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February 1st, 2012 (01:00pm - 02:00pm)

Seminar: Seminar on Mathematics in the Bio and Geo Sciences
Title: Dynamics of membranes and molecules at the endothelial cell surface
Speaker: Peter J. Butler, Dept of Bioengineering, Penn State
Location: MB106

Our group seeks to understand how cells convert force into biochemical signals. I will present evidence that the cell membrane is stressed by tension and out of plane fluctuations and that these stresses lead to perturbation of membrane microdomains. These domains may, in turn, participate in lipid and protein sorting that results in changes in biochemical signaling in the cells. Specifically, I will present results of molecular dynamics simulations of lipids and corresponding molecular scale spectroscopic measurements of lipid areal changes accompanying tension and fluctuations. In addition, I will present the first direct evidence for the participation of membrane domains in mechanosensation at the cell surface. We seek mathematical formulations that might capture these phenomenon and lead to predictive models of mechanochemical signal transduction.

February 1st, 2012 (02:30pm - 03:20pm)

Seminar: Applied Algebra Seminar
Title: Combinatorics arising from the study of tensors
Speaker: Claudiu Raicu, Princeton
Location: MB106
Abstract: http://www.math.princeton.edu/~craicu/

I will explain a polarization technique that allows one to translate basic algebro-geometric questions arising from the study of tensors into very concrete combinatorial problems via representation theory. In particular, I will describe the relationship between the syzygies of Segre and Veronese varieties and the homology groups of the clique complexes associated to certain graphs.

February 2nd, 2012 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Cyclotomic constructions of strongly regular Cayley graphs and difference sets
Speaker: Qing Xiang, University of Delaware
Location: MB106

The idea of constructing dierence sets and strongly regular Cayley graphs from cyclotomic classes of nite elds goes back to Paley. In the mid- 20th century, this idea was pursued vigorously by many researchers, such as Baumert, Chowla, Hall, Lehmer, Van Lint, Schrijver, Storer, Whiteman, Yamamoto, etc. However, this method for constructing dierence sets has had only very limited success. Let q be a prime power and N|(q-1), N > 1. It is known that a single cyclotomic class of order N of F_q can form a dif- ference set in (F_q,+) if N = 2, 4 or 8 and q satisfies certain conditions. It was conjectured that the converse is also true. Namely, if the nonzero N-th powers of F_q form a difference set in (F_q,+), then N is necessarily 2, 4, or 8. This conjecture has been verified up to N = 20. There is a conjecture of a similar nature for cyclotomic strongly regular graphs. We will report new constructions of both strongly regular Cayley graphs and skew Hadamard difference sets by using unions of cyclotomic classes of very large orders. Implications on association schemes will be discussed. The main tools we used are Gauss sums, instead of cyclotomic numbers. The talk is based on joint work with Tao Feng.

February 2nd, 2012 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: Reciprocity and p-adic groups, 3
Speaker: Nigel Higson, Penn State
Location: MB106

Frobenius reciprocity connects the operations of induction and restriction in group representation theory. In the 1980's Bernstein discovered that for p-adic groups, the roles of parabolic induction and restriction can be exchanged, more or less, leading to a second reciprocity, or adjointness theorem. This is the foundation for much of p-adic representation theory. I'll try to give an account (over several lectures) of Bernstein's theorem. I'll examine a recent geometric account to due Bezrukavnikov and Kazhdan, as well as Bernstein's original argument.

February 2nd, 2012 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Partial hyperbolicity and the topology of 3-manifolds
Speaker: Jana Rodriquez Hertz
Location: MB114

A partially hyperbolic diffeomorphism is one having an invariant splitting of the tangent bundle into 3 directions: one expanding -unstable- direction, one contracting -stable- direction, and one intermediate -center- direction. It is one of the natural generalizations of Anosov diffeomorphisms. Interestingly, 3-dimensional topology is a crucial ingredient in the study of such systems. Here we survey directions of research and open problems relating these two fields.

