# Math Calendar

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<>October 2014
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A live feed of seminars and special events in the upcoming week.

October 1st, 2014 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Chain theorems with period six
Speaker: Arseniy Akopyan, IITP Russ. Acad. Sci, visiting PSU.
Location: MB114

The Poncelet and Steiner theorems are probably the most famous chain theorems. In my talk I will demonstrate a class of similar theorems which are usually related with a triangle and have period 6.

October 1st, 2014 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Permutohedral Arrangements, Simplicial Decompositions and a Geometrization of the Classical Worpitzky Identity
Speaker: Nick Early, Penn State
Location: MB106

In forthcoming joint work with Adrian Ocneanu, we prove a symmetric group character formula conjectured several years ago by the latter as he was studying certain polyhedra emerging from hyperplane arrangements in simplices. We reveal the geometric content which lies behind the classical Worpitzky identity, which expands a cubical number $r^{n-1}$ in terms of the Eulerian numbers. Our proof suggests a new geometric interpretation of combinatorial results of Sagan-Shareshian-Wachs on Eulerian quasi-symmetric functions.

October 1st, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Some problems on the two-phase flows with diffuse interface-part II
Speaker: Yinghua Li, South China Normal University
Location: MB106

We consider the well-posedness of 1-D compressible Navier-Stokes/Cahn-Hilliard system, 1-D compressible Navier-Stokes/Allen-Cahn system, and the blow-up criterion of incompressible Navier-Stokes/Allen Cahn system with different densities in 2-D and 3-D.

October 1st, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: How Mathematicians Gain Conviction
Speaker: Attendees, Penn State
Location: MB102

Mathematics is often thought of as a discipline that gains certainty by deductive reasoning rather than empirical or authoritarian evidence. In practice, however, this may not be entirely true. This week, we read a paper on this very topic and discuss if we teach the practice of mathematics honestly.
Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49(1), 36-58.

October 2nd, 2014 (10:00am - 10:50am)
Seminar: Hyperbolic and Mixed Type PDEs Seminar
Title: Set-up of a mixed type problem for the pressure gradient system
Speaker: Yuxi Zheng, Penn State
Location: MB216

We will collect relevant information around the edge of the hyperbolic region to form the free boundary and data for the interior elliptic domain.

October 2nd, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: A reciprocity law for Drinfeld modules
Speaker: Mihran Papikian, Penn State University
Location: MB106

First, I will explain what is a "reciprocity law". Then I will describe such law arising from Drinfeld modules. Finally, I will apply this law to derive a criterion for the splitting modulo primes of a class of non-solvable polynomials over $\mathbb{F}_q(T)$ that was studied by Abhyankar. (This is a joint work with Alina Cojocaru.)

October 2nd, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Stimulus space geometry and topology from neural activity
Speaker: Carina Curto, Penn State University
Location: MB114

Neural activity data can be used to infer subsets of co-active neurons in a network. By considering neurons in the hippocampus that encode position information, I will show how these data can be used to infer topological and geometric features of the stimulus space the neurons are encoding. Our results rely on an unexpected application of the Nerve Lemma from algebraic topology.

October 2nd, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Modeling Electrodiffusion and Osmosis in Physiological Systems
Speaker: Yoichiro Mori, University of Minnesota (Host: Chun Liu)
Location: MB114

Electrolyte and cell volume regulation is essential in physiological systems. After a brief introduction to cell volume control and electrophysiology, I will discuss the classical pump-leak model of electrolyte and cell volume control. I will then generalize this to a PDE model that allows for the modeling of tissue-level electrodiffusive, convective and osmotic phenomena. This model will then be applied to the study of cortical spreading depression.

October 3rd, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Numerical approximations and analysis for phase-field equations
Speaker: YANG Jiang, Penn State
Location: MB315

In this presentation, we concentrate on numerical approximations and analysis for two phase-field equations, namely the Allen-Cahn equation and the Cahn Hilliard equations. Based on the stabilized semi-implicit scheme, which is unconditionally energy stable with only first order accuracy, we use the spectral deferred correction (SDC) methods to produce high order accurate solutions. A local p-adaptive strategy is proposed to balance the accuracy and overall energy stability. Another part focuses on the numerical stability analysis for Allen-Cahn equations. Apart from extensively studied energy stability, we establish the numerical maximum principle and the uniform L^2 stability for finite difference methods and Fourier spectral methods, respectively.

October 3rd, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Ergodicity of avalanche transformations
Speaker: Manfred Denker, PSU
Location: MB106

An avalanche transformation is a product transformation followed by an avalanche dynamics. The talk will provide a precise definition. I will discuss the question when such a transformation is ergodic, besides other questions like topological transitivity and central limit theorems.

October 4th, 2014 (08:00am - 06:00pm)
Seminar: GAP Seminar
Title: Joint Cornell-Penn State Symplectic Geometry Seminar
Speaker: Various Speakers, Various Affiliations
Location: MB114
Abstract: http://www.math.psu.edu/stienon/cornellpennstate/schedule_FA14.pdf

Yuri Berest (Cornell University), David Li-Bland (University of California, Berkeley), Sasha Patotski (Cornell University), Nick Early (Penn State University), and Jae-Suk Park (Center for Geometry and Physics, IBS & POSTECH) See link for schedule.

October 6th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Data driven methods for dynamical systems: Extracting spatiotemporal patterns from high-dimensional time series
Speaker: Dimitrios Giannakis, New York University (Host: J Harlim)
Location: MB114

Large-scale datasets generated by dynamical systems arise in many applications in science and engineering. A research topic of current interest in this area involves using data collected through observational networks or output by numerical models to extract the salient modes of variability from high-dimensional data, and create low-order models to forecast these modes. In this talk we discuss applied mathematics techniques to address this topic blending ideas from machine learning, harmonic analysis, and delay-coordinate embeddings of dynamical systems. We illustrate these techniques with applications to climate atmosphere ocean science.

October 6th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Extracting and predicting spatiotemporal patterns from data with dynamics-adapted kernels
Speaker: Dimitrios Giannakis, New York University (Host: J Harlim)
Location: MB106

Kernel methods provide an attractive way of extracting features from data by biasing their geometry in a controlled manner. In this talk, we discuss a family of kernels for dynamical systems featuring an explicit dependence on the dynamical vector field operating in the phase-space manifold, estimated empirically through finite differences of time-ordered data samples. The associated diffusion operator for data analysis is adapted to the dynamics in that it generates diffusions along the integral curves of the dynamical vector field. We present applications to toy dynamical systems and comprehensive climate models. We also discuss a technique for analog forecasting based on these kernels. In this empirical forecasting technique, kernels are used to create weighted ensembles of states (analogs) with high similarity to the initial data from a record of historical observations, and the future values of observables are predicted from the historical evolution of the ensemble.

