# Math Calendar

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<>October 2012
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A live feed of seminars and special events in the upcoming week.

October 1st, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Unipotent cocycle rigidity in higher rank Lie groups
Speaker: Zhenqi Wang, Yale University
Location: MB106
October 1st, 2012 (08:00pm - 09:00pm)
Seminar: Marker Lecture Series
Title: The Classical Theory of L-functions
Speaker: Enrico Bombieri
Location: MB114

This lecture is in part on the history and evolution of the theory of zeta and L-functions, from Euler to the recent conjectures about the connection of the distribution of values of zeta and L-functions with the distribution of eigenvalues of random orthogonal, unitary, or symplectic matrices.

October 2nd, 2012 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: From Linear Algebra and Graphs to Oriented Matroids.
Speaker: Leandro Junes, Cal U of PA
Location: MB106

This is the first of a series of two talks. In this talk I will introduce the concept of oriented matroids and show how they are a natural generalization of linear algebra and directed graphs. I will also show a strong connection between oriented matroids and topology.

October 2nd, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Linear differential operators on contact manifolds
Speaker: Valentin Ovsienko, University of Lyon 1
Location: MB106

(Joint with Charles Conley) We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. Our main result is an intrinsically defined "subsymbol" of a differential operator, which is a differential invariant of degree one lower than that of the principal symbol. In particular, this subsymbol associates a contact vector field to an arbitrary second order linear differential operator.

October 2nd, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Old and new perspectives on K-trivials
Speaker: Phil Hudelson, Pennsylvania State University
Location: MB315
Abstract: http://www.math.psu.edu/simpson/papers/rmpc.pdf
October 2nd, 2012 (04:30pm - 05:30pm)
Seminar: Marker Lecture Series
Title: The Rosetta Stone of L-functions
Speaker: Enrico Bombieri
Location: MB114

This lecture deals with the deep interconnections among different L-functions, comparing the three different ways of looking at L-functions: Motivic, Galois, Automorphic, and why it should all be the same through the Langlands Program.

October 3rd, 2012 (12:10pm - 01:10pm)
Seminar: SIAM Student Chapter Seminar
Title: Molecular dynamics models and coarse-grained molecular dynamics models
Speaker: Xiantao Li, Penn State University, Department of Mathematics
Location: MB106
Abstract: http://

I will introduce some basic elements in molecular dynamics (MD) models, along with some ideas to reduce MD models to coarse-grained models with much smaller dimension. This is particularly useful for the numerical implementation purpose.

October 3rd, 2012 (12:20pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Van Kampen diagrams and algorithmic group theory
Speaker: Mark Sapir, Vanderbilt
Location: MB114

I will show how to solve complicated group theory problems using simple 2-dimensional pictures.

October 3rd, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Aspherical groups and manifolds
Speaker: Mark Sapir, Vanderbilt University
Location: MB106

I will show how to construct wild aspherical manifolds.

October 3rd, 2012 (04:30pm - 05:30pm)
Seminar: Marker Lecture Series
Title: L-functions and Diophantine Equations
Speaker: Enrico Bombieri
Location: MB114

Through the theory of elliptic curves and zeta and L-functions over finite fields, there are important applications of zeta and L-functions to the theory of diophantine equations.

October 4th, 2012 (09:00am - 10:10am)
Seminar: Mathematical Biology & Physiology Seminar
Title: mathematical biology seminar
Speaker: Sheereen Majd, Bioengineering, PSU
Location: MB114
Abstract: http://www.math.psu.edu/treluga/mmbs.html

Title: Nano-Scale Pores for Sensing and Single-Molecule Characterization Abstract: Biological protein pores and pore-forming peptides can generate a pathway for the flux of ions and other charged and polar species across otherwise impermeable cellular membranes. In nature, these nanopores have diverse and essential functions that range from maintaining cell homeostasis and participating in cell signaling to activating or killing cells. The combination of nano-scale dimensions and inherent sophisticated functionality of these biological pores have them made particularly attractive for the growing field of bionanotechnology where their applications range from single-molecule sensing to drug delivery and targeted killing of malignant cells. Recently, nano-scale pores fabricated in synthetic materials have also emerged as powerful platforms for single-molecule sensing and characterization. In this talk, I present two examples of application of biological and synthetic nanopores for detection and characterization of molecular processes on lipid membranes. In the first example, we applied an ion channel-forming peptide, gramicidin A, for sensing and detection of membrane-associated enzymatic activities and binding interactions. In the second example, we modified a synthetic nanopore by coating its walls with non-fouling lipid bilayers to enable sensing and characterization of single protein molecules as well as molecular processes on lipid bilayers.