February 2nd, 2012 (04:40pm - 05:30pm)

Seminar: SIAM Student Chapter Seminar
Title: Career advice from a successful applied mathematician
Speaker: Tim Reluga, Penn State
Location: MB315

The Penn State SIAM student chapter is pleased to host our own Tim Reluga, assistant Professor of Mathematics and Biology and a member of Penn State's Center for Infectious Disease Dynamics. Professor Reluga will talk about the early-career success that he's enjoying as an interdisciplinary researcher and share his thoughts on how we might all be so successful while we all enjoy SIAM-provided pizza.

February 3rd, 2012 (12:20pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Zooming for curl and divergence
Speaker: M. Kawski, Arizona State University
Location: MB114

We explain our JAVA program "vector field analyzer."

February 3rd, 2012 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: A conservation law modeling a highly re-entrant manufacturing system
Speaker: M. Kawski, Arizona State University
Location: MB106

We study a model for microchip manufacturing

February 6th, 2012 (03:35pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Genericity of non-uniform hyperbolicity in dimension 3
Speaker: Jana Rodriguez Hertz, IMERL, Montevideo
Location: MB106

In 1982 Mañé announced (later proved by Bochi) that generic conservative surface diffeomorphisms are either Anosov or else all Lyapunov exponents vanish almost everywhere. He pointed out the difficulties of obtaining similar results for higher dimensional manifolds, including the fact that conservative diffeomorphisms are not necessarily symplectic. Here we show that for a generic conservative diffeomorphism in a 3-manifold, either all Lyapunov exponents vanish almost everywhere, or else the system is non-uniformly hyperbolic. It is known that the generic non-uniformly hyperbolic diffeomorphism is ergodic, and its Oseledets splitting is globally dominated.

February 7th, 2012 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Slaman-Woodin Coding (I)
Speaker: Adrian Maler, Pennsylvania State University
Location: MB315

The talk presents a theorem, due to Slaman and Woodin, that every countable relation is uniformly definable in the structure of the Turing degrees.

February 7th, 2012 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: Not quite Kodaira vanishing theorems in characteristic p
Speaker: Karl Schwede, Penn State
Location: MB106

In this talk I will discuss the Kodaira vanishing theorem, the fact that it doesn't hold for varieties in positive characteristic, and a potential replacement for it in this setting. To motivate this replacement, I will discuss the role multiplier ideals play in the complex setting. I also hope to discuss some applications.

February 7th, 2012 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Applications of topology of three-dimensional manifolds to dynamics, I.
Speaker: Raul Ures, IMERL, Montevideo
Location: MB216

We will show that some tools of the theory of foliations, laminations and decompositions of 3-manifolds are very useful in the study of ergodic properties of partially hyperbolic diffeomorphisms. In this talk we plan to show what happens if a partially hyperbolic diffeomorphism does not satisfy the accessibility property. This leads to three type of obstructions that we will describe and, as a consequence, we will prove that on nilmanifolds any conservative partially hyperbolic diffeomorphism is accessible.

February 7th, 2012 (04:00pm - 05:00pm)

Seminar: Applied Analysis Seminar
Title: "Nonlinear continuity equations"
Speaker: Pierre Emmanuel Jabin, Mathematics Department, University of Maryland
Location: MB106

Recent developments in the modeling of various complex transport phenomena (from bacteria to pedestrians' flows) have produced new and challenging equations. In particular those models have a very different behaviour from the usual fluid dynamics when the density is locally high, usually as a consequence of a strict bound on the maximum number of indivivuals that one can have at a given point. The corresponding non linear continuity equations combine the features of both scalar conservation laws and transport equations with rough velocity fields. Their study, both theoretically and numerically, hence presents unique challenges. We are able to derive new critical regularity estimates for this class of models, which are compatible with shocks and the singular advection phenomenon.

February 7th, 2012 (05:00pm - 06:10pm)

Seminar: Slow Pitch Seminar
Title: Arnold diffusion and waves in lattices
Speaker: Mark Levi, Penn State
Location: MB106

I will give a quick overview of some interesting phenomena, and will mention some open problems, in dynamics of chains or arrays of oscillators.

