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<>February 2016  




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 February 1st, 2016 (02:30pm  03:30pm)
 Seminar: Computational and Applied Mathematics Colloquium
Title: ShapeSelective Growth of Colloidal Nanocrystals: Multiscale theory and Simulation
Speaker: Kristen A. Fichthorn
Location: MB106Achieving the controlled synthesis of colloidal nanomaterials with selected shapes and sizes is an important goal for a variety of applications that can exploit their unique properties (e.g., optical, catalytic, magnetic, etc.). In the past decade, a number of promising solutionphase synthesis techniques have been developed to fabricate various nanostructures. A deep, fundamental understanding of the phenomena that promote selective growth and assembly in these syntheses would enable tight control of nanostructure morphologies in nextgeneration techniques. I will discuss our efforts to understand how colloidal nanostructures assume selective shapes during their synthesis. To highlight one of our research directions, I will discuss our efforts to understand the workings of PVP, a structuredirecting molecule that facilitates the formation of selective Ag nanoparticle shapes. In these studies, we use firstprinciples densityfunctional theory, molecular dynamics (MD) simulations, and continuum theory to predict PVPinduced Ag nanocrystal shapes in the 10100 nm size range. [15] References [1] W. AlSaidi, H. Feng, and K. A. Fichthorn, “Adsorption of polyvinylpyrrolidone on Ag surfaces: Insight into a structuredirecting agent”, Nano Letters, 2012, 12, 9971001. [2] W. A. Saidi, H. Feng, and K. A. Fichthorn, “The binding of PVP to Ag surfaces: Insight into a structuredirecting agent from dispersioncorrected densityfunctional theory,” J. Phys. Chem. C, 2013, 117, 11631171. [3] Y. Zhou, W. A. Saidi, and K. A. Fichthorn, “Comparison of the binding of PVP and PEO to Ag surfaces: Elements of a successful structuredirecting agent”, J. Phys. Chem. C, 2013, 117, 1144411448. [4] Y. Zhou, W. A. Saidi, and K. A. Fichthorn, “A force field for describing the PVPmediated solutionphase synthesis of shapeselective Ag nanocrystals”, J. Phys. Chem. C, 2014, 118, 33663374. [5] X. Qi, T. Balankura, Y. Zhou, and K. A. Fichthorn, “How structuredirecting agents control nanocrystal shape: PVPmediated growth of Ag nanocubes”, Nano Letters 2015, 15, 7711–7717.
 February 2nd, 2016 (02:30pm  03:30pm)
 Seminar: GAP Seminar
Title: Jacobi manifolds and their coisotropics
Speaker: Luca Vitagliano, Università degli Studi di Salerno
Location: MB106Jacobi structures on manifolds were introduced by Kirillov and Lichnerowicz in the 70s. They generalize and unify several interesting geometric structures like Poisson, contact and locally conformal symplectic structures. The talk is divided into two parts. In the first part I will review the fundamentals of the geometry of Jacobi structures. In particular, I will present several examples and a local form theorem. The second part is more technical and it is based on joint work with Hông Vân Lê, YongGeun Oh and Alfonso Tortorella: I will discuss coisotropic submanifolds of Jacobi manifolds and the Linfinity algebra controlling their formal deformations.
 February 2nd, 2016 (02:30pm  03:45pm)
 Seminar: Logic Seminar
Title: Fine Structure and Algorithmic Randomness
Speaker: Jan Reimann, Penn State
Location: MB315Jensen's fine structure theory allows for a canonical definition of codes for levels of Goedel's constructible universe similar to how the Turing jump codes levels of the arithmetic hierarchy. In this talk, we will show how Jensen's codes and algorithmic randomness behave mutually orthogonal. This allows us in turn to derive a metamathematical result about randomness with respect to continuous measures.
 February 2nd, 2016 (02:30pm  03:29pm)
 Seminar: Center for Dynamics and Geometry Colloquium
Title: A survey of C^1 generic ergodic theory
Speaker: Jairo Bochi, Pontifical University of Chile
Location: MB114I'll survey what is known about the ergodic theory of C^1generic conservative diffeomorphisms, culminating with the following theorem of Avila, Crovisier, and Wilkinson: C^1generic volumepreserving diffeomorphisms either have zero metric entropy or are ergodic and ``semiuniformly Anosov''. I'll explain informally the main ideas used in the proofs.
 February 2nd, 2016 (03:32pm  06:02pm)
 Seminar: Working Seminar: Dynamics and its Working Tools
Title: Lecture series on Lyapunov exponents III
Speaker: Daren Wei, Penn State
Location: MB114  February 2nd, 2016 (04:15pm  05:30pm)
 Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://This seminar will example aspects of the representation theory of SL(2,R)
 February 3rd, 2016 (03:30pm  04:20pm)
 Seminar: Theoretical Biology Seminar
Title: Optimal Control for MultiTargeted Cancer Therapies: Results and Open Problems
Speaker: Urszula Ledzewicz, Southern Illinois University Edwardsville, USA and Lodz University of Technology, Poland
(Host: Leonid Berlyand)
Location: MB106Modern cancer treatment protocols are multitargeted and take into account highly diverse subpopulations of cancerous cells with widely varying therapeutic sensitivities all embedded into the tumor microenvironment. This includes the vasculature as well as the elements of the immune system. Because of this complexity, dosage, frequency and sequencing of therapeutic agents may have a major effect on the outcome of treatment. There is mounting medical evidence that "more is not necessarily better" and a properly calibrated dose which takes into account this complexity can lead to a better outcome. This has generated a search for what is called the biologically optimal dose (BOD) in the medical literature. Formulating mathematical models with an objective that reflects the overall goal of the therapy, like minimizing the tumor size and side effects, maximizing immune system etc., leads to optimal control problems where mathematical analysis can answer some of these questions in a theoretical framework. In this talk, we present some of these problems starting with a model for heterogeneous tumor populations under chemotherapy and consider models for monotherapy of the antiangiogenic inhibitors alone and combined with chemo and radiotherapy. Tumorimmune interactions under treatment will also be addressed leading to a singleinput multitarget model for metronomic chemotherapy which is a new treatment protocols currently widely discussed in the medical literature. The resulting optimal control problems will be analyzed with the tools of geometric optimal control giving raise to challenging aspects related to singular controls, chattering controls and an overall synthesis of solutions. Some results and open questions coming from this analysis will be presented which are relevant and interesting both from the mathematical point of view and biomedical perspective. This is joint research with Heinz Schaettler (Washington University, St. Louis, USA).
 February 4th, 2016 (02:30pm  03:30pm)
 Seminar: Noncommutative Geometry Seminar
Title: Operator spaces, representations of reductive groups, and a Kasparov product
Speaker: Nigel Higson, Penn State
Location: MB106This is joint work with Pierre Clare and Tyrone Crisp. Lafforgue gave a geometric proof of the ConnesKasparov conjecture for real reductive groups (a representationtheoretic proof had previously been sketched by Wassermann) and in his 2002 ICM address he used this as the starting point for a new approach to HarishChandra's classification of the discrete series. The new approach requires the computation of some Kasparov products, which are fortunately easy because the underlying Hilbert spaces are finitedimensional. It is interesting to attempt to extend Lafforgue's approach to limits of discrete series, since these account for the rest of the Ktheory of the reduced group C*algebra. But now the Kasparov products are more difficult, because among other things the underlying Hilbert spaces are infinitedimensional, and are only geometrically defined as operator spaces (the Hilbert space structure requires the Plancherel theorem).
 February 4th, 2016 (03:35pm  04:35pm)
 Seminar: Department of Mathematics Colloquium
Title: Free Boundary Problems Arising in Biology
Speaker: Professor Avner Friedman, Ohio State University
Location: MB114In a free boundary problem one seeks to solve a system of PDEs in a domain G whose boundary, or a part of it, is unknown, and to also determine the free boundary. Classical free boundary problems include contact problems in elasticity, melting of ice, propagation of jets, and cavitational flows. In recent years new free boundary problems arose in the context of biological or biomedical processes. Examples include the healing of a wound, the growth of a tumor, the formation of a plaque in the artery, the development of granulomas in tuberculosis, and biofilms. In this talk I will introduce some of the biological free boundary problems, focus on rigorous mathematical results, and describe some open problems.
 February 5th, 2016 (02:30pm  03:30pm)
 Seminar: Probability and Financial Mathematics Seminar
Title: Useful information and small probabilities
Speaker: Yuri Suhov, Penn State University
Location: MB106One of most famous (and practically useful) results of Shannon's information theory is the Noiseless coding theorem providing a basis for Datacompression. In short, the theorem says that discarding data with low information enables us to reduce the amount of the used memory by a factor involving the information/entropy rate of the source (but not more). However, in modern practices, we are often inundated with information that is not particularly useful to us (if at all). Consequently, we may be interested in storing only those data which carry a certain weight/utility which is, typically, contextdependent. This leads to an idea of a {\it selected} Datacompression and a problem of a further reduction of the used memory. The concept of {\it weighted} information/entropy emerges, in conjunction with Large deviation probabilities, which allows us to assess the amount of memory needed to store data that are relevant (i.e., have a high utility rate). This is a joint work with I. Stuhl (University of Denver). I will not require preliminary knowledge of Probability or Information theory and plan to introduce the related concepts and facts in the course of the presentation.
 February 8th, 2016 (02:30pm  03:30pm)
 Seminar: Computational and Applied Mathematics Colloquium
Title: Weak solutions to compressible NavierStokes
Speaker: PierreEmmanuel Jabin, University of Maryland
Location: MB106I will give an overview of the global existence theory for weak solutions to the compressible NavierStokes equations. The main goal is to introduce the basic Lions and Feireisl's theory and the connections with renormalized solutions and the well posedness theory for advection equations. Some recent developments and remaining open questions will also be presented.
 February 8th, 2016 (03:35pm  04:35pm)
 Seminar: Dynamical systems seminar
Title: Exponential Decays and Topological Entropy
Speaker: Peng Sun, Central University of finance and Economics, Beijing, China
Location: MB114We study exponential decays of Lebesgue numbers and expansive constants under dynamics. We find some interesting properties, especially their relations with topological entropy.
 February 9th, 2016 (02:30pm  03:30pm)
 Seminar: GAP Seminar
Title: Hamiltonian and Lagrangian structures in an integrable hierarchy: spacetime duality
Speaker: Vincent Caudrelier, City University of London
Location: MB106In the context of integrable systems, the object known as the classical rmatrix emerged from two remarkable discoveries: 1) integrable PDEs can be written as a Hamiltonian system by introducing an appropriate Poisson bracket of the (infinite dimensional) phase space; 2) combined with the Lax pair formulation and motivated by the question of canonical quantization of such Hamiltonian systems, certain fundamental Poisson brackets can be written as a commutator involving a special matrix (the r matrix). Understanding these observations on a fundamental level led to the discovery of PoissonLie groups and the modern theory of classical integrable systems. However, from the point of view of the independent variables (x,t) involved in the original PDEs, the entire theory is asymmetric. It is based only on "one half" of the Lax pair: the matrix describing the space evolution in the auxiliary problem at fixed time. In this talk, I will introduce some motivations to treat both independent variables x and t on equal footing. Using ideas from covariant field theory, the following observation will be made: it is possible to construct a new Poisson bracket on the phase space of an integrable hierarchy for which the fundamental Poisson brackets of the other half of the Lax pair have exactly the same structure as the usual one, with the same r matrix. Perhaps ironically, this observation actually raises more questions than it answers and I will mention some of them.
 February 9th, 2016 (03:32pm  06:02pm)
 Seminar: Working Seminar: Dynamics and its Working Tools
Title: Ergodic theory of C^1 generic conservative diffeomorphisms: I.
Speaker: Jairo Bochi, Pontifical University of Chile
Location: MB114In this pair of talks, I'll survey what is known about the ergodic theory of C^1generic volumepreserving and symplectic diffeomorphisms, and what are the various perturbation techniques used to prove those results. In the first part, I'll explain a statement of Mañé (generic areapreserving diffeomorphisms either have zero Lyapunov exponents a.e. or are Anosov), and its higherdimensional generalizations. In the second part, I'll explain more recent results, culminating with the following theorem of Avila, Crovisier, and Wilkinson: C^1generic volumepreserving diffeomorphisms either have zero Lyapunov exponents a.e. or the volume measure is ergodic, hyperbolic, and moreover the splitting into stable and unstable spaces is globally uniformly dominated.
 February 9th, 2016 (04:15pm  05:30pm)
 Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://This seminar will example aspects of the representation theory of SL(2,R)
 February 11th, 2016 (11:15am  12:05pm)
 Seminar: Algebra and Number Theory Seminar
Title: Connections Between Path Partitions and Restricted mary Partitions
Speaker: James Sellers, Penn State University
Location: MB106In this talk, we will describe unique path partitions (whose motivation comes from representation theory of the symmetric group). Once this introduction is complete, we will discuss an explicit characterization of the unique path partitions of n (or uppartitions for short) in terms of partitions we call strongly decreasing (and which are closely related to the nonsquashing partitions of Sloane and JAS). We then discuss numerous connections between uppartitions and certain types of binary partitions. Thanks to such connections with binary partitions, we conjecture and prove various arithmetic properties of u(n), the number of unique path partitions of n. We will close the talk with a discussion of generalizations to certain types of mary partitions as well as very recent work on arithmetic properties satisfied by such mary partition functions. This talk will touch on joint works of Christine Bessenrodt, Jorn Olsson, and JAS; George Andrews, Aviezri Fraenkel, and JAS; and George Andrews, Eduardo Brietzke, Oystein Rodseth, and JAS.
 February 11th, 2016 (02:30pm  04:30pm)
 Seminar: CCMA PDEs and Numerical Methods Seminar Series
Title: Numerical Modeling of Ice Sheets
Speaker: David Pollard, Pennsylvania State University
Location: MB315A brief overview of continentalsized ice sheets will be given, both for today (Greenland and Antarctica) and the past (North American and Eurasian). Basic physical processes and the equations describing icesheet variations through time will be described. The numerical techniques used to solve for the slow flow of ice deforming under its own weight will be outlined, focusing on the sparsematrix solution of the horizontal stretching equations. The performance of the sparsematrix solver used in our model will be assessed, and advice sought on how to improve on this performance.
 February 11th, 2016 (03:35pm  04:35pm)
 Seminar: Department of Mathematics Colloquium
Title: Firstpassage percolation
Speaker: Arjun Krishnan, University of Utah
Location: MB114Firstpassage percolation is a random growth model on the cubic lattice Z^d. It models, for example, the spread of fluid in a random porous medium. This talk is about the asymptotic behavior of the firstpassage time T(x), which represents the time it takes for a fluid particle released at the origin to reach a point x on the lattice. The firstorder asymptotic  the law of large numbers  for T(x) as x goes to infinity in a particular direction u, is given by a deterministic function of u called the timeconstant. The first part of the talk will focus on a new variational formula for the timeconstant, which results from a connection between firstpassage percolation and stochastic homogenization for discrete HamiltonJacobiBellman equations. The secondorder asymptotic of the firstpassage time describes its fluctuations; i.e., the analog of the central limit theorem for T(x). In two dimensions, the fluctuations are (conjectured to be) in the KardarParisiZhang (KPZ) or random matrix universality class. We will present some new results (with J. Quastel) in the direction of the KPZ universality conjecture. The analysis of this problem will involve tools and ideas from probability, PDEs, and ergodic theory.
 February 15th, 2016 (12:20pm  01:10pm)
 Seminar: CCMA Luncheon Seminar
Title: What is new for incompressible Euler?
Speaker: Dong Li
Location: MB114I will discuss some new exciting developments for incompressible Euler and related fluid equations in recent years, with a focus on understanding the solution operator, wellposedness issues and (harmonic) analysis perspectives.
 February 15th, 2016 (02:30pm  03:30pm)
 Seminar: Computational and Applied Mathematics Colloquium
Title: Norm inflation in hydrodynamics
Speaker: Dong Li, UBC
Location: MB106I will discuss a number of recent results concerning the norm inflation phenomena of fluid equations in various functional spaces. In particular I will focus on some new techniques to explore (beyond) the limitation of traditional energy type methods. Time permitting I will also discuss some new developments in related KatoPonce type inequalities and new fractional Leibniz rules. (Part of the work is joint with Jean Bourgain).
 February 15th, 2016 (03:35pm  04:35pm)
 Seminar: Dynamical systems seminar
Title: Postive loops  on a question by EliashbergPolterovich and a contact systolic inequality
Speaker: Peter Albers, University of Muenster, Germany
Location: MB114In 2000 EliashbergPolterovich introduced the concept of positivity in contact geometry. The notion of a positive loop of contactomorphisms is central. A question of EliashbergPolterovich ist whether C^0small positive loops exist. We give a negative answer to this question. Moreover we give sharp lower bounds for the size which, in turn, gives rise to a L^\inftycontact systolic inequality. This should be contrasted with a recent result by Abbondandolo et. al. that on the standard contact 3sphere no L^2contact systolic inequality exists. The choice of L^2 is motivated by systolic inequalities in Riemannian geometry. This is joint work with U. Fuchs and W. Merry.
 February 16th, 2016 (02:30pm  03:30pm)
 Seminar: GAP Seminar
Title: Jordan Groups, Abelian Varieties and Conic Bundles
Speaker: Yuri Zarhin, Penn State
Location: MB106A classical theorem of Jordan asserts that each finite subgroup of the complex general linear group GL(n) is ``almost commutative": it contains a commutative normal subgroup with index bounded by a universal constant that depends only on n. We discuss an analogue of this property for the groups of birational (and biregular) automorphisms of complex algebraic varieties and the groups of diffeomorphisms of real manifolds. This is a report on a joint work with Tatiana Bandman (BarIlan).
 February 16th, 2016 (02:30pm  03:45pm)
 Seminar: Logic Seminar
Title: Fine Structure Theory and Algorithmic Randomness (II)
Speaker: Jan Reimann, Penn State
Location: MB315Jensen's fine structure theory allows for a canonical definition of codes for levels of Goedel's constructible universe similar to how the Turing jump codes levels of the arithmetic hierarchy. In this talk, we will show how Jensen's codes and algorithmic randomness behave mutually orthogonal. This allows us in turn to derive a metamathematical result about randomness with respect to continuous measures.
 February 16th, 2016 (03:32pm  06:02pm)
 Seminar: Working Seminar: Dynamics and its Working Tools
Title: Ergodic theory of C^1 generic conservative diffeomorphisms: II.
Speaker: Jairo Bochi, Pontifical University of Chile
Location: MB114In this pair of talks, I'll survey what is known about the ergodic theory of C^1generic volumepreserving and symplectic diffeomorphisms, and what are the various perturbation techniques used to prove those results. In the first part, I'll explain a statement of Mañé (generic areapreserving diffeomorphisms either have zero Lyapunov exponents a.e. or are Anosov), and its higherdimensional generalizations. In the second part, I'll explain more recent results, culminating with the following theorem of Avila, Crovisier, and Wilkinson: C^1generic volumepreserving diffeomorphisms either have zero Lyapunov exponents a.e. or the volume measure is ergodic, hyperbolic, and moreover the splitting into stable and unstable spaces is globally uniformly dominated.
 February 16th, 2016 (04:15pm  05:30pm)
 Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://This seminar will example aspects of the representation theory of SL(2,R)
 February 18th, 2016 (11:15am  12:05pm)
 Seminar: Algebra and Number Theory Seminar
Title: Cones of higher codimension cycles
Speaker: Izzet Coskun, University of Illinois at Chicago
Location: MB106There is a welldeveloped theory of effective and nef divisors on projective varieties. In contrast, the theory of higher codimension cycles is much more difficult and we lack good criteria for determining when cycle classes are effective or nef. In this talk, I will discuss joint work with John Lesieutre on higher codimension pseudoeffective cones of blowups of projective space. In particular, we show that for a very general point blowup of projective space which is a Mori Dream Space all higher codimension effective cones are finitely generated. This is false for blowups of projective space along higher dimensional subvarieties. If time permits, I will discuss joint work with Dawei Chen on higher codimension cycles on moduli spaces of curves.
 February 18th, 2016 (03:35pm  04:35pm)
 Seminar: Department of Mathematics Colloquium
Title: Positivity in contact geometry
Speaker: Peter Albers, University of Muenster, Germany
Location: MB114The notion of positivity in contact geometry was introduced in 2000 by Eliashberg and Polterovich. For example, geodesic flows (and more generally Reeb flows) are positive. This and other examples will be explained during the talk. Positivity has connections to many phenomena such as contact (non)squeezing and biinvariant partial orders. Positivity leads to a generalization of the classical BottSamelson theorem and has connection to the famous Weinstein conjecture. Examples will be presented throughout the talk.
 February 22nd, 2016 (12:20pm  01:10pm)
 Seminar: CCMA Luncheon Seminar
Title: Phase field formulations and their numerical approximations of deterministic and stochastic mean curvature flows
Speaker: Xiaobing H. Feng, University of Tennessee
Location: MB114Discuss some recent developments and main issues on numerical methods for phase field models of (geometric) moving interface problems. Deterministic and stochastic mean curvature flows will be used as examples to present the ideas.
 February 22nd, 2016 (02:30pm  03:30pm)
 Seminar: Computational and Applied Mathematics Colloquium
Title: Some recent developments on numerical methods for second order fully nonlinear PDEs
Speaker: Xiaobing H. Feng, University of Tennessee
Location: MB106In the first part of the talk, a brief review of some recent highlights of numerical fully nonlinear second order PDEs including MongeAmpere (MA) type equations and HamiltonJacobiBellman (HJB) type equations. Those numerical methods include finite difference methods, semiLagrangian methods, finite element methods, discontinuous Galerkin methods. In the second part of the talk, describe a recent effort/approach to bridge the gap between advances on numerical methods for the HJBtype and for the MAtype fully nonlinear PDEs and to use the wealthy numerical techniques for HJBtype equations to solve MA type equations on general triangular and rectangular grids.
 February 23rd, 2016 (03:32pm  06:02pm)
 Seminar: Working Seminar: Dynamics and its Working Tools
Title: Lecture series on Lyapunov exponents IV
Speaker: Qiao Liu, Penn State
Location: MB114  February 23rd, 2016 (04:15pm  05:30pm)
 Seminar: Special Event
Title: SL(2,R) seminar
Speaker: Various, Penn State
Location: MB315
Abstract: http://This seminar will example aspects of the representation theory of SL(2,R)
 February 25th, 2016 (11:15am  12:05pm)
 Seminar: Algebra and Number Theory Seminar
Title: Zetapolynomials for modular form periods
Speaker: Larry G. Rolen III, Penn State University
Location: MB106Answering problems of Manin, we use the critical $L$values of even weight newforms $f$ to define zetapolynomials $Z_f(s)$ which satisfy the functional equation $Z_f(s)=\pm Z_f(1s)$, and which obey the Riemann Hypothesis: if $Z_f(\rho)=0$, then $\Re(\rho)=1/2$. The zeros of the $Z_f(s)$ on the critical line in $t$aspect are distributed in a manner which is somewhat analogous to those of classical zetafunctions. These polynomials are assembled using (signed) Stirling numbers and "weighted moments" of critical values $L$values. In analogy with Ehrhart polynomials which keep track of integer points in polytopes, the $Z_f(s)$ keep track of arithmetic information. Assuming the BlochKato Tamagawa Number Conjecture, they encode the arithmetic of a combinatorial arithmeticgeometric object which we call the "BlochKato complex" for $f$. Loosely speaking, these are graded sums of weighted moments of orders of \v{S}afarevi\v{c}Tate groups associated to the Tate twists of the modular motives.
 February 25th, 2016 (03:35pm  04:35pm)
 Seminar: Department of Mathematics Colloquium
Title: Datadriven stochastic model reduction in nonlinear dynamical systems
Speaker: Fei Lu, University of California, Berkeley
Location: MB114Prediction of highdimensional chaotic dynamic systems is often difficult when only partial observations are available, because such systems are often expensive to solve in full and the initial data will be incomplete. The development of reduced models for the observed variables is thus needed. The challenges come from the nonlinear interactions between the observed variables and the unobserved variables, and the difficulties in quantifying uncertainties from discrete data. We address these challenges by developing discretetime stochastic reduced systems for the observable variables, by using data and statistical methods to account for the impact of the unobserved variables. A key ingredient in the construction of the stochastic reduced systems is a discretetime stochastic parametrization based on inference of nonlinear time series. We demonstrate our approach on the twolayer Lorenz 96 system and the KuramotoSivashinsky equation. A theoretical understanding of such a datadriven modeling problem requires ideas from dynamical systems, PDEs, probability and statistics. Open questions will be discussed.
 February 26th, 2016 (09:30am  12:00pm)
 Seminar: Ph.D. Thesis Defense
Title: "Asymptotic formulae in analytic number theory"
Speaker: Ayla Gafni  Adviser: R. Vaughan, Penn State
Location: MB114
Abstract: http://This dissertation is composed of two main results. The first is an asymptotic formula for $p^k(n)$, the number of partitions of a number $n$ into $k$th powers. As an immediate consequence of this formula, we derive an asymptotic equivalence for $p^k(n)$ which was claimed without proof in a 1918 paper of Hardy and Ramanujan. The result is established using the HardyLittlewood circle method. As a necessary step in the proof, we obtain a nontrivial bound on exponential sums of the form $\sum_{m=1}^q e(am^k/q)$. The second result is an asymptotic formula for the number of rational points near planar curves. More precisely, if $f:\mathbb{R}\rightarrow\mathbb{R}$ is a sufficiently smooth function defined on the interval $[\eta,\xi]$, then the number of rational points with denominator no larger than $Q$ that lie within a $\delta$neighborhood of the graph of $f$ is shown to be asymptotically equivalent to $(\xi\eta)\delta Q^2$. This result has implications to the field of metric Diophantine approximation.
 February 26th, 2016 (02:30pm  03:30pm)
 Seminar: Probability and Financial Mathematics Seminar
Title: Special Analysis Seminar: Resonances in scattering by two magnetic fields at large separation and a complex scaling method
Speaker: Ivana Alexandrova, University at Albany
Location: MB106We study the quantum resonances in magnetic scattering in two dimensions. The scattering system consists of two obstacles by which the magnetic fields are completely shielded. The trajectories trapped between the two obstacles are shown to generate the resonances near the positive real axis, when the distance between the obstacles goes to infinity. The location is described in terms of the backward amplitudes for scattering by each obstacle. A difficulty arises from the fact that even if the supports of the magnetic fields are largely separated from each other, the corresponding vector potentials are not expected to be well separated. To overcome this, we make use of a gauge transformation and develop a new type of complex scaling method. We can cover the scattering by two solenoids at large separation as a special case. The obtained result heavily depends on the magnetic fluxes of the solenoids. This indicates that the Aharonov–Bohm effect influences the location of resonances. This is joint work with Hideo Tamura.