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October 1st, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Prime factors of dynamical sequences
Speaker: Xander Faber, McGill University
Location: MB106

Euclid's proof that there are infinitely many primes can be recast as a statement about the existence of primitive prime factors of a certain sequence defined by a polynomial dynamical system on the projective line. I will describe a few generalizations of this dynamical statement for arbitrary rational functions. On the arithmetic side, this gives infinitely many new proofs that there are infinitely many primes. On the geometric side, it gives information about the mod p structure of orbits for dynamical systems. The proofs are an amusing mixture of ideas from number theory and complex dynamics.

October 1st, 2009 (02:30pm - 03:20pm)

Seminar: MASS Colloquium
Title: Discovering and proving theorems by physical reasoning
Speaker: Mark Levi, Penn State
Location: MB113

Physics often provides mathematics not only with a problem, but also with the idea of a solution. Some calculus problems can be solved more quickly without calculus, by using physics instead. A few examples of such problems will be given in a part of this talk. In addition to these problems, quite a few theorems which may seem somewhat mysterious become completely obvious when given a proper physical incarnation. This is the case for both ``elementary" theorems (the Pythagorean theorem, Pappus' theorems, some trig identities, and many, many more) and the less elementary ones: Noether's theorem, the preservation of Poincare's integral invariants, the Gauss-Bonnet theorem, the Riemann Mapping Theorem, Green's theorem, Moser's theorem on uniformization of density, etc. (no familiarity with any of these is assumed). I will describe a miscellaneous sampling from the above list, according to the audience's interest. No background beyond calculus and basic mechanics will be assumed in this talk.

October 1st, 2009 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Sieves and their applications
Speaker: Emmanuel Kowalski, ETH, Zurich
Location: MB114

Sieve methods are among the basic tools to study the distribution of primes in various sequences, and the variety of techniques available is quite remarkable (small, larger and larger sieves may be used depending on the problem at hand). Viewed somewhat abstractly, the underlying principles have even wider applications. The talk will recall some of the classical achievements of sieve and present more recent ones, emphasizing the more surprising and unusual ones, which are of interest well beyond analytic number theory. Random 3-manifolds, elliptic divisibility sequences, random walks on discrete groups with Property (T), families of algebraic varieties over finite fields, and the Quantum Unique Ergodicity Conjecture may be mentioned, depending on time.

October 2nd, 2009 (12:00pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Introduction to traffic modeling with partial differential equations
Speaker: Harald Hanche-Olsen, Norwegian University of Science and Technology
Location: MB114

The mathematical study of traffic flow stems back at least to 1955, with a paper by Lighthill and Whitham and one by Richards. I will explain these models, in the process giving a brief introduction to nonlinear first order conservation laws and their solutions using characteristics and shock waves. I will then move on to more modern developments using higher order models. The highway is littered with failed models, but there are also several successful ones. This talk will serve as an introduction to the afternoon CAM Colloquium.

October 2nd, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Vacuum on the highway
Speaker: Harald Hanche-Olsen, Norwegian University of Science and Technology
Location: MB106

The study of traffic flow using nonlinear conservation laws stems back at least to 1955, with a paper by Lighthill and Whitham and one by Richards. These first order models have been quite successful, but have their limitations which many authors have tried to address with various higher order models. I will touch briefly of the history and arrive quickly at a model developed by Aw and Rascle in the form of a 2×2 system of conservation laws (or balance laws, if a relaxation term is included). This system is a Temple system, and hence its well-posedness is easily established. That is, unless vacuum (i.e., stretches of roadway with no traffic) can occur. In this case, strict hyperbolicity breaks down and we lose control over the total variation of the solution. I shall outline two existence proofs, and discuss questions of uniqueness and stability. This is joint work with Marte Godvik.

October 5th, 2009 (10:10am - 11:00am)

Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Quadrature and GFEM
Speaker: Uday Banerjee, Syracuse University
Location: MB114

October 5th, 2009 (02:30pm - 03:30pm)

Seminar: The Pritchard Lab Seminar
Title: Interfacial instabilities of reactive micellar fluids
Speaker: Andrew Belmonte, Dept of Mathematics, Penn State University
Location: MB216

Many fluid instabilities involving free surfaces are governed by interfacial forces - the classic example being surface tension. However, complex fluids often have other surface forces due to physical processes not present in the bulk. A striking example of this has been observed for viscoelastic micellar fluids, in which long tubelike aggregates form at low concentrations due to the presence of an organic salt/cosurfactant, without which the micelles are spherical and the fluid is completely Newtonian. I will present some recent experimental observations and modeling of instabilities occurring when two such Newtonian fluids react at their interface to produce a fragile elastic micellar material, including droplet splashes, sedimentation, and Hele-Shaw fingering.

October 5th, 2009 (04:00pm - 05:00pm)

Seminar: Student Geometric Functional Analysis Seminar
Title: TBA
Speaker: TBA
Location: MB315
Abstract: http://

October 6th, 2009 (11:15am - 12:05pm)

Seminar: Combinatorics/Partitions Seminar
Title: q,t-Catalan numbers and partition numbers
Speaker: Dr. Kyungyong Lee, Purdue University
Location: MB106

The q,t-Catalan numbers naturally occur in the study of Macdonald polynomials, which are an important family of multivariable orthogonal polynomials introduced by Macdonald in 1988 with applications to a wide variety of subjects including Hilbert schemes, harmonic analysis, representation theory, mathematical physics, and algebraic combinatorics. Haiman and Garsia-Haglund proved that they are polynomials of q and t with positive coefficients. Finding coefficients of the n-th q,t-Catalan number is equivalent to counting how many Catalan paths in the n*n square have the same statistics. We give simple upper bounds on coefficients in terms of partition numbers, and describe all coefficients which achieve the upper bounds.