February 8th, 2012 (02:30pm - 03:20pm)

Seminar: Applied Algebra Seminar
Title: Approximation Errors of Deep Belief Networks
Speaker: Guido Montufar, Penn State
Location: MB106

The Deep Belief Network (DBN) is a kind of artificial learning system with an efficient learning algorithm introduced by Hinton in 2006 and which has revolutionized the machine learning research field Deep Learning. The DBN has a graphical representation including several layers of hidden binary variables with directed pairwise connections between subsequent layers and undirected pairwise connections between the last two hidden layers. The representational power of these models is far from being completely understood. In particular, the smallest number of hidden variables for which the DBN model is able to represent any probability distribution as its marginal visible distribution is still unknown. In this talk, I discuss submodels of DBNs and use them to bound, for the first time, the maximal Kullback-Leibler approximation errors of the DBNs depending on the number of hidden layers. These results yield, in particular, bounds for the minimal number of hidden layers of a DBN universal approximator.

February 9th, 2012 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: D-module structure of local cohomology modules
Speaker: Jen-Chieh Hsiao, Purdue University
Location: MB106

Let R be a polynomial ring and I be an ideal of R. It is well known that the local cohomology modules of R supported at I have finite length as D-modules. They are in fact holonomic D-modules. In this talk, I will define these terms and will try to illustrate this classical result by a simple example and explain how to generalize it to the case where R is a toric algebra and I is a monomial ideal of R. Some computations of characteristic varieties of local cohomology modules will also be discussed.

February 9th, 2012 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: Stable triviality criterion for associated noncommutative line bundles
Speaker: Piotr Hajac, Polish Academy of Sciences
Location: MB106

February 9th, 2012 (02:30pm - 03:30pm)

Seminar: PMASS Colloquium
Title: Lake fish population estimates and mixing properties
Speaker: Jana Rodriguez Hertz, IMERL, Uruguay
Location: MB113

A mark-and-recapture method of lake fish population estimate consists in collecting and tagging a random sample of, for instance, 1000 fish, and counting the tagged fish in a second random capture, after releasing and allowing a period of mixing. A number of, for instance, 10 tagged fish would give an estimate of 100,000 fish in the lake. Is this a good estimate? We will see how this depends on the way the fish get mixed.

February 9th, 2012 (02:30pm - 03:30pm)

Seminar: Symplectic Topology Seminar
Title: A simple proof of the Conley conjecture for Hamiltonian diffeomorphisms C^1-close to the identity
Speaker: Marco Mazzucchelli, Penn State University
Location: MB315
Abstract: http://

The Conley conjecture, recently established by Hingston, asserts that every Hamiltonian diffeomorphism of a standard symplectic 2n-torus admits infinitely many periodic points. While this conjecture has been extended to more general closed symplectic manifolds, all the known proofs require sophisticated machinery and somehow lack transparency. In this talk, we use generating function techniques in symplectic geometry to give a simple proof of the conjecture for those Hamiltonian diffeomorphisms of the torus that are C^1-close to the identity.

February 9th, 2012 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Directed last passage percolation
Speaker: Jinho Baik, University of Michigan
Location: MB114

http://www.math.lsa.umich.edu/~baik/Welcome.html Imagine that one travels from the origin to a site (M,N) through a sequence of neighboring integer lattice sites. The condition is that only north-moves and east-moves are allowed. It takes certain amount of time to pass through a given site and this time is different from site to site. If the passage times at sites are random, what is the maximal time to go from (0,0) to (M,N)? This question is related to 2-D random growth models, interacting particle systems and tandem queues. Moreover for some special choice of random variables, the answer is related to random matrix theory and also combinatorics of partitions. We will survey some results and recent developments related to this question.

February 10th, 2012 (12:20pm - 01:30pm)

Seminar: CCMA Luncheon Seminar
Title: Schroedinger operators and Regularity results via blow-up techniques
Speaker: Bernd Ammann, Regensburg University
Location: MB114

This talk is an introduction to the afternoon talk in which regularity results for Schroedinger operators and for boundary values on polyhedral domains will be discussed. These regularity results have an impact in the design of numerical methods.

