd, 2012 (04:35pm - 05:45pm)
Seminar: Logic Seminar
Title: Unions of chains of signatures
Speaker: Alice Medvedev, University of California, Berkeley
Location: MB315

We meditate on a particularly naive notion of a limit of a sequence of theories: a union of conservative expansions. That is, we consider a sequence of nested signatures $L_1 \subset L_2 \subset \ldots$, each one a subsignature of the next, and a sequence of $L_i$-theories $T_i$ where each $T_i$ is precisely the set of $L_i$-consequences of $T_{i+1}$. It turns out that many model-theoretic properties then pass from all $T_i$ to their union $T$; these include consistency, completeness, quantifier limination, partial quantifier elimination such a model-completeness, elimination of imaginaries, stable embeddedness of some definable set, characterization of algebraic closure; stability, simplicity, rosiness, dependence. Our motivating example is the theory $T$ of fields with an action by $(\mathbb{Q}, +)$, seen as a limit of (theories of) fields with $(\mathbb{Z}, +)$-actions.

November 5th, 2012 (10:30am - 12:00pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Multigrid Method for Fluid-Structure Interfaction"
Speaker: Kai Yang, Adviser: Jinchao Xu, Penn State
Location: 113 Sackett Building
Abstract: http://

Fluid-Structure Interactions (FSI) is a common physical phenomemon. It requires complicated models and introduces numerical difficulties. Numerous studies have been done on the partitioned approach and the monolithic approach. In our work, the coupling of heat equations and wave equations is considered. And we keep interface conditions of FSI in this model in order to show the monolithic approach we are considering. Geometric multigrid method is applied to solve the discretized problem on each time step and the performance is shown. We also present some future works about multigrid method for FSI.

November 5th, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Gap Distributions and Homogeneous Dynamics
Speaker: Jayadev Athreya, University of Illinois at Urbana-Champaign
Location: MB106

The Farey sequence F(Q) is the collection of fractions between [0,1] whose denominator (when written in lowest terms) is at most Q. As Q grows, these points become uniformly distributed in the interval, so in some sense, look `random'. However, when you look at the gaps between them, they do not behave like those for uniformly distributed random variables, but instead follow an unusual law known as Hall's Distribution. We will explain a proof of this result that uses horocycle flow on the space of lattices SL(2,R)/SL(2, Z), and, time permitting discuss how this picture can be generalized to understanding gaps between directions of saddle connections on Veech surfaces. This talk will include elements from joint work with Y. Cheung, joint work with J. Chaika, and joint work with J. Chaika and S. Lelievre.

November 6th, 2012 (09:00am - 10:00am)
Seminar: Computational and Applied Mathematics Colloquium
Title: Modeling and simulation of the self-assembly of crystalline microstructures
Speaker: Maciek Korzec, Technical University Berlin
Location: MB216
Abstract: http://

To optimize materials that are used in photovoltaic applications — in particular for third generation solar cells — realistic continuum models are sought that can lead to a more efficient approach for finding improved growth parameters. The usual trial and error approach has lead to many good results, mostly however with the downside that many experiments had to be carried out for that end. Fundamental knowledge has to be united to derive realistic models that allow for a fast simulation. Eventually this can lead to a reduction of the number of experiments by supporting the work with optimized growth parameters. In this talk a model for Stranksi-Krastanov growth of quantum dots is presented, a small-slope approximation is carried out, pseudospectral methods with various time-stepping possibilities are introduced and numerical results are presented. In the last part of the presentation ongoing challenges are discussed, i.e. the dewetting of thin silicon films during annealing and grain growth.

November 6th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA, TBA
Location: MB216
November 6th, 2012 (01:20pm - 02:20pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Short time symptotics for solutions of parabolic equations
Speaker: Victor Nistor, Penn State Math
Location: MB106

I will present a new method to solve parabolic equations. The method is based on short time asymptotics for the solution and a bootstrap procedure to extend this approximation to larger times. Our main applications are to the equations that arise in Finance, but this method can be in principle applied to any evolution equation. One of the technical advances that makes this method work is an approximate computation of the perturbative integrals (Dyson series) that were widely studied in Physics. The method is unconditionally stable and numerical tests show that it is very efficient. The results presented in my talk are joint work with W. Cheng, R. Constantinescu, N. Costanzino, J. Liechty, and A. Mazzucato.