October 4th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Liquid Crystal Wave System of Equations
Speaker: Yuxi Zheng
Location: MB216

A survey of the current status of research in the area of liquid crystal waves systems of equations will be given and the cutting-edge open problems presented.

October 4th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: No talk this week
Speaker: Enrico Bombiero, is the Marker Lecturer
Location: MB106
October 4th, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: A differential complex for CAT(0) cubical spaces
Speaker: Nigel Higson, Penn State
Location: MB106
October 4th, 2012 (02:30pm - 03:30pm)
Seminar: MASS Colloquium
Title: A new approach to CRC processing
Speaker: Donald Newhart, NSA
Location: MB113

High-speed digital communications must anticipate the possibility of channel errors in transmission. Nontrivial mathematical approaches to this date back to 1948, and constitute the subject of Algebraic Coding Theory. The principle of using the coefficients of polynomial remainders as a checksum to detect errors goes back to at least 1961; this idea blended well with the technology of shift registers, and is used in everything from the GPS system to the internet. Advances in modern technology such as Field Programmable Gate Arrays (FPGA), allows for very efficient vector addition of long binary inputs, and open new possibilities. This talk will explain CRC checksums from first principles, show how abstract algebra plays a pivotal role, and finally, present a new mathematical algorithm (developed at NSA) to process them. Although the approach will be explained with some simple linear algebra, it implicitly takes advantage of an underlying quotient-ring context that is usually ignored. Potential advantages for FPGA use will be discussed.

October 4th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Application of Hermite expansion in Kalman Filtering method
Speaker: Yicun Zhen, Math Dept, Penn State University
Location: MB216

Kalman Filtering is a commonly used method in data assimilation in many scientific areas. In this presentation we will mainly focus on a method of improving the rate of Kalman Filtering. We will not deal with real data today but we will try attacking a localizer matrix which has been used in weather prediction. We will utilize the Hermite expansion to speed up the matrix-vector multiplication process so that conjugate gradient method has the potential to be used to compute $A^{-1}*b$ for matrix $A$ and vector $b$. If the size of the matrix $A$ is n*n, the algorithm for computing the matrix-vector multiplication is hopefully of computational complexity O(n) despite setting up.

October 4th, 2012 (04:30pm - 05:30pm)
Seminar: Department of Mathematics Colloquium
Title: A Problem on Sums of Two Squares
Speaker: Enrico Bombieri
Location: MB114

Even apparently simple questions about integers that are representable as a sum of two squares take a life of their own when examined in detail. This lecture shows how combinatorics, algebraic and arithmetic geometry, elliptic curves and their L-functions can all play a role in a problem on sum of two squares arising from a model in mathematical physics. (Joint work with Jean Bourgain)

October 4th, 2012 (04:30pm - 05:30pm)
Seminar: Marker Lecture Series
Title: A Problem on Sums of Two Squares
Speaker: Enrico Bombieri
Location: MB114

Even apparently simple questions about integers that are representable as a sum of two squares take a life of their own when examined in detail. This lecture shows how combinatorics, algebraic and arithmetic geometry, elliptic curves and their L-functions can all play a role in a problem on sum of two squares arising from a model in mathematical physics. (Joint work with Jean Bourgain)

October 5th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Traveling water waves in two and three dimensions
Speaker: Vishal Vasan, Penn State Mathematics
Location: MB114

Water waves are a common phenomena but their mathematical description can be quite complicated. In this talk I will present the equations governing the motion of the free surface of an inviscid, irrotational flow over a flat bed. If we limit ourselves to traveling waves we obtain a free boundary-value problem for Laplace's Equation. Finally I will present a method to numerically compute these traveling wave solutions.

October 5th, 2012 (02:20pm - 03:20pm)
Seminar: Seminar on Probability and its Application
Title: Universally Typical Sets for Ergodic Sources of Multidimensional Data
Speaker: Guido Montufar, Penn State University
Location: MB106

We lift important results of the theory of samples of discrete ergodic information sources to the multidimensional setting. We use the technique of packings and coverings with multidimensional windows in entropy estimation and universal lossless compression. In particular, we construct sequences of multidimensional array sets which, in the limit, build the generated samples of any ergodic source of entropy rate below an h0 with probability 1 and whose cardinality grows at most at exponential rate h0. Thereby we extrapolate mathematical framework relevant for universal source coding of multi-dimensionally correlated data.

