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Eberly College of Science Mathematics Department

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November 1st, 2013 (12:00pm - 03:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Accurate coarsening of H1-, Hcurl- and Hdiv- conforming finite element spaces by element agglomeration on unstructured 3d meshes
Speaker: Ilya Lashuk, Penn State Univeristy
Location: MB315

We present the ideas on how to coarsen the finite element spaces, so that two properties are preserved: the exactness of de Rham complex, and local interpolation of (scalar or vector) polynomials. Our approach is based on element agglomeration: we group together nearby fine elements to get coarse elements (generally, of rather wild shape). We then construct the coarse shape functions associated with coarse elements, "coarse faces" (faces of coarse elements), "coarse edges", etc. We discuss at length the lowest-order case, then proceed (if time permits) to higher-order construction for Hdiv case, and finish with the standalone (not dependent on Hcurl and Hdiv) construction for H1. Note: the talk starts at 1:30 PM.

November 1st, 2013 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Stochastic stability of stable-like Markov models
Speaker: Nikola Sandric, Mathematics Department, University of Zagreb
Location: MB106

In this talk, we will focus on a long-time behavior, in particular on the recurrence, transience and ergodicity, of so-called stable-like models. Roughly speaking, a stable-like model can be understood as a state-dependent stable model (random walk or Levy process), i.e., its index of stability depends on the current position of the process. We will give sufficient conditions for the recurrence, transience and ergodicity for this class of Markov models and, as a special case, we will give a new proof for the recurrence and transience of stable random walks and Levy processes.

November 4th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Nearshore Sticky Waters
Speaker: Juan M. Restrepo, University of Arizona
Location: MB114
Abstract: http://math.arizona.edu/~restrepo/

Abstract: Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, not subject to inertial effects, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters

November 4th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Mathematical Challenges in Climate Variability
Speaker: Juan M. Restrepo, University of Arizona
Location: MB106
Abstract: http://math.arizona.edu/~restrepo/

Abstract: A fundamental challenge in climate science is to make sense of very limited and poorly constrained data. A notable problem in this realm is the question of whether global warming is an industrial era trend or not. Even though many data gathering campaigns are taking place or are being planned, the very high dimensional state space of the system makes the prospects of climate variability analysis from data alone very tenuous, especially in the near term. The use of models and data, via data assimilation, is one of the strategies pursued to improve climate predictions and retrodictions. I will review some of the challenges with this process, cover some of our group's efforts to meet these. Problems in which progress can be made by a combination of deterministic and statistical techniques are endemic in climate science and other geosciences. I will also enumerate a prioritized list of problems, which if addressed with careful mathematical treatment, will have a significant impact on climate variability and a variety of other geoscience problems.

November 4th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Livsic Theorem for cocycles with values in Banach Algebras and the group of diffeomorphisms.
Speaker: Misha Guysinsky, Penn State
Location: MB114

We will generalize the Livsic Theorem that a Holder continuous cocycle over a transitive Anosov map is a coboundary if and only if the product of the values over every periodic orbit is the identity element. This theorem was proved for cocycles with values in abelian groups by Livsic, in matrix (and more generally Lie groups) by B.Kalinin. We will prove it for cocycles with values in Banach Algebras and groups of diffeomorphisms of compact manifolds.

November 4th, 2013 (04:00pm - 05:30pm)
Seminar: Tensor Networks and Applications Seminar
Title: Inequivalent Quantum Entanglements
Speaker: Sara Jamshidi, Penn State University
Location: MB315

This talk discusses LOCC and SLOCC equivalences of quantum entangled systems. We use the SLOCC notion of equivalence to discuss some inequivalent entanglements of a two, three, and four qubit systems. Finally, I discuss possible approaches for larger systems entanglements. This is an informal talk meant primarily for a mathematical audience.

November 5th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Remarks on the p-system of isentropic gas dynamics
Speaker: Alberto Bressan, Penn State
Location: MB216

The talk will be concerned with two long standing open problems, for entropy solutions of the p-system: (i) global existence of BV solutions with large initial data, and (ii) emergence of vacuum in finite time.