November 6th, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: T-duality for nonprincipal circle bundles and noncommutative geometry
Speaker: Jonathan Rosenberg, University of Maryland
Location: MB106

"Topological T-duality", which was first discovered by physicists, gives an involution on the set of pairs (p: X --> Z, H), where p: X --> Z is a principal S^1 bundle and H is a 3-dimensional cohomology class on X. Recently David Baraglia pointed out that this theory can be extended to cover the case of nonprincipal circle bundles as well. In recent work with Varghese Mathai, we show that Baraglia's results can be reproduced in two ways: a) via a homotopy-theoretic approach à la Bunke-Schick, and b) via noncommutative geometry and crossed products. The latter method leads to the general analysis of K-theory for crossed products by the semidirect product of Z/2 acting on the reals.

November 6th, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Gale-Stewart games and Blackwell games
Speaker: Daisuke Ikegami, University of California, Berkeley
Location: MB315

Starting from the determinacy of Chess by Zermelo, the theory of determinacy of games with perfect information has been developed exclusively. Among those games, Gale-Stewart games are general infinite games which have applications to set theory, model theory, and theoretical computer science. Apart from that, the research in games with imperfect information has started in game theory since von Neumann's minimax theorem, and Blackwell games are one of the few infinite games with imperfect information which are tractable to discuss their determinacy. In this talk, we discuss the connection between the determinacy of Gale-Stewart games and that of Blackwell games. Our main result is that assuming the Axiom of Dependent Choice, the axiom of determinacy of Blackwell games with reals is equivalent to that of Gale-Stewart games with reals. This is joint work with W. Hugh Woodin.

November 6th, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Algebraic K-theory and its applications to dynamics, I
Speaker: Kurt Vinhage, Penn State
Location: MB216
November 8th, 2012 (09:00am - 10:10am)
Seminar: Mathematical Biology & Physiology Seminar
Title: mathematical biology seminar
Speaker: TBA, TBA
Location: MB114
Abstract: http://www.math.psu.edu/treluga/mmbs.html
November 8th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA, Penn State
Location: MB216
November 8th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Wooley's recent work on the Vinogradov Mean Value Theorem
Speaker: Robert C. Vaughan, Penn State
Location: MB106

I will give a brief overview of the history of Vinogradov's Mean Value Theorem and discuss Trevor Wooley's recent work on this subject along with some of the consquences.

November 8th, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: The structure of simple operator algebras
Speaker: Nate Brown, Penn State
Location: MB106
November 8th, 2012 (02:30pm - 03:30pm)
Seminar: MASS Colloquium
Title: Seeing Invisible: Mathematics of Medical Imaging
Speaker: Peter Kuchment, Texas A&M University
Location: MB113

In this talk I will attempt to give the attendees the idea of what kind of mathematics is involved into contemporary medical imaging. Most of you have probably heard of CAT scan, MRI, and maybe some other CT (computed tomography) types. However, it is not that often that people know that tomographic images are not actual images, but rather results of intricate mathematical procedures. Advanced mathematical tools play a huge role. The mathematics of this subject is beautiful, hard, and diverse. Just to give you an idea, it deals in particular with differential equations, differential and integral geometry, group representations, harmonic analysis, numerical analysis, and surely, computer programming. This is what has kept the speaker and many others hooked up on tomography for years. Several brand new cheap, effective, and safe tomographic methods are being developed by engineers right now, which requires new mathematical techniques. Similar techniques are used for industrial non-destructive testing and geophysical imaging.

November 8th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Preconditioning discretizations of systems of partial differential equations
Speaker: Lu Wang, Dept. of Mathematics Penn State
Location: MB216
November 8th, 2012 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: The nodal count mystery
Speaker: P. Kuchment, Texas A&M University
Location: MB114

In this talk we address the nodal count (i.e., the number of nodal domains) for eigenfunctions of Schroedinger operators with Dirichlet boundary conditions in bounded domains (billiards). The classical Sturm theorem claims that in dimension one, the nodal and eigenfunction counts coincide: the n-th eigenfunction has exactly n nodal domains. The Courant Nodal Theorem claims that in any dimension, the number of nodal domains of the n-th eigenfunction cannot exceed n. However, it follows from a stronger upper bound by Pleijel that in dimensions higher than 1 the equality can hold for only finitely many eigenfunctions. Thus, in most cases a ``nodal deficiency'' arises. Moreover, examples are known of eigenfunctions with an arbitrarily large index n that have just two nodal domains. One can say that the nature of the nodal deficiency had not been understood. We show that, under some genericity conditions, the answer can be given in terms of a functional on an infinite dimensional variety of partitions of the billiard, whose critical points correspond exactly to the nodal partitions and Morse indices coincide with the nodal deficiencies. This is joint work with G. Berkolaiko and U. Smilansky, just published on-line in GAFA.