October 5th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Onsager's Maximum Dissipation Principle, General Diffusions and Optimal Transport
Speaker: Chun Liu, Penn State Mathematics
Location: MB106

In the talk, I will explore the general framework of energetic variational approaches, especially Onsager's Maximum Dissipation Principles, and their particular applications in generalized diffusions. We will discuss the roles of different stochastic integrations (Ito's form, Stratonovich's form and other possible forms), and the procedure of optimal transport in the context of general framework of theories of linear responses.

October 8th, 2012 (01:25pm - 02:15pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Applications of the Heston model to option pricing
Speaker: Camelia Pop, University of Pennsylvania Mathematics
Location: 223 Thomas

In this talk that is designed for non mathematicians, I will discuss properties of the Heston model that are relevant for option pricing. The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order degenerate elliptic partial differential operator. We present results concerning existence, uniqueness and regularity of solutions to the Heston equation, and show their relevance for option pricing. This is joint work with Paul Feehan, Rutgers University

October 8th, 2012 (02:30pm - 03:30pm)
Seminar: Applied Analysis Seminar
Title: Fluids and the skew mean curvature flow.
Speaker: Boris Khesin, University of Toronto
Location: MB216
Abstract: http://

We show that an approximation of the incompressible Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for higher-dimensional vortex filaments and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively. This framework, in particular, allows one to define the symplectic structures on the spaces of vortex sheets. Preprint: arXiv:1201.5914

October 8th, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Morse index, stability and multiplicity of closed geodesics,
Speaker: Huagui Duan, Nankai University, visiting Penn State
Location: MB106

A closed geodesic can be regarded as a critical point of the energy functional with positive energy. The closed geodesic problem is a traditional and important topic in dynamical systems and differential geometry. There is a longstanding conjecture that there exist infinitely many distinct closed geodesics on every compact Riemannian manifold. The current interest on this problem is on compact simply connected manifolds, specially spheres. In this talk, I shall give a survey on the study of this problem and explain how the Morse indices are applied to study the stability and multiplicity of closed geodesics on compact simply connected Riemannian (, or Finsler) manifolds.

October 9th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Lipschitz metrics for non-smooth evolutions
Speaker: Alberto Bressan, Penn State
Location: MB216

This second talk will be concerned with evolution problems where the flow is not contractive w.r.t. the natural distance generated by a norm, and where continuous dependence cannot be obtained by a Gronwall type argument. In this case, some results on well posedness can be achieved by introducing a weighted distance, possibly generated by a Riemann type metric. Examples will be discussed, including the Hunter-Saxton and the Camassa-Holm equations, and a second order variational wave equation.

October 9th, 2012 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Still Yet even More Congruence Properties of the Restricted Partition Function p(n,m)
Speaker: Brandt Kronholm, Juniata College
Location: MB106

Ramanujan congruences for the unrestricted partition function p(n) are well known and have been studied in great detail. p(n,m) is the restricted partition function that enumerates the number of partitions of n into exactly m parts. The close relationship between p(n) and p(n,m) is clear: p(n)=p(n,1)+p(n,2)+ ... +p(n,n-1)+p(n,n). Until recently, the existence of Ramanujan-type congruences was virtually unknown for p(n,m). Let l be an odd prime. In this presentation we will establish explicit Ramanujan-type congruences for p(n,m) modulo any prime l. In this presentation we will discuss an intriguing extension of a previous result regarding p(n,m), the restricted partition function that enumerates the number of partitions of n into exactly m parts. This extension reveals further symmetries of the generating function for p(n,m) and may allow us to gain a better understanding of these Ramanujan-like congruences. Moreover, this extension agrees with the Hardy-Ramanujan-Rademacher formula for p(n) when n is negative, namely, p(n)=0. We may also discuss recent rank and crank statistics computed by our friend Dennis Eichhorn for p(n,m) mod l - though I really don't know too much about them.

October 9th, 2012 (01:20pm - 02:20pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Holder continuity for solutions to the Heston variational equation and inequality
Speaker: Camelia Pop, University of Pennsylvania Math
Location: MB106

The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order degenerate elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. With the aid of weighted Sobolev spaces, we prove supremum bounds, a Harnack inequality, and H\"older continuity near the boundary for solutions to elliptic variational equations defined by the Heston partial differential operator, as well as H\"older continuity up to the boundary for solutions to elliptic variational inequalities defined by the Heston operator. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. This is joint work with Paul Feehan, Rutgers University.