October 6th, 2009 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Automatic groups
Speaker: John Clemens, Penn State
Location: MB315

I will give a short introduction to the area of automatic groups, beginning with an overview of finite state automata and problems decidable via automata. I will discuss various ways in which a structure such as a group can be presented by an automaton, and some of the structural properties of such structures.

October 6th, 2009 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Entropy in measurable dynamics, II
Speaker: Lewis Bowen, Texas A & M University
Location: MB216

This is the second talk in a 3-part series. It will be an introduction to my work in extending entropy theory to actions of free groups and more generally, sofic groups. One of the main results is a complete classification of Bernoulli shifts over a countable linear group.

October 6th, 2009 (05:00pm - 06:00pm)

Seminar: Slow Pitch Seminar
Title: Behavioral modelling in ecology and epidemiology.
Speaker: Timothy Reluga, Penn State University
Location: MB106

Behavior, social interactions, and their consequences are potentially the most maliable aspects of human and animal populations that influence the health and wellbeing of those individuals and communities. Many open mathematical problems can be found in this field, with both theoretical and applied flavors. In this talk, I'll outline some of my ongoing work on the analysis of behavior problems in epidemiology and ecology. Time-permitting, I'll discuss optimal social distancing in a flu pandemic, management of disease transmission in a spatially distributed population, and selfish herd theory.

October 7th, 2009 (12:15pm - 01:15pm)

Seminar: Geometry Luncheon Seminar
Title: Variation on a theme of Luroth
Speaker: Yuri Zarhin, Penn State
Location: MB114

Let X -> Y be a finite covering of compact Riemann surfaces. It is well known that if X is the Riemann sphere then Y is also the Riemann sphere. (An algebraic version of this result is called a theorem of Luroth.) It turns out that for a given g>1 a natural generalization of Luroth's theorem holds true only for ``almost all" X of genus g . We discuss explicit examples (and counterexamples).

October 7th, 2009 (03:30pm - 05:00pm)

Seminar: Logic Seminar
Title: Automatic structures
Speaker: Bakh Khoussainov, Cornell University and University of Auckland
Location: MB114

In this talk we introduce the concept of automatic structure, give examples, and prove some of the basic theorems about them. We provide results of positive character. For example, we explain why the isomorphism problems for automatic well-ordered sets and Boolean algebras are decidable. We also give examples of negative character. For example, we explain as to why the isomorphism problem for automatic structures is Sigma_1^1-complete. Time permitting, we outline some techniques of proving non-automaticity through the use of advanced group theory and additive combinatorics results.

October 8th, 2009 (11:00am - 12:30pm)

Seminar: Teaching Seminar
Title: The Virtual Office Hour
Speaker: Stan Smith
Location: MB114

As the H1N1 virus takes its toll and prevents students from attending class, the virtual office hour is one tool we, as instructors, can use to help confined students whilst minimizing personal exposure. This short seminar will introduce instructors to a convenient tool to open up a virtual office at no cost, complete with two-way audio, a chat tool, whiteboard, and the capability to share your desktop applications. As the interface is java based, it works well on all platforms with a java enabled browser.

October 8th, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Zeta functions of Complexes arising from PGL(n)
Speaker: Ming-hsuan Kang, Penn State University
Location: MB106

We define and investigate the properties of the zeta functions on the complex, which arises from a finite quotient of the affine Bruhat-Tits building on a general linear group over a local field. These zeta functions are analogue of varieties' zeta functions. Briefly speaking, for each type of simplex of dimension $k$, we define a zeta function which counts the number of $k$-dimensional closed straight geodesics containing the simplex of that type. Several important properties of zeta functions are concluded as follows. First, these zeta functions are rational functions and have closed-form expressions in terms of parahoric Hecke operators. Second, the alternating production of the zeta functions satisfies an identity which is involved in the Euler characteristic of the complex. Finally, we show that the Ramanujan property of complexes is equivalent to the condition on the absolute values of zeta functions' roots.

October 8th, 2009 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: C*-Algebras, Foliations and K-Theory 2
Speaker: John Roe, Penn State
Location: MB106
Abstract: http://www.math.psu.edu/roe/NCG/notes-index.html

October 8th, 2009 (02:30pm - 03:30pm)

Seminar: MASS Colloquium
Title: Two problems in combinatorial plane geometry
Speaker: Anton Petrunin, Penn State
Location: MB113

It is a story, how I was making exercises for school students and what happened after it.

October 8th, 2009 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: A journey into computable structures
Speaker: Bakh Khoussainov, University of Auckland, New Zealand, and Cornell University
Location: MB114

The theory of computable structures is a branch of mathematical logic which has connections to computability theory, model theory, algebra and theoretical computer science. The theory is motivated by questions about the effective content of mathematical results, issues related to complexity of mathematical structures, building specific models that satisfy given axioms, and decision problems. The aim of this talk is twofold. One is to explain computable structures, present basic definitions, give examples, and outline some of the main themes in the area. The other is to talk about several fundamental results and say a few words about their proofs. We emphasize issues related to computable isomorphisms and building computable structures with specific properties.