November 5th, 2013 (10:10am - 11:00am)
Seminar: Combinatorics/Partitions Seminar
Title: Partitions with non-repeating odd parts and combinatorial identities
Speaker: Krishnaswami Alladi, University of Florida
Location: MB106

We will study partitions with non-repeating odd parts combinatorially by representing them in terms of 2-modular graphs. We obtain certain weighted identities with free parameters. By special choices of these parameters, we connect them to the Gollnitz-Gordon partitions, and combinatorially prove a modular identity and some parity results. Finally we deduce a shifted partition identity mod 32 of Andrews.

November 5th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Algorithmic randomness and stochastic processes.
Speaker: Adrian Maler, Pennsylvania State University
Location: MB315

Universal tests for Martin-L"of randomness can be defined for a wide class of probability spaces. We discuss some results pertaining to Martin-L"of random sample paths of Brownian motion (with respect to the Wiener measure). We define effective Skorokhod space, a suitable setting for generalizing to Martin-L"of random sample paths of discontinuous stochastic processes, e.g., the Poisson process.

November 5th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Integrable Curve Flows in Centroaffine Geometry
Speaker: Annalisa Calini, College of Charleston, SC
Location: MB106

I will discuss integrable evolution equations for closed curves in centroaffine geometry. The planar setting is motivated by Pinkall's flow, a Hamiltonian evolution equation for closed star-shaped planar curves closely related to the KdV equation, and whose projectivization is the Schwarzian KdV equation. I will describe the relation between invariant curve evolutions in projective and centro-affine geometry and the associated geometric Hamiltonian structures, and construct examples of closed solutions of Pinkall's flow corresponding to periodic finite-gap KdV potentials. In the three-dimensional setting, I will describe the construction of integrable hierarchies of curve evolutions through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. The induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and the restricted hierarchy of flows on curves that project to conics in $\mathbb{RP}^2$ induces the Kaup-Kuperschmidt hierarchy at the curvature level. This is joint work with Tom Ivey (College of Charleston), and Gloria Mar ́ı Beffa (University of Wisconsin- Madison).

November 5th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Algebraic K-theory and its applications to dynamics, new progress, II.
Speaker: Kurt Vinhage, Penn State
Location: MB216
November 7th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA
Location: MB216
November 7th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Rankin-Selberg Theory of L-functions
Speaker: Mahdi Asgari, Cornell
Location: MB106

I will give an introduction to the so-called Rankin-Selberg method of constructing automorphic L-functions, mostly through examples. I will then report on joint work with J. Cogdell and F. Shahidi, developing a Rankin-Selberg integral for the product of general spin and general linear groups. This generalizes parts of results of D. Ginzburg and D. Soudry and Gelbart-Piatetski-Shapiro-Rallis for classical groups.

November 7th, 2013 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Adding and counting
Speaker: Ken Ono, Emory University
Location: MB114

This lecture will only be about adding and counting. There are many difficult problems related to these seemingly simple tasks. Here we address the problem of finding an exact formula for p(n), the number of partitions of n, and we explain a comprehensive theory of congruence properties.

November 7th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Unitary representations of groups and C*-algebras
Speaker: Caleb Eckhardt, Miami University
Location: MB106

Quasidiagonality is a natural representation theoretic property of C*-algebras, but has not been heavily studied with regards to unitary group representations. Recent advances by Matui and Sato suggest it is time to study quasidiagonality of group representations. We will explain why this is this case and some recent progress in this direction for polycyclic groups.

November 7th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Special numbers and special functions
Speaker: Ken Ono, Emory University
Location: MB114

"I discovered very interesting functions recently which I call 'Mock' theta-functions. Unlike the 'False'-functions (studied partially by Prof. Rogers in his interesting paper) they enter into mathematics as beautifully as the ordinary theta functions." These are Ramanujan's words from his famous enigmatic deathbed letter. The mathematics inspired by this letter is a 'hot topic' with applications in subjects including black hole entropies, elliptic curves, Moonshine, probability theory, to name a few. This lecture will be about two very recent works in which these functions play an important roles: Quantum modular forms, and Birch and Swinnerton-Dyer Conjecture. Special Note: The talk will be followed by a short break and then a screening of the documentary "The Genius of Srinivasa Ramanujan." The film is about one hour long.