November 9th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Possible Stack for Parallel Programming Models for Scientific Computing
Speaker: Zeyao Mo, Institute of Applied Physics and Computational Mathematics
Location: MB114

This talk reports on the possible stack for parallel programming models for scientific computing on the petascale or more powerful machines. The goal is to identify potential layers for parallel applications, numerical stencils, algorithms, implementation and run-time optimization oriented to more complex applications and more complex machines. The instance of JASMIN framework is used to illustrate such stacks.

November 9th, 2012 (02:20pm - 03:20pm)
Seminar: Seminar on Probability and its Application
Title: Robust sensitivity analysis for stochastic systems
Speaker: Henry Lam, Boston University
Location: MB106

Sensitivity analysis for stochastic systems is typically carried out via derivative estimation, which critically requires parametric model assumptions. In many situations, however, we want to evaluate model misspecification effect beyond certain parametric family of models, or in some cases, there plainly are no parametric model to begin with. Motivated by such deficiency, we propose a sensitivity analysis framework that is parameter-free, by using the Kulback-Leibler divergence as a measure of model discrepancy, and obtain well-defined derivative estimators. These estimators are robust in that they automatically choose the worst (and best)-case directions to move along in the (typically infinite-dimensional) model space. They require little knowledge to implement; the distributions of the underlying random variables can be known up to, for example, black-box simulation. Methodologically, we identify these worst-case directions of the model as changes of measure that are the fixed points of a class of functional contraction maps. These fixed points can be asymptotically expanded to obtain derivative estimators that are expressed in closed-form formula in terms of the moments of certain ``symmetrizations" of the system, and hence are readily computable.

November 9th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Nanogeometry
Speaker: Vincent Crespi, Physics Dept PSU
Location: MB106

This will be an informal talk on the roles of geometrical concepts in the physical properties of nanometer-scale systems, including systems of reduced dimensionality (2D) embedded in 3D space, and also the behavior of chemistry when confined and constrained geometrically.

November 12th, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Global rigidity of abelian Anosov actions on tori
Speaker: Zhiren Wang, Yale University
Location: MB106

As part of a more general conjecture by A. Katok and R. Spatzier, the following statement was expected to hold: if a smooth $\mathbb Z^r$-action $\alpha$ on a torus contains one Anosov element and has no rank-1 factor, then it must be smoothly conjugate to its linearization $\alpha_0$, which is an action by toral automorphisms. D. Fisher, B. Kalinin and R. Spatzier showed this holds under the assumption that $\alpha$ has at least one Anosov element in every Weyl chamber of the linearization action. We will verify that this assumption is redundant, hence fully establish the statement above. This is a joint work with Federico Rodriguez Hertz.

November 13th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discussion session
Speaker: TBA
Location: MB216
November 13th, 2012 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: A Graph-Theoretical Approach to Euclidean Oriented Matroids
Speaker: Leandro Junes, Cal U of PA
Location: MB106

This is the second of a series of two talks. I will address my research with euclidean oriented matroids. The euclidean property in oriented matroids resembles the euclidean property in the n-dimensional space, and it is characterized by a graph. My research introduces a new characterization of euclidean oriented matroids using a new graph. The new graph is an improvement in the following sense: it provides a strong connection between the new graphs of an oriented matroid program and its dual. As an application, I will provide a graph theoretical proof for Fukuda’s duality of the Euclidean property.