October 9th, 2009 (12:00pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Introduction to Lie groups, variational integrators, and geometric optimal control
Speaker: Melvin Leok, Department of Mathematics, University of California, San Diego
Location: MB114

This will serve as an introduction to the afternoon CAM Colloquium.

October 9th, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Lie group and homogeneous variational integrators and their applications to geometric optimal control theory
Speaker: Melvin Leok, Department of Mathematics, University of California, San Diego
Location: MB106

The geometric approach to mechanics serves as the theoretical underpinning of innovative control methodologies in geometric control theory. These techniques allow the attitude of satellites to be controlled using changes in its shape, as opposed to chemical propulsion, and are the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation. We will discuss the application of geometric structure-preserving numerical schemes to the optimal control of mechanical systems. In particular, we consider Lie group variational integrators, which are based on a discretization of Hamilton's principle that preserves the Lie group structure of the configuration space. In contrast to traditional Lie group integrators, issues of equivariance and order-of-accuracy are independent of the choice of retraction in the variational formulation. The importance of simultaneously preserving the symplectic and Lie group properties is also demonstrated. Recent extensions to homogeneous spaces yield intrinsic methods for Hamiltonian flows on the sphere, and have potential applications to the simulation of geometrically exact rods, structures and mechanisms. Extensions to Hamiltonian PDEs and uncertainty propagation on Lie groups using noncommutative harmonic analysis techniques will also be discussed. We will place recent work in the context of progress towards a coherent theory of computational geometric mechanics and computational geometric control theory, which is concerned with developing a self-consistent discrete theory of differential geometry, mechanics, and control. This research is partially supported by NSF grants DMS-0714223, DMS-0726263, and DMS-0747659.

October 12th, 2009 (03:30pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: The irregular set for the beta transformation has full topological entropy (= log beta) and full Hausdorff dimension (=1)
Speaker: Daniel Thompson, Penn State
Location: MB106

A recent weakening of the specification property provides new tools to study interesting systems beyond the scope of the standard theory of uniformly hyperbolic dynamics such as the beta-transformation. This property was introduced by Pfister and Sullivan as the g-almost product property. The version we study is a priori slightly weaker and we rename it the almost specification property. We show that for dynamical systems with almost specification, the set of points for which the Birkhoff average of a continuous function does not exist (which we call the irregular set) is either empty or has full topological entropy. Every beta-shift satisfies almost specification and we show that the irregular set for any beta-shift or beta-transformation is either empty or has full topological entropy and Hausdorff dimension. The talk is in three parts. Firstly, we give some history on results about the topological entropy and Hausdorff dimension of the irregular set. Secondly, we discuss our abstract results and try to give some intuition as to why they are true. Thirdly, we discuss in detail the application to the beta-transformation. In particular, we give some intuition on the almost specification property and show why it is satisfied by the beta-transformation.

October 12th, 2009 (04:00pm - 05:00pm)

Seminar: Student Geometric Functional Analysis Seminar
Title: TBA
Speaker: TBA
Location: MB315
Abstract: http://

October 13th, 2009 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: LR-reducibility and LK-reducibility
Speaker: Stephen G. Simpson, Penn State
Location: MB315
Abstract: http://www.math.psu.edu/simpson/papers/aedsh.pdf

Let A and B be Turing oracles. We say that A is LR-reducible to B if every X which is random relative to B is random relative to A. We say that A is LK-reducible to B if K^B(tau) < K^A(tau) + O(1), where K^A denotes prefix-free Kolmogorov complexity relative to A. Recently Kjos-Hanssen, Miller and Solomon discovered that LR-reducibility and LK-reducibility coincide. Moreover, A is LR-reducible to B if and only if every set of positive measure which is effectively closed relative to A includes a set of positive measure which is effectively closed relative to B. We sketch the proof of these and related results.

October 13th, 2009 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Entropy in measurable dynamics, III
Speaker: Lewis Bowen, Texas A & M University
Location: MB216

This is third talk in a 3-part series. Now that the definition of entropy has been extended to free groups and sofic groups, which classical results also extend? Markov chains can be defined over free groups. The theory is analogous to classical Markov chains and is a useful tool in extending some classical formulas including the Abramov-Rohlin formula and Yuzvinskii's addition formula. I will discuss these and other results, which depending on time and interest might include an analogue of the asymptotic equipartition property, applications to random regular graphs, f-invariants for non-free groups and more.

October 14th, 2009 (12:15pm - 01:15pm)

Seminar: Geometry Luncheon Seminar
Title: Module categories in geometry and topology
Speaker: Jonathan Block, University of Pennsylvania
Location: MB114

We discuss the rational homotopy theory of spaces with finite homotopy group as an illustration of the title.