November 7th, 2013 (04:30pm - 06:00pm)
Seminar: MASS Colloquium
Title: Ramanujan
Speaker: Ken Ono
Location: MB114
Abstract: http://
November 7th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

November 8th, 2013 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Random 3D surfaces and tehir asymptotic behavior
Speaker: Leonid Petrov, Northeastern University
Location: MB114

I will discuss the model of uniformly random tilings of polygons drawn on the regular triangular lattice by lozenges of three types (equivalent formulations: dimer models on the honeycomb lattice, or random 3D stepped surfaces glued out of 1x1x1 boxes). Asymptotic questions about these tilings have received a significant attention over the past years. Kenyon, Okounkov, and their co-authors (1998-2007) proved the law of large numbers: when the polygon is fixed and the mesh of the lattice goes to zero, the random surface concentrates around a deterministic limit shape which is algebraic in a certain sense. Via an explicit understanding of the correlations in the model, I managed to obtain finer asymptotics of random surfaces. I will discuss the local geometry of the surfaces, behavior of interfaces between phases (which manifests the Kardar-Parisi-Zhang universality), and global fluctuations of random surfaces (described by the Gaussian Free Field).

November 8th, 2013 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Markov dynamics on interlacing arrays
Speaker: Leonid Petrov, Northeastern University
Location: MB106

Since the end of 1990's there has been a significant progress in understanding the long time nonequilibrium behavior of certain integrable (1+1)-dimensional interacting particle systems and random growth models in the Kardar-Parisi-Zhang (KPZ) universality class. The miracle of integrability in most cases (with the notable exception of the partially asymmetric simple exclusion process) can be traced to an extension of the Markovian evolution to a suitable (2+1)-dimensional random growth model whose remarkable properties yield the solvability. So far, there have been two sources of such extensions. The first one originated from a classical combinatorial bijection known as the Robinson-Schensted-Knuth correspondence (RSK, for short) in the works of Johansson, O'Connell and their co-authors. The second approach introduced by Borodin-Ferrari was based on an idea of Diaconis-Fill of extending intertwined "univariate" Markov chains to a "bivariate" Markov chain that projects to either of the initial ones. In a recent joint work with A.Borodin, we presented a way to unify these two approaches using a fairly general framework of Macdonald processes. This also provides new examples of integrable KPZ particle systems.

November 8th, 2013 (04:40pm - 05:30pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Setting the Tone
Speaker: Attendees, Penn State University
Location: MB106

What are your goals for the first week? How much does it affect the rest of the semester? This week, we will discuss how first impressions of your class (and of you) can affect the rest of the semester. Please note that this week, we will be meeting in 102 instead of 106. We will have limited seating. For more information about this discussion group, please visit http://bit.ly/19ySDan

November 11th, 2013 (11:15am - 12:05pm)
Seminar: Special Talk
Title: Spectral stability of the complex Laplacian
Speaker: Siqi Fu, Rutgers University- Camden
Location: MB106

The d-bar-Neumann Laplacian is a prototype of an elliptic operator with non-coercive boundary condition. Its spectral behavior is more sensitive to the underlying geometric and algebraic structures than the usual Dirichlet or Neumann Laplacian. In this talk, we will discuss results on interplays between spectral behavior of the d-bar-Neumann Laplacian and the underlying geometric and algebraic structures, with emphasis on spectral stability.

November 11th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Big Data and Small Model - A New Approach in “Dry” Biology
Speaker: Qing Nie, University of California, Irvine
Location: MB114
Abstract: http://www.math.uci.edu/~qnie/

The explosion of publicly available data on sequences, structures, and images in life sciences allows non-biologists easy access to original and unexplored information to make fundamental discoveries. While more data increases capability of realizing sophisticated models that may be less useful when the data size is small, can small models be utilized to explore big data? In this talk, I will discuss several of our attempts in this direction, including a new method that integrates prior network information and heterogeneous spatial and temporal data during embryo development.

November 11th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Robust and Stochastic Dynamics in Signal Transduction, Stem Cells, and Development Patterning
Speaker: Qing Nie, University of California, Irvine
Location: MB106
Abstract: http://www.math.uci.edu/~qnie/

Noise and stochastic effect exist in most biological systems due to many intrinsic and extrinsic factors. In this talk, I will discuss strategies and principles for noise attenuation and robustness to genetic and environmental perturbations in signal transduction, embryonic patterning, and regeneration driven by stem cells. In one case, I will introduce a critical quantity that dictates capability of attenuating temporal noise in feedback systems. In another case, I will show that noise in gene regulations actually enables reduction of stochastic effects in spatial patterns during embryonic development. Finally, novel experimental data that support our modeling and computational predictions will be presented and several multi-scale, stochastic, and computational modeling frameworks that are required for simulating such complex biological systems will be introduced.

