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February 1st, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Fixed-Point Based Proximity Algorithms for Convex Optimization Problems in Signal and Image Processing
Speaker: Yuesheng Xu, Syracuse University
Location: MB114

We consider in this talk a class of convex optimization problems in the context of signal and image processing. The computational challenges of these problems are the nonlinearity and non-differentiability of the object function. We characterize the solutions of these problems in terms of fixed-point equations via the proximity operators of the functions that appear in the object function. Efficient algorithms are developed based on the characterization. We introduce the notion of the weakly firmly non-expansive operators to analyze the convergence of the proposed algorithms. Many well-known algorithms are re-interpreted as special cases of the proposed algorithms and new algorithms are shown numerically more efficient than the existing ones.

February 1st, 2013 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Fixed-Point Based Proximity Algorithms for Convex Optimization Problems in Signal and Image Processing
Speaker: Yuesheng Xu, Purdue U. Mathematics
Location: MB106

This talk will present the details of the results introduced in the Luncheon seminar.

February 4th, 2013 (10:45am - 11:45am)
Seminar: Job Candidate Talk
Title: Long-term behavior of Markov processes and applications to actuarial sciences
Speaker: Achim Wuebker
Location: MB114

We investigate the long-term behavior of Markov processes. General spectral gap conditions are derived for time discrete Markov chains in terms of isoperimetric constants. Moreover, we analyze the Brownian Motion with Jump Boundary process as well as the Fiber Lay-down process by analytic and probabilistic techniques. Finally, we introduce a Fleming-Viot interaction particle process and discuss a related model with applications to survival analysis.

February 5th, 2013 (02:30am - 04:00am)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Smooth Particle Hydrodynamics: Fundamentals, projection schemes and computational considerations
Speaker: Nathaniel Trask, Applied Mathematics Department, Brown University
Location: MB023

Smooth Particle Hydrodynamics (SPH) is a meshless collocation methods for solving PDEs with origins in solving astrophysics problems in the late 70's. Recently the method has gained popularity due to its ability to robustly simulate multiphase and low Reynolds number flows. In recent years the method has been put on more sound theoretical footing and many researchers are using the SPH discretization in the same algorithms that are typically used in finite element/volume codes. In this talk the fundamentals of SPH approximation will be reviewed with a focus on recent developments in error analysis and current work using a stiffly stable projection technique for low Reynolds number flows will be presented.

February 5th, 2013 (09:30am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discussion session
Speaker: TBA
Location: MB216
February 5th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Partial randomness and strong separations, part 2.
Speaker: Phil Hudelson, Pennsylvania State University
Location: MB315
Abstract: http://www.personal.psu.edu/wmh129/abstract_for_logic_seminar.pdf

Algorithmic randomness and Kolmogorov complexity respectively provide recursion-theoretic frameworks for the study of probability theory and information theory. In this talk we will prove a new strong separation for partial randomness concepts. Two partial randomness definitions, pwt-f-random and dwt-f-random, can be characterized in terms of Kolmogorov complexity by generalizations of Schnorr's theorem: X is dwt-f-random if and only if KP(X_n)>f(n)+O(n) for all n, and X is pwt-f-random if and only if KA(X_n)>f(n)+O(n), where KP and KA mean prefix-free and a priori complexity respectively, and X_n means the length n initial segment of X. We will prove using a forcing argument that under suitable conditions on the function f, there is an X such that KP(X_n)>f(n) for all n, but no Y recursive in X satisfies KP(Y_n)>f(n)+2log_2(f(n))+O(1) for all n (also the analogous result for KA). This theorem, which will be published in The Journal of Symbolic Logic, generalizes the theorem of Miller that there exists a Turing degree of effective Hausdorff dimension exactly 1/2. The new theorem also implies that there exists an X of effective Hausdorff dimension 1 which does not compute a Martin-Lof random, a result originally due to Greenberg and Miller.

February 5th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: I. Orbit method and geometric quantization. Mathematical models of classical and quantum mechanics. Quantization.
Speaker: Alexandre Kirillov, University of Pennsylvania
Location: MB216
February 5th, 2013 (03:45pm - 04:45pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Understanding the shape of mortality in practice
Speaker: Achim Wuebker, Hanover Re
Location: MB114

We explain the importance of a precise understanding of different survival curves for insurance companies. A simple frailty model shows how the mortality ratio of two different risk groups develops in time in dependence of the underlying frailty distribution. Moreover, we will see how quasistationary distributions naturally appear in survival analysis.