February 10th, 2012 (02:20pm - 03:20pm)

Seminar: Seminar on Probability and its Application
Title: Latency analysis for a tandem of queues with exponentially distributed service times
Speaker: Jinho Baik, University of Michigan
Location: MB106

When a customer arrives in a tandem of queues, this person joins a queue at the first server. After being served, this person proceeds to the next server and joins a queue there, and so on. Now suppose that all the queues were empty and a batch of N customers arrive at the first queue. How long does it take for the Nth customer to exit from the queue M? When M and N are large, does one or two slow servers matter in the asymptotics? We discuss this question and connection to random matrix theory. This is a joint work with Raj Rao (UM EECS).

February 10th, 2012 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Regularity results for Schroedinger operators
Speaker: Bernd Ammann, Regensburg University, Germany
Location: MB106

The talk will present regularity statements for elliptic operators with certain types of singularities. Regularity results are often an important ingredient in the design of numerical methods. The main application is to Schroedinger operators. In fact, we will consider two types of singularities: at first we study operators similar to the Schroedinger operator, i.e. elliptic differential operators with a potential comparable to $r^{-s}$ where $r$ is the distance to a submanifold and where $s$ is positive, but smaller than the order of the operator. In this frist case, we consider the points with infinite potential as singularities. Secondly we study elliptic operators on bounded domains, with non-smooth but piecewise smooth boundary. In this case we consider the non-smooth boundary points as singularities. In both cases, one cannot expect the usual regularity results in the standard Sobolev spaces close to the singularity. In the talk we use blow-up methods to derive suitable Sobolev spaces which are well-adapted the geometry of the singularities. In these modified Sobolev spaces, one obtains regularity results, generalizing the standard regularity statements to operators on domains with non-smooth but piecewise smooth boundary and to Schr\"odinger type operators. The blow-up method is formalized in the language of Lie manifolds, a class of non-compact complete manifolds. This class of manifolds contains b-manifolds in the sense of Melrose, asymptotically hyperbolic manifolds and many more. We then describe a systematic way to conformally blow-up a Lie-manifold along a given submanifold, and the result will be a Lie manifold with "new" points at infinity. The results I will present are joint work with Victor Nistor, Catarina Carvalho, Robert Lauter, and Alexandru Ionescu.

February 13th, 2012 (03:35pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Global rigidity of maximal rank Anosov abelian actions
Speaker: Federico Rodriguez Hertz, Penn State
Location: MB106

February 14th, 2012 (11:15am - 12:05pm)

Seminar: Combinatorics/Partitions Seminar
Title: Symmetric Group, cont.
Speaker: Matt Katz
Location: MB106

February 14th, 2012 (12:30pm - 02:30pm)

Seminar: Ph.D. Thesis Defense
Title: "Orthogonality and Extendability of Latin Squares and Related Structures"
Speaker: Serge Ballif, Adviser: Gary Mullen
Location: 203 EE West
Abstract: http://

Two of the most important topics in the study of latin squares are questions of orthogonality and extendability. A latin square of order $n$ is an $n \times n$ array consisting of $n$ symbols such that each of $n$ distinct symbols occurs precisely once in each row and column. Two latin squares are said to be orthogonal if no two cells contain the same ordered pair of symbols when the squares are superimposed. There are many generalizations of latin squares, and in these generalizations there is a natural notion of orthogonality. In particular, we can view a latin square as a coloring of a graph. We say that two colorings of a graph are orthogonal if, whenever two vertices share a color in one coloring, then they have a different color in the other coloring. It is well known that there cannot be more than $n-1$ pairwise orthogonal latin squares of order $n$. Given a graph, $G$, we seek a bound on the maximum size of a set of pairwise orthogonal colorings of $G$. We derive several upper bounds based on parameters of the graph such as the number of vertices and edges, the maximum degree of a vertex, or the existence of large cliques. As a consequence we establish upper bounds on the maximum cardinality of a set of pairwise orthogonal colorings for several latin structures including latin rectangles, row latin squares, single diagonal latin squares, and double diagonal latin squares. We show that these bounds are the best possible. Questions about the extendability of latin squares are related to obtaining a latin square from a partially filled latin square. A partial latin square of order $n$ is an $n\times n$ array consisting of $n$ symbols such that each of $n$ symbols occurs at most once in each row and column. It is an NP-complete problem as to whether a partial latin square can be completed to a latin square of the same order. In 1974 Alan Cruse derived necessary and sufficient conditions to extend a partial latin rectangle to a latin square. Here we provide an alternate proof of Cruse's Theorem. Then we use the tools of this proof to prove an analogous theorem for frequency squares. A frequency square of type $F(n;\lambda_1,\ldots,\lambda_k)$ is an $n\times n$ array filled with $k$ symbols if the symbol $i$ occurs in each row and column precisely $\lambda_i$ times.

