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IMA Newsletter #360

October 2006

2006-2007 Program

Applications of Algebraic Geometry

See http://www.ima.umn.edu/2006-2007 for a full description of the 2006-2007 program on Applications of Algebraic Geometry.

Blackwell-Tapia Conference: The Blackwell-Tapia Conference is the premier national event concerned with under-represented minorities in mathematical research. The 2006 Blackwell-Tapia Conference will be held at the IMA on November 3-4 with over 100 participants and an exciting program. You can find more information about this event on the conference web page. A registration form is at the web site. A few places are still available.
IMA Events

IMA Workshop

Negative Index Materials

October 2-4, 2006

Organizers: Maria-Carme T. Calderer (University of Minnesota Twin Cities), Sharon C. Glotzer (University of Michigan), Charles Y-C Lee (US Air Force Research Laboratory), Graeme Milton (University of Utah), Arje Nachman (US Air Force Research Laboratory), Peter Palffy-Muhoray (Kent State University)

IMA Annual Program Year Workshop

Software for Algebraic Geometry

October 23-27, 2006

Organizers: Michael E. Stillman (Cornell University), Jan Verschelde (University of Illinois)
Schedule

Monday, October 2

8:30a-9:15aRegistration and coffeeEE/CS 3-176 SW10.2-4.06
9:15a-9:30aWelcome to the IMADouglas N. Arnold (University of Minnesota Twin Cities)EE/CS 3-180 SW10.2-4.06
9:30a-10:20aConceptual foundations of metamaterials: from superlensing to negative indexGennady Shvets (University of Texas)EE/CS 3-180 SW10.2-4.06
10:20a-11:00aDiscussion and coffee breakEE/CS 3-180 SW10.2-4.06
11:00a-11:50aCloaking and opaque perfect lensesGraeme Milton (University of Utah)EE/CS 3-180 SW10.2-4.06
11:50a-1:30pDiscussion and lunch break SW10.2-4.06
1:30p-2:20pTwisted material gainsAkhlesh Lakhtakia (Pennsylvania State University)EE/CS 3-180 SW10.2-4.06
2:20p-3:00pDiscussion and coffee breakEE/CS 3-180 SW10.2-4.06
3:00p-3:30pSecond chances, a discussion period to revisit workshop topics and issues and look towards future directions.EE/CS 3-180 SW10.2-4.06
3:30p-3:40pGroup photo SW10.2-4.06
3:40p-6:00pReception and poster sessionLind Hall 400 SW10.2-4.06
Radiation enhancement and radiation suppression by a left-handed metamaterialAllan Boardman (University of Salford)
Directed seeding of three-dimensional metal-semiconductor nanocomposites for negative index metamaterialsRachel S. Goldman (University of Michigan)
Novel metamaterial using Cubic high dielectric resonatorsAnand Gopinath (University of Minnesota Twin Cities)
Jaewon Kim (University of Minnesota Twin Cities)
Optical hyperlens : Far-field imaging beyond the diffraction limit Zubin Jacob (Princeton University)
Error analysis of mixed finite element methods for wave propagation in double negative metamaterialsJichun Li (University of Nevada)
A boundary integral method and adaptive treecode for the linear Poisson-Boltzmann equationPeijun Li (University of Michigan)
Optimization and control of energy transmission across photonic crystal slabsRobert P. Lipton (Louisiana State University)
Nonlinear transmission in layered structures containing thin film of negative index materialNatalia Litchinitser (University of Michigan)
Nanoparticle susceptibilities and the bianisotropic formalismJeremy Neal (Kent State University)
Observation of increased transmission in sol-gel nanocompositesPeter Palffy-Muhoray (Kent State University)
"Negative" nanophotonics: controlling diffraction limit and group velocity in anisotropy-based NIMsViktor Podolskiy (Oregon State University)
Maximization of the quality factor of an optical resonatorFadil Santosa (University of Minnesota Twin Cities)
A homogenization-based study of the scattering resonances of a microstructured slabHaiping Shen (New York University)
Homogenization theory of negative index materials in the optical rangeGennady Shvets (University of Texas)

Tuesday, October 3

9:00a-9:30aCoffeeEE/CS 3-176 SW10.2-4.06
9:30a-10:20aEmpowering Optical Metamaterials with Gain and NonlinearitiesVladimir Shalaev (Purdue University)EE/CS 3-180 SW10.2-4.06
10:20a-11:00aDiscussion and coffee breakEE/CS 3-180 SW10.2-4.06
11:00a-11:50aMultifunctional composites with negative refractive indexSia Nemat-Nasser (University of California, San Diego)EE/CS 3-180 SW10.2-4.06
11:50a-1:30pDiscussion and lunch break SW10.2-4.06
1:30p-2:20pPlane-wave solutions to frequency-domain and time-domain scattering from negative permittivity and permeability slabsArthur Yaghjian (US Air Force Research Laboratory)EE/CS 3-180 SW10.2-4.06
2:20p-3:00pDiscussion and coffee break SW10.2-4.06
3:00p-3:50pSimulation environments for electromagnetic scatteringLeslie F. Greengard (New York University)EE/CS 3-180 SW10.2-4.06
4:00p-4:30pSecond chances, a discussion period to revisit workshop topics and issues and look towards future directions.EE/CS 3-180 SW10.2-4.06