February 6th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Polynomial actions of unitary operators: some new results and conjectures
Speaker: Vitaly Bergelson, Ohio State University
Location: MB114
February 7th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA
Location: MB216
February 7th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Expander families and variation of Galois representations
Speaker: Chris Hall, University of Wyoming
Location: MB106

Given a pair of curves U,V over the complex numbers, one can associate to a finite unramified map V-->U a finite Cayley-Schreier graph. In this talk we consider families of maps V_i-->U indexed by a parameter i such that the family of associated graphs is an expander family. As we will explain, the expander hypothesis has remarkable geometric implications, e.g. the set of V_i such that the gonality of V_i is less than your favorite positive number N is finite. We will also explain some of the arithmetic implications, e.g. for all but finitely many V_i, there are only many points on V_i defined over some extension of K of degree at most N. As one an application, we can derive results on the variation of Galois representations in a one-parameter family of abelian varieties defined over a number field.

February 7th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Tempered representations from the point of view of C*-algebras, I
Speaker: Nigel Higson, Penn State
Location: MB106
February 7th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Quasirandom groups
Speaker: Vitali Bergelson, Ohio State University
Location: MB114

A finite group G is called D-quasirandom for some parameter D, if all non-trivial unitary representations of G have dimension greater or equal to D. For example, the group SL(2, F_p) is (p-1)/2 quasirandom for any prime p. Informally, a finite group is quasirandom if it is D-quasirandom for a large value of D. We will discuss some recent results involving quasirandom groups, including a new mixing theorem obtained in a joint work with T. Tao.

February 8th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations
Speaker: James Adler, Tufts University Mathematics
Location: MB114

This work is on the numerical approximation of incoming solutions to Maxwell's equations, whose energy decays exponentially with time (asymptotically disappearing), meaning that the leading term of the back-scattering matrix becomes negligible. For the exterior of a sphere, such solutions are obtained by Colombini, Petkov and Rauch by specifying a maximal dissipative boundary condition on the sphere and setting appropriate initial conditions. We consider a mixed finite element approximation of Maxwell's equations in the exterior of a polyhedron whose boundary approximates the sphere. We use the standard Nedelec-Raviart-Thomas elements and a Crank-Nicholson scheme to approximate the electric and magnetic fields. We set discrete initial conditions with standard interpolation, modified so that these initial conditions are divergence-free. We prove that with such initial conditions, the fully discrete approximation to the electric field is weakly divergence-free for all time. We show numerically that the finite-element solution approximates well the asymptotically disappearing solutions constructed analytically when the mesh size becomes small.

February 8th, 2013 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Constrained First-Order System Least Squares for Improved Mass Conservation and Complex Fluids
Speaker: James Adler, Tufts University Mathematics
Location: MB106

In complex fluid flow simulations, there is a tradeoff between obtaining solutions that are accurate with a reasonable amount of computational work and satisfying certain conservation laws exactly. For instance, in incompressible fluid flow, conservation of mass takes the form of making sure the fluid velocities are divergence-free. In magnetohydrodynamics, one must satisfy conservation of mass as well as the solenoidal constraint that the magnetic field is divergence-free (i.e. there are no magnetic monopoles). Many methods have been applied to such systems, some being conservative at the cost of accuracy of the momentum equations and others at the cost of efficiency in the solver. First-order system least-squares approaches have also been applied and yield efficient methods for approximating solutions to coupled fluid mechanics problems. However, without proper care, the auxiliary conservation equations may not be solved to a sufficient accuracy. In this talk, we propose a constrained least-squares approach, where we augment the first-order system and minimize the least-squares functional subject to some constraint. Here, we only look at a simple diffusion equation, but present the main ideas, including what types of finite-element spaces to use and the solution algorithm. A domain decomposition or multilevel approach is employed to solve the constrained problem on local subdomains and coarse grids and used to update the unconstrained solution as needed. Thus, we approximate the solution accurately and efficiently using the least-squares method, while still conserving the appropriate quantity.