November 13th, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Formal Hecke algebras and oriented cohomology theories
Speaker: Alexander Hoffnung, Temple
Location: MB106

The affine Hecke algebra can be constructed geometrically on the equivariant K-theory of the Steinberg variety. Many related convolution constructions appear in geometric representation on various (co)homology theories. It seems natural to work towards a theory of higher representation theory in order to find a unified framework for such geometric constructions. We implement formal methods to study the role of arbitrary oriented cohomology theories in analogues of geometric constructions in representation theory. We generalize the construction of the nil Hecke ring of Kostant and Kumar to the context of an arbitrary oriented cohomology theory of Levine and Morel, e.g. to Chow groups, connective K-theory, elliptic cohomology, or algebraic cobordism. In particular, we define formal (affine) Demazure algebras and formal (affine) Hecke algebras. These depend on one-dimensional commutative formal group laws and specialize to known variants of the Hecke algebra at the additive and multiplicative formal group laws. In general, this family of formal Hecke algebras satisfies equations that we call ´oriented braid relations´, which agree with the usual braid relations at the additive and multiplicative formal group laws. Joint work w. José Malagón Lopez, Alistair Savage, and Kirill Zainoulline

November 13th, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Computable randomness and martingales a la probability theory
Speaker: Jason Rute, Carniegie Mellon University
Location: MB315

In this talk, I will outline a martingale characterization of computable randomness that goes beyond the usual one. An infinite sequence of coin flips is said to be computably random if one cannot win arbitrarily large amounts of money while betting on the flips with a computable strategy (called a martingale) and a limited starting capital. In this talk I will extend the notion of computable betting strategy to the martingale definition more commonly used in probability theory. In probability theory, a martingale is a pair (M,F), where M={M_n} is sequence of random variables and F={F_n} is a sequence of increasing sigma-algebras (called a filtration), such that E[M_{n+1} | F_n] = M_n for all n. The L^1 bound of a martingale M is the supremum over n of the L^1 norm of M_n. The limit F_infty of a filtration F is the sigma-algebra generated by the union of all F_n. I will show that a point x in a computable Polish space with a computable Borel measure is computably random if an only if for all computable martingales (M,F) such that the L^1 bound is computable and F_infty is computable, the sequence M_n(x) is Cauchy. Not only does this result extend the usual definition, but it covers most (if not all) known gambling characterizations of computable randomness. It also is easily adapted to characterize Schnorr and Martin-Lof randomness This result draws together a number of tools from computable analysis and randomness. I will define what it means for a point to be computably random on a computable Borel measure. I will define what it means for a martingale and a sigma-algebra to be computable. I will also discuss various measure theoretic lemmas that are not only useful in proving this result, but are useful in proving many facts about algorithmic randomness.

November 13th, 2012 (02:30pm - 03:20pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Modeling and simulation of the self-assembly of crystalline microstructures
Speaker: Maciek Korzec, Technical University Berlin
Location: MB216
Abstract: http://

To optimize materials that are used in photovoltaic applications — in particular for third generation solar cells — realistic continuum models are sought that can lead to a more efficient approach for finding improved growth parameters. The usual trial and error approach has lead to many good results, mostly however with the downside that many experiments had to be carried out for that end. Fundamental knowledge has to be united to derive realistic models that allow for a fast simulation. Eventually this can lead to a reduction of the number of experiments by supporting the work with optimized growth parameters. In this talk a model for Stranksi-Krastanov growth of quantum dots is presented, a small-slope approximation is carried out, pseudospectral methods with various time-stepping possibilities are introduced and numerical results are presented. In the last part of the presentation ongoing challenges are discussed, i.e. the dewetting of thin silicon films during annealing and grain growth.

November 13th, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Algebraic K-theory and its applications to dynamics, II
Speaker: Kurt Vinhage, Penn State
Location: MB216
November 14th, 2012 (09:05am - 09:55am)
Seminar: Computational and Applied Mathematics Colloquium
Title: Norm inflation for the 2D Debye-Hu ̈ckel system in Besov Spaces
Speaker: Chao Deng, University of Colorado at Boulder
Location: MB315
Abstract: http://

Based on the construction of Bourgain and Pavlovi\'{c} ``{\it JFA {\bf 255}(2008):\! 2233--2247}" for the Navier-Stokes equations in periodic case, we demonstrate that the solutions to the Cauchy problem for the two dimensional Debye-H\"uckel system can develop norm inflations in with data in $B^{-\frac{3}{2}}_{4,\infty}(R^2)$.

November 14th, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Alexandrov geometry and isometric actions
Speaker: Anton Petrunin, Penn State
Location: MB106

It is a survey talk on applications of ALexandrov geometry in study of isometric group actions via Alexandrov geometry.