November 11th, 2013 (03:35pm - 04:25pm)
Seminar: Multiscale Modeling and Simulations Seminar
Title: Traveling wave solutions to reaction diffusion equations with fractional Laplacians
Speaker: Changfeng Gui, National Science Foundation
Location: MB106

In this talk, I will discuss the existence and asymptotic behavior of traveling wave solutions to Allen-Cahn equation with fractional Laplacians where the double well potenotial has unequal depths. A key ingredient is the estimate of the speed of the traveling wave in terms of the potential, which seems new even for the classical Allen-Cahn equation. I will also discuss nonexistence of traveling wave solutions to a nonlocal combustion model. The talk is based on recent results obtained jointly with Tingting Huan and with Mingfeng Zhao respectively.

November 11th, 2013 (04:00pm - 05:30pm)
Seminar: Tensor Networks and Applications Seminar
Title: Some Topics in Quantum Physics
Speaker: Yufei Shen, Penn State University
Location: MB315

In this talk, I planned to focus on two parts. First I will give a brief introduction on quantum mechanics, in particular, what are pure states and mixed states, and how to describe them mathematically. Then, for the second part, I would like to give some examples on physics models, in particular, Ising model, Heisenberg model, and Hubbard. I will show that solutions to these models in 1D has already been given, either exactly or numerically.

November 12th, 2013 (09:30am - 11:15am)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Mathematical and Numerical Analysis of Nonlocal Models"
Speaker: Xiaochuan Tian, Adviser: Qiang Du, Penn State
Location: 103 Osmond Laboratory

The peridynamic (PD) model is an integral-type nonlocal model of materials which provides an alternative set-up to classical continuum mechanics based on partial di erential equations (PDEs). In this talk, numerical methods for nonlocal di usion that can be applied to various singular kernels will be developed and basic properties of these discrete schemes such as discrete maximum principles will be discussed. We pay particular attention to the issue of convergence in both the nonlocal setting and the local limit. The latter reveals that while some methods tend to converge to the intended solutions, other methods lead to the possibility of convergence to unintended local limits. Thus we reveal the risks of discretizing nonlocal models when the modeling parameter is tied to the discretization parameter. Motivated by this phenomenon, we develop an abstract mathematical framework to help us nd asymptotically compatible schemes as robust discretization of nonlocal models that can be applied to a general state-based peridynamic system under minimum regularity assumptions. The framework may be used to guide computational studies of nonlocal problems; in particular, we develop a non-conforming method for nonlocal problems and its convergence can be proved within the framework. In order to apply the framework to the convergence of non-conforming methods for nonlocal problems, a more general compactness result of limiting behaviors of nonlocal energy norms is needed, which is an extension of a compactness result of Bourgain, Brezis and Mironescu.

November 12th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion
Speaker: TBA
Location: MB216
November 12th, 2013 (10:10am - 11:00am)
Seminar: Combinatorics/Partitions Seminar
Title: Permutations, multicolored partitions and Feynman diagrams
Speaker: Adrian Ocneanu, PSU
Location: MB106

We describe a new tree decomposition of permutations. The nodes of the tree are called primitive permutations, and their generating function involves imaginary gaussians. An algorithm pairs them with 2-connected fermionic Feynman diagrams, describing electrons and photons in quantum field theory. The combinatorics is based on multicolored partitions, for which we find Eulerian type recursions.

November 12th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Strong reductions between combinatorial problems
Speaker: Damir Dzhafarov, University of Connecticut
Location: MB315

I will discuss recent investigations of various reducibility notions between Pi^1_2 principles of second-order arithmetic, the most familiar of which is implication over the subsystem RCA_0. In many cases, such an implication is actually due to a considerably stronger reduction holding, such as a uniform (a.k.a. Weihrauch) reduction. (Here, we say a principle P is uniformly reducible to a principle Q if there are fixed reduction procedures Phi and Gamma such that for every instance A of P, Phi(A) is an instance of Q, and for every solution S to Phi(A), Gamma(A + S) is a solution to A.) As an example, nearly all the implications between principles lying below Ramsey's theorem for pairs are uniform reductions. In general, the study of when such stronger implications hold and when they do not gives a finer way of calibrating the relative strength of mathematical propositions. In addition, this analysis sheds light on several open questions from reverse mathematics, including that of whether the stable form of Ramsey's theorem for pairs (SRT^2_2) implies the cohesive principle (COH) in \omega (standard) models of RCA_0.