February 11th, 2013 (04:00pm - 06:30pm)
Seminar: Ph.D. Thesis Defense
Title: "Partial randomness and Kolmogorov complexity"
Speaker: Phil Hudelson; Adviser: Stephen Simpson, Penn State
Location: MB113
Abstract: http://www.personal.psu.edu/wmh129/abstract_for_defense.pdf

Algorithmic randomness and Kolmogorov complexity provide a computational framework for the study of probability theory and information theory. In this dissertation we prove some theorems about partial randomness. Ten notions of partial randomness are considered, based on the definition of Martin-Lof randomness and its equivalents. Under suitable hypotheses every variant of partial randomness can be defined in terms of either a priori or prefix-free complexity, using a strengthening of Schnorr's theorem. In addition, using Kolmogorov complexity arguments we can weakly separate various notions of partial randomness. For example, under suitable conditions on the function f, there exists an X such that KP(X_n)>f(n) for all n but KP(X_n)=f(n)+O(1) infinitely often. A similar result holds with KP replaced by KA. Here KP and KA denote prefix-free and a priori complexity respectively, X is an infinite sequence of 0's and 1's, and X_n is the length n initial segment of X. A major new theorem is that under suitable conditions on f, there is an X such that KP(X_n)>f(n) for all n, but no Y recursive in X satisfies KP(Y_n)>f(n)+2log_2(f(n))+O(1) for all n (also the analogous result for KA). This theorem, which will be published in The Journal of Symbolic Logic, generalizes the theorem of Miller that there exists a Turing degree of effective Hausdorff dimension 1/2. The new theorem also implies that there exists an X of effective Hausdorff dimension 1 which does not compute a Martin-Lof random, a result originally due to Greenberg and Miller.

February 12th, 2013 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Euler's partition theorem with upper bounds on multiplicities.
Speaker: Ae Ja Yee, PSU
Location: MB106

In 1972, George Andrews obtained a theorem on equivalent upper bound sequences of multiplicities, from which the Euler partition theorem on partitions into distinct parts and odd parts can be deduced. In this talk, I will revisit Boulet's four parameter formula for partitions and discuss a unification of Bressenrodt's alternating sum refinement and Andrews' generalization of the Euler theorem.

February 12th, 2013 (02:00pm - 03:00pm)
Seminar: Job Candidate Talk
Title: Reduced Stochastic Models for Filtering Turbulent Dynamical Systems
Speaker: John Harlim
Location: MB114

Fundamental issues in advancing real-time filtering problems are model errors even when expensive high-dimensional global weather forecasting models are used. For example, the modern operational weather models poorly reproduce the tropical observational records even with 10^9 state variables; this long-standing issue hinders the global weather model forecasting skill to improve from weekly to monthly, as reported in a recent article in the World Meteorological Organization bulletin. In this talk, I will discuss a class of computationally fast reduced stochastic models to help filtering. I will try to convince you that such a filtering approach can provide practical guidelines to improve estimation of moisture coupled tropical waves. Furthermore, I'd like to use mathematical theory to convince you that one can achieve ``optimal filtering" with judicious choice of reduced stochastic models.

February 12th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Partial randomness and strong separations, part 3.
Speaker: Phil Hudelson, Pennsylvania State University
Location: MB315
Abstract: http://www.personal.psu.edu/wmh129/abstract_for_logic_seminar.pdf

Algorithmic randomness and Kolmogorov complexity respectively provide recursion-theoretic frameworks for the study of probability theory and information theory. In this talk we will prove a new strong separation for partial randomness concepts. Two partial randomness definitions, pwt-f-random and dwt-f-random, can be characterized in terms of Kolmogorov complexity by generalizations of Schnorr's theorem: X is dwt-f-random if and only if KP(X_n)>f(n)+O(n) for all n, and X is pwt-f-random if and only if KA(X_n)>f(n)+O(n), where KP and KA mean prefix-free and a priori complexity respectively, and X_n means the length n initial segment of X. We will prove using a forcing argument that under suitable conditions on the function f, there is an X such that KP(X_n)>f(n) for all n, but no Y recursive in X satisfies KP(Y_n)>f(n)+2log_2(f(n))+O(1) for all n (also the analogous result for KA). This theorem, which will be published in The Journal of Symbolic Logic, generalizes the theorem of Miller that there exists a Turing degree of effective Hausdorff dimension exactly 1/2. The new theorem also implies that there exists an X of effective Hausdorff dimension 1 which does not compute a Martin-Lof random, a result originally due to Greenberg and Miller.

February 12th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: K-theory for some noncommutative orbifolds
Speaker: Yi-Jun Yao, Fudan University
Location: MB106

In this talk (based on joint work with Xiang Tang), I plan to discuss the computation of K-theory groups of some crossed-product C*-algebras using an equivariant version of Rieffel's strict deformation.