November 15th, 2012 (09:00am - 10:10am)
Seminar: Mathematical Biology & Physiology Seminar
Title: mathematical biology seminar
Speaker: TBA, TBA
Location: MB114
Abstract: http://www.math.psu.edu/treluga/mmbs.html
November 15th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion
Speaker: TBA
Location: MB216
November 15th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: F-pure thresholds of quasi-homogeneous polynomials
Speaker: Daniel Hernandez, University of Minnesota
Location: MB106

The F-pure threshold of a polynomial over a finite field is a numerical invariant which measures the singularities of the associated hypersurface. Amazingly, this prime characteristic invariant is closely related to the log canonical threshold, a well-known invariant of singularities in characteristic zero. In this talk, we recall the relationship between these two invariants, and will present recent work regarding the computation of F-pure thresholds for quasi-homogeneous polynomials. This is joint work with Luis Nunez Betancourt, Emily Witt, and Wenliang Zhang. Note that some of our methods are based on ideas of Bhargav Bhatt and Anurag Singh.

November 15th, 2012 (01:00pm - 02:00pm)
Seminar: Game Theory Seminar
Title: Imitation Dynamics of Altruists and Egoists in an Overlapping Neighborhood Local Interaction Network Model
Speaker: Kyle Wray, Depts of Mathematics, Computer Science and Applied Research Laboratory, PSU
Location: MB114

An overlapping neighborhoods local interaction network model with imitation learning dynamics is presented in which the local of interaction of neighbors is to engage in Prisoner’s Dilemma games with one another. Karl Sigmund, Avner Shaked et al, published a thorough characterization of 1-dimensional networks (integral points on lines and circles) but had stalled exploring 2-dimensional networks, specifically the torus Zn x Zn , the direct extension of the circles Zn they had cataloged. We replaced the torus with the geodesic dome as a 2-dimensional network more closely resembling the globe, though not entirely regular, and in subsequent research have begun dropping the regularity condition altogether to begin cataloging local neighborhood patterns of interaction. We also consider 4 related learning rules with subtle but important differences. In this talk I will present the global model, the learning rules, and patterns of convergence observed in numerous simulation trials. I will also show proofs of a few local neighborhood dynamic patterns and two global patterns that we have proven. We are far from proving all of the observed dynamics, but I will show visualizations created with openGL, in an effort to gain insight into the dynamics.

November 15th, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Noncommutative covering dimension
Speaker: Nicola Watson, University of Toronto
Location: MB106

There have been many fruitful attempts to define noncommutative versions of the covering dimension of a topological space, ranging from the stable and real ranks to the decomposition rank. In 2010, Winter and Zacharias defined the nuclear dimension of a C*-algebra, which has turned out to be a major development in the study of nuclear C*-algebras. In this talk, we introduce nuclear dimension, discuss the differences between it and other dimension theories, and focus on why nuclear dimension is so important.

November 15th, 2012 (02:30pm - 03:30pm)
Seminar: MASS Colloquium
Title: A short look at the long history of the lemniscate of Bernoulli
Speaker: Joel Langer, Case Western Reserve University
Location: MB113

Could a beautiful plane curve launch a thousand propositions? To make the case for the lemniscate, this talk will romp through hundreds (ok thousands!) of years of history: From the spiric sections of Perseus, to the planetary orbits of Cassini, to mechanical linkages of Watt and others; not to mention the ``Enigma of Viviani's Temple" and the early investigations on the theory of elasticity by Bernoulli himself. But above all, the lemniscate is tied to the birth of elliptic functions and their connections to the theory of equations and numbers through the discoveries of Count Fagnano, Euler, Gauss and Abel. All of this predates the fuller view of the lemniscate as a Riemann surface of genus zero--i.e., a sphere--sitting in the complex projective plane. In this setting, the ever-elegant lemniscate turns out to have octahedral symmetry. In fact, with the help of pictures, this talk will attempt to provide some impression of the lemniscate as a disdyakis dodecahedron.