October 14th, 2009 (03:30pm - 04:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: On topological aspects of the Dvoretzky Theorem
Speaker: S. Ivanov, Steklov Institute, St. Petersburg and Penn State
Location: MB106

October 15th, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: The metric theory of diophantine approximation
Speaker: Robert Vaughan, Penn State
Location: MB106

October 15th, 2009 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: C*-Algebras, Foliations and K-Theory 3
Speaker: Tyrone Crisp, Penn State
Location: MB106
Abstract: http://www.math.psu.edu/roe/NCG/notes-index.html

October 15th, 2009 (02:30pm - 03:30pm)

Seminar: MASS Colloquium
Title: Braid groups and their applications
Speaker: Frederick Cohen, University of Rochester
Location: MB114
Abstract: http://

Braids are easy to picture. The purpose of this talk is to describe Borromean braids as well as what these 'measure'.

October 15th, 2009 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Generalized moment-angle complexes
Speaker: Frederick Cohen, University of Rochester
Location: MB114

A subspace of a product space known as 'the generalized moment-angle complex' was first defined in generality by Neil Strickland extending constructions of Davis-Januskiewicz, Buchstaber-Panov-Ray, and Goresky-MacPherson. Definitions, examples, as well as connections to other topics will be addressed. One notable case is given by subspaces of products of infinite dimensional complex projective space 'indexed by a finite simplicial complex'. These spaces encode features ranging from the structure of toric varieties in one guise, Stanley-Reisner rings of simplicial complexes, as well as 'motions of certain types of robotic legs' in other guises. What do these spaces have to do with the motions of legs of a cockroach ? This feature will be illustrated with slides. Features of these spaces such as their cohomology as well as stable structure are developed within the context of classical homotopy theory based on joint work with A. Bahri, M. Bendersky, and S. Gitler. Applications to the motion of legs of a cockroach are based on joint work with G. Haynes and D. Koditschek.

October 15th, 2009 (05:15pm - 06:30pm)

Seminar: Topology/Geometry Seminar
Title: Secondary Chern-Euler forms and the Law of Vector Fields
Speaker: Zhaohu Nie, Penn State
Location: MB106

In this talk, I will present results generalizing those in my previous related talks. The improvement comes from removing the restrictive condition that the metric on the manifold is locally product near its boundary. The outline of the talk is as follows. In his famous proof of the Gauss-Bonnet theorem, Chern transgressed the Euler curvature form of a Riemannian manifold on the tangent sphere bundle. For a manifold with boundary, the restriction of Chern's transgression form to the tangent sphere bundle on the boundary is closed, and we call it the secondary Chern-Euler form. In this talk, we will show that this form is exact, up to a pullback form, away from the inward and outward unit normal vectors of the boundary by explicitly constructing a primitive. I should emphasize again that we can do this for any metric on the manifold, not necessary locally product near the boundary. Using Stokes' theorem, this then evaluates some boundary term and thus proves the Law of Vector Fields in a differential geometric fashion. Recall that the Law of Vector Fields is a relative version of the Poincar\'e-Hopf theorem and expresses the Euler characteristic of a manifold with boundary in terms of the indices of a generic vector field and the inner part of its tangential projection on the boundary. Some related results will also be mentioned.

October 16th, 2009 (12:00pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Asymptotic and numerical analysis of PDE models for suspensions of micro-swimmers: interaction and effective viscosity.
Speaker: Vitaliy Gyrya, Penn State University, Mathematics Department
Location: MB114

      Recently, there have been a number of experimental studies convincingly demonstrating that a suspension of self-propelled bacteria (microswimmers in general) may have an effective viscosity significantly smaller than the viscosity of the fluid without inclusions. This is in sharp contrast with suspensions of rigid passive inclusions, whose presence always increases the effective viscosity.
      We introduce two PDE models for a suspension of microswimmers in a Newtonian fluid and study their well-posedness. The first model was used for an asymptotic study of swimmer-swimmer interactions at large distances (with L. Berlyand, I. Aronson, and D. Karpeev).
      The second model (with K. Lipnikov, I. Aronson, and L. Berlyand) was used to analyze the effective viscosity of suspensions of microswimmers in two regimes:
  - small concentration (dilute, no swimmer-swimmer interactions)
  - moderate concentration (all swimmer-swimmer and swimmer-fluid interactions resolved).
The dilute regime was studied analytically using symmetries of the model, the background flow, and the swimmers. The moderate concentration regime is not tractable for analytical analysis and therefore was studied numerically, using the novel Mimetic Finite Difference discretization for Stokes equation (developed jointly with L. Beirao da Veiga, K. Lipnikov and G. Manzini). Our theoretical results agree with experiments performed at Argonne. Based on our analysis, we were able to identify and explain the nature of the mechanisms responsible for the decrease of the effective viscosity in physical experiments.

October 16th, 2009 (02:30pm - 03:25pm)

Seminar: Seminar on Probability and its Application
Title: Disordered media, slow dynamics, aging and trapping
Speaker: Gerard Ben Arous, Courant Institute
Location: MB106

I will discuss some universal scenarii for the phenomenon of slow dynamics in random media. Examples will be drawn from recent results on random walks on supercritical and critical percolation clusters and trees, and on dynamics of spin glasses.