October 9th, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Langlands Parameters and Algebraic Varieties
Speaker: Roger Plymen, Southampton University
Location: MB106

The local Langlands conjecture relates arithmetic data, based on a local nonarchimedean fi eld F, with the representation theory of re- ductive groups such as GL(n; F). In this talk, we will show how the extended quotient, an idea from noncommutative geometry, is useful in this context. We will focus on the general linear group GL(n). In this case, Langlands parameters form complex algebraic varieties. We will describe these varieties explicitly. This will be a non-technical talk. Joint work with Anne-Marie Aubert and Paul Baum.

October 9th, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Borel combinatorics, recursion theory, and countable Borel equivalance relations
Speaker: Andrew Marks, California Institute of Technology
Location: MB315

We use determinacy to settle several questions in Borel combinatorics related to colorings and matchings of n-regular graphs. We then describe how these results can be used to show that recursive isomorphism on 2^\omega is not a universal countable Borel equivalence relation in a "nicely uniform" way.

October 9th, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Index Theory for Symplectic Matrix Paths with Applications I
Speaker: Huagui Duan, Nankai University, visiting Penn State
Location: MB216

In these two lectures, I shall give an introduction of the Maslov-type index theory for symplectic matrix paths and its iteration theory with applications to the multiplicity and stability of periodic orbits for Hamiltonian systems and closed geodesics on compact manifolds.

October 10th, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: On fundamental groups of manifolds without conjugate points.
Speaker: Sergei Ivanov, Steklov Institute, SPb University, visiting Penn State
Location: MB106
October 11th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: Yuxi Zheng, Penn State
Location: MB216
October 11th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The Skewes Number
Speaker: Roger Plymen, Southampton University
Location: MB106

Let pi(x) denote the number of primes less than or equal to x, let li(x) denote the logarithmic integral \int_0^x dt/log t. The prime number theorem says pi(x)~li(x). The evidence from any table of primes suggests that pi(x) < li(x) for all x. Littlewood's theorem (1914) says that the diff erence pi(x)-li(x) changes sign infi nitely often. This implies that there is a least crossover, a least number X for which pi(X) > li(X). What is X? No-one knows. However, successive upper bounds have been given, starting with the famous bound due to Skewes: 10^10^10^43 We will bring the subject up to date with two papers from 2010: Chao-Plymen and Saouter-Demichel. The current world record is held by Stefanie Zegowitz: her upper bound is around exp(727.9513), a number with 316 digits. The statement is There exists an x < exp(727:9513) such that pi(x) > li(x). This work depends on the Riemann Explicit Formula { I'll begin with this formula.

October 11th, 2012 (01:00pm - 02:00pm)
Seminar: Special Event
Title: Solutions of an epidemic game with linear social distancing cost
Speaker: Tim Reluga, Penn State Mathematics
Location: MB106

Epidemics can put peopleʼs health at risk, and people often change their behaviors during epidemics to increase their social distance from others and thus to reduce their risk of infection. Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior depend on the course of the epidemic, which itself depends on peopleʼs behaviors. Differential population game theory provides one approach resolving this interdependence. I'll present an analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear, with a zero lower bound. Complete closed-form results are obtained in the infinite-horizon case, followed by some discussion of the finite-time case and other generalizations.

October 11th, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: A differential complex for CAT(0) cubical spaces, 2
Speaker: Nigel Higson, Penn State
Location: MB106
October 11th, 2012 (02:30pm - 03:30pm)
Seminar: MASS Colloquium
Title: On the use of computers in Mathematics and Science: the good, the bad, and what we should do about them
Speaker: Sheldon Newhouse, Michigan State University
Location: MB113

Computers have become a fundamental part of our lives. They are used in appliances ranging from cell phones to rocket launchers, in controlling our air travel, in describing models for financial management, and in large parts of Mathematics and Science. Can we trust what computers tell us? How can we improve the verification of various types of computation? These are questions of fundamental importance to all of us. In this lecture, we will explore some ideas and examples related to computation as it applies to Dynamical Systems--the branch of mathematics which deals with how various systems evolve in time. We will see that modern methods for verified computation can provide tests for finding certain computational errors as well as providing proofs of theorems which are, at the present time, unattainable with traditional methods.