October 6th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: The Random Minkowski Theorem and Values of Polynomials at Lattice Points
Speaker: Jayadev Athreya, University of Illinois at Urbana-Champaign
Location: MB114

Motivated by problems of unipotent flows on homogeneous spaces, in 2008 we (the speaker and G. Margulis) proved a "Random Minkowski" theorem on the probability a randomly chosen unimodular lattice mises a large subset of Euclidean space. In this talk, we give applications of this theorem to give error terms (for almost every quadratic form) in the Quantitative Oppenheim results of Eskin-Margulis-Mozes. This is joint work with G. Margulis.

October 7th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Composite likelihood ratio tests for detecting natural selection
Speaker: Michael DeGiorgio, Penn State
(Host: Tim Reluga)
Location: MB106

The study of genetic variation is fundamental to population and evolutionary genetics, as it provides a basis for understanding differences among individuals, populations, and species. This talk will focus on the development of statistical approaches for identifying the adaptive processes that have shaped the current distribution of genetic variation in populations. Three main adaptive forces are positive, negative, and balancing selection. In the first half of the talk, I will discuss an extension to a method for detecting recent positive selection that can take into account the effects of long-term negative selection, both of which can yield similar patterns in the genome. In the second half, I will introduce the first set of likelihood-based methods to scan for signals of long-term balancing selection. Simulation results show that these methods for detecting balancing selection are robust to population demography and are the most powerful developed to date.

October 7th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Fermions as functors
Speaker: Zifeng Yang, Penn State and Capital Normal University, China
Location: MB106

Bosons and Fermions are fundamental concepts in many constructions related to the representations of quantum (affine) algebras in theoretical physics and mathematical physics. Recently, we need to lift these concepts to functors of some categories, which might reflect some geometric constructions. In this talk, I will explain how to construct the categorical Fermions based on Khovanov's categori cation of Heisenberg algebra, and how these categori ed Fermions are related to the classical Boson-Fermions correspondence.

October 7th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: The Muchnik topos
Speaker: Sankha Basu, Penn State
Location: MB315

A. A. Muchnik in his 1963 paper titled "Strong and weak reduciblity of algorithmic problems" described how mass problems under weak reduciblity form a model for intuitionistic propositional calculus. This interpretation formalized the well known 'Calculus of problems' introduced by Kolmogorov in 1932. A recent paper, submitted for publication, authored by the speaker and Stephen Simpson, discusses an extension of this semantics to higher-order intuitionistic logic and mathematics. This model has been named as the Muchnik topos. The paper also introduces a new class of intuitionistic real numbers, called the Muchnik reals, which are different from the Cauchy and the Dedekind reals. Within the Muchnik topos, we obtain a choice principle (\forall x\exists y A(x,y))\implies(\exists w\forall x A(x,wx)) and a bounding principle (\forall x\exists y A(x,y))\implies(\exists z\forall x\exists y (y\le_{\mathrm{T}}(x,z)\land A(x,y)), where x,y,z range over Muchnik reals, w ranges over functions from Muchnik reals to Muchnik reals, and A(x,y) is a formula not containing w or z.

October 7th, 2014 (03:40pm - 05:40pm)
Seminar: Ph.D. Oral Comprehensive Examination
Title: "Local time of discrete stochastic processes and a homogenization problem”
Speaker: Xiaofei Zheng, Adviser: Manfred Denker, Penn State
Location: MB114

Suppose {X_i} are i.i.d or strictly stationary, S_n is the partial sum of {X_i}. We are interested in studying the time that S_n spends at a certain level and its limiting behavior. For continuous stochastic processes, it is described by local time. Levy first introduced Brownian local time in 1939. For discrete processes, we are looking for a good definition of local time. We defined the local time of a random walk, it turns out that after a proper scaling, the local time converges to the Brownian local time. For discrete martingale, I will introduce how to embed it into the path of a Brownian motion, and study the downcrossing number. In the second part of my talk, I will introduce the problem of homogenization driven by fractional Brownian motion. Based on the work of Iyer, Komorowski, Novikov and Ryzhik, we conjecture that the solution to dX_t=-AV(X_t)dt+dB^H(t) converges to Brownian motion weakly. The possible method is to introduce stopping times and study the number of downcrossings.

October 7th, 2014 (05:45pm - 06:45pm)
Seminar: Teaching Seminar
Title: Midsemester Evaluations and Interpreting SRTEs
Speaker: Larkin Hood, Research Associate and Instructional Consultant at SITE
Location: MB114
October 8th, 2014 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Planar Fronts of the Bidomain-Bistable Equation
Speaker: Yoichiro Mori, University of Minnesota
Location: MB114

The bidomain model is the standard model of cardiac electrophysiology, and is used extensively in computational simulations of normal and pathological cardiac electrical activity. Despite its importance, very little is known about its mathematical properties. In its simplest form, the bidomain model can be seen as a reaction-diffusion type system of Fitz-Hugh Nagumo type, where the diffusion operator is replaced by a more general non-local second order operator. We study the scalar case of the bidomain-bistable equation. We show that planar fronts of the bidomain bistable equation can become unstable, in drastic contrast to the Allen Cahn equation. This is joint work with Hiroshi Matano of the University of Tokyo.

October 8th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Numerical approximations and analysis for phase-field equations
Speaker: Jiang Yang, Penn State University
Location: MB106

In this presentation, we concentrate on numerical approximations and analysis for two phase-field equations, namely the Allen-Cahn equation and the Cahn Hilliard equation. Based on the stabilized semi-implicit scheme, which is unconditionally energy stable with only first order accuracy, we use the spectral deferred correction (SDC) methods to produce high order accurate solutions. A local p-adaptive strategy is proposed to balance the accuracy and overall energy stability. Another part focuses on the numerical stability analysis for Allen-Cahn equations. Apart from extensively studied energy stability, we establish the numerical maximum principle and the uniform L^2 stability for finite difference methods and Fourier spectral methods, respectively.

October 8th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: How Mathematicians Use Examples To Understand Proofs
Speaker: Attendees, Penn State
Location: MB102

Everyone knows mathematicians use examples to explore conjectures... except for many undergraduate students. This week, we read a paper that details how mathematicians use examples when exploring a conjecture and discuss its implications for undergraduate education.
Lockwood, Elise, Amy B. Ellis, and Eric Knuth. "Mathematicians’ example-related activity when proving conjectures." 16TH Annual Conference on Research in Undergraduate Mathematics Education 1 (n.d.): 16-30. Web. 20 Aug. 2014.

October 9th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: A quick tour of discrepancy theory
Speaker: William Chen, MacQuarie University
Location: MB106

The birth of geometric discrepancy theory is usually attributed to the fundamental work of Klaus Roth in 1954. The present scope of the subject is due in no small part to the many important results of Wolfgang Schmidt in the 1960s and 1970s. It is fair to say that every subsequent worker in the subject have been motivated and encouraged, directly or indirectly, by these two pioneers and their work. Lower bound results in discrepancy theory exhibit the limitations to just point distributions, whereas upper bound results lead to point distributions that are close to best possible under such limitations. In this expository talk, we shall discuss some of the main results obtained over the last 60 years, and introduce to the audience a number of lower and upper bound techniques. We shall also briefly discuss some open questions.

October 9th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: On the inviscid limit and stability of boundary layers of Navier-Stokes
Speaker: Toan Nguyen, Penn State University
Location: MB114

I will overview several recent results concerning the inviscid limit and stability / instability of boundary layers in fluid dynamics (precisely, for 2D incompressible Navier-Stokes equations). These issues are very classical: in fact, there are major works by prominent physicists such as Lord Rayleigh, W. Orr, A. Sommerfeld, Tollmien, C.C. Lin, among others, on the subject, using the spectral analysis and the Fourier normal mode theory. Physicists are interested in the estimation of the critical Rayleigh number (typically, very large) for laminar flows as well as the transition from laminar to turbulent flows. One of the results that I will discuss is to rigorously prove that there is always a non-empty range of wave numbers and Reynolds numbers between which generic laminar boundary layer flows are spectrallly unstable, despite the fact that at the infinite Reynolds number, the profiles are stable. The instability is therefore due to the presence of viscosity! Next, we use this instability result to show that boundary layer expansions in the inviscid limit are generally invalid. We also make a formal link of our construction with the multi-layer analysis and the classical Kato's criterium for the validity of the inviscid limit. Several other significant progresses in the subject will also be briefly discussed. This talk is intended to be accessible to graduate students.

October 10th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: How do dispersed inertial particles modify turbulent flows ?
Speaker: Said Elghobashi, University of California, Irvine (Host: J Xu)
Location: MB114

Turbulent flows laden with inertial particles are ubiquitous in nature (e.g. aerosols in clouds, and dust storms on Earth and Mars) and in industrial applications (e.g. liquid fuel and pulverized coal sprays in combustion chambers). Experimental and numerical studies of these flows are quite challenging due to the wide spectra of length- and time- scales of the dispersed particles in addition to the spectra of scales intrinsic to the carrier fluid turbulence. The two-way and and four-way nonlinear interactions between the dispersed particles and the turbulence result in complex multi-scale physical phenomena. The lecture focuses on the physical mechanisms of interactions between dispersed spherical particles and isotropic turbulence using Direct Numerical Simulation (DNS). Particles whose diameter is smaller than the Kolmogorov length scale are simulated as point particles. Larger particles with diameter of the order of Taylor microscale are fully resolved using the Immersed Boundary method.

October 10th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: How do dispersed inertial particles modify turbulent flows ?
Speaker: Said Elghobashi, University of California, Irvine
Location: MB315

Turbulent flows laden with inertial particles are ubiquitous in nature (e.g. aerosols in clouds, and dust storms on Earth and Mars) and in industrial applications (e.g. liquid fuel and pulverized coal sprays in combustion chambers). Experimental and numerical studies of these flows are quite challenging due to the wide spectra of length- and time- scales of the dispersed particles in addition to the spectra of scales intrinsic to the carrier fluid turbulence. The two-way and and four-way nonlinear interactions between the dispersed particles and the turbulence result in complex multi-scale physical phenomena. The lecture focuses on the physical mechanisms of interactions between dispersed spherical particles and isotropic turbulence using Direct Numerical Simulation (DNS). Particles whose diameter is smaller than the Kolmogorov length scale are simulated as point particles. Larger particles with diameter of the order of Taylor microscale are fully resolved using the Immersed Boundary method.

October 10th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: On infinitely divisible semimartingales
Speaker: Jan Rosinski, University of Tennessee
Location: MB106

Semimartingales play a fundamental role in stochastic analysis and mathematical finance. Concerning the latter, the discounted asset price process must be a semimartingale in order to preclude arbitrage opportunities. The question whether a given process with long memory, possible jumps and/or heavy tails is a semimartingale is also of importance in stochastic modeling, where such processes are used as a driving random motion for stochastic differential equations. We consider this question in the context of infinitely divisible processes, which include fractional processes, moving averages, and Ornstein-Uhlenbeck processes driven by stable, multi-stable, and tempered stable L\'evy processes, and their mixtures. We show that the problem when any such process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible process is of finite variation. This gives the key to fully characterize the semimartingale property for many processes of interest, including processes mentioned above. This talk is based on a joint work with Andreas Basse-O'Connor of Aarhus University.

October 13th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Boltzmann and Fokker-Planck Equations for Economic Modeling
Speaker: Bruce Boghosian, Tufts University (C Liu)
Location: MB106

The Boltzmann equation provides a continuum description of a population of particles undergoing pairwise interactions in which they can exchange momentum and energy. An economy consists of economic agents who engage in pairwise transactions in which they can exchange wealth. It has long been suggested that it ought to be possible to write a Boltzmann equation that describes an economy. This work describes how to do exactly that for a simplified microeconomic model, called the "Yard-Sale Model." We also show how, in the limit of small transactions, this Boltzmann equation reduces to a nonlinear Fokker-Planck equation for the probability distribution function of wealth. Stability of a market economy is one of the fundamental tenets of classical and neoclassical economics, dating back at least to Adam Smith's "invisible hand" concept. In spite of that, we find that our model market economy is highly unstable, with a strong tendency toward oligarchy. Mathematically, its time-asymptotic state is a singular distribution. It can be stabilized by adding some mechanism for wealth redistribution, such as a wealth tax, in which case its steady state is shown to be similar to the the famous Pareto distribution, with a cutoff at very low values of wealth and power-law decay at very high values. Indeed, this appears to be the first detailed microeconomic explanation of Pareto's century-old law of wealth distribution, a key observation of macroeconomics.

October 13th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: New examples of polynomial Julia sets of positive area
Speaker: Mikhail Lyubich, SUNY Stony Brook
Location: MB114

The problem of Lebesgue area of polynomial Julia sets goes back to classical work of Fatou. When the polynomial is reasonably hyperbolic then the Julia set has zero area, and there are plenty of examples of this kind. First examples of polynomial Julia sets of posiive area were constructed around 2006 by Buff and Cheritat. However, these examples are rare and topologically wild". In the talk, we will describe a new class of examples that are tame" and observable", with explicit topological models and computable images. The corresponding parameter set has a reasonable size (positive Hausdorff dimension). Existence of such Julia sets goes against intuition coming from hyperbolic geometry and theory of Kleinian groups. It is a joint work with Artur Avila.

October 14th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Two problems in partitions
Speaker: George Andrews, PSU
Location: MB106

The talk will consider to different questions. (1) (joint work with Beck and Robbins) What is the nature of the generating function for partitions in which the difference between largest and smallest parts is fixed? (2) (joint work with Simay) Find a formula for g_m(n,k), the number of partitions of n in which k is the m-th largest summand (i.e there are exactly m-1 distinct parts (each of which may be repeated arbitrarily) that are larger than k).

October 14th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Modeling Actin Regulation in Cancer Metastasis
Speaker: Nessy Tania, Smith College
(Host: Jessica Conway)
Location: MB106

Directed cell movement, chemotaxis, is a part of normal physiological processes such as wound healing, immune response and embryogenesis. However, this pathway can also be hijacked during tumor development, allowing cancer cells to metastasize. In this talk, I will discuss an ongoing collaborative work in modeling the regulation of actin cytoskeleton in mammary carcinoma motility. I will survey results from a temporal ODE model of the regulation of cofilin, an actin regulatory protein that is upregulated in invasive carcinoma. Second, I will present a spatio-temporal model of actin growth to look at the collective effects of two actin regulatory proteins. At the end, I will motivate our current effort in studying invadopodia, a dynamic actin-based structure that allows cancer cell to 'dig' through its surrounding environment. This work is done jointly with John Condeelis (Albert Einstein College of Medicine) and Leah Edelstein-Keshet (University of British Columbia).

October 14th, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: Families of Harish Chandra modules connecting compact and noncompact Lie groups
Speaker: Eyal Subag, Tel Aviv University
Location: MB106

Families of representations naturally appear in the representation theory of real reductive Lie groups. In my talk I will demonstrate how the Lie groups themselves come in families and how families of representations (of non-isomorphic groups) play a significant role in representation theory. I’ll be focusing on the groups SU(1,1), SU(2) and their Cartan motion group. Furthermore, I will show that there exists an algebraic family of Harish Chandra pairs that is associated with these groups. We shall see how families of Harish Chandra modules relate representations of SU(1,1), SU(2) and their Cartan motion group. These families of HC modules will finally be used to provide some insights into the theory of contraction of representations and the Mackey bijection.

October 14th, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Hausdorff dimension
Speaker: Manfred Denker, Penn State
Location: MB315

It is a difficult problem to calculate the Hausdorff dimension of a set. In general, this number is hard to compute with some given precision. For some sets, like the Cantor set, a formula for the dimension is known. In other cases, like the attractor of the Henon map computer calculations showed varying results. Box counting methods are a bit more reliable, but they may not calculate Hausdorff dimension, but the Minkowski dimension. Grassberger and Procaccia introduced a new type of dimension, called correlation dimension. Although it does not calculate the Hausdorff dimension in general, it is a notion which is estimable in the sense of regression analysis. I will review this method and the mathematical theory needed for such an approach.

October 14th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Dynamics of dissipative polynomial automorphisms of C^2
Speaker: Mikhail Lyubich, SUNY Stony Brook
Location: MB114

Two-dimensional complex dynamics displays a number of phenomena that are not observable in dimension one. However, if f is moderately dissipative then there are deeper similarities between the two fields. In particualar, a nearly complete classification of periodic Fatou components has been recently obtained: Theorem 1 (joint with Han Peters): Any periodic component of the Fatou set is either an attracting basin or parabolic basin, or the basin of a rotation domain (Siegel disk or Herman ring). In complex and real one-dimensional world, structurally stable maps are dense. In dimension two this fails because of the Newhouse phenomenon caused by homoclinic tangencies. Palis conjectured that in the real two-dimensional case this is the only reason for failure. We prove a complex version of this conjecture: Theorem 2 (joint with Romain Dujardin): Any moderately dissipative polynomial automorphism of C^2 is either weakly stable" or it can be approximated by a map with homoclinic tangency.

October 14th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Invariant distributions in elliptic dynamics,I
Speaker: Alejandro Kocsard, Fluminense Federal University, Brazil
Location: MB216

Invariant distributions appear as natural obstructions for the existence of smooth solutions for cohomological equations and they have been extensively used for estimating ergodic deviations, especially for certain parabolic and hyperbolic systems. In general, such systems exhibit infinitely many invariant distributions. On the other hand, within elliptic dynamical systems ergodic rigid translations on tori are the archetypal examples of such systems and they are distributionally uniquely ergodic, i.e. the Lebesgue measure is the only (up to multiplication by a constant) invariant distribution. In these talks we shall discuss some results and conjectures about distributionally uniquely ergodic systems.

October 14th, 2014 (05:45pm - 06:45pm)
Seminar: Teaching Seminar
Title: Student Motivation
Speaker: Jackie Bortiatynski, Senior Lecturer and Director for Excellence in ECoS
Location: MB114
October 15th, 2014 (12:05pm - 01:20pm)
Seminar: Geometry Luncheon Seminar
Title: Symplectic and Hamiltonian Rigidities
Speaker: Augustin Banyaga, PennState
Location: MB114

In this talk, I will explain the recent short proof due to Buhovsky that the Eliashberg-Gromov symplectic rigidity is an immediate consequence of Oh-Muller theorem on uniqueness of Hamiltonians of hameomorphisms ( a hameomorphism is a limit of Hamiltonian diffeomorphisms in the Hofer topology). Using a theorem of uniqueness of generators of ssympeomorphisms ( a limit of symplectic diffeomorphisms in the Hofer-like topology) of Banyaga-Tchuiaga, one can prove that a smooth hameomorphism is a Hamiltonian diffeomorphism, a theorem on Hamiltonian rigidity. This theorem was proved before by Seyfaddini using different methods.

October 15th, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Well-posedness and Long-time Behavior of a Non-autonomous Cahn-Hilliard-Darcy System with Mass Source Modeling Tumor Growth-II
Speaker: Jie Jiang, Wuhan Institute of Physics and Mathematics
Location: MB106

We talk about our recently result on an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term modeling tumor growth. Existence of global weak solutions as well as the existence of unique local strong solutions are given in both 2D and 3D. Then we investigate the qualitative behavior of solutions in details when the spatial dimension is two. More precisely, we prove that the strong solution exists globally and it defines a closed dynamical process. Then we study the longtime behavior of the 2D strong solutions to our problem under suitable assumptions on the external source term.

October 15th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: A Uniform Standard for Evaluating Proofs?
Speaker: Attendees, Penn State
Location: MB102

Courses as basic as Calculus incorporate proofs. Is the mathematical community consistent in how it evaluates such basic proofs? This week, we read a paper that explores different standards used by mathematicians and discuss if there exists a uniform standard by which we judge proofs.
Inglis, M., Mejia-Ramos, J.P., Weber, K., & Alcock, L. (2013). On mathematicians' different standards when evaluating elementary proofs. Topics in Cognitive Science 5(2), 270-282

October 15th, 2014 (05:01pm - 06:01pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: Seiberg-Witten invariants
Speaker: Damien Broka
Location: MB216

Tomorrow I’ll be talking about Seiberg-Witten invariants. These are invariants cooked up from the topology of moduli spaces of solutions to the Seiberg-Witten equations. The latter are defined on compact, oriented, Riemannian, smooth four-manifolds with Spin^c(4) structure as nonlinear PDEs whose solutions are states of a very simple classical gauge field theory with much milder behavior than non-abelian Yang-Mills. The interest stems from being extra-sensitive to the differential structure, yielding invariants that sometimes allows one to distinguish different smooth structures in the same topological family. My goal tomorrow is to introduce four-dimensional spin geometry (a lot of simplifications/identifications arise which are essential to the developments of SW theory, due to quaternionic calculus being available) and study the moduli space of solutions (modded out by gauge equivalences) using the theory of elliptic PDEs and index theory. We will see it is in fact a compact, smooth, and (if time permits) a *finite dimensional* (w/ a sketch of proof) manifold! The room is 216, the time is 5pm. See you then! Best, Damien

October 16th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: The divisor function on arithmetic progressions
Speaker: Robert C. Vaughan, Penn State University
Location: MB106
October 16th, 2014 (01:15pm - 02:15pm)
Seminar: MASS Colloquium
Title: Ramsey Theory and Dynamics
Speaker: Vitaly Bergelson, Ohio State University
Location: MB113

We will start the talk with formulating and discussing some of the classical results of Ramsey theory, a branch of combinatorics which studies the structure of mathematical objects that is preserved under partitions. Next, we will show that some of these results can be naturally viewed as dynamical questions about the recurrence in topological and/or volume preserving systems. We will conclude with the discussion of some of the recent developments and open problems.

October 16th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Entropy methods and the SL(2,R) action on Moduli space.
Speaker: Alex Eskin, Dynamical Systems Speaker, University of Chicago (Host: Boris Kalinin)
Location: MB114

I will outline the first part of my recent proof with Maryam Mirzakhani of the measure classification theorem for this action. This part is an entropy based argument, closely related to that of Einsiedler-Katok-Lindenstrauss and others. (No knowledge of Teichmuller theory is required).

October 17th, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Well-posedness and Robust Preconditioners for Discretized Fluid-Structure Interaction Systems
Speaker: Kai Yang, Penn State
Location: MB315

In our work we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point problems and prove the uniform well-posedness. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust preconditioners for the discretized fluid-structure interaction systems.

October 17th, 2014 (03:30pm - 04:30pm)
Seminar: Center for Interdisciplinary Mathematics Seminar
Title: Phase-field modeling of collective migration of eukaryotic cells
Speaker: Igor Aronson, Argone National Lab and Northwestern University
Location: MB113

Self-propelled motion, emerging spontaneously or in response to external cues, is a hallmark of living organisms. Systems of self-propelled synthetic particles are also relevant for multiple applications, from targeted drug delivery to the design of self-healing materials. Self-propulsion relies on the force transfer to the surrounding. While self-propelled swimming in the bulk of liquids is fairly well characterized, many open questions remain in our understanding of self-propelled motion along substrates, such as in the case of crawling cells or related biomimetic objects. How is the force transfer organized and how does it interplay with the deformability of the moving object and the substrate? How do the spatially dependent traction distribution and adhesion dynamics give rise to complex cell behavior? How can we engineer a specific cell response on synthetic compliant substrates? Here we developed model for a crawling cell by incorporating locally resolved traction forces and substrate deformations. The model captures the generic structure of the traction force distribution and faithfully reproduces experimental observations, like the response of a cell on a gradient in substrate elasticity (durotaxis). It also exhibits complex modes of cell movement such as “bipedal” motion.The model is extended to multiple migrating cells by introducing individual phase field for each cell. Depending on the model parameters we obtained a transition to collective migration or rotation of multiple cells.

October 17th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: Heavy-traffic limits for a fork-join network in the Halfin-Whitt regime
Speaker: Hongyuan Lu, PSU, Industr. & Manufact. Engineering
Location: MB106

We study a fork-join network with a single class of jobs, which are forked into a fixed number of parallel tasks upon arrival to be processed at the corresponding parallel service stations. After service completion, each task will join a buffer associated with the service station waiting for synchronization, called unsynchronized queue". The synchronization rule requires that all tasks from the same job must be completed, referred to non-exchangeable synchronization". Once synchronized, jobs will leave the system immediately. Service times of the associated parallel tasks of each job can be correlated and form a sequence of i.i.d. random vectors with a general continuous joint distribution function. Each service station has multiple statistically identical parallel servers. We consider the system in the Halfin-Whitt (Quality-and-Efficiency-Driven, QED) regime, in which the arrival rate of jobs and the number of servers in each station get large appropriately so that all service stations become critically loaded asymptotically. We develop a new method to study the joint dynamics of the service processes and the unsynchronized queueing processes at all stations and the synchronized process. The waiting processes for synchronization after service depend on the service dynamics at all service stations, and thus are extremely difficult to analyze exactly. The main mathematical challenge lies in the resequencing of arrival orders after service completion at each station. We represent the dynamics of all the aforementioned processes via a multiparameter sequential empirical process driven by the service vectors of the parallel tasks. We show a functional law large number (FLLN) and a functional central limit theorem (FCLT) for these processes. Both the service and unsynchronized queueing processes in the limit can be characterized as unique solutions to the associated integral convolution equations driven by the arrival limit process and a generalized multiparameter Kiefer process driven by the service vectors.

October 20th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: The Phase Field Crystal Model: An Introduction to a Continuum Framework for Studying Phase Transformations on Atomic Length and Diffusive Time Scales
Speaker: Steven Wise, University of Tennessee
Location: MB114

This is an introduction to the afternoon talk on Phase Field Crystal methods.

October 20th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: The Phase Field Crystal Model: A Continuum Framework for Studying Phase Transformations on Atomic Length and Diffusive Time Scales
Speaker: Steven Wise, University of Tennessee (Host: M Metti)
Location: MB106

Crystalline materials contain atomic-scale imperfections in the form of defects – such as vacancies, grain boundaries, and dislocations – and controlling, or at least predicting, the formation and evolution of such imperfections during phase transformation is a major challenge. The phase field crystal (PFC) methodology has emerged as a important, increasingly-preferred modeling framework for studying materials with atomic-scale structures on diffusive time scales. In contrast to molecular dynamics models, the fast atomic vibrational time-scale phenomena are averaged out, in essence, but the atomic spatial resolution is preserved. In this talk, I will describe some analysis (existence and uniqueness), approximation, and fast computation of solutions to PFC and PFC-type equations, a family of highly nonlinear hyperbolic-parabolic PDE and integro-PDE. I will also discuss a new PFC framework for multi-spatial-scale modeling based on the recent method of amplitude expansions. This presentation will be accessible to graduate students.

October 20th, 2014 (03:00pm - 05:00pm)
Seminar: Special Event
Title: Office hour for math 231
Speaker: Jingchi Huang
Location: MB315
Abstract: http://
October 20th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Arnold diffusion: two and half degrees of freedom and beyond
Speaker: Ke Zhang, University of Toronto
Location: MB114

Arnold diffusion concerns the instability of nearly integrable systems, where much progress has been made recently in the case of 2.5 degrees of freedom. We will discuss the ideas behind the 2.5 degrees of freedom result, and the generalization to higher degrees of freedom. This is based on joint works with V. Kaloshin.

October 20th, 2014 (03:35pm - 04:25pm)
Seminar: Special Talk
Title: Invariants and symmetries I
Speaker: Ke Wu, Capital Normal University, Beijing
Location: MB106

In this survey talk, I will explain some symmetries related to invariants of moduli spaces which arise in mathematical physics, for example, the action of the Heisenberg algebra on the homology or $K_0$ groups of Hilbert schemes of surfaces. I will also talk about the Nekrasov partition functions and the related symmetries.

October 21st, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Modeling tuberculosis, from cells to populations
Speaker: Leonid Chindelevitch, MIT
(Host: Tim Reluga)
Location: MB106

Tuberculosis continues to afflict millions of people and causes over a million deaths a year worldwide. Multi-drug resistance is also on the rise, causing concern among public-health experts. This talk will give an overview of my work on modeling tuberculosis at various scales. On the cellular side I will describe models of the metabolism of M. tuberculosis, where insights from duality led to a consistent analysis of existing models, a systematic method for reconciling discrepant models, and the identification of putative drug targets. On the population side I will describe models of strain evolution, where a new metric combined with an optimization-based approach resulted in an accurate classification of complex infections as originating from mutation or mixed infection, as well as the identification of the strains composing these complex infections.

October 21st, 2014 (02:30pm - 03:30pm)
Seminar: GAP Seminar
Title: An odd-dimensional counterpart of generalized complex geometry
Speaker: Aissa Wade, Penn State University
Location: MB106

In 2002, Hitchin introduced the theory of generalized complex structures which, has been developed since then. Generalized complex structures on an even-dimensional manifold M are generalizations of symplectic and complex structures on M. More precisely, any generalized complex structure on M can be viewed as a complex structure on the vector bundle $TM \oplus T^*M$. After a brief review of generalized complex geometry, we will discuss its odd-dimensional counterpart. The odd-dimensional analogues of generalized complex structures are called generalized contact structures. They include contact, cosymplectic, and normal almost contact structures. Our new concept provide a natural framework for all these geometric objects on odd-dimensional manifolds. However, there is a sharp contrast with generalized complex geometry. Non-trivial examples can be constructed using a Boothby-Wang construction type. This is a joint work with Yat Sun Poon.

October 21st, 2014 (02:30pm - 03:45pm)
Seminar: Logic Seminar
Title: Uniform distribution and algorithmic randomness
Speaker: Jeremy Avigad, Carnegie Mellon University
Location: MB315

A seminal theorem due to Weyl states that if (a_n) is any sequence of distinct integers, then, for almost every real number x, the sequence (a_n x) is uniformly distributed modulo one. In particular, for almost every x in the unit interval, the sequence (a_n x) is uniformly distributed modulo one for every *computable* sequence (a_n) of distinct integers. Call such an x *UD random*. Every Schnorr random real is UD random, but there are Kurtz random reals that are not UD random. On the other hand, Weyl's theorem still holds relative to a particular effectively closed null set, so there are UD random reals that are not Kurtz random.

October 21st, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Invariant distributions in elliptic dynamics,II
Speaker: Alejandro Kocsard, Fluminense Federal University, Brazil
Location: MB216

Invariant distributions appear as natural obstructions for the existence of smooth solutions for cohomological equations and they have been extensively used for estimating ergodic deviations, especially for certain parabolic and hyperbolic systems. In general, such systems exhibit infinitely many invariant distributions. On the other hand, within elliptic dynamical systems ergodic rigid translations on tori are the archetypal examples of such systems and they are distributionally uniquely ergodic, i.e. the Lebesgue measure is the only (up to multiplication by a constant) invariant distribution. In these talks we shall discuss some results and conjectures about distributionally uniquely ergodic systems.

October 22nd, 2014 (02:30pm - 03:20pm)
Seminar: Applied Algebra and Network Theory Seminar
Title: Algebraic geometry of tree tensor networks
Speaker: Sara Jamshidi, Penn State
Location: MB106

Tree tensor networks have been used to model the ground states of Hamiltonians in condensed matter physics and quantum chemistry. Exactly which quantum states can be represented by a tree tensor network with a given topology and given restrictions on the parameter tensors? When the restrictions are algebraic, the set of states is a projective algebraic variety. We describe those varieties, using techniques originally developed for phylogenetics.

October 22nd, 2014 (03:30pm - 05:00pm)
Seminar: Complex Fluids Seminar
Title: Well-posedness and Long-time Behavior of a Non-autonomous Cahn-Hilliard-Darcy System with Mass Source Modeling Tumor Growth
Speaker: Jie Jiang, Wuhan Institute of Physics and Mathematics
Location: MB106

We talk about our recently result on an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term modeling tumor growth. Existence of global weak solutions as well as the existence of unique local strong solutions are given in both 2D and 3D. Then we investigate the qualitative behavior of solutions in details when the spatial dimension is two. More precisely, we prove that the strong solution exists globally and it defines a closed dynamical process. Then we study the longtime behavior of the 2D strong solutions to our problem under suitable assumptions on the external source term.

October 22nd, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Opportunities for Theoretical Thinking
Speaker: Attendees, Penn State
Location: MB102

The majority of lower-level curriculum provides little in the way of theoretical assignments. Is it, however, possible to incorporate activities that encourage high-level thinking in 100- or 200-level curriculum? This week, we read a paper that explores this issue and we consider if its suggestions could be realistically incorporated into the classroom.
Challita, Dalia, and Nadia Hardy. "Providing calculus students with opportunities to engage in theoretical thinking." 16TH Annual Conference on Research in Undergraduate Mathematics Education 1 (n.d.): 16-30. Web. 20 Aug. 2014.

October 22nd, 2014 (03:35pm - 04:35pm)
Seminar: Geometry Working Seminar
Title: Tarski numbers
Speaker: Mark Sapir, Vandrebilt University
Location: MB114

This is a joint work with Mikhail Ershov and Gili Golan. The Tarski number of a group is the minimal number of pieces in a paradoxical decomposition. We prove that there are 2-generated groups with arbitrary large Tarski numbers and construct groups with Tarski numberd 5 and 6.

October 22nd, 2014 (03:35pm - 04:25pm)
Seminar: Special Talk
Title: Invariants and symmetries II
Speaker: Ke Wu, Capital Normal University, Beijing
Location: MB315

In this survey talk, I will explain some symmetries related to invariants of moduli spaces which arise in mathematical physics, for example, the action of the Heisenberg algebra on the homology or $K_0$ groups of Hilbert schemes of surfaces. I will also talk about the Nekrasov partition functions and the related symmetries.

October 22nd, 2014 (05:01pm - 06:01pm)
Seminar: Student Geometric Functional Analysis Seminar
Title: moment map and representation theory
Location: MB216

On Wednesday I will talk about the momentum map: this is a map from a symplectic manifold to the dual of the Lie algebra of the group acting on it. After covering a few basic facts and examples, I will focus on the geometry of the momentum map and some of its applications in representation theory.

October 23rd, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: Algebraic independence of derivatives of Carlitz periods
Speaker: Dale Brownawell, Penn State University
Location: MB106
October 23rd, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Evolution of resistance to white pine blister rust in high-elevation pines
Speaker: Simon Tavener, Colorado State University
Location: MB114

Five-needle white pines play an important role in high-elevation ecosystems but are highly susceptible to white pine blister rust (WPBR) caused by a nonnative fungal pathogen. We construct a nonlinear, stage-structured infection model to investigate the effect of WPBR on the dynamics and stand structure of high-elevation five-needle white pines. Management decisions are by definition short-term perturbations that require analysis of transient behavior and we have developed a general software package to examine both transient and equilibrium sensitivities and elasticities. The presence in a population of a resistant genotype can modify both transient and equilibrium behaviors and suggest potential new control strategies. We extend our model to include a resistant allele at a single genetic locus and provide preliminary results. This work was conducted as part of an NSF sponsored undergraduate research program (FEScUE) at the intersection of mathematics and biology.

October 23rd, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: A posteriori error analysis for multirate, multiphysics problems
Speaker: Simon Tavener, Colorado State University (Host: Andrew Belmonte)
Location: MB114

Finite element methods are well-established and popular techniques for solving systems of partial differential equations. A priori analyses of finite element methods seek to establish error bounds in appropriate norms and to determine rates of convergence with mesh refinement. Adjoint-based a posteriori analyses seek to estimate the error in a functional of the solution (a “quantity of interest”) for a given numerical calculation. Computation plays an essential role in many areas of science and technology where we seek to understand complex systems involving multiple physical processes which often evolve on distinctly different time scales. Complicating matters, the model parameters and even computational domains may be uncertain. Further, specific numerical approaches such as finite volume methods or explicit time integration techniques may be entrenched within particular scientific communities. The goal of this work is to use mathematically appealing adjoint-based a posteriori ideas to develop accurate a posteriori error estimates for a range of computational problems encountered in practice and to use the insights gained in to the multiple sources of error to construct adaptive computational strategies.

October 24th, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: When does a mixture of products contain a product of mixtures?
Speaker: Jason Morton, PSU
Location: MB106

We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and convex geometry. We give implications and equivalences relating RBM-representable probability distributions, perfectly reconstructible inputs, Hamming modes, zonotopes and zonosets, point configurations in hyperplane arrangements, linear threshold codes, and multi-covering numbers of hypercubes. As a motivating application, we prove results on the relative representational power of mixtures of product distributions and products of mixtures of pairs of product distributions (RBMs) that formally justify widely held intuitions about distributed representations. In particular, we show that an exponentially larger mixture of products, requiring an exponentially larger number of parameters, is required to represent the probability distributions represented as products of mixtures.

October 27th, 2014 (12:20pm - 01:30pm)
Seminar: CCMA Luncheon Seminar
Title: Adaptive Learning and Optimization for Machine Intelligence
Speaker: Haibo He, University of Rhode Island
Location: MB114

With the recent development of brain research and modern technologies, scientists and engineers will hopefully find efficient ways to develop brain- like intelligent systems that are highly robust, adaptive, scalable, and fault tolerant to uncertain and unstructured environments. Yet, developing such truly intelligent systems requires significant research on both fundamental understanding of brain intelligence as well as complex engineering design. This talk aims to present the recent research developments in computational intelligence to advance the machine intelligence research and explore their wide applications across different critical engineering domains. Specifically, this talk covers numerous aspects of the foundations and architectures of adaptive learning and control. The key objective is to achieve cognitive‐alike optimization and prediction capability through learning. An essential component of this talk is a recent development of a new adaptive dynamic programing (ADP) architecture for improved learning and optimization capability over time. This architecture integrates a hierarchical goal generator network to provide the system a more informative and detailed goal representation to guide its decision-making. Various real-world applications including smart grid, robotics, cyber‐physical systems, and big data analysis, will be presented to demonstrate the broader and far‐reaching applications of our research.

October 27th, 2014 (02:30pm - 03:30pm)
Seminar: Computational and Applied Mathematics Colloquium
Title: Discretization of time-dependent quantum systems: propagation of the evolution operator
Speaker: Joseph Jerome, Northwestern University
Location: MB106

The talk represents joint work with Eric Polizzi and is based on a paper of similar title recently published online in Applicable Analysis. We discuss time-dependent quantum systems on bounded domains; these represent closed systems and are relevant for application to Carbon Nanotubes and molecules. Included in our framework are linear iterations involved in time-dependent density functional theory as well as the global nonlinear model which includes the Hartree potential. A key aspect of the analysis of the algorithms is the use of time-ordered evolution operators, which allow for both a well-posed problem and its approximation. The approximation theorems we obtain are operator extensions of classical quadrature theorems. The global existence theorem uses the Leray-Schauder fixed point theorem, coupled to a modified conservation of energy principle. The simulations were performed by Eric Polizzi using his algorithm FEAST. The evolution operators used in the talk are due to T. Kato and their properties will be summarized. Application areas make significant use of these operators, particularly chemical physics. In the mathematical literature, the Euclidean space problem has been studied by T. Cazenave and others, employing the Strichartz inequalities. These are ultimately based on semi-groups. Our results appear to be complementary to results of this type. The solutions we discuss are strong solutions. We are currently studying more general potentials via weak solutions. This work is in-progress.

October 27th, 2014 (03:35pm - 04:35pm)
Seminar: Dynamical systems seminar
Title: Dynamical properties of conformally symplectic systems
Speaker: Rafael de la Llave, Georgia Tech
Location: MB114

When one considers the dynamics of mechanical systems with a friction proportional to the velocity one obtains a system with the remarkable property that a symplectic form is transformed into a multiple of itself. The same phenomenon happens when one minimizes the action after discounting it by an exponential factor (these models are very common in economics when one minimizes the present cost and includes inflation). We will present several results for this systems: 1) A KAM theory for these systems that leads to efficient algorithms. 2) Absence of Birkhoff invariants near Lagrangian tori. 3) Numerical experiments at the breakdown of tori 4) Analyticity domains of expansions for KAM tori. All these works are in collaboration with R. Calleja and A. Celletti (the numerical work reported is by R. Calleja, A. Celletti, J.L - Figueras)

October 28th, 2014 (11:15am - 12:05pm)
Seminar: Combinatorics/Partitions Seminar
Title: Multiplicative properties of the number of $k$-regular partitions.
Speaker: Olivia Beckwith
Location: MB106

Earlier this year, Bessenrodt and Ono proved surprising multiplicative properties of the partition function. In this project, we deal with $k$-regular partitions. Extending the generating function for $k$-regular partitions multiplicatively to a function on $k$-regular partitions, we show that it takes its maximum at an explicitly described small number of partitions, and thus can be easily computed. The basis for this is an extension of a classical result of Lehmer, from which we prove an inequality for the number of $k$-regular partitions which seems not to have been noticed before.

October 28th, 2014 (01:00pm - 01:50pm)
Seminar: Theoretical Biology Seminar
Title: Graph Limits and Dynamics of Large Networks
Speaker: Georgi Medvedev, Drexel University
Location: MB106

The continuum limit is an approximate procedure, by which coupled dynamical systems on large graphs are replaced by an evolution integral equation on a continuous spatial domain. This approach has been instrumental for studying dynamics of diverse networks throughout physics and biology. We use the ideas and results from the theories of graph limits and nonlinear evolution equations to develop a rigorous justification for using the continuum limit in a variety of dynamical models on deterministic and random graphs. As a specific application, we discuss synchronization in small-world networks of Kuramoto oscillators. References: Georgi S. Medvedev, The nonlinear heat equation on dense graphs and graph limits, SIAM J. Math. Anal., 46(4), 2743-2766, 2014; Georgi S. Medvedev, The nonlinear heat equation on W-random graphs, Archive for Rational Mechanics and Analysis, 212(3), 781-803, 2014; Georgi S. Medvedev, Small-world networks of Kuramoto oscillators, Physica D, 266, 13-22, 2014.

October 28th, 2014 (02:30pm - 03:30pm)
Seminar: Center for Dynamics and Geometry Colloquium
Title: Some geometric mechanisms for Arnold Diffusion
Speaker: Rafael de la Llave, Georgia Tech
Location: MB114

We consider the problem whether small perturbations of integable mechanical systems can have very large effects. It is known that in many cases, the effcts of the perturbations average out, but there are exceptional cases (resonances) where the perturbations do accumulate. It is a complicated problem whether this can keep on happening because once the instability accumulates, the system moves out of resonance. V. Arnold discovered in 1964 some geometric structures that lead to accumulation in carefuly constructed examples. We will present some other geometric structures that lead to the same effect in more general systems and that can be verified in concrete systems. In particular, we will present an application to the restricted 3 body problem. We show that, given some conditions, for all sufficiently small (but non-zero) values of the eccentricity, there are orbits near a Lagrange point that gain a fixed amount of energy. These conditions (amount to the non-vanishing of an integral) are verified numerically. Joint work with M. Capinski, M. Gidea, T. M-Seara

October 28th, 2014 (03:30pm - 06:00pm)
Seminar: Working Seminar: Dynamics and its Working Tools
Title: Finer structure of minimal systems, the Bohr problem and its higher version
Speaker: Xiangdong Ye, University of Science and Technology of China
Location: MB216

In this talk first I will explain why the regionally proximal relation of order d is an equivalence relation and why the quotient space is a d-step nilsystem for minimal systems. Then we will discuss the Bohr problem, i.e. if the difference of a syndetic set conatains a Bohr_0 set, and its higher version.

October 29th, 2014 (03:35pm - 04:25pm)
Seminar: Teaching Mathematics Discussion Group Seminar
Title: Preparing Students for Calculus
Speaker: Attendees, Penn State
Location: MB102

Last week, we considered ways of preparing calculus students for higher-level classes. This week, we consider what it takes to adequately prepare students for calculus.
Judd, April B., and Terry Crites. "Preparing students for calculus." 16TH Annual Conference on Research in Undergraduate Mathematics Education 1 (n.d.): 96-105. Web. 20 Aug. 2014.

October 30th, 2014 (11:15am - 12:05pm)
Seminar: Algebra and Number Theory Seminar
Title: To be announced
Speaker: Kirsten Eisentraeger, Penn State University
Location: MB106
October 30th, 2014 (01:25pm - 02:25pm)
Seminar: MASS Colloquium
Title: Random walks: simple and self-avoiding
Speaker: Greg Lawler, University of Chicago
Location: MB113

Many phenomena are modeled by walkers that wander randomly. The case of complete randomness is well understood -- I will survey some of the key facts including the idea that the set of points visited by a random walker in any dimension (greater than one) is two. I will then discuss a much harder problem -- what happens when you do not allow the walker to return to points? Many of the interesting questions about this "self-avoiding walk" are still open mathematical problems.

October 30th, 2014 (03:30pm - 04:20pm)
Seminar: Department of Mathematics Colloquium
Title: Understanding planar self-avoiding walks
Speaker: Greg Lawler, University of Chicago (Host: Victoria Sadovskaya)
Location: MB114

The self-avoiding walk was introduced by Paul Flory in the mid twentieth century as a model of polymer chains. While it was a simple model to state, it is still an open problem to analyze it rigorously. However, we do understand the (conjectured) scaling limit which is a self-avoiding continuous process with paths of fractal dimension 4/3. I will give an introduction to this area and hope to show how the polymer problem in two dimensions is both very well understood and yet a big open problem. This talk is intended for a general mathematical audience.

October 31st, 2014 (03:30pm - 05:00pm)
Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: On computer simulation of multiscale processes in porous electrodes of Li-ion batteries
Speaker: Oleg Iliev, Fraunhofer Institute for Industrial Mathematics, ITWM
Location: MB315
Abstract: http://www.itwm.fraunhofer.de/en/departments/flow-and-material-simulation/employees/prof-dr-oleg-iliev.html

Li-ion batteries are widely used in automotive industry, in electronic devices, etc. In this talk we will discuss challenges related to the multiscale nature of batteries, mainly the understanding of processes in the porous electrodes at pore scale and at macroscale. A software tool for simulation of isothermal and non-isothermal electrochemical processes in porous electrodes will be presented. The pore scale simulations are done on 3D images of porous electrodes, or on computer generated 3D microstructures, which have the same characterization as real porous electrodes. Finite Volume and Finite Element algorithms for the highly nonlinear problems describing processes at pore level will be shortly presented. MOR and DEIM-MOR algorithms for acceleration of the computations will be discussed. Next, homogenization of the equations describing the electrochemical processes at the pore scale will be presented, and the results will be compared to the engineering approach based on Newman’s 1D+1D model. Simulations at battery cell level will also be addressed. Finally, the challenges in modeling and simulation of degradation processes in the battery will be discussed and our first simulation results in this area will be presented. This is joint work with A.Latz (DLR), M.Taralov, V.Taralova, J.Zausch, S.Zhang from Fraunhofer ITWM, and Y.Efendiev from Texas A&M.

October 31st, 2014 (03:35pm - 04:35pm)
Seminar: Probability and Financial Mathematics Seminar
Title: TBA
Speaker: Alexei Novikov, PSU
Location: MB106