February 12th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: II. Moment map, relation to integrable systems, weight multiplicities, Okounkov concavity theorem, functional dimension.
Speaker: Alexandre Kirillov, University of Pennsylvania
Location: MB114
February 12th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: Algebraic Multigrid Method and Its Parallelization
Speaker: Xiaozhe Hu, Pennsylvania State University
Location: MB106

Developing parallel algorithms for solving large-scale sparse linear systems is an important and challenging task in scientific computing and practical applications. In this talk, I will introduce the unsmoothed aggregation algebraic multigrid method for solving large-scale linear systems. I will give theoretical justifications of its optimality for model problems and its parallelization, especially on GPUs. Two different parallel approaches will be discussed and numerical results will be presented to demonstrate their efficiency.

February 13th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: An information theoretic approach to Sobolev and isoperimetric inequalities
Speaker: Deane Yang, NYU - Poly
Location: MB114

I will describe connections among information theoretic, Sobolev-type, and isoperimetric inequalities and how these ideas can be used to establish new results.

February 14th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Atkin and Swinnerton-Dyer Congruences
Speaker: Ling Long, Cornell and Louisiana State Universities
Location: MB106

In the study of modular forms for noncongruence subgroups of SL(2,Z), despite the lack of effective Hecke operators, the coefficients of noncongruence modular forms satisfy some remarkable congruences called Atkin and Swinnerton-Dyer (ASD) congruences. They are often viewed as p-adic Hecke operators and are of fundamental importance to the study of noncongruence modular forms. More generally, it has been observed that special sequences arising from combinatorics, arithmetic, or differential equations also satisfy ASD type congruences. Some of them turned out to be p-adic analogues of Ramanujan type formula for 1 over Pi. In this talk, we will introduce Atkin and Swinnerton-Dyer congruences, survey some recent developments, and discuss their applications and connections to other areas.

February 14th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Tempered representations from the point of view of C*-algebras, II
Speaker: Nigel Higson, Penn State
Location: MB106
February 14th, 2013 (02:30pm - 03:20pm)
Seminar: PMASS Colloquium
Title: Fractals and dimension
Speaker: Victoria Sadovskaya, Penn State
Location: MB113

Fractals can be described as self-similar sets that have a fine structure at arbitrarily small scales. We will consider a variety of fractals and discuss their properties, which will lead us to their non-integer dimension. We will define and explore the notion of box dimension.

February 14th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: A mozaic of mathematical problems
Speaker: Dima Burago, Penn State University
Location: MB114

This won't be a typical colloquium lecture. Instead I'll give a number of mini-talks on very different topics. The only thing linking the topics together is that they have all been of interest to me in the past several years, and the most important part of the lecture will be the presentation of open problems. These will be formulated using no more than the material of our graduate student qualifying exams.

February 15th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: An introduction to Monge-Ampere equations
Speaker: Ovidiu Savin, Columbia Mathematics
Location: MB114

We present a brief overview of the classical theory for Monge-Ampere equations. In particular we'll discuss weak solutions, viscosity solutions and some applications to optimal transportation problems.

February 15th, 2013 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Boundary regularity for Monge-Ampere equation
Speaker: Ovidiu Savin, Columbia University, Mathematics
Location: MB106

Boundary estimates for second derivatives of solutions to the Dirichlet problem for the Monge-Ampere equation were first obtained by Ivockina in 1980. A few years later independently Krylov and Caffarelli-Nirenberg-Spruck obtained $C^{2,\alpha}$ regularity of solutions and this led to the solvability of the classical Dirichlet problem in the case when the data is sufficiently smooth. In our talk we will discuss some more recent results about boundary regularity under optimal assumptions on the data.

February 15th, 2013 (04:00pm - 05:00pm)
Seminar: GAP Seminar
Title: Splitting and replicating of operads, Manin products and Rota-Baxter operators
Speaker: Li Guo, Rutgers University at Newark
Location: MB315

Many new algebraic structures have emerged in recent year from diverse background, that are related to the three traditionally studied structures of associative, Lie and commutative algebras. The relationship can be vaguely described as either splitting or replicating the operations in the traditional structures, but it is not clear how it works precisely until recently. We will describe a general procedure that put these new structures together. We will also discuss the relationship of this procedure with Manin products and Rota-Baxter related operators.