October 11th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Divergence free condition for maxwell equation
Speaker: Yicong Ma, Math Dept, Penn State University
Location: MB216
October 11th, 2012 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Low dimensional dynamics with abstract time
Speaker: John Franks, Northwestern University
Location: MB114

We consider the dynamics of (non-compact) group actions on surfaces which are conservative and non-chaotic systems (technically with elements having zero topological entropy). A structure theorem for the dynamics of many such elements combined with the much better understood positive entropy case permits us to provide applications to group actions especially in the analytic case and leads to some interesting conjectures. New results represent joint work with Michael Handel.

October 12th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Introduction to the well-posedness of the hydrostatic limit in fluid mechanics
Speaker: Michael Renardy, Virginia Tech Math
Location: MB106

This talk is an introduction for students to the afternoon talk (with a similar title).

October 12th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: On the well-posedness of the hydrostatic limit in fluid mechanics
Speaker: Michael Renardy, Virginia Tech Math
Location: MB106

The talk will review some recent results on the well-posedness of the hydrostatic Euler equations. In particular, the role of boundary conditions (walls or free surface) will be emphasized. The results show that well-posedness of these equations is not a local property, for instance, it turns out that flows with one free surface are well-posed while flows with two free surfaces are ill-posed. It is also shown that magnetic fields or fluid elasticity can restore the well-posedness of the equations. I shall also discuss the implications for boundary layers in high Weissenberg number viscoelastic flows

October 15th, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Index Theory for Symplectic Matrix Paths with Applications II. ATTENTION! This is a part of the Tuesday lecture series at the Working seminar ; TIME: 3:35-5:30pm
Speaker: Huagui Duan, Nankai University, visiting Penn State
Location: MB106
October 16th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discuss session
Speaker: Qin Wang, Shanghai Jiaotong University
Location: MB216
October 16th, 2012 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Wilf-equivalence in permutation patterns
Speaker: Andrew Baxter, PSU
Location: MB106

In partition theory, it is often interesting when the number of partitions of n satisfying condition X equals the number of partitions satisfying condition Y. We will consider the analogous question for permutations of length n, where the conditions are phrased in terms of patterns which the permutations must avoid. Two patterns are Wilf-equivalent if the number of n-permutations avoiding one equals the number of n-permutations avoiding the other, and I will present some of the more powerful techniques to create such equivalences.

October 16th, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: T-duality for Langlands dual groups
Speaker: Calder Daenzer, Penn State University
Location: MB106

I will give a quick tour of T-duality, followed by a quick tour of Langland’s duality. The ﬁrst duality is a relation between a pair of principal torus bundles with NS-ﬂux, while the second is the relation between a pair of Lie groups whose root and co-root data is interchanged. A priori, these two have nothing to do with one another, but I will describe how in many cases Langlands may be realized as a T-dualization. This is joint work with Erik Van Erp.

October 16th, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: The structure of non-atomic randomness
Speaker: Jan Reimann, Pennsylvania State University
Location: MB315

We study the set NCR of infinite binary sequences that are never random with respect to a continuous Borel probability measure. We show that such sequences occur all the way through the hyperarithmetical hierarchy, and construct examples that are non-ranked, i.e. not a member of a countable effectively closed set.

October 16th, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Index Theory for Symplectic Matrix Paths with Applications,III . ATTENTION! There will be an extra lecture the day before: Monday October 15, at 3:35-5:30.
Speaker: Huagui Duan, Nankai University, visiting Penn State
Location: MB216

In these two lectures, I shall give an introduction of the Maslov-type index theory for symplectic matrix paths and its iteration theory with applications to the multiplicity and stability of periodic orbits for Hamiltonian systems and closed geodesics on compact manifolds

October 17th, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Relative spectral theory and nonconventional averages
Speaker: Jean-Paul Thouvenot, University of Paris, VI
Location: MB106

The norm convergence of non conventional averages of Z^d actions can, in the linear case, proved by T. Tao, be interpreted as the production of a new transformation, namely the diagonal action on a joining of d copies of the original action. We shall, using the relative spectral theory, describe an important object, the algebra of invariant sets of this diagonal action.

October 18th, 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
October 18th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discussion session
Speaker: Geng Chen, Penn State
Location: MB216
October 18th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Generating an algebra from the probabilistic standpoint
Speaker: Bogdan Petrenko, SUNY Brockport
Location: MB106

Let A be a ring whose additive group is free abelian of finite rank. The topic of this talk is the following question: what is the probability that several random elements of A generate it as a ring? After making this question precise I will show that it has an interesting answer which can be interpreted as a local-global principle. Some applications will be discussed. This talk will be based on my joint work with with Rostyslav Kravchenko (University of Chicago) and Marcin Mazur (Binghamton University).