February 14th, 2012 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Slaman-Woodin Coding (II)
Speaker: Adrian Maler, Pennsylvania State University
Location: MB315

The talk presents a theorem, due to Slaman and Woodin, that every countable relation is uniformly definable in the structure of the Turing degrees.

February 14th, 2012 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Applications of topology of three-dimensional manifolds to dynamics, II.
Speaker: Raul Ures, IMERL, Montevideo
Location: MB216

We will show that some tools of the theory of foliations, laminations and decompositions of 3-manifolds are very useful in the study of ergodic properties of partially hyperbolic diffeomorphisms. In this talk we consider one of the obstructions mentioned in the first talk, namely the presence of a 2-torus with hyperbolic dynamics. We plan to show that these objects exist only in some especial families of 3-manifolds.

February 14th, 2012 (04:00pm - 05:00pm)

Seminar: Applied Analysis Seminar
Title: Using Mathematics to Understand Biological Function
Speaker: Jim Keener, Mathematics Department, University of Utah
Location: MB106

Recent advances in biology have resulted in an explosion of information about the parts of biological organisms. The much larger remaining challenge is to understand how those parts work together to function at the level of a cell or a multicellular organism. The purpose of this talk is to give an introduction to the fascinating world of Mathematical Physiology, that is, how mathematical thinking and modeling can give insight into the ways in which biological systems work. Specifically, the goal is to show how two fundamental processes, namely molecular diffusion and chemical reaction are exploited by living organisms to accomplish a variety of important tasks. Perhaps more importantly, I will show that there are common mathematical features (i.e., transferable principles) that underlie apparently disparate biological phenomena. Specific biological examples that I will discuss include endosomal protein sorting, bacterial quorum sensing, calcium signaling, and acid pumping into the stomach. The equations that are used to describe all of these quite different processes are of diffusion-advection-reaction type and have similar mathematical features, which is why/how mathematicians can get involved in this endeavor. The necessary background for this talks includes some knowledge of ordinary and partial differential equations, although not at a technical level.

February 14th, 2012 (04:00pm - 05:00pm)

Seminar: Student Geometric Functional Analysis Seminar
Title: The K-theory of the triple-pullback C*-algebra of Toeplitz quantum projective spaces
Speaker: Jan Rudnik, Mathematical Institute of the Polish Academy of Science
Location: MB315

Any triple-pullback C*-algebra is isomorphic with a certain iterated-pullback C*-algebra. This leads to a general method of computing the K-theory of triple-pullback C*-algebras. This method will be applied to determine the K-groups of the C*-algebras of the Toeplitz quantum real and complex projective spaces in dimension 2. The real case also needs an explicit formula for the even-to-odd connecting homomorphism in the six-term Mayer-Vietoris exact sequence. This formula will be recalled and applied to derive the torsion part of the even K-group.

February 15th, 2012 (02:30pm - 03:20pm)

Seminar: Applied Algebra Seminar
Title: Applied Algebraic Geometry
Speaker: Jason Morton, Penn State
Location: MB106

I will survey some recent successes and future directions in applied algebraic geometry.