November 15th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Analysis of the Navier-Stokes-Poisson-Nernst-Planck SYSTEM
Speaker: Shixin Xu, Dept. of Maths Penn State University
Location: MB216
November 15th, 2012 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Contractions of Lie Groups and Representation Theory
Speaker: N. Higson, Department of Mathematics, Penn State
Location: MB114

The contraction of a Lie group G to a subgroup K is a new Lie group, usually easier to understand than G itself, that approximates G to first order near K. The name comes from the mathematical physicists, who examined the Galilean group as a contraction of the Poincare group of special relativity. My focus will be on a related but different class of examples: the prototype is the group of isometric motions of Euclidean space, viewed as a contraction of the group of isometric motions of hyperbolic space. It is natural to expect some sort of limiting relation between representations of the contraction and representations of G itself. But in the 1970s George Mackey discovered an interesting rigidity phenomenon: as the contraction group is deformed to G, the representation theory remains in some sense unchanged. In particular the irreducible representations of the contraction group parametrize the irreducible representations of G. I shall formulate a reasonably precise conjecture along these lines that was inspired by subsequent developments in C*-algebra theory and noncommutative geometry, and describe the evidence in support of it, which is by now substantial. However a conceptual explanation for Mackey's rigidity phenomenon remains elusive.

November 16th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Mathematical Analysis of linearized peridynamics
Speaker: Tadele Mengesha, Mathematics PSU
Location: MB114

We analyze the linearized bond-based peridynamic model of continuum mechanics. The focus is on models of isotropic elastic materials that allow an indefinite micromodulus kernel. Using standard variational techniques we prove the well posedness of the system of equilibrium equations, given as a nonlocal boundary value problem. We will also study the Cauchy problem of the time dependent equations of motion. In the event of vanishing nonlocality solutions of the nonlocal system are shown to converge to the Navier system of classical elasticity. Our analysis is based on some nonlocal Poincare-type inequalities and compactness of the corresponding nonlocal operators.

November 16th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Mathematical theory for charged particles: from kinetic equations to continuum models
Speaker: Hao Wu, Mathematics, Fudan University, China
Location: MB106

The impact of charged-particles on the human's life is constantly increasing, due to their importance in such domains as plasma physics, industrial processes, biology, etc. It is related to a large variety of physical situations and has complex multiscale character. In this talk, I will explore the mathematical theory for the charged particles including the kinetic equations and continuum field models. In particular, I will discuss the diffusion limit of Vlasov-Poisson-Fokker-Planck (VPFP) equations to the Poisson-Nernst-Planck (PNP) equations for multispecies charged particles, which are widely used to describe the drift-diffusion of electrons and holes in semiconductors, as well as the movement of ions in solutions and protein channels. Besides, I will discuss the well-posedness and long-time behavior of the PNP equations with a nonlinear generation-recombination rate.

November 20th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discussion session
Speaker: geng Chen, penn State
Location: MB216
November 22nd, 2012 (09:00am - 10:10am)
Seminar: Mathematical Biology & Physiology Seminar
Title: mathematical biology seminar
Speaker: TBA, TBA
Location: MB114
Abstract: http://www.math.psu.edu/treluga/mmbs.html
November 22nd, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discussion session
Speaker: TBA
Location: MB216
November 22nd, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No talk this week
Speaker: Mr Turkey, Thanksgiving
Location: MB106
November 26th, 2012 (03:00pm - 05:00pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Tensor Networks, Complexity Theory, and Algebraic Geometry"
Speaker: Jacob Turner, Adviser: Jason Morton, Penn State
Location: 319 Sackett Building

Tensor networks are a tool that have many applications to different fields. I am particularly interested in its connections to complexity theory and algebraic geometry. First I'll discuss applications of tensor networks in finding polynomial time algorithms. Then I'll talk about how the hardness of counting problems implies relations on varieties.

November 26th, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: The Statistics of Self-Intersections of Closed Curves on Orientable Surfaces
Speaker: Matthew Wroten, SUNY, Stoney Brook
Location: MB106

Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case of closed surfaces) as a cyclic word of minimal length in terms of the fundamental group's generators. The self-intersection number of a conjugacy class is the minimal number of transverse self-intersections of representatives of the class. By using Markov chains to encapsulate the exponential mixing of the geodesic flow and achieve sufficient independence, we can use a form of the central limit theorem to describe the statistical nature of the self-intersection number. For a class chosen at random among all classes of length n, the distribution of the self intersection number approaches a Gaussian when n is large. This theorem generalizes the result of Steven Lalley and Moira Chas to include the case of closed surfaces.