February 18th, 2013 (03:30pm - 05:30pm)
Seminar: Ph.D. Thesis Defense
Title: "Some Problems in Poisson Geometry"
Speaker: Wei Hong, Adviser: Ping Xu, Penn State
Location: MB113

I will discuss two main topics. First, I will compute the Poisson cohomology of Del Pezzo Surfaces for all holomorphic Poisson structures. Then I will introduce a unifying structure of hypercomplex structure and holomorphic symplectic structure from the point of Courant algebroid, and some of the properties of such structure are studied.

February 18th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Reeb dynamics and symplectically degenerate extrema
Speaker: Doris Hein, Institute for Advanced Study, Princeton
Location: MB114

In this talk, I will discuss the dynamics of the Reeb flow and show that the Reeb vector field of every contact form supporting the tight three-sphere has at least two periodic orbits. Moreover, the existence of a special periodic orbit, a contact analog of a symplectically degenerate maximum, implies that there are infinitely many periodic orbits on a certain class of contact manifolds. The methods are taken from Hamiltonian dynamics on symplectic manifolds, in particular from the proof of the Hamiltonian Conley conjecture, and an isomorphism between local Floer homology and local contact homology.

February 19th, 2013 (09:30am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion
Speaker: TBA
Location: MB216
February 19th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Manifolds from simplicial polytopes
Speaker: Bin Zhang, Sichuan University
Location: MB106

From Delzant polytopes, we can construct complex manifolds and their real forms, a natural question is, can we construct manifolds from simplicial polytopes? In this talk, we address this question, and we prove that we can construct smooth manifolds from simplicial polytopes. The key ingredient is the local Z_2 systems on polytopes, and we use our recent results on cones and subdivisions to prove the existence. This is joint work with Bohui Chen and Anmin Li.

February 19th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: ATTENTION: The date and time of this lecture has been changed to THURSDAY, Feb. 21, 4:45pm
Speaker: Alexandre Kirillov, University of Pennsylvania
Location: MB114
February 21st, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: Geng chen
Location: MB216
February 21st, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Using Frobenius to produce global sections in characteristic p
Speaker: Karl Schwede, Penn State University
Location: MB106

In characteristic zero, one common way to prove that sections of line bundles exist is to set up various short exact sequences and use Kodaira vanishing (and generalizations). These vanishing theorems are false in characteristic p. Fortunately, I'll describe some methods which can be used to produce global sections of line bundles and discuss some recent applications (some by me, some not).

February 21st, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Tempered representations from the point of view of C*-algebras, III
Speaker: Nigel Higson, Penn State
Location: MB106
February 21st, 2013 (04:45pm - 07:15pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: III. Algebraic approach: enveloping algebra, infinitesimal characters, Kontsevich theorem, family algebras.
Speaker: Alexandre Kirillov, University of Pennsylvania
Location: MB114
Abstract: http://
February 22nd, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Gamma-Convergence and Minimizing Energies
Speaker: Marta Lewicka, University of Pittsburgh
Location: MB114

We shall introduce the definition and main properties of Gamma-convergence, which is the the key concept in the Calculus of Variations. We will explain how this concept plays central role in the mathematical theory of Elasticity, Phase Transitions and Homogenization.

February 22nd, 2013 (03:35pm - 04:25pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Isometries on Surfaces, Elasticity, and Calculus of Variations
Speaker: Marta Lewicka, University of Pittsburgh
Location: MB106

Elastic materials exhibit qualitatively different responses to different kinematic boundary conditions or body forces. As a first step towards understanding the related evolutionary problem, one studies the minimizers of an appropriate nonlinear elastic energy functional. We shall give an overview of recent results, rigorously deriving 2d elasticity theories for thin 3d shells around mid-surfaces of arbitrary geometry. One major ingredient is the study of Sobolev spaces of infinitesimal isometries on surfaces, their density and matching properties. Another one relates to the non-Euclidean version of 3d nonlinear elasticity, conjectured to explain the mechanism for spontaneous formation of non-zero stress equilibria in growing tissues (leaves, flowers).