Wednesday, October 4

9:00a-9:30aCoffeeEE/CS 3-176 SW10.2-4.06
9:30a-10:20aMetamaterials, plasmonics and optical nanocircuitsNader Engheta (University of Pennsylvania)EE/CS 3-180 SW10.2-4.06
10:20a-11:00aDisussion and coffee break SW10.2-4.06
11:00a-11:50a"Optical Hyperspace": Negative refractive index and sub-wavelength imaging in strongly anisotropic mediaEvgenii Narimanov (Princeton University)EE/CS 3-180 SW10.2-4.06
11:15a-12:15pAlgebraic geometry and applications seminar: An experimental approach to numerical Godeaux surfacesFrank-Olaf Schreyer (Universität des Saarlandes)Lind Hall 409 AGS
11:50a-1:30pDiscussion and lunch break SW10.2-4.06
1:30p-2:20pNegative refractive index metamaterials based on transmission linesAnthony Grbic (University of Michigan)EE/CS 3-180 SW10.2-4.06
2:20p-3:00pDiscussion and coffee breakEE/CS 3-180 SW10.2-4.06
3:00p-3:50pAbnormal refraction of EM waves in periodic metamaterialsAlexander Figotin (University of California)EE/CS 3-180 SW10.2-4.06
3:50p-4:30pClosing discussion SW10.2-4.06

Thursday, October 5

11:15a-12:15pReal algebraic geometry tutorial: A first order language for ordered ringsKenneth R. Driessel (Iowa State University)Lind Hall 409 RAG

Wednesday, October 11

11:15a-12:15pAlgebraic geometry and applications seminar: Examples of exact results from inexact methodsChris Peterson (Colorado State University)Lind Hall 305 AGS

Friday, October 13

1:25p-2:25pIndustrial Problems Seminar: Arun Verma (Bloomberg)Room 6 Vincent Hall (tentative) IPS

Wednesday, October 18

11:15a-12:15pAlgebraic Geometry and Applications SeminarChris Peterson (Colorado State University)Lind Hall 409 AGS

Friday, October 20

1:25p-2:25pIndustrial Problems Seminar: Jae Lew (Eaton Corporation)Room 6 Vincent Hall (tentative)

Monday, October 23

8:30a-9:15aRegistration and coffeeEE/CS 3-176 W10.23-27.06
9:15a-9:30aWelcome to IMADouglas N. Arnold (University of Minnesota Twin Cities)EE/CS 3-180 W10.23-27.06
9:30a-10:20aMacaulay 2, a software system for algebraic geometryDaniel R. Grayson (University of Illinois at Urbana-Champaign)EE/CS 3-180 W10.23-27.06
10:20a-10:50aCoffeeEE/CS 3-176 W10.23-27.06
10:50a-11:40aSAGE — Software for algebra and geometry experimentationWilliam Stein (University of Washington)EE/CS 3-180 W10.23-27.06
11:40a-1:40pLunch W10.23-27.06
1:40p-2:30pWhat should a software package for numerical algebraic geometry be?Charles W. Wampler (General Motors Corporation)EE/CS 3-180 W10.23-27.06
2:30p-3:00pCoffeeEE/CS 3-176 W10.23-27.06
3:00p-3:50pTBAPablo A. Parrilo (Massachusetts Institute of Technology)EE/CS 3-180 W10.23-27.06
4:00p-6:00pSoftware installation/poster session/receptionLind Hall 400 W10.23-27.06
9:00p-9:00pSoftware for partial differential equationsWenyuan Wu (University of Western Ontario)EE/CS 3-180

Tuesday, October 24

9:00a-9:30aCoffeeEE/CS 3-176 W10.23-27.06
9:30a-10:20aResolution of singularities from the practical point of view Anne Frühbis-Krüger (Universität Kaiserslautern)EE/CS 3-180 W10.23-27.06
10:20a-10:50aCoffeeEE/CS 3-176 W10.23-27.06
10:50a-11:40aTowards a black-box solver for finite games: The Gambit systemTheodore L. Turocy (Texas A & M University)EE/CS 3-180 W10.23-27.06
11:40a-1:40pLunch W10.23-27.06
1:40p-2:30pTBATangan Gao (California State University)EE/CS 3-180 W10.23-27.06
2:30p-3:00pCoffeeEE/CS 3-176 W10.23-27.06
3:00p-3:50pOn computing using FGb/RS softwareFabrice Rouillier (Institut National de Recherche en Informatique Automatique (INRIA))EE/CS 3-180 W10.23-27.06
4:00p-4:10pGroup picture W10.23-27.06
4:20p-6:00pChallenge problemsEE/CS 3-180 W10.23-27.06

Wednesday, October 25

9:00a-9:30aCoffeeEE/CS 3-176 W10.23-27.06
9:30a-10:20aCoCoALib, a C++ library for computations in commutative algebraAnna M. Bigatti (Università di Genova)EE/CS 3-180 W10.23-27.06
10:20a-10:50aCoffeeEE/CS 3-176 W10.23-27.06
10:50a-11:40a4ti2 — Computation of Hilbert bases, Graver bases, toric Gröbner bases and moreRaymond Hemmecke (Otto-von-Guericke-Universität Magdeburg)EE/CS 3-180 W10.23-27.06
11:40a-1:40pLunch W10.23-27.06
1:40p-2:30pParallel implementation of the polyhedral homotopy method for polynomial systemsMasakazu Kojima (Tokyo Institute of Technology)EE/CS 3-180 W10.23-27.06
2:30p-3:00pCoffeeEE/CS 3-176 W10.23-27.06
3:00p-3:50pSYNAPS, a library for symbolic-numeric computationBernard Mourrain (Institut National de Recherche en Informatique Automatique (INRIA))EE/CS 3-180 W10.23-27.06
4:00p-6:00pTutorial/Demo SessionLind Hall 400 W10.23-27.06