November 27th, 2012 (03:30am - 05:30am)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Numerical modeling of multicomponent multiphase reactive flow in porous media"
Speaker: Changhe Qiao, Adviser: Jinchao Xu, Penn State
Location: 307 Boucke Building
Abstract: http://

The development of robust and efficient oil reservoir simulator is crucial to the petroleum engineering industry. The efficient computational solution of this multi-physics system is challenging. The complexity and difficult arises from the strongly coupled, highly nonlinear phenomena that describe multiphase flow,transport, thermodynamics, and geochemical reaction. A very large range of length and time scales are involved and the balancing between systems added to the difficulty. The solution of such system is meaningful, both in theoretical and practical aspects. In my comprehensive exam, I will talk about mathematical models, existing numerical schemes, some preliminary results and future research.

November 27th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion
Speaker: Geng chen
Location: MB216
November 27th, 2012 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Combinatorial interpretations as two-line array for the mock theta functions
Speaker: Plinio Santos, UNICAMP
Location: MB106

The mock theta functions introduced by Ramanujan have been studied by many authors both analytically and combinatorically. The combinatorial interpretations that are known for some of them are quite different in nature. In this paper we present combinatorial interpretation as two-line array for many of the classical mock theta functions.

November 27th, 2012 (01:20pm - 02:20pm)
Seminar: Probability and Financial Mathematics Seminar
Title: On zero-sum stochastic differential games with unbounded controls
Speaker: Song Yao, University of Pittsburgh Mathematics
Location: MB106

We study a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The pay-offs of the game are defined via a (decoupled) forward-backward stochastic differential equation. We prove that each player's priority value satisfies a weak dynamic programming principle and thus solves the associated Hamilton-Jacobi-Bellman-Isaacs equation in the viscosity sense. This is joint work with Erhan Bayraktar.

November 27th, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Fock space and Renormalization
Speaker: Si Li, Boston University
Location: MB106

I'll explain the classical idea of quantization on Fock space via Costello's renormalization scheme, and some geometric applications to topological string theory on Calabi-Yau manifolds.

November 27th, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Explicit and implicit definability over the integers, part 1
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315

We begin with a discussion of implicit and explicit definability in general, mentioning Beth's Definability Theorem. We then specialize to definability over the ring of integers. (So now we are talking about what recursion theorists call arithmetical sets versus arithmetical singletons.) The main part of the talk consists of three examples. Example 1: a set X which is implicitly definable but not explicitly definable. Namely, X = the Tarski truth set for arithmetic. Example 2: an implicitly definable pair of sets X, Y such that Y by itself is not implicitly definable. Namely, X = the Tarski truth set and Y = a set which is explicitly definable from X and Cohen-generic for arithmetic. Example 3: a pair of sets X, Y such that X is implicitly definable, Y is implicitly definable, X is not explicitly definable from Y, and Y is not explicitly definable from X. This is an unpublished result of Leo Harrington.

November 27th, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Higher cohomology for group actions with hyperbolic structure, I.
Speaker: Felipe Ramirez, University of Bristol
Location: MB216
November 28th, 2012 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: An algebraic perspective on tensor network states
Speaker: Jason Morton
Location: MB106
November 28th, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: CANCELLED
Speaker: Igor Rivin - CANCELLED
Location: MB106
November 29th, 2012 (09:00am - 10:10am)
Seminar: Mathematical Biology & Physiology Seminar
Title: mathematical biology seminar
Speaker: TBA, TBA
Location: MB114
Abstract: http://www.math.psu.edu/treluga/mmbs.html
November 29th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion
Speaker: TBA
Location: MB216
November 29th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Singularities of graded sequences of ideals
Speaker: Mircea Mustata, University of Michigan
Location: MB106

Instead of studying singularities of a hypersurface or an ideal, in many settings one is led to studying singularities for certain sequences of ideals. In this talk I will discuss various asymptotic invariants that one can attach to such sequences and connections to valuation theory.