October 16th, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Arbitrarily slow convergence of sequences of linear operators
Speaker: Frank Deutsch, Department of Mathematics, Penn State
Location: MB106

Our objective is to study the rate of convergence of a sequence of linear operators that converges pointwise to a linear operator. Our main interest is in characterizing the slowest type of pointwise convergence possible. A sequence of linear operators (Ln) is said to converge to a linear operator L arbitrarily slowly (resp., almost arbitrarily slowly) provided that (Ln) converges to L pointwise, and for each sequence of real numbers (φ(n)) converging to 0, there exists a point x = xφ such that ||Ln (x) − L(x|| ≥ φ(n) for all n (resp., for infinitely many n). The main results in this paper are two “lethargy” theorems. The first one characterizes almost arbitrarily slow convergence. The second one gives a useful sufficient condition that guarantees arbitrarily slow convergence. In the particular case when the sequence of linear operators is generated by the powers of a single linear operator, it turns out that almost arbitrarily slow convergence and arbitrarily slow convergence are equivalent. In this case we obtain a “dichotomy” theorem that states the perhaps surprising result that either there is linear (fast) convergence or arbitrarily slow convergence; no other type of convergence is possible. The first lethargy theorem is applied to show that a large class of polynomial operators (e.g., Bernstein, Hermite-Fejer, Landau, Fejer, and Jackson operators) all converge almost arbitrarily slowly to the identity operator. It is also shown that all the classical quadrature rules (e.g., the composite Trapezoidal Rule, composite Simpson’s Rule, and Gaussian quadrature) converge almost arbitrarily slowly to the integration functional. Finally, the dichotomy theorem is applied in Hilbert space to generalize and sharpen: (1) the von Neumann-Halperin cyclic pro jections theorem, (2) the rate of convergence for randomly ordered pro jections, and (3) a theorem of Xu and Zikatanov.

October 19th, 2009 (03:30pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Local rigidity of partially hyperbolic actions
Speaker: Zhenqi Wang, Penn State
Location: MB106

We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. The local differentiable rigidity for such actions comes from geometric Katok-Damjanovic way and the conclusions based on progress to- wards computations of the Schur multipliers of these non-split groups.

October 19th, 2009 (03:35pm - 04:25pm)

Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Splines over T-meshes and Applications
Speaker: Falai Chen, Department of Mathematics, University of Science and Technology of China.
Location: MB216

In this talk, I will introduce a new spline representation - splines over T-meshes, for geometric modeling and scientific computing. I will present methods for the construction of basis spline functions and discuss their properties. Then several applications are presented including surface fitting, segmentation, simplification, etc. The promising application in adaptive iso-geometric analysis (a possible substitute for finite element method) is also discussed.

October 19th, 2009 (04:00pm - 05:00pm)

Seminar: Student Geometric Functional Analysis Seminar
Title: TBA
Speaker: TBA
Location: MB315
Abstract: http://

October 20th, 2009 (11:15am - 12:05pm)

Seminar: Combinatorics/Partitions Seminar
Title: An Overview of Generalized Frobenius Partitions
Speaker: Dr. James Sellers, Penn State
Location: MB106

In 1984, George Andrews wrote an AMS Memoir entitled "Generalized Frobenius Partitions" in which he studied two families of partitions functions which naturally generalize ordinary partitions. As he notes in the introduction of the Memoir, he was motivated to consider these generalized Frobenius partitions, or F-partitions for short, while working with Rodney Baxter on Regime III of the Hard Hexagon Model in statistical mechanics. F-partitions also are of natural significance in group representation theory and elliptic theta functions. In the early 1990s, I became very interested in Ramanujan-like congruences that are satisfied by F-partitions (some of which were proven by Andrews in his Memoir). In this talk, I will focus on several of these congruence results with the goal of introducing this subject to our seminar group. In the process, I hope to provide sufficient background for our group in preparation for Peter Paule's seminar talk next week.

October 20th, 2009 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: Hall Algebras and Canonical Bases
Speaker: Zongzhu Lin, Kansas State University
Location: MB106

Ringel described the Hall algebras of finite type quiver via representations of the quivers over finite fields and proved that the Hall algebra is isomorphism (with an certain twisted) to the positive part of the quantized enveloping algebra of the Lie algebra whose Dynkin diagram is the underlying graph of the quiver. Lusztig used the geometric approach to Ringel's construction and discovered a basis for the positive part of the quantized enveloping algebra as the simple perverse sheaves over classes of representation varieties. Such construction was generalized to other quivers with out loops. In this talk I will outline Lusztig's construction and various ways to describe the canonical basis for affine quivers using representation theory properties of the affine quivers.

October 20th, 2009 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Measure rigidity for Zariski dense groups, I.
Speaker: Jean-Francois Quint, University of Paris-13
Location: MB216
Abstract: http://www.math.psu.edu/katok_a/Quint-lectures.pdf

October 20th, 2009 (04:00pm - 04:55pm)

Seminar: Applied Analysis Seminar
Title: Sailing On Diffusion
Speaker: Tom Peacock, MIT
Location: MB106

When a density-stratified fluid encounters a sloping boundary, diffusion alters the fluid density adjacent to the boundary, producing spontaneous along-slope flow. Since stratified fluids are ubiquitous in nature, this phenomenon plays a vital role in environmental transport processes, including salt transport in rock fissures and ocean-boundary mixing. Here we show that diffusion-driven flow can be harnessed as a remarkable means of propulsion, acting as a diffusion-engine that extracts energy from microscale diffusive processes to propel macroscale objects. Like a sailboat tacking into the wind, forward motion results from fluid flow around an object, creating a region of low pressure at the front relative to the rear. In this case, however, the flow is driven by molecular diffusion and the pressure variations arise due to the resulting small changes in the fluid density. This mechanism has implications for a number of important systems, including environmental and biological transport processes at locations of strong stratification, such as pycnoclines in oceans and lakes. There is also a strong connection with other prevalent buoyancy-driven flows, such as valley and glacier winds, significantly broadening the scope of these results and opening up a new avenue for propulsion research.