November 12th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Three Hopf algebras and their common algebraic and categorical background
Speaker: Ralph Kaufman, IAS and Purdue University
Location: MB106

We discsuss the renormalization Hopf algebra of Connes and Kreimer, Gontcharov's Hopf algebra for multi-zeta values and the Hopf algebra appearing in Baues' double cobar construction. We show that these are a examples of a common algebraic framework. Moreover this framework is a manifestation of one of the properties of Feynman categories, which we briefly define and discuss at the end.

November 12th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Some number--theoretic tools, I
Speaker: Svetlana Katok, Penn State
Location: MB216
November 12th, 2013 (04:15pm - 05:15pm)
Seminar: GAP Seminar
Title: GRT-equivariance of Tamarkin's construction
Speaker: Brian Paljug, Temple University
Location: MB114

Given two homotopy algebras and an infinity-morphism between them, it is natural to ask that, if we can modify the two homotopy algebras in some structured way, can we modify the infinity-morphism in some similar way, so as to preserve the new structures? In this talk we describe a situation in which the answer is yes, and indicate how it is possible. We will also give an application of these results, to show that Tamarkin´s construction of formality morphisms is equivariant with respect to the action of the Grothendieck-Teichmuller group.

November 13th, 2013 (03:00pm - 04:30pm)
Seminar: Complex Fluids Seminar
Title: Variational analysis of Nash equilibria for the Lighthill-Whitham model of traffic flow (Part 3)
Speaker: Fang YU, Penn State University
Location: MB315
November 13th, 2013 (03:35pm - 04:35pm)
Seminar: Center for Dynamics and Geometry Seminars
Title: Polynomials, eigenvalues, and Thurston's Theorem
Speaker: Sarah Koch, University of Michigan
Location: MB114

In William Thurston's last paper, "Entropy in Dimension One," he completely characterizes which numbers arise as exp(entropy(f)), where f is a critically finite real polynomial map of a closed interval. Inspired by his work (and the spectacular fractal picture on page 1 of his manuscript), we consider a particular dynamical quantity associated to critically finite rational maps. Following earlier work of Thurston, a critically finite rational map induces a holomorphic endomorphism on a Teichmueller space, and this endomorphism has a unique fixed point. We study the spectrum of the derivative of this endomorphism and prove that there is a prominent spectral gap in the case of quadratic polynomials. We plot a picture for this data (analogous to Thurston's entropy picture), revealing some incredible fractal structure. This is joint work with X. Buff and A. Epstein.

November 13th, 2013 (07:00pm - 08:30pm)
Seminar: Complex Fluids Seminar
Title: Nonlinear Wave Equations, formation of Singularities-Fritz John
Speaker: Tao Huang, Penn State University
Location: MB216
November 14th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA
Location: MB216
November 14th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Hecke Properties of Drinfeld modular forms
Speaker: Aleksandar Petrov, Texas A&M University at Qatar
Location: MB106

The theory of modular forms and their properties with respect to the Hecke operators is one of the cornerstones of modern number theory. In this talk, we will consider the Hecke properties of Drinfeld modular forms. After a brief review of the differences and similarities with the classical theory of modular forms, we will focus on the theory of $A$-expansions with its consequences and limitations.

November 14th, 2013 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Mating habits of polynomials
Speaker: Sarah Koch, University of Michigan
Location: MB114

Given two suitable complex polynomial maps, one can construct a new dynamical system by mating the polynomials; that is, by "gluing'' the polynomials together in a dynamically meaningful way. In this talk, we focus on quadratic polynomials -- we begin with a brief discussion of parameter space for quadratic polynomials (the Mandelbrot set), we then define the mating of two quadratic polynomials, and finally we explore examples where the mating does exist, and examples where it does not.

November 14th, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: The rapid decay property and some aspects of ergodic theory: the case of SL(2,R)
Speaker: Adrien Boyer, University of Aix-Marseille
Location: MB106

We will study property RD in terms of convergence of the integral of matrix coefficients for a unitary representations of a locally compact group, and we will give some applications. Then we will focus only on the case of SL(2,R), and study the unitary representation on its Furstenberg boundary (which is just the circle), and more precisely its restriction to a lattice of SL(2,R). In this case, we will make connections with ergodic theory.

November 14th, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: George Andrews and the Gollnitz theorem
Speaker: Krishnaswami Alladi, University of Florida
Location: MB114

A Rogers-Ramanujan (R-R) type partition theorem is one that equates partitions whose parts satisfy difference conditions with partitions whose parts satisfy congruence conditions. One of the deepest R-R type partition theorems is a 1967 identity due to Gollnitz. His proof of this identity is very difficult. Andrews is one of the very few to have understood Gollnitz' proof. Andrews subsequently simplified the proof, and in his famous CBMS Lecture Notes asks for an approach to Gollnitz' theorem that would clearly explain the underlying structure. Such an approach was provided by Alladi-Andrews-Gordon in 1995 who viewed a generalization and refinement of Gollnitz theorem as emerging from a remarkable key identity in three free parameters. Andrews' proof of this key identity is a classic achievement. Subsequently, Andrews proved two other key identities for Gollnitz' theorem discovered by Alladi using combinatorial reformulations. And most recently, Andrews found an intriguing new companion to Gollnitz' theorem which was shown by Alladi to also emerge from the 1995 key identity. In this talk the role of Andrews over the years in the exploration of the many facets of Gollnitz' theorem will be described, and in that process, links with a number of fundamental and classical theorems on partitions and q-hypergeometric series will be discussed. The talk will be accessible to non-experts.

November 14th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

November 15th, 2013 (12:00pm - 03:30pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Accurate coarsening of H1-, Hcurl- and Hdiv- conforming finite element spaces by element agglomeration on unstructured 3d meshes, Part II
Speaker: Ilya Lashuk, Penn State Univeristy
Location: MB315

We present the ideas on how to coarsen the finite element spaces, so that two properties are preserved: the exactness of de Rham complex, and local interpolation of (scalar or vector) polynomials. Our approach is based on element agglomeration: we group together nearby fine elements to get coarse elements (generally, of rather wild shape). We then construct the coarse shape functions associated with coarse elements, "coarse faces" (faces of coarse elements), "coarse edges", etc. We discuss at length the lowest-order case, then proceed (if time permits) to higher-order construction for Hdiv case, and finish with the standalone (not dependent on Hcurl and Hdiv) construction for H1. Note: the talk starts at 1:30 PM.

November 15th, 2013 (04:40pm - 05:30pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Homework that Works
Speaker: Attendees, Penn State University
Location: MB106

What do you believe is the purpose of homework? How do you achieve that? This week, we will discuss the methods we employ when designing homework. For more information about this discussion group, please visit http://bit.ly/19ySDan

November 18th, 2013 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: The classical Laplacian and the fractional Laplacian as limits of nonlocal diffusion operators
Speaker: Marta D'Elia, Sandia Nat. Lab.
Location: MB114
Abstract: http://sites.google.com/site/martadeliawebsite/Home

In this talk we introduce nonlocal operators and discuss their properties and possible applications. Using the nonlocal vector calculus, the nonlocal counterpart of the classical vector calculus, we analyze the connections between nonlocal diffusion operators and the local and fractional Laplacian. In particular, we show that as the nonlocal interactions vanish the nonlocal operators approach the classical Laplacian and as the nonlocal interactions become infinite they approach the fractional Laplacian and other fractional differential operators. In the latter case, we also show one-dimensional test cases that illustrate the theoretical results.

November 18th, 2013 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: The fractional differential operators on bounded domains as special cases of the nonlocal diffusion operator
Speaker: Marta D'Elia, Sandia Nat. Lab.
Location: MB106
Abstract: http://sites.google.com/site/martadeliawebsite/Home

In this talk we analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several applications. In our analysis, a recently developed nonlocal vector calculus is exploited to define a weak formulation of the nonlocal problem. We demonstrate that, when sufficient conditions on certain kernel functions hold, the solution of the nonlocal diffusion equation converges to the solution of the fractional Laplacian equation on bounded domains as the nonlocal interactions become infinite. We also introduce a continuous Galerkin finite element discretization of the nonlocal weak formulation and we derive a priori error estimates. Through several numerical examples we illustrate the theoretical results and we show that by solving the nonlocal problem it is possible to obtain accurate approximations of the solutions of fractional differential equations circumventing the problem of treating infinite-volume constraints.

November 18th, 2013 (04:00pm - 05:30pm)
Seminar: Tensor Networks and Applications Seminar
Title: A Tensor Network Theory of Operator-State and Channel-Operator Dualities
Speaker: Ville Bergholm, ISI Foundation
Location: MB315

We present several important and mostly well-known theorems regarding the duality between linear maps and bipartite quantum states, and the duality between quantum channels and linear operators, in diagrammatic form. The tensor network presentation makes the proofs very compact and in some cases even intuitive. This work adds to the theory, expressiveness and potential range of applicability of map- and channel- dualities.

November 19th, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Wave interactions for P-system
Speaker: Jiequan Li, Beijing normal University
Location: MB216
November 19th, 2013 (10:10am - 11:00am)
Seminar: Combinatorics/Partitions Seminar
Title: Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao
Speaker: James Sellers, PSU
Location: MB106

In this talk, we revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to $2,3,4,6 \pmod 6$, together with a generalization by Andrews and another by Subbarao. Then we develop a unified bijective proof for all three theorems involved, and obtain a natural further generalization as a result. This is joint work with Shishuo Fu, Chongqing University, China.

November 19th, 2013 (11:00am - 01:00pm)
Seminar: Teaching Seminar
Title: Myths Regarding Student Learning
Speaker: Carla Firetto
Location: MB114
Abstract: http://
November 19th, 2013 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Lindstr"om's characterization of first-order logic
Speaker: Kostas Hatzikiriakou, University of Thessaloniki, Greece
Location: MB315

In 1969 Per Lindstr"om characterized first-order logic as the strongest (most expressive) logical system for which (a) both the Compactness theorem and the L"owenheim-Skolem theorem hold (First Theorem), and (b) the L"owenheim-Skolem theorem holds and its set of valid sentences is recursively enumerable (Second Theorem). We will go through the proof of the First Lindstr"om's Theorem.

November 19th, 2013 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Some number-theoretic tools, II
Speaker: Svetlana Katok, Penn State
Location: MB216
November 20th, 2013 (12:00pm - 01:30pm)
Seminar: Geometry Luncheon Seminar
Title: Globalizations and Applications
Speaker: Nan Li, Penn State
Location: MB114

We will discuss some Globalization Theorems for Alexandrov spaces (length spaces with curvature bounded from below in the comparison sense) and a possibility to use it to solve some open questions.

November 20th, 2013 (03:00pm - 04:30pm)
Seminar: Complex Fluids Seminar
Title: G-equation in the modeling of turbulent flame speed
Speaker: Yifeng Yu, University of California, Irvine
Location: MB315

G-equation is a well known simplified model in turbulent combustion to describe the flame propagation. It is a level set Hamilton-Jacobi equation. A significant project is to use this model to understand the dependence of the turbulent flame speed (effective burning velocity) on turbulence intensity. In this talk, I will present some old and recent analytic results related to this project. This is mainly based on joint works with Jack Xin.

November 20th, 2013 (04:40pm - 05:30pm)
Seminar: Applied Algebra Seminar
Title: Tensor Contractions for #SAT
Speaker: Jacob Biamonte, ISI Foundation
Location: MB106
Abstract: http://qubit.org/jacob-biamonte.html

Boolean formula satisfiability and solution counting are foundational topics faced in theoretical computer science with numerous practical applications. Recently, the simulation of quantum systems has experienced advancements due to the development of tensor network algorithms and associated quantum physics based techniques. Taking inspiration from these physics based algorithms, we propose a tensor contraction algorithm for \#SAT instances which we show has $O(t2^c)$ complexity, (where $t$ is the polynomial bounding the computation of contracting a tree tensor network and $c$ is the number of COPY tensors in the network. The broader implications of this line of work involve the use of tensor network methods as a language uniting parts of quantum theory and computer science.

November 21st, 2013 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Discussion session
Speaker: TBA
Location: MB216
November 21st, 2013 (11:00am - 01:00pm)
Seminar: Mathematical Biology and Physiology Seminar
Title: Scaling from life-cycles to population dynamics: insights from combining models & empirical biology
Speaker: William Nelson, Queen's University
Location: MB216

Many biological organisms has strong ontogenetic stage-structure that impacts the instantaneous rates of development, mortality and reproduction. In this seminar, I will discuss two systems where the combination of mathematical modelling and experimentation/empirical observation has been used to gain insight into the effect that stage-structure has on population dynamics.

November 21st, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: A geometric application of tensor networks
Speaker: Shamil Shakirov, UC Berkeley
Location: MB106

An important geometric property of a surface is the volume that it bounds. This volume is invariant under SL(n) transformations; for quadratic surfaces (ellipsoids) it is simply the inverse square root of the determinant. I will tell how, more generally, for algebraic surfaces of higher degree, the bounded volume is a function of the elementary SL(n) invariants of the surface -- the tensor networks. I will demonstrate on examples that this function is typically of hypergeometric type, derive the differential equations that it satisfies, and argue that its singularities are determined by the discriminant of the surface. This last property is especially interesting and could have further applications in statistical physics, which I will mention if time permits.

November 21st, 2013 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: We vote, but do we get what we want?
Speaker: Don Saari, UC Irvine
Location: MB114

We vote to select the choice of a pizza, of a member to a social group, of congress, of rankings of football teams, of almost everything. But, does the outcome reflect what the voters really wanted? Mathematics is providing that there is much to worry about. Indeed, by the end of this presentation, some in the audience will worry about some personal election in which she or he was involved.

November 21st, 2013 (02:30pm - 03:30pm)
Seminar: Noncommutative Geometry Seminar
Title: Higgs bundles and index theory
Speaker: Eric Korman, University of Pennsylvania
Location: MB106

Secondary index theorems give information about additional structures on the index bundle (e.g. a flat connection), which are not detectable by the usual families index theorem. In this talk, I will discuss such an index theorem for Higgs bundles. I will describe the characteristic classes of Higgs bundles that are used in the theorem and also explain the connections with Bismut and Lott's index theorem for flat vector bundles.

November 21st, 2013 (03:35pm - 04:25pm)
Seminar: Department of Mathematics Colloquium
Title: Mathematics and the astronomical mystery of "Dark Matter"
Speaker: Don Saari, UC Irvine
Location: MB114

One of the more compelling scientific mysteries in the last 35 years has been the one from astronomy called "dark matter." What is it? In answering this question, it will become apparent that the central issue is one of mathematics, not astronomy. As described during this lecture, the answers coming from mathematics contradict long held beliefs about the amount of this mysterious stuff that is supposed to be out there.

November 21st, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA

November 22nd, 2013 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Dispersive Hydrodynamics of Viscous Fluid Conduits
Speaker: Mark Hoefer, North Carolina State University
Location: MB315
Abstract: http://www4.ncsu.edu/~mahoefer/

Solitary waves and small amplitude dispersive radiation are important solution components of nonlinear wave problems. A dispersive shock wave (DSW) represents the combination of solitary and dispersive waves into one coherent, expanding modulated wavetrain. The generation of DSWs represents a universal mechanism to resolve hydrodynamic singularities in dispersive media. Physical manifestations include undular bores on shallow water and in the atmosphere, nonlinear diffraction patterns in optics and ultracold atoms. After a brief discussion of recent theory and observation of magnetic solitons, this talk will focus on the dispersive hydrodynamics associated with interfacial waves of viscous fluid conduits. The derivation of an interfacial wave equation, modulation theory for DSWs, and experimental observations will be presented. It will be argued that this system is particularly well-suited to the careful, laboratory study of universal dispersive hydrodynamics.

November 26th, 2013 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Thanksgiving
Speaker: No Seminar
Location: MB106
November 28th, 2013 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Thanksgiving
Speaker: No seminar
Location: MB106
November 28th, 2013 (05:00pm - 06:30pm)
Seminar: SIAM Student Chapter Seminar
Title: TBA
Speaker: TBA
Location: MB106
Abstract: http://

TBA