February 15th, 2012 (03:35pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: TBA
Speaker: Walter Neumann, Columbia University
Location: MB106

February 16th, 2012 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Hilbert-Kunz Multiplicities
Speaker: Florian Enescu, Georgia State University
Location: MB106

The talk will discuss the notion of Hilbert-Kunz multiplicity for rings of positive prime characteristic, presenting its general theory and listing some of the outstanding open problems together with recent progress on them. Some of the work is joint with Ian M. Aberbach.

February 16th, 2012 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: A new perspective on the Inonu-Wigner contractions
Speaker: Eyal Subag, Technion
Location: MB106

Many physical theories approximate other theories under certain limits. Segal, İnönü and Wigner were the first to consider what are the implications of these limits on the corresponding symmetry groups. Contraction is a formal way of applying these limits to Lie groups, Lie algebras and their representations. In recent work we have shown that any contraction of Lie algebra representations is intrinsically a direct limit construction. Moreover, for any İnönü-Wigner contraction of a real three dimensional Lie algebra, we obtained the corresponding contractions of the irreducible representations in a canonical way by pointwise convergence of differential operators. In this talk I’ll review contraction of Lie algebras and their representations focusing on the methods of İnönü and Wigner. I will present several examples, some of which are new and show how the direct limit construction arises naturally. This work was done in collaboration with E. M. Baruch, J. L. Birman and A. Mann.

February 16th, 2012 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Fredholm meets Hodgkin, Huxley, Fokker, Planck, Keizer and Gillespie
Speaker: Jim Keener, University of Utah
Location: MB114

One fascinating aspect of the study of Mathematical Biology is the way in which certain fundamental mathematical ideas show up in widely varying contexts. In this talk we will take a quick tour of a variety of stochastic biological and chemical processes all of which have a common mathematical feature, namely that the underlying dynamics is on a manifold of lower dimension, and the existence of this manifold is a consequence of the Fredholm alternative theorem. The biological problems we will discuss include spontaneous release of calcium in cardiac cells, extinction dynamics of enzyme reactions, ion channel kinetics, progression of molecular motors and spontaneous firing of action potentials in nerve cells. Names associated with these biological processes and their mathematical models include Hodgkin and Huxley, Fokker-Planck, Keizer and Gillespie.

February 17th, 2012 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: Computational Issues in Numerical Weather Prediction
Speaker: Fuqing Zhang, Penn State Metereology
Location: MB106

February 17th, 2012 (04:40pm - 05:30pm)

Seminar: SIAM Student Chapter Seminar
Title: A Mathematical Career in Industry
Speaker: Jennifer Deang, Lockheed Martin-IS&GS
Location: MB106

In this talk, I will give an overview of my experiences working as a mathematician at Lockheed Martin. Lockheed Martin is a very large technology corporation with major activities in aerospace, energy, information technology, satellites, and simulation. An unbelievable array of problems arise from these activities, and can land on a the desk of the computational scientist, with the plea "Can you help?" The reason it's a problem is nobody has seen something quite like this before. The reason they're coming to you is that your more generalized experience, and ability to construct new algorithms from old ones, you might be able to guide them to an acceptable solution. I'll try to suggest the range of problems you could find yourself working on if you choose a research or programming job in an industrial environment such as mine. Industrial firms hire mathematicians and computational scientists because their training means they can be given almost any kind of problem, and figure out a reasonable way to analyze and solve it. The industrial setting includes some features not found in academia, including time and cost constraints, and work in large projects. Surprisingly, there can also be room for research projects.

February 20th, 2012 (09:00am - 11:00am)

Seminar: Ph.D. Thesis Defense
Title: "The divisor function in arithmetic progressions"
Speaker: Prapanpong Pongsriiam, Adviser: Robert Vaughan
Location: 110 Sackett Building
Abstract: http://

We will discuss and compare average results on primes and on the divisor function in arithmetic progressions. We will show how we apply Hooley's method and Vaughan's method to obtain the results which improve significantly Motohashi's result on the distribution of the divisor function in arithmetic progressions. This is the work in my thesis under the guidance of Professor R.C. Vaughan.