Thursday, October 26

9:00a-9:30aCoffeeEE/CS 3-176 W10.23-27.06
9:30a-10:20aD-modules for Macaulay 2Anton Leykin (University of Minnesota Twin Cities)EE/CS 3-180 W10.23-27.06
10:20a-10:50aCoffeeEE/CS 3-176 W10.23-27.06
10:50a-11:40aNew recombination techniques for polynomial factorization algorithms based on Hensel liftingGrégoire Lecerf (Université Versailles/Saint Quentin-en-Yvelines)EE/CS 3-180 W10.23-27.06
11:40a-1:40pLunch W10.23-27.06
1:40p-2:30pAPAtools: A Maple/Matlab toolbox for approximate polynomial algebraZhonggang Zeng (Northeastern Illinois University)EE/CS 3-180 W10.23-27.06
2:30p-3:00pCoffeeEE/CS 3-176 W10.23-27.06
3:00p-3:50pComputing tropical varietiesAnders Nedergaard Jensen (Aarhus University)EE/CS 3-180 W10.23-27.06
4:00p-6:00pTutorial/Demo SessionTBD W10.23-27.06

Friday, October 27

9:00a-9:30aCoffeeEE/CS 3-176 W10.23-27.06
9:30a-10:20aAlgebra & algorithms for differential elimination & completionEvelyne Hubert (Institut National de Recherche en Informatique Automatique (INRIA))EE/CS 3-180 W10.23-27.06
10:50a-11:40aApplication of numerical algebraic geometry to partial differential equationsGreg Reid (University of Western Ontario)EE/CS 3-180 W10.23-27.06
11:40a-1:40pLunch W10.23-27.06
1:40p-2:30pIntroduction to Bertini: a software package for numerical algebraic geometry Daniel J. Bates (University of Minnesota Twin Cities)EE/CS 3-180 W10.23-27.06
2:30p-3:00pCoffeeEE/CS 3-176 W10.23-27.06
3:00p-3:50pDemo Presentation: Maple 11 Jürgen Gerhard (Maplesoft)EE/CS 3-180 W10.23-27.06
4:00p-5:20pAnswers to challengesEE/CS 3-180 W10.23-27.06
5:20p-5:30pClosing DiscussionEE/CS 3-180 W10.23-27.06
Abstracts
Software installation/poster session/reception
Abstract: Software developers will offer their software for installation on the laptops of the participants at various booths.
Daniel J. Bates (University of Minnesota Twin Cities) Introduction to Bertini: a software package for numerical algebraic geometry
Abstract: Bertini is a new software package for computation in the field of numerical algebraic geometry. Among other things, Bertini is capable of producing all complex isolated solutions of a given polynomial as well as points on each positive-dimensional irreducible component. Bertini makes use of adaptive multiprecision, singular endgames, straight-line programs, and several other useful tools. This talk will cover some of the capabilities of Bertini as well as some of the implementation details.
Anna M. Bigatti (Università di Genova) CoCoALib, a C++ library for computations in commutative algebra
Abstract: For almost 20 years the CoCoA project has been conducting research into computational commutative algebra, developing new algorithms and offering implementations in the interactive program "CoCoA." Recently we took the decision to rebuild the software from scratch with the specific aim of making excellent implementations available to all researchers. The implementations will be accessible in three distinct ways: as a standalone interactive system, as a networked service (via an OpenMath-like communications channel), as a C++ library, called CoCoALib (free and open in the sense of the GPL). CoCoALib, being the core of the project, is also its most evolved part, and is the part that we shall look at most closely.
Allan Boardman (University of Salford) Radiation enhancement and radiation suppression by a left-handed metamaterial
Abstract: Joint work with K. Marinov (Photonics and Nonlinear Science Group, Joule Laboratory, Department of Physics, University of Salford, Salford M5 4WT, UK). It is shown that the perfect lens property of the left-handed metamaterials can be exploited to control the radiation efficiency of an electromagnetic radiation source (e.g. an antenna). In particular, the radiation characteristics of two identical sources, in the focal planes of the lens can be controlled depending on the relative phase difference between their feeding voltages. When the feeding voltages are pi-out-of-phase the resulting system behaves as a non-radiating configuration with a strong electromagnetic field confined in the space between the lens and the emitters and almost no electromagnetic radiation emitted. It is shown that such a system can be used as a very sensitive detector since any object disturbing the configuration of the electromagnetic fields inside the system stimulates radiation. Even objects of subwavelength dimensions are able to produce a substantial increase of the total power emitted by the system, and thus their presence can be revealed. The finite-difference time-domain (FDTD) numerical analysis performed allows a realistic system performance evaluation to be made. It is shown that if a pair of identical sources driven with in-phase feeding voltages are used in the same resonant configuration this results in an increase of the radiation resistance of each of the sources. The latter property can be useful for small antennas.
Nader Engheta (University of Pennsylvania) Metamaterials, plasmonics and optical nanocircuits
Abstract: Metamaterials, which are engineered composite media with unconventional electromagnetic and optical properties, can be formed by embedding sub-wavelength inclusions as artificial molecules in host media in order to exhibit specific desired response functions. They can have exciting characteristics in manipulating and processing RF, microwave, IR and optical signal information. Various features of these media are being investigated and some of the fundamental concepts and theories and modeling of wave interaction with a variety of structures and systems involving these material media are being developed. From our analyses and simulations, we have found that the devices and components formed by these media may be ultracompact and subwavelength, while supporting resonant and propagating modes. This implies that in such structures RF, microwave, IR and optical signals can be controlled and reshaped beyond the diffraction limits, leading to the possibility of miniaturization of optical interconnects and design and control of near-field devices and processors for the next generation of information technology. This may also lead to nano-architectures capable of signal processing in the near-field optics, which has the potential for significant size reduction in information processing and storage. Furthermore, the nanostructures made by pairing these media can be compact resonant components, resulting in either enhanced wave signatures and higher directivity or in transparency and scattering reduction. We are also interested in nano-optics of metamaterial structures that effectively act as lumped nano-circuit-elements. These may provide nano-inductors, nano-capacitors, nano-resistors, and nanodiodes as part of field nanocircuits in the optical regimes or optical-field nanoelectronics--, and can provide roadmaps to more complex nanocircuits and systems formed by collection of such nanostructures. All these characteristics may offer various potential applications in high-resolution near-field imaging and microscopy, enhancement or reduction of wave interaction with nano-particles and nano-apertures, nanoantennas and arrays, far-field sub-diffraction optical microscopy (FSOM), nano-circuit-filters, optical data storage, nano-beam patterning and spectroscopy, optical-molecular signaling and optical coupling and interfacing with cells, to name a few. In this talk, we present an overview of the concepts, salient features, recent developments, and some of the potential applications of these metamaterials and structures, and will forecast some futures ideas and directions in this area.