February 25th, 2013 (03:30pm - 05:00pm)
Title: Private
Location: MB106
February 26th, 2013 (09:30am - 11:00am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: discussion session
Speaker: TBA
Location: MB216
February 26th, 2013 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Partitions with part difference conditions and Bressoud's conjecture
Speaker: Ae Ja Yee, PSU
Location: MB106

In the theory of partitions, the Rogers-Ramanujan identities have been the starting point for a great deal of insightful work into both analytic and combinatorial questions. Strongly motivated by the Rogers-Ramanujan identities, Isaai Schur searched for further analogous partition identities, and in 1926, he proved a mod 3 anaglogue of the Rogers-Ramanujan identities. In 1948, Henry Alder showed that if further identities exist, then more complex conditions than those stated in Schur’s theorem would be required. However, in his pathbreaking paper, by relaxing the part difference conditions of the Rogers-Ramanujan identities, Basil Gordon accomplished a remarkable partition theoretic extension of the Rogers-Ramanujan identities, which was extensively generalized by George Andrews and David Bressoud. In particular, in 1980, David Bressoud established an analytic identity, which serves as a master theorem for most of the well known partition theorems including the Rogers-Ramanujan identities. This analytic identity led him to define two partition functions as combinatorial counterparts of his identity. Bressoud then proved those functions are equal in some special cases and conjectured that this holds true in general. In my talk, I will discuss his conjecture. This talk is based on joint work with Sun Kim from Ohio State University.

February 26th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Rankin-Cohen operators for symmetric pairs
Speaker: Michael Pevzner, Universite de Reims
Location: MB106

Rankin-Cohen brackets play an important role in analytic number theory and deformation quantization. These specific bi-differential operators can also be interpreted as intertwining operators for some infinite dimensional representations of the Lie group SL(2,R). We present their analogues that appear in the framework of breaking symmetries for a large class of reductive symmetric pairs and explain in a systematic way why such equivariant differential operators are described in terms of Jacobi orthogonal polynomials. It is a joint work with T. Kobayashi.

February 26th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: On arithmetical equivalence relations.
Speaker: Keng Meng (Selwyn) Ng, Nanyang Technological University, Singapore
Location: MB315
Abstract: http://www.math.psu.edu/simpson/seminar/130226-ng.pdf

To be provided.

February 26th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: IV. Analytic problems: integral character formula, complementary series, infinite-dimensional case.
Speaker: Alexandre Kirillov, University of Pennsylvania
Location: MB114
February 26th, 2013 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Efficient solver of the Smoothed Partical Hydrodynamics equation
Speaker: Kai Yang, Dept. of Maths, Penn State University
Location: MB023
February 26th, 2013 (03:45pm - 05:00pm)
Title: Private
Location: MB106
February 27th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Non-existence of Einstein metrics compatible with some symplectic forms
Speaker: Augustin Banyaga, PSU
Location: MB114

Let $(M,\omega)$ be a symplectic manifold. We exhibit a reimannian type necessary and sufficient condition for the existence of an $\omega$-compatible Einstein metric. This was motivated by the Goldberg conjecture saying that if a compact symplectic manifold admits an $\omega$- compatible Einstein metric, then it is Kaehler.

February 28th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA
Location: MB216
February 28th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: On Lech's conjecture
Speaker: Linquan Ma, University of Michigan
Location: MB106

I will talk about the long-standing conjecture of Lech on the multiplicities of a faithfully flat extension of local rings. I will start with some historical results and several attempts to attack this conjecture. And I will show how this conjecture is related to some questions on modules of finite length and projective dimension and discuss some recent progress.

February 28th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Tempered representations from the point of view of C*-algebras, IV
Speaker: Nigel Higson, Penn State
Location: MB106
February 28th, 2013 (02:30pm - 03:20pm)
Seminar: PMASS Colloquium
Title: Geometry and arithmetic of Apollonian gasket
Speaker: Alexandre Kirillov, University of Pennsylvania
Location: MB113
Abstract: http://www.math.psu.edu/katok_s/Gasket.pdf

One of oldest and beautiful examples of a fractal set is the Apollonian gasket, arising as a maximal tiling of 2-dimensional sphere by non-intersecting discs. There are (at least) two remarkable facts: 1. The Descartes theorem, which gives the algebraic relation between the curvatures of four pair-wise tangent circles on the plane. I shall give the proof based on the geometry of Minkowski space. 2. The existence of integral realisations of the Apollonian gasket, where all curvatures are integers. I show some arithmetic properties of these curvatures and formulate several open questions. I attached a picture of one integral realisation.

February 28th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Symplectic realizations of Poisson manifolds
Speaker: Ping Xu, Penn State University
Location: MB114

Poisson brackets were invented in the early 19th century to provide a framework for optics and classical mechanics. Poisson geometry developed into a separate branch of mathematics during the 1960s, with applications to various aspects of physics, as well as to other areas of mathematics such as representation theory and integrable systems. In this talk, I will discuss the problem of symplectic realizations of Poisson manifolds, a classical question which can be traced back to Sophus Lie.