February 20th, 2012 (03:35pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: The structure of the space of ergodic measures
Speaker: Vaughn Climenhaga, University of Toronto
Location: MB106

Many interesting dynamical systems have the property that the set of ergodic measures is dense in the space of all invariant measures. This implies, among other things, that the set of ergodic measures is arc-connected. In this talk, I will describe how techniques for selecting continuous paths of ergodic measures yield information about various statistical properties of the system, and give results that extend these techniques to new classes of systems.

February 21st, 2012 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Degree of Randomness versus Turing degree
Speaker: William Calhoun, Bloomsburg University
Location: MB315

February 21st, 2012 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Global rigidity of Riemannian manifolds of non-positive curvature, after Ballmann, Brin, Burns, Eberlein, Spatzier, III.
Speaker: Weisheng Wu, Penn State
Location: MB216

February 23rd, 2012 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: To be announced
Speaker: Anurag Singh, University of Utah
Location: MB106

February 23rd, 2012 (11:30am - 01:00pm)

Seminar: Teaching Seminar
Title: "Academic Integrity-facts, myths, and classroom realities"
Speaker: Dr. James Sellers, Penn State
Location: MB114

All of us have read the university's statement on academic integrity and have posted the relevant information in our syllabus materials. Many of us have also experienced that sinking feeling when we realize that a student has stepped "over-the-line", and that we will need to take remedial action. Our shared history with academic integrity includes many myths, urban legends, quirky stories, serious and potentially confrontational moments, and at times regrets that we did not act differently in specific situations. Please join us at our Feb 23, 11:30-1:00 Teaching Seminar, when Dr. James Sellers, Associate Head for Undergraduate Studies in the Mathematics Department will "lay bare the facts" by sharing his experiences as a member of the college's academic integrity committee, and as the initial point-of-contact for academic integrity issues within the mathematics department. This informal talk will discuss the current academic integrity policies of the college, the online academic integrity resources currently available, and most importantly, Dr. Sellers' experiences with the implementation of these policies. There will be plenty of time for Q&A so please bring your concerns, questions, and "sanitized" stories.

February 23rd, 2012 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: C*-algebraic intertwiners for SL(2,R)
Speaker: Pierre Clare, Penn State
Location: MB106

February 23rd, 2012 (02:30pm - 03:30pm)

Seminar: PMASS Colloquium
Title: The Continuum Hypothesis
Speaker: Jan Reimann, The Pennsylvania State University
Location: MB113

In the late 19th century the German mathematician Georg Cantor tried to show that every uncountable subset of the real numbers can be mapped bijectively onto the real line. He was unable to prove this, and the question became the Continuum Hypothesis (CH). It was the first question on Hilbert's famous problem list of 1900. Seminal works by Gödel and Cohen showed that CH can neither be proved nor disproved from Zermelo-Fraenkel set theory (ZF), a basic axiom system for sets that captures most of modern mathematics. In other words, CH is independent of ZF. In this talk I will sketch the history of the Continuum Hypothesis, how it influenced the development of logic and set theory in the 20th century, and I will outline how one can show that a statement is independent of ZF.

February 23rd, 2012 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: The number of equations defining an algebraic set
Speaker: Anurag Singh, University of Utrah
Location: MB114

Given an algebraic set---i.e., the solution set of a family of polynomial equations---what is the minimal number of polynomials needed to define this set? The question is surprisingly difficult, with a rich history. We will give a partial survey, and discuss results and questions coming from local cohomology theory.

February 27th, 2012 (03:35pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: TBA
Speaker: Marlies Gerber, Indiana University
Location: MB106

February 28th, 2012 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Automorphisms of the Turing Degrees
Speaker: Keita Yokoyama, Tokio Institute of Technology and Pennsylvania State University
Location: MB315

February 29th, 2012 (01:00pm - 02:00pm)

Seminar: Seminar on Mathematics in the Bio and Geo Sciences
Title: TBA
Speaker: Reka Albert, Dept of Physics, Penn State
Location: MB106

February 29th, 2012 (03:35pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: TBA
Speaker: Tim Austin, Brown University
Location: MB106