Alexander Figotin (University of California) Abnormal refraction of EM waves in periodic metamaterials
Abstract: Joint work with I Vitebskiy. Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the minimal translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such important features as negative refraction and/or opposite phase and group velocities for certain directions of light propagation can be found in almost any photonic crystal. The only reservation is that unlike hypothetical uniform left-handed media, photonic crystals are essentially anisotropic at frequency range of interest. Consider now a plane wave incident on a semi-infinite photonic crystal. One can assume, for instance, that in the case of positive refraction, the normal components of the group and the phase velocities of the transmitted Bloch wave have the same sign, while in the case of negative refraction, those components have opposite signs. What happens if the normal component of the transmitted wave group velocity vanishes? Let us call it a "zero-refraction" case. At first sight, zero normal component of the transmitted wave group velocity implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possibility. Instead, the transmitted wave can appear in the form of an abnormal grazing mode with huge amplitude and nearly tangential group velocity. This spectacular phenomenon is extremely sensitive to the frequency and direction of propagation of the incident plane wave. We also discuss some possible applications of this effect. REFERENCES: - A. Figotin, and I. Vitebskiy. Phys. Rev. E68, 036609 (2003). - J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy. Phys. Rev. E71, (2005).
Anne Frühbis-Krüger (Universität Kaiserslautern) Resolution of singularities from the practical point of view
Abstract: In the 1960s H.Hironaka proved the existence of a resolution of singularities in arbitrary dimension over a field of characteristic zero; but it was not before the late 1980s/early 1990s that the first algorithmic approaches to this task appeared which were at that time considered to be purely of theoretical use. By now there are two independent implementations and in this talk I would like to focus on the computational issues and modifications to the algorithm which are necessary to keep the very high time and memory consumption of the algorithm as low as possible and hence make it usable for non-trivial examples.
Rachel S. Goldman (University of Michigan) Directed seeding of three-dimensional metal-semiconductor nanocomposites for negative index metamaterials
Abstract: Negative index of refraction materials (NIMs) are promising for several applications including near-field imaging and steering of EM radiation. Although NIMs have been demonstrated using hybrid metamaterials at microwave frequencies, high losses and narrow bandwidths are presently limiting their wide application. We are developing a novel approach to fabricating low-loss high density NIM semiconductor-metal nanocomposites, which consists of alternating sequences of focused-ion beam nanopatterning of metallic droplet arrays and film growth using molecular-beam epitaxy. We will discuss the formation and ordering of Ga and In droplets and droplet motifs on a variety of semiconductor surfaces. In addition, we will discuss the extension of this approach to 3D. In particular, information from scattering measurements of 1D and 2D droplet motifs will be input into theoretical NIMs calculations to guide the fabrication of 3D arrays of appropriate motifs.
Anand Gopinath (University of Minnesota Twin Cities), Jaewon Kim (University of Minnesota Twin Cities) Novel metamaterial using Cubic high dielectric resonators
Abstract: Simulations have been performed on a novel metamaterial structure generated by periodic placement of identical high dielectric cubic resonators, in a low dielectric background. These resonators have degenerate modes, which implies that the TE and TM modes are resonant at the same frequency. Negative index behavior is deduced from these simulations near their resonant frequency. The periodic cubic structure with these high dielectric resonators results in a metamaterial, without any plasmonic metallic material, and should be low loss.
Daniel R. Grayson (University of Illinois at Urbana-Champaign) Macaulay 2, a software system for algebraic geometry
Abstract: Macaulay 2 supports research in algebraic geometry and commutative algebra. Its versatile framework, based on Buchberger's algorithm for computing Groebner bases, combined with an object-oriented interpreted language supporting the introduction of new high-level mathematical types, allows advanced algorithms to be coded. I'll demonstrate it, and I will describe recent improvements aimed to support third-party development of code, including the package system, the debugger, and the documentation processor.
Anthony Grbic (University of Michigan) Negative refractive index metamaterials based on transmission lines
Abstract: This talk will describe negative refractive index metamaterials that are based on transmission-line networks. It will focus on microwave structures that consist of transmission lines loaded with reactive elements. Both planar and volumetric negative refractive index metamaterials will be presented and their operation explained. Finally, ways to push these transmission-line based structures to optical frequencies using plasmonic materials will be described.
Leslie F. Greengard (New York University) Simulation environments for electromagnetic scattering
Abstract: We will review the analytic and computational foundations of Green's function-based methods for electromagnetic scattering, including high order integral representations, fast solvers, and quasi-periodicity. We will then discuss the development of easy-to-use numerical simulation environments, and present some applications to photonic crystals, random microstructures, and negative index materials.