October 21st, 2009 (12:15pm - 01:15pm)

Seminar: Geometry Luncheon Seminar
Title: Topological and metric rigidity for actions of nonabelian groups
Speaker: Jean-Francois Quint, Paris
Location: MB114

In this talk, I will present some recent results on the subject above, part of which are jointly due to Yves Benoist and myself. For example, if $\Gamma$ is a non virtually solvable subgroup of $SL(2,\mathbb Z)$ (resp. $SL(2,\mathbb R)$), every $\Gamma$-orbit in $\mathbb T^2$ (resp. $SL(2,\mathbb R)/SL(2,\mathbb Z)$) is finite or dense.

October 21st, 2009 (03:30pm - 04:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Alexandrov meets Lott--Villani--Sturm
Speaker: A. Petrunin, Penn State
Location: MB106

show compatibility of two definition of generalized curvature bounds --- the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvature in the sense of Lott--Villani--Sturm.

October 22nd, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Reversed Dickson Polynomials and Related Polynomials
Speaker: Xiang-dong Hou, South Florida University
Location: MB106

Let D_n(x,y) be the polynomial over Z such that x_1^n+x_2^n=D_n(x_1+x_2,x_1x_2) and fix an element a\in F_q^*. The polynomial D_n(x,a) is the well known Dickson polynomial; the polynomial D_n(a,x) is the reversed Dickson polynomial recently introduced. Reversed Dickson polynomials are a rich source of permutation polynomials over finite fields and are closely related to the ubiquitous APN (almost perfect nonlinear) functions in cryptography. The ultimate goal is to determine all pairs (q,n), called desirable pairs, for which D_n(1,x) is a permutation polynomial on F_q. We will survey the known families of desirable pairs and introduce a new family. Together, these families cover all desirable pairs (q,n) with q<200. We cautiously conjecture that all desirable pairs have been found. We also introduce a q-ary version of reversed Dickson polynomials which coincide with D_n(1,x) when q=2. The permutation properties of the q-ary version will be discussed.

October 22nd, 2009 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: Continuous fields of Hilbert spaces
Speaker: Nigel Higson, Penn State
Location: MB106

October 22nd, 2009 (02:30pm - 03:20pm)

Seminar: MASS Colloquium
Title: Minimal surfaces in sub-Riemannian geometry
Speaker: Luca Capogna, University of Arkansas
Location: MB113

October 22nd, 2009 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Holomorphic linking numbers
Speaker: Boris Khesin, University of Toronto
Location: MB114

The Gauss linking number of two curves in three-space has a complex counterpart. In the talk we define the holomorphic linking number for complex curves in complex three-folds. Moreover, one can define "polar homology" groups of complex projective manifolds by regarding meromorphic forms on their submanifolds as a complex analogue of orientation, and taking the residue as the boundary operator. We also discuss gauge-theoretic aspects of the above correspondence, and, in particular, its relation to the holomorphic Chern--Simons theory.

October 23rd, 2009 (12:00pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Random Matrix Theory and Covariance Estimation (NOTE: this will be an extended lunch seminar of 45 minutes.)
Speaker: Jim Gatheral, New York University and Merrill Lynch
Location: MB114

Sophisticated optimal liquidation portfolio algorithms that balance risk against impact cost involve inverting the covariance matrix. Eigenvalues of the covariance matrix that are small (or even zero) correspond to portfolios of stocks that have nonzero returns but extremely low or vanishing risk; such portfolios are invariably related to estimation errors resulting from insufficient data. One of the approaches used to eliminate the problem of small eigenvalues in the estimated covariance matrix is the so-called random matrix technique. In this talk I will discuss the basis of random matrix theory, how to apply RMT to the estimation of covariance matrices and whether the resulting covariance matrix performs better than (for example) the Barra covariance matrix.

October 23rd, 2009 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: Poisson geometry of directed networks and integrable lattices
Speaker: Michael Gekhtman, Notre Dame
Location: MB315

Recently, Postnikov used weighted directed planar graphs in a disk to parametrize cells in Grassmannians. We investigate Poisson properties of Postnikov's map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grasmannian is viewed as a Poisson homogeneous space GL(n) equipped with an appropriately chosen R-matrix Poisson-Lie structure. We generalize Postnikov's construction by defining a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. This family includes, for a particular kind of networks, the Poisson bracket associated with the trigonometric R-matrix. We use a special kind of directed networks in an annulus to study a cluster algebra structure on a certain space of rational functions and show that sequences of cluster transformations connecting two distinguished clusters are closely associated with Backlund-Darboux transformations between Coxeter-Toda flows in GL(n).

October 23rd, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Statistical Arbitrage in the U.S. Equities Market
Speaker: Marco Avellaneda, Courant Institute, New York University
Location: MB106

We study model-driven statistical arbitrage strategies in U.S. equities. Trading signals are generated in two ways: using Principal Component Analysis and using sector ETFs. In both cases, we consider the residuals, or idiosyncratic components of stock returns, and model them as a mean-reverting process, which leads naturally to "contrarian'' trading signals. The main contribution of the paper is the back-testing and comparison of market-neutral PCA- and ETF- based strategies over the broad universe of U.S. equities. Back-testing shows that, after accounting for transaction costs, PCA-based strategies have an average annual Sharpe ratio of 1.44 over the period 1997 to 2007, with a much stronger performances prior to 2003: during 2003-2007, the average Sharpe ratio of PCA-based strategies was only 0.9. On the other hand, strategies based on ETFs achieved a Sharpe ratio of 1.1 from 1997 to 2007, but experience a similar degradation of performance after 2002. We introduce a method to take into account daily trading volume information in the signals (using "trading time'' as opposed to calendar time), and observe significant improvements in performance in the case of ETF-based signals. ETF strategies which use volume information achieve a Sharpe ratio of 1.51 from 2003 to 2007. The paper also relates the performance of mean-reversion statistical arbitrage strategies with the stock market cycle. In particular, we study in some detail the performance of the strategies during the liquidity crisis of the summer of 2007. We obtain results which are consistent with Khandani and Lo (2007) and validate their "unwinding'' theory for the quant fund drawndown of August 2007.

October 24th, 2009 (07:30am - 07:30pm)

Seminar: AMS Sectional Meeting
Title: AMS 2009 Fall Eastern Sectional Meeting
Speaker: Various, Various
Location: First and Second Floor Thomas Building

October 25th, 2009 (07:30am - 07:30pm)

Seminar: AMS Sectional Meeting
Title: AMS 2009 Fall Eastern Section Meeting
Speaker: Various, Various
Location: First and Second Floor Thomas Building

October 26th, 2009 (03:30pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Applications of algebraic $K$-theory to rigidity problems in dynamics: An overview
Speaker: Anatole Katok, Penn State
Location: MB106

Remarkable Ph. D. thesis of Zhenqi Wang constitutes a major new progress in the direction started in the joint work of 2004 Ph.D. Danijela Damjanovic and the present speaker. Wang had a chance to speak at the seminar last week but clearly the audience had difficulties following due to both complexities of the subject and lack of experience of the speaker. This talk with attempt to present the setting and the background for the problem describe the general method in sufficient detail and clearly explain what is the novelty of Wang's work. The audience will have another chance to hear Wang at the Dynamical Systems and related topics workshop on Saturday October 31.

October 26th, 2009 (03:35pm - 04:25pm)

Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: The effect of numerical integration on the finite element approximation
Speaker: Hengguang Li, Syracuse University
Location: MB216

It is well known that the discretization of a finite element method results in a linear system of equations, in which the matrix and the load vector are usually computed by numerical integration. The inexact integration may lead to a different linear system, and consequently, produce a different finite element solution. In this talk, we will first discuss the existing results on the impact of quadrature rules on the finite element approximation in the energy norm. Then, a sharp estimate on the convergence rate of the finite element approximation with numerical integration for linear functionals will be presented.

October 26th, 2009 (04:00pm - 05:00pm)

Seminar: Student Geometric Functional Analysis Seminar
Title: TBA
Speaker: TBA
Location: MB315
Abstract: http://

October 27th, 2009 (11:15am - 12:05pm)

Seminar: Combinatorics/Partitions Seminar
Title: A Proof of Sellers' Conjecture
Speaker: Dr. Peter Paule, Research Institute for Symbolic Computation, University of Linz, Austria
Location: MB106

In 1994 James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In joint work with Silviu Radu (RISC) we were able to prove Sellers' conjecture for all powers of 5.

October 27th, 2009 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Measure-theoretic regularity and LR-reducibility
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315
Abstract: http://www.math.psu.edu/simpson/papers/massmtr.pdf

Let S be a Lebesgue measurable set in Euclidean space. It is well known that we can find closed sets C included in S such that the measure of S minus the measure of C is as small as desired. This phenomenon is known as measure-theoretic regularity. Using tools from the theory of computability and algorithmic randomness, we analyze the "descriptive complexity" or "logical strength" of the closed sets which are needed in order to implement measure-theoretic regularity. One of the tools is Nies's notion of LR-reducibility.

October 27th, 2009 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: A Lefschetz number theorem for differential operators
Speaker: Ajay Ramadoss, Cornell University
Location: MB106

Let $X$ be a compact, complex manifold and let $E$ be a holomorphic vector bundle on $X$. Let $ Diff^{\bullet}(E)$ be the Dolbeault resolution of the sheaf of holomorphic differential operators on $E$. A construction due to Feigin, et. al , gives a linear functional on the $0$-th Hochschild homology of $Diff^{\bullet}(E)$. This functional "extends" to a linear functional on the "completed" $0$-th Hochschild homology of $Diff^{\bullet}(E)$ ,thereby giving a linear functional $I_E$ on the top cohomology $\text{H}^{2n} (X,\mathbb C)$ of $X$ with complex coefficients. The main result is that $I_E$ is just integration over $X$. As a consequence, one obtains a Lefschetz number formula for a global holomorphic differential operator on $E$.

October 27th, 2009 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Measure rigidity for Zariski dense groups, II.
Speaker: Jean-Francois Quint, University of Paris-13
Location: MB216
Abstract: http://www.math.psu.edu/katok_a/Quint-lectures.pdf

October 27th, 2009 (04:00pm - 04:55pm)

Seminar: Applied Analysis Seminar
Title: Trajectories of a Control System in a Cone
Speaker: Richard Vinter, Imperial College London
Location: MB106

Suppose we have a a solution to a differential inclusion (an F-trajectory). How close is it to the class of F-trajectories that evolve in a closed subset of the state space (the so-called `feasible' F-trajectories)? This question is of great importance in state constrained optimal control and system theory. Whether there exist suitable estimates of the distance to the set of feasible F-trajectories has implications for the non-degeneracy of standard optimality conditions, the characterization of the minimum cost function in terms of solutions to the Hamilton Jacobi equation and the reformulation of optimal control problems to improve their conditioning for numerical solution. The talk will focus on cases when the state constraint set has a edge (intersection of two half-spaces, for example). It is demonstrated by means of a recent counter-example that, contrary to expectations, a linear estimate of the distance in terms of the state violation h is not valid. We report the results of recent research, establishing the validity of 'superlinear' h log h estimates, and the optimality of the h log h estimate structure; also on the special cases for which linear estimates are now known to hold, notably that when the velocity set is strictly convex. We discuss the implications of these findings for systems theory and optimal control.

October 28th, 2009 (03:30pm - 04:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Non-Kahler Calabi-Yau manifolds via hyperbolic geometry
Speaker: D. Panov, Imperial College
Location: MB106

In this talk we will present a construction of simply connected non-Kahler Calabi-Yau manifolds of real dimension 6. Non algebraic Calabi-Yaus have two types - symplectic and complex. It turns out that simply- connected 4-dimensional hyperbolic orbifolds produce symplectic examples while hyperbolic knots in S^3 produce complex examples. In particular there exists an infinte series of complex structures on 2(S^3 x S^3)#(S^2 x S^4) with trivial canonical bundle. This is a joint project with Joel Fine.

October 29th, 2009 (08:00am - 04:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Dynamical Systems and Related Topics Workshop
Speaker: Various, Various
Location: MB114

October 29th, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Special values of Goss L-functions and log-algebraicity
Speaker: Matt Papanikolas, University of Texas
Location: MB106

We will consider special values of Goss L-functions for Dirichlet characters at positive integers, which take values in the completion of the rational function field in one variable over a finite field. Building on work of Anderson for the case of L(1,chi), we will deduce various power series identities on tensor powers of the Carlitz module that are "log-algebraic" and in turn use these formulas to access values L(n,chi) for arbitrary n > 0. Moreover, we will relate these L-series values to powers of the Carlitz period and values of Carlitz polylogarithms at algebraic points.

October 29th, 2009 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: TBA
Speaker: Jean Renault, Universite d'Orleans, France
Location: MB106

October 29th, 2009 (02:30pm - 03:20pm)

Seminar: MASS Colloquium
Title: [0,1] is not a minimality detector of [0,1]^2
Speaker: Jon Chaika
Location: MB113

This talk will introduce the notion of minimal sequences. It will then show that [0,1]^2 can detect the minimality of sequences in any compact metric space. However, [0,1] can not detect the minimality of sequences in [0,1]^2.

October 29th, 2009 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Invariant distribution and scaling for parabolic flows
Speaker: G. Forni, University of Maryland
Location: MB114
Abstract: http://

October 29th, 2009 (05:00pm - 07:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Various Speakers Throughout the Day
Speaker: Various, Various
Location: MB114
Abstract: http://

October 30th, 2009 (08:00am - 06:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Dynamical Systems and Related Topics Workshop
Speaker: Various, Various
Location: MB114

October 30th, 2009 (12:00pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Relaxation Schemes for Hyperbolic Conservation Laws
Speaker: James A. Rossmanith, University of Wisconsin - Madison Department of Mathematics
Location: MB106

I will briefly describe finite volume methods for solving hyperbolic conservation laws, and in particular focus on Riemann solvers. I will explain what relaxation systems are, and how these can be used to construct approximate Riemann solvers. I will mostly focus on the 1D case, but time-permitting briefly discuss multidimensional approximate Riemann solvers.

October 30th, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Discontinuous Galerkin Methods for Problems in Plasma Physics
Speaker: James Rossmanith, Department of Mathematics, University of Wisconsin
Location: MB106

Plasma is a state of matter in which electrons disassociate from their nuclei, resulting in electrically conducting clouds of positively and negatively charged ions. Mathematically, plasma can be modeled on a variety of scales, resulting in various kinetic, fluid, and hybrid models. In this talk we first we consider the simplest plasma fluid model: the ideal MHD (magnetohydrodynamic) system. We review some of the mathematical difficulties associated with the divergence-free condition on the magnetic field. We will then describe a class of discontinuous Galerkin (DG) methods for approximately solving this system. Next we consider two genuinely two-fluid models of plasma: Euler-Maxwell (5-moments) and extended Euler-Maxwell (10-moments). We focus our discussion on the problem of collisionless magnetic reconnection. We first describe this problem and then our efforts to apply two-fluid models to it, again using discontinuous Galerkin methods.

October 31st, 2009 (08:00am - 06:00pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Dynamical Systems and Related Topics Workshop
Speaker: Various, Various
Location: MB114