October 18th, 2012 (01:00pm - 02:00pm)
Seminar: Game Theory Seminar
Title: Modeling Marvin Minsky: Game Theoretic Implications of The Society of Mind
Speaker: Eli Byrne, Dept of Mathematics and Applied Research Laboratory, PSU
Location: MB114

In his 1988 book The Society of Mind, Marvin Minsky, cognitive scientist and co-founder of MIT’s artificial intelligence laboratory, puts forth a concept of decision making based on the emergent dynamics of a collection of agents governed by local interaction rules, not an overall executive. Decision making control passes from one agent to another based on localized, heterogeneous, endogenous concepts of the relative “strength” of agents. Control shifts when the controlling agent loses strength relative to another. Agents may have a hierarchical structure, with sub-agents, and conflict between sub-agents weakens the parent agent. Environmental stimuli can increase or decrease the strength of agents. I will present a short summary of ideas for integrating these ideas with traditional game theory models, followed by an example model of players in a repeated prisoner’s dilemma or social dilemma game. Methodologies include mathematical convergence and equilibrium analysis as well as computer simulation analysis. Discussion also includes modeling the effects of Karma, i.e. non-random initial conditions.

October 18th, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: D-modules and differential forms in noncommutative geometry
Speaker: Jonathan Block, University of Pennsylvania
Location: MB106
October 18th, 2012 (02:30pm - 03:30pm)
Seminar: MASS Colloquium
Title: Number of collisions of n balls on the infinite billiard table after Burago-Ferleger-Kononenko.
Speaker: Anton Petrunin, Penn State
Location: MB113

Consider a system of n hard balls moving freely and colliding elastically in Euclidean space. We will give an upper bound for the number of collisions in such a system. The proof is a simple application of Alexandrov geometry. The talk is based on work of D. Burago, S Ferleger and A. Kononenko

October 18th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Auxiliary Space Multigrid Method
Speaker: Lu Wang, Math Dept, Penn State University
Location: MB216
October 19th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Towards understanding the evolution of the universe
Speaker: Christian Klingenberg, Wuerzburg University, Germany
Location: MB114

As a teaser for the afternoon Computational and Applied Math colloquium, I will show some numerical simulations related to the evolution of the universe. This will go beyond our own contributions and also show simulations of my collaborators Volker Springel and Fritz Roepke.

October 19th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: New numerical solvers for Hydro- and Magnetohydrodynamics using the relaxation approach
Speaker: Christian Klingenberg, Wuerzburg University, Germany
Location: MB106

We present a relaxation system for the Euler equations and for ideal MHD, from which one may derive approximate Riemann solvers. The solvers satisfy a discrete entropy inequality, and preserve positivity of density and pressure under a subcharacteristic condition. Next we consider the practical implementation, and derive explicit wave speed estimates satisfying the stability conditions. We put this into an astrophysical application by comparing our new positive and entropy stable approximate Riemann solver with state-of the-art algorithms for astrophysical fluid dynamics. We show some of the astrophysics applications that have been computed with our method. This is joint work with F. Bouchut and K. Waagan.

October 22nd, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: The ball in R^3 is a local minimizer of the optimal lattice packing density.
Speaker: Fedor Nazarov, Kent University
Location: MB106

We will show that any 3-dimensional symmetric convex body sufficiently close to the ball admits a lattice packing of higher density than the ball itself unless it is an ellipsoid, in which case the density is the same. This is joint work with Yoav Kallus.

October 23rd, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: A nonlinear variational wave equation
Speaker: Alberto Bressan, Penn State
Location: MB216

The talk will focus on the nonlinear wave equation u_tt - c(u) (c(u) u_x)_x = 0 The first part will review some earlier results. In particular, by a change in the independent and dependent variables, the equation can be reformulated as a semiinear system, and solved by a standard fixed point argument. The second part will discuss open problems: structurally stable singularities, dissipative solutions, multi-dimensional radially symmetric solutions, uniqueness and continuous dependence on the initial data.

October 23rd, 2012 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Coloring Statistics of an m × n grid
Speaker: Jocelyn Quaintance, Rutgers University
Location: MB106

You are given an m × n chess board and c cans of paint. Each can of paint has its own paint brush. The goal is to color each square of the chess board using this selection of c colors. There is one catch. Before painting each square you must shut your eyes and arbitrarily select a paint brush. When you are ﬁnished how many edge adjacent squares share the same color? This talk explains how humans and computers apply probabilistic methods to answer such a question.