Raymond Hemmecke (Otto-von-Guericke-Universität Magdeburg) 4ti2 — Computation of Hilbert bases, Graver bases, toric Gröbner bases and more
Abstract: Hilbert bases, Graver bases and toric Gröbner bases are at the heart of many problems arising in mathematics or in practice. In this talk we present the main functionality and the algorithmic theory behind the software package 4ti2. Furthermore, we present applications (theoretical and computational) from various mathematical fields such as toric algebra, integer programming or statistics. Within this workshop, this talk is accompanied by a tutorial on 4ti2 by Peter Malkin.
Evelyne Hubert (Institut National de Recherche en Informatique Automatique (INRIA)) Algebra & algorithms for differential elimination & completion
Abstract: Differential algebra provides an algebraic viewpoint on nonlinear differential systems. The motivating questions for this talk are:
  • How do we define the general solution of a nonlinear equations
  • What are the conditions for a differential system to have a solution
  • How do we measure the "degrees of freedom" for the solution set of a differential system
Theory and algorithms for those are extensions of commutative algebra (prime ideal decomposition, Hilbert polynomials) and Groebner bases techniques. The library diffalg in Maple supports this introduction to constructive differential algebra. It has been developed by F. Boulier (1996) and the speaker afterwards. A recent extension of differential algebra to non-commutative derivations, and its implementation in diffalg, allow to treat systems bearing on differential invariants.
Zubin Jacob (Princeton University) Optical hyperlens : Far-field imaging beyond the diffraction limit
Abstract: Joint work with Leonid V. Alekseyev and Evgenii Narimanov. We propose an approach to far-field optical imaging beyond the diffraction limit. The proposed system allows image magnification, is robust with respect to material losses and can be fabricated by adapting existing metamaterial technologies in a cylindrical geometry.
Anders Nedergaard Jensen (Aarhus University) Computing tropical varieties
Abstract: The tropical variety of a polynomial ideal I in n variables over Q is a polyhedral complex in n-dimensional space. We may consider it as a subfan of the Groebner fan of I. The polyhedral cones in the Groebner fan can be computed using Groebner bases and by applying "Groebner walk" techniques. This gives one method for computing the tropical variety of I. We show how the method can be refined by applying a connectivity result for tropical varieties of prime ideals and an algorithm for constructing tropical bases of curves. The presented algorithms have been implemented in the software package Gfan. This is joint work with T. Bogart, K. Fukuda, D. Speyer, B. Sturmfels and R. Thomas.
Masakazu Kojima (Tokyo Institute of Technology) Parallel implementation of the polyhedral homotopy method for polynomial systems
Abstract: The polyhedral homotopy method is known to be a powerful numerical method for approximating all isolated solutions of a system of polynomial equations. We discuss a parallel implementation of the polyhedral homotopy method, a dynamic enumeration of all fine mixed cells which is used in constructing a family of polyhedral homotopy functions and extensions of the Hornor Scheme to multivariate polynomials for efficient evaluation of a system of polynomials and their partial derivatives in the polyhedral homotopy method.
Akhlesh Lakhtakia (Pennsylvania State University) Twisted material gains
Abstract: A twisting and turning tale promises unimaginable gains for the savvy investor of time and effort in metamaterials research.
Grégoire Lecerf (Université Versailles/Saint Quentin-en-Yvelines) New recombination techniques for polynomial factorization algorithms based on Hensel lifting
Abstract: Multivariate polynomial factorization algorithms are necessary ingredients to several tasks in computational algebraic geometry such as prime and primary decompositions. They are also extremely useful in many places where they are not necessary but where they lead to major speedups by splitting problems into several smaller ones. In this talk I will present recent results concerning the factorization reductions from several to two variables via Bertini's theorem, and then from two to one variable. These reductions are based on the very classical Hensel lifting strategy and new fast recombination devices. Over a prime coefficient field, I will show that the irreducible factorization of a bivariate polynomial of bidegree (m,n) roughly reduces to the factorization of a univariate polynomial of degree n, a Hensel lifting to precision m+1, and O~( m n^2 ) arithmetic operations to recombine the lifted factors. Finally we will report on practical performances of the new algorithms, and on comparisons with other software.
Anton Leykin (University of Minnesota Twin Cities) D-modules for Macaulay 2
Abstract: The package D-modules for Macaulay 2 implements the majority of the now classical algorithms in the computational D-module theory. Based on the ability of Macaulay 2 engine to compute Gröbner bases in the Weyl algebra, the package provides, in particular, tools to work with holonomic D-modules such as the algorithms for b-functions, localized modules, restriction, etc. Amongst the applications there are computation of the local cohomology modules, polynomial and rational solutions, and A-hypergeometric systems. (Joint work with Harry Tsai)
Jichun Li (University of Nevada) Error analysis of mixed finite element methods for wave propagation in double negative metamaterials
Abstract: In this paper, we develop both semi-discrete and fully-discrete mixed finite element methods for modeling wave propagation in three-dimensional double negative metamaterials. Optimal error estimates are proved for Nedelec spaces under the assumption of smooth solutions. To our best knowledge, this is the first error analysis obtained for Maxwell's equations when metamaterials are involved.
Peijun Li (University of Michigan) A boundary integral method and adaptive treecode for the linear Poisson-Boltzmann equation