November 29th, 2012 (01:00pm - 02:00pm)
Seminar: Game Theory Seminar
Title: Rational behavior in an epidemic game
Speaker: Dongmei Zhang, Dept of Mathematics, Penn State University
Location: MB106

Epidemics of infectious diseases, like smallpox, cholera, and HIV, have been a major health issue around the world. Some infectious diseases, like HIV and malaria, continue to reduce global health, in part because of poor treatment options and the absence of effective vaccines. This leaves behavior-based interventions as people’s primary tool for managing risk., and changes in behavior often come at a price. Therefore, people have to consider balancing the risk of illness against the costs of prevention. Due to the feedback loop between behavior and disease prevalence, the optimal behavior of one person depends on the behavior of everybody else. In this talk, I present the use of games in epidemiology to model such interaction and identify the non-trivial Nash equilibrium behavior strategy when the epidemic dynamics reach certain steady-state with numerical simulation. To be more realistic, our model takes in to account the heterogeneity of the population regarding both time since infection and time since birth (age) on a continuous level. Several transmission cases have been investigated in detail as examples.

November 29th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Lab-on-a-Chip Technologies Enabled by Acousto-Opto-Fluidics
Speaker: Tony Jun Huang, Department of Engineering Science and Mechanics, Penn State University
Location: MB216

The past decade has witnessed an explosion in lab-on-a-chip research. This rapid development has occurred mainly because of the continuous fusion of new physics into microfluidic domains. In recent years, researchers have made significant progress in joining acoustic and optical technologies with microfluidics. Optofluidics, the merger between optics and microfluidics, enables the creation of reconfigurable optical components that are otherwise difficult to implement with solid-state technology. Acoustofluidics, on the other hand, offers noninvasive solutions for many on-chip biomedical applications. In this talk, I will present several lab-on-a-chip innovations enabled by acoustofluidics and optofluidics, including acoustic tweezers, tunable optofluidic lenses, and miniature fluorescence-activated cell sorters (FACS). These technological innovations have many advantages and are packaged in simple, elegant designs. For example, our acoustic tweezers operate at ~107 times lower power intensity than current optical tweezers. The low power intensity renders our technology non-invasive toward delicate biological samples, as confirmed by experimental results. Moreover, the acoustic tweezers are amenable to miniaturization and versatile—they can be applied to virtually any type of cell or microparticle regardless of size, shape, or electrical/magnetic/optical properties. With these advantages in versatility, miniaturization, power consumption, and technical simplicity, our acoustic tweezers technique are expected to become a powerful tool in many applications, including tissue engineering, microarrays, stem cell biology, and drug screening/discovery.

November 29th, 2012 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Singularities: characteristic zero versus positive characteristic
Speaker: M. Mustata, University of Michigan
Location: MB114

A very basic invariant of the singularities of a polynomial at a point is its multiplicity. I will discuss two ``fancy" versions of this invariant, and connections between them. The first one lives (mostly) in characteristic zero and can be described as an integrability exponent. The second one lives in positive characteristic, and owes its existence to the Frobenius homomorphism.

November 30th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Besov spaces and the Littlewood-Paley decomposition
Speaker: Roman Shvydkoy, UI Chicago
Location: MB114

This lecture will introduce some of the tools from harmonic analysis that will be used in the main talk of the speaker. Besov spaces and their several equivalent definitions will be the central topic of discussion. We will review the Bernstein's inequalities and the Littlewood-Paley decomposition.

November 30th, 2012 (02:20pm - 03:20pm)
Seminar: Seminar on Probability and its Application
Title: Stochastic Integration of Two-Parameter Semimartingales and Weak Convergence
Speaker: Brian Nowakowski, Penn State University
Location: MB106

We present an extension of work by Jakubowski, Memin and Pages to the setting of stochastic processes with a multidimensional time parameter. In particular, we demonstrate that under suitable conditions, convergence of the pair (X_n,Y_n) to (X,Y) implies the convergence of \int Y_n dX_n to \int Y dX. An extension of the relevant topologies, as well as a new approach to multi-parameter stochastic integrals, will also be discussed.

November 30th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Anomalous energy dissipation and intermittency in ideal fluids
Speaker: Roman Shvydkoy, UI Chicago
Location: MB106

A long standing hypothesis of Onsager states that the minimal regularity of a velocity field of an ideal fluids that guarantees energy conservation is Holder-1/3. He also conjectures that there should exist a weak solution of regularity 1/3 that dissipates energy. In this talk we will given on overview of the current state of the Onsager conjecture and draw connections to the Kolmogorov theory of turbulence and intermittency.