October 23rd, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Turing equivalence as a Borel equivalence relation
Speaker: Jake Pardo, Pennsylvania State University
Location: MB315

The talk first presents some important facts on countable Borel equivalence relations. Feldman and Moore showed that any such relation is obtained as the orbit equivalence of some countable group action. This yields, among other things, the existence of a universal countable Borel equivalence relation. The second part then covers a result due to Slaman and Steel: Turing equivalence is not hyperfinite, or, equivalently, it is not generated by a Z-action.

October 23rd, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Non-uniform non-stationary normal forms, I
Speaker: Boris Kalinin, Penn State
Location: MB216
October 23rd, 2012 (04:00pm - 05:00pm)
Seminar: Applied Analysis Seminar
Title: Adaptive evolution and concentrations in parabolic PDEs
Speaker: Benoit Perthame, Unviversity Paris 6
Location: MB114

Living systems are characterized by variability; they are subject to constant evolution through the three processes of population growth, selection and mutations, a principle established by C. Darwin. In a very simple, general and idealized description, their environment can be considered as a nutrient shared by all the population. This alllows certain individuals, characterized by a 'phenotypical trait', to expand faster because they are better adapted to use the environment. This leads to select the 'fittest trait' in the population (singular point of the system). On the other hand, the new-born individuals undergo small variations of the trait under the effect of genetic mutations. In these circumstances, is it possible to describe the dynamical evolution of the current trait? A new area of population biology that aims at describing mathematically these processes is born in the 1980's under the name of 'adaptive dynamics' and, compared to population genetics, considers usually asexual reproduction, a continuous phenotypical trait and population growth. We will give a self-contained mathematical model of such dynamics, based on parabolic equations, and show that an asymptotic method allows us to formalize precisely the concepts of monomorphic or polymorphic population. Then, we can describe the evolution of the 'fittest trait' and eventually to compute various forms of branching points which represent the cohabitation of two different populations. The concepts are based on the asymptotic analysis of the above mentioned parabolic equations once appropriately rescaled. This leads to concentrations of the solutions and the difficulty is to evaluate the weight and position of the moving Dirac masses that desribe the population. We will show that a new type of Hamilton-Jacobi equation, with constraints, naturally describes this asymptotic. Some additional theoretical questions as uniqueness for the limiting H.-J. equation will also be addressed. Several other modeling methods have been proposed, stochastic individual based models, evolutionary game theory, dynamical systems. Connections will be presneted too. This talk is based on collaborations with G. Barles, J. Carrillo, S. Cuadrado, O. Diekmann, M. Gauduchon, S. Genieys, P.-E. Jabin, S. Mirahimmi, S. Mischler and P. E. Souganidis.

October 24th, 2012 (03:35pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Tits Geometry and Positive Curvature
Speaker: Karsten Grove, University of Notre Dame
Location: MB106

There is a well known link between (maximal) irreducible polar representations and isotropy representations of irreducible symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns - Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and compact topological spherical irreducible buildings of rank at least three. In joint work with Fang and Thorbergsson we discover and exploit a rich structure of a (connected) chamber system of finite (Coxeter) type "M" associated with any polar action of cohomogeneity at least two on any simply connected (closed) positively curved manifold. Although this chamber system is typically not a (Tits) geometry of type "M", we prove in all cases but one that its universal (Tits) cover indeed is a building. We construct a topology on this universal cover making it into a compact topological building in the sense of Burns and Spatzier. Our work shows that the exception indeed provides a new example (also discovered by Lytchak) of a Tits "C_3" geometry whose universal cover is not a building. We use this structure to prove the following Rigidity Theorem: Any polar action of cohomogeneity at least two on a simply connected positively curved manifold is smoothly equivalent to a polar action on a rank one symmetric space. The analysis and methods used in the reducible case (including the case of fixed points), the case of cohomogeneity two, and the general irreducible case in cohomogeneity at least three are quite different from one another. Throughout the local approach to buildings by Tits plays a significant role.

October 25th, 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
October 25th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: Geng Chen, Penn State
Location: MB216
October 25th, 2012 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Locally nilpotent derivations and the AK (ML) invariant
Speaker: Leonid Makar-Limanov, Wayne State University
Location: MB106

In my talk I will define the invariant and show in several examples how the invariant can be computed and used.

October 25th, 2012 (11:30am - 01:00pm)
Seminar: Teaching Seminar
Title: Data Collection and Analysis in the Math Department – what we are learning about our students, our intervention programs, and maybe ourselves.
Speaker: Jim Hager, PSU
Location: MB114
Abstract: http://
October 25th, 2012 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: K-theory for semigroup C*-algebras
Speaker: Xin Li, University of Muenster
Location: MB106

In this talk, I will explain how to compute K-theory for semigroup C*-algebras. It turns out that the Baum-Connes conjecture plays an important role in our computations. As an application, we will discuss the case of ax+b-semigroups over rings of integers in number fields.

October 25th, 2012 (02:30pm - 03:20pm)
Seminar: MASS Colloquium
Title: Mathematical Puzzles that S-t-r-e-t-c-h Your Intuition
Speaker: Peter Winkler, Dartmouth College
Location: MB113

Humans are not born with perfect mathematical intuition, to say the least, yet most decisions we make are based on "feel", not calculation. Today you will hear some mind-boggling puzzles (some with solutions, some without) that are designed to help you adjust your intuition when it's about to run off the rails.

October 25th, 2012 (02:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Proof of the auxiliary multigrid
Speaker: Lu Wang, Dept. of Maths Penn state
Location: MB216
October 25th, 2012 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: A Cop and Robber Solve the Kakeya Needle Problem
Speaker: P. Winkler, Dartmouth College
Location: MB114

We show that when pitted against each other, optimal strategies for a certain pursuit-and-evasion game construct a small region in the plane containing unit-length line segments at all angles. Joint work with Y. Babichenko, Y. Peres, R. Peretz, and P. Sousi.

October 26th, 2012 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Foundations of Density Functional Theory in context
Speaker: Paul Lammert, Physics Dept. PSU
Location: MB106

This talk will preview the long afternoon talk on foundations of Density Functional Theory, as well as fill in some context and background related to electronic structure calculation.

October 26th, 2012 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Foundations of Density Functional Theory Revisited
Speaker: Paul Lammert, Physics Dept. PSU
Location: MB106

This talk will be an exploration of the foundations of Density Functional Theory (DFT). Density Functional Theory is the basis of electronic structure calculations of high accuracy at acceptable computational cost for systems of up to hundreds of atoms and thus has a wide and growing impact in physics, chemistry and materials science. Our emphasis, however, will be on DFT as a distinct viewpoint on quantum many-body systems interesting for its own sake. There is some tendency to regard the foundations of the theory as a finished and straighforward story, but we will see that the structure is less sturdy and more unruly that one would like. To tame the troubles coming from arbitrarily short distance scales, we formulate a non-traditional "coarse-grained" approach and show that it is well-behaved.

October 29th, 2012 (03:30pm - 05:30pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: On rich surface dynamics arising from algebraic dynamics on $S^3\times S^3$.
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB106

Abstract: In this talk we shall analyze the dynamics of $f(x,y)=(y,xy)$ on $S^3\times S^3$. We shall relate it to a family of area preserving diffeomorphisms of $S^2$. We will discuss open problems coming from this dynamics on $S^2$, like the coexistence phenomena. This study arose from conversation with Klaus Schmidt when trying to understand the dynamics of $f$.

October 30th, 2012 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: Geng Chen, Penn State
Location: MB216
October 30th, 2012 (01:20pm - 02:20pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Cancelled. Will be rescheduled soon: On zero-sum stochastic differential games with unbounded controls
Speaker: Song Yao, University of Pittsburgh
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.

October 30th, 2012 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Advances in the minimal model program and open questions.
Speaker: Ray Lai, Purdue University
Location: MB106

In the course of birational classification of smooth complex projective varieties, the Good minimal model (GMM) conjecture is a natural generalization of the study of surfaces by Italian schools. The minimal model program is a generalization in higher dimensions of creating (relative) minimal surfaces. We will give a review on the theory of minimal model program, some recent results, and related open questions.

October 30th, 2012 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: A model of intuitionism based on Turing degrees
Speaker: Sankha Basu, Pennsylvania State University
Location: MB315

For any topological space T, let Sh(T) be the category of sheaves of sets over T. It is well known that the topos Sh(T) is a model of higher-order intuitionistic logic. We now consider the special case T = D = the partial ordering of Turing degrees with the topology of upward closed sets. We argue that the Muchnik topos, Sh(D), is a rigorous implementation of Kolmogorov's nonrigorous 1932 interpretation of intuitionism as a "calculus of problems."

October 30th, 2012 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Non-uniform non-stationary normal forms, II
Speaker: Boris Kalinin, Penn State
Location: MB216