Abstract: Joint work with Robert Krasny. A boundary integral method (BIM) is developed for computing the electrostatic potential of biomolecules governed by the linear Poisson--Boltzmann equation (PBE). Compared with finite difference method and finite element method, the BIM provides a rigorous treatment on issues of the singular charges, the solute-solvent interfaces, and the infinite domain associated with the PBE. However, the BIM involves singular kernels. Their accurate integration is an important issues. Rather than investing in the development of complicated quadratures, we employ simple regularization techniques to evaluate surface integrals with regularized kernels. Furthermore, the high computational cost incurred in the conventional BIM is reduced by using an adaptive treecode algorithm based on Taylor approximation in Cartesian coordinates, and necessary Taylor coefficients are computed by recurrence relations. Numerical experiments are included to show the efficiency and accuracy of the proposed method.
Robert P. Lipton (Louisiana State University) Optimization and control of energy transmission across photonic crystal slabs
Abstract: A variational approach is developed for the design of defects within a two-dimensional lossless photonic crystal slab to create and manipulate the location of high Q transmission spikes within band gaps. This phenomena is connected to the appearance of resonant behavior within the slab for certain crystal defects. The methodology is applied to design crystals constructed from circular dielectric rods embedded in a contrasting dielectric medium. This is joint work with Stephen Shipman and Stephanos Venakides.
Natalia Litchinitser (University of Michigan) Nonlinear transmission in layered structures containing thin film of negative index material
Abstract: Co-authors: Ildar R. Gabitov, Andrei I. Maimistov, and Vladimir M. Shalaev. We investigate analytically and numerically nonlinear transmission in a bilayer structure consisting of a slab of positive index material with Kerr-type nonlinearity and a thin layer of negative index material (NIM). We find that a sub-wavelength layer of NIM significantly modifies the bistable nonlinear transmission characteristics of the considered bilayer structure and leads to nonreciprocal transmission with enhanced operational range, potentially enabling novel photonic devices such as optical diodes. The demonstrated high sensitivity of the nonlinear response of the structure to the material parameters of NIMs suggests that optical bistability in these structures has a strong potential for developing new tools for NIM characterization.
Graeme Milton (University of Utah) Cloaking and opaque perfect lenses
Abstract: We show how a slightly lossy superlens of thickness d cloaks collections of polarizable line dipoles or point dipoles or finite energy dipole sources that lie within a distance of d/2 of the lens. In the limit as the loss in the lens tends to zero, these become essentially invisible from the outside through the cancelling effects of localized resonances generated by the interaction of the source and the superlens. The lossless perfect Veselago lens has attracted a lot of debate. It is shown that as time progresses the lens becomes increasingly opaque to any physical dipole source located within a distance d/2 from the lens and which has been turned on at time t=0. Here a physical source is defined as one which supplies a bounded amount of energy per unit time. In fact the lens cloaks the source so that it is not visible from behind the lens either. For sources which are turned on exponentially slowly there is an exact correspondence between the response of the perfect lens in the long time constant limit and the response of lossy lenses in the low loss limit. This is joint work with Nicolae Nicorovici and Ross McPhedran.
Bernard Mourrain (Institut National de Recherche en Informatique Automatique (INRIA)) SYNAPS, a library for symbolic-numeric computation
Abstract: SYNAPS (SYmbolic Numeric APplications) is a C++ library devoted to symbolic and numeric computations. It provides data-structures for the manipulation of basic algebraic objects, such as vectors, matrices (dense, sparse, structured), univariate and multivariate polynomials. It contains solvers for univariate and multivariate polynomials, including generalized normal form or subdivision solvers, tools for the manipulatiion of algebraic numbers, for the construction of resultants, ... In this talk, we will describe shortly its design, its main features and functionalities, show some applications in computational geometry for algebraic curves and surfaces and explain how it can be embbeded in an interpreter such as mathemagix or a modeling tool such as axel.
Evgenii Narimanov (Princeton University) "Optical Hyperspace": Negative refractive index and sub-wavelength imaging in strongly anisotropic media
Abstract: We develop a new approach to negative index materials and subwavelength imaging in the far field based on strong anisotropy of the dielectric response. In contrast to conventional negative refraction systems, our method does not rely on magnetic resonance and does not require periodic patterning--leading to lower losses and high tolerance to fabrication defects.
Jeremy Neal (Kent State University) Nanoparticle susceptibilities and the bianisotropic formalism
Abstract: Since the spatial extent of nanoparticles is not negligible compared to the wavelength of light, non-local effects may be expected in the electric and magnetic response of nanoparticles at optical frequencies. It has been suggested that such spatially non-local response may be taken into account via the bianisotropic formalism for the constitutive equations. We have calculated the susceptibilities of pairs of nanowires as a function of orientation relative to the incident fields using the discrete dipole approximation. We compare the results of our simulations with predictions of the bianisotropic description, and summarize our observations.
Sia Nemat-Nasser (University of California, San Diego) Multifunctional composites with negative refractive index
Abstract: We outline recent achievements in creating structural composite materials with controlled electromagnetic properties, as an integral part of a multifunctional material system. The electromagnetic response is tailored by incorporating within the material small amounts of suitably configured, periodically distributed, electric conductors to produce distributed electric inductance and capacitance. The small-scale response of the conductors can be homogenized to give overall macroscopic EM material properties at wavelengths that are orders of magnitude larger than the dimensions of the periodicity of the structure. Periodic arrays of inductive elements such as thin straight wires, loop-wires, coils, and other conductive thin metallic structures can modify the effective electric permittivity and the effective magnetic permeability of a composite and make it negative. I will discuss the process of design, analysis, manufacturing, and measurement of such composites. In particular, I will review the UCSD's work on the design, production, and experimental characterization of a 2.7 mm thick composite panels having negative refractive index between 8.4 and 9.2 GHz. I will also examine our work on a flat lens having a gradient variation of negative index of refraction that can focus in the 10GHz range, showing excellent agreement with full-wave simulations.
Peter Palffy-Muhoray (Kent State University) Observation of increased transmission in sol-gel nanocomposites
Abstract: Nanocomposites made of Ag nanowires imbedded in a sol-gel host have been morphologically and optically investigated. Sonication during solidification significantly improved nanowire dispersal. The data from the nanocomposites were compared to the data from pure sol-gels in order to determine the effects of the nanowires. Reflectometry data at 1064 nm show that the presence of ~5% nanowires (by volume) results in a decrease from 1.17 to ≈1.1 in the real part of the index of refraction accompanied by an increase in the imaginary part. Transmission loss in the pure sol-gel is mainly due to scattering from inhomogeneities, and the inclusion of nanowires (or the process of doing so) results in a reduction of optical loss at VIS-NUV wavelengths in several samples.
Chris Peterson (Colorado State University) Algebraic geometry and applications seminar: Examples of exact results from inexact methods
Abstract: In this talk, some examples will be presented that illustrate how exact equations can often be recovered from numerically approximated generic points on a variety.
Viktor Podolskiy (Oregon State University) "Negative" nanophotonics: controlling diffraction limit and group velocity in anisotropy-based NIMs
Abstract: We explore the perspectives of a new type of materials with negative index of refraction - non-magnetic NIMs. In contrast to conventional NIMs, based either on magnetism or on periodicity, our design is non-magnetic and relies on the effective-medium response of anisotropic meta-materials in waveguide geometries. Being highly-tolerable to fabrication defects, anisotropic systems allow a versatile control over the magnitude and sign of effective refractive index and open new ways to efficiently couple the radiation from micro-scale optical fibers to nm-sized waveguides followed by sub-diffraction light manipulation inside sub-critical waveguiding structures. Specific applications include photonic funnels, capable of transferring over 25% of radiation from conventional telecom fiber to the spots smaller than 1/30-th of a wavelength, and NIM-based lenses with a far-field resolution of the order of 1/10-th of a wavelength. We also investigate the perspectives of active nanoscale NIMs and demonstrate that material gain can not only eliminate problems associated with absorption, but is also a powerful tool to control the group velocity from negative to "slow" positive values.
Greg Reid (University of Western Ontario) Application of numerical algebraic geometry to partial differential equations
Abstract: In Numerical Algebraic Geometry, solution components of polynomial systems are characterized by witness points. Such nice points are computed efficiently by continuation methods. In this talk, which is joint work with Wenyuan Wu and Jan Verschelde, I will outline progress on extending these methods to Partial Differential Equations. I will describe the jet geometric picture of PDE in their jet space, to which the methods of Numerical Algebraic Geometry are applied. In particular witness points in jet geometry are cut out by the intersection of random linear spaces with submanifolds in jet space (there will be nice pictures). Applications to constrained mechanical systems; overdetermined systems for symmetries of differential equations will also be described.
Fabrice Rouillier (Institut National de Recherche en Informatique Automatique (INRIA)) On computing using FGb/RS software
Abstract: The goal of this lecture is to show how to use efficiently FGb and RS software for solving various kinds of polynomial systems. Such software can nowadays be used as a "black box" in many cases (J. Gehrard's presentation) for computing/studying real roots of polynomial systems, but the objective here is to show how to use them in extreme situations. We will introduce, step by step, several tricks and advanced options, including the related mathematical background, and show how to solve some examples presented in the tutorial which took place at IMA in September (http://www.ima.umn.edu/2006-2007/T9.15-16.06/).
Fadil Santosa (University of Minnesota Twin Cities) Maximization of the quality factor of an optical resonator
Abstract: We consider resonance phenomena for the scalar wave equation in an inhomogeneous medium. Resonance is a solution to the wave equation which is spatially localized while its time dependence is harmonic except for decay due to radiation. The decay rate, which is inversely proportional to the qualify factor, depends on the material properties of the medium. In this work, the problem of designing a resonator which has high quality factor (low loss) is considered. The design variable is the index of refraction of the medium. Finding resonance in a linear wave equation with radiation boundary condition involves solving a nonlinear eigenvalue problem. The magnitude of the ratio between real and imaginary part of the eigenvalue is proportional to the quality factor Q. The optimization we perform is finding a structure which possesses an eigenvalue with largest possible Q. We present a numerical approach for solving this problem and describe results obtained by our method.
Frank-Olaf Schreyer (Universität des Saarlandes) Algebraic geometry and applications seminar: An experimental approach to numerical Godeaux surfaces
Abstract: A (numerical) Godeaux surface is a minimal surface X of general type with K_2=1 and p_g=0, hence also q=0 and H_1(X,Q)=0. So in some sense these are the surfaces of general type with smallest possible invariants. Godeaux constructed a family of such surfaces as quotients of a quintic hypersurface by a fixed point free action of Z_5. By the work of Miyaoka it is known that the torsion group T=H_1(X,Z) is a cyclic group of order at most 5. The surfaces with T=Z_d for d=3,4,5 have a moduli space which consists of one 8 dimensional component by work of Reid and Miyaoka. For T=Z_2 or T=0 much less is known. Existence of such surfaces was proved by Rebecca Barlow, by a complicated quotient construction. Traditionally there are two approaches to construct numerical Godeaux surfaces: Either by a Godeaux approach as a quotient of a simpler surface by a possibly non free group action, or by a Campedelli approach as a double plane branched along a curve with a specific configuration of singularities. In this talk I present a third approach based on homological algebra and computer algebra.
Vladimir Shalaev (Purdue University) Empowering Optical Metamaterials with Gain and Nonlinearities
Abstract: Metamaterials, i.e. artificial engineered structures with properties not available in nature are expected to open a gateway to unprecedented electromagnetic properties and functionality unattainable from naturally occurring materials. Negative-refractive index metamaterials create entirely new prospects for guiding light on the nanoscale, some of which may have revolutionary impact on present-day optical technologies. We review this new emerging field of metamaterials and recent progress in demonstrating a negative refractive index in the optical range, where applications can be particularly important. We also discuss strategies how to push the wavelength region of negative refractive index into the visible range by using plasmon resonant metal nanostructures.
Haiping Shen (New York University) A homogenization-based study of the scattering resonances of a microstructured slab
Abstract: This poster studies the scattering resonance problem associated with a waveguide consisting of an infinite slab with 2-D microstructure embedded in a homogeneous material. The main goal is to understand how resonances are affected by the presence of the microstructure in the slab. Our method is similar to the prior work of S. Moskow, F. Santosa and M. Vogelius, as the investigation concentrates on the first order correction to the homogenized resonance. The outgoing radiation condition at infinity makes the problem non-selfadjoint. Furthermore, there are boundary layers on the edges of the slab, due to the presence of rapidly vaying coefficients in the highest order term of the underlying equation. Our main result is a formula for the first order correction. The formula indicates strong influence of the way microstructure hits the edges of the slab.
Gennady Shvets (University of Texas) Homogenization theory of negative index materials in the optical range
Abstract: The challenge in engineering negative index materials in the optical frequency range involves designing sub-wavelength building blocks that exhibit both electric and magnetic activity. Achieving strong magnetic response is particularly challenging because magnetic moment of a structure scales as the square of the unit cell size. We address this challenge by employing higher order (multipole) electrostatic resonances that have a non-vaishing magnetic moment for a finite unite cell size. This approach provides a natural starting point for a perturbation theory that uses the ratio of the building block size to vacuum wavelength as the smallness parameter. Perturbative calculation yields the effective parameters of the metamaterial: effective epsilon and mu tensors. Those can be compared with the effective parameters extracted from fully electromagnetic simulations. Examples are given for two and three dimensional structures.
William Stein (University of Washington) SAGE — Software for algebra and geometry experimentation
Abstract: The goal of SAGE is to create an optimal software environment for research and experimentation in algebra, geometry, number theory, cryptography, and related areas. The speaker started SAGE in 2005 by combining together the very best of existing free software (e.g., Singular, PARI, GAP, Macaulay2, Maxima, gfan, etc), creating interfaces to non-free software (e.g., MAGMA, Maple, Mathematica), and beginning to fill in the gaps with new code. Now many developers have joined him in working on filling these gaps and making SAGE a polished and efficient piece of software. This talk will demo SAGE, and explain how it works.
Theodore L. Turocy (Texas A & M University) Towards a black-box solver for finite games: The Gambit system
Abstract: An intriguing fact about the celebrated Nash equilibrium concept in finite games is that it can be expressed mathematically in a variety of ways: as a fixed point, a solution to a complementarity program, a (global) minimizer, or a solution to a system of polynomial equations and inequalities. As a result, there are general-purpose algorithms to compute Nash equilibria on finite games. Many of these algorithms relate specifically to well-studied areas of numerical programming, including linear programming, homotopy path-following, and solving polynomial systems. Game theory appears in a broad range of disciplines, and is taught broadly at the undergraduate level. Students and practitioners alike need a tool to specify and analyze games without needing to worry about the computational details of finding equilibria. The Gambit system is an Open Source (GPL) set of software tools for specifying and analyzing games, with the goal of packaging quality implementations of numerical codes from experts in a convenient form for general use. This talk will introduce the Gambit system and outline current implementations of algorithms for computing equilibrium, with special emphasis on the role of a method for computing all equilibria which uses the PHCPACK system as a backend.
Charles W. Wampler (General Motors Corporation) What should a software package for numerical algebraic geometry be?
Abstract: It has been approximately twenty years since the initial germination of numerical continuation as an approach to finding solution points of systems of polynomial equations and ten years since its flowering into numerical algebraic geometry, which facilitates description of solution sets of any dimension and operations on these, such as intersection and fiber products. We will attempt to step back from the torrent of recent developments to sketch out the big picture of what a general software package for numerical algebraic geometry should be: what core functions are necessary, how these can be organized into higher level algorithms, and how this might be wedded to user interfaces that allow access by non-experts while still being open to new advances in algorithms.
Wenyuan Wu (University of Western Ontario) Software for partial differential equations
Abstract: In this talk both symbolic and numerical software will be described for overdetermined systems of Partial Differential Equations. The symbolic software is the rifsimp package which is available in distributed Maple. Examples and applications of the use of this software will be given. The numeric-symbolic methods are implemented using Jan Verschelde's PHCPack for numerical polynomial continuation together with Maple programs. Again examples will be given. This is joint work with Greg Reid, Jan verschelde and Allan Wittkopf and is a partner to the earlier talk Application of Numerical Algebraic Geometry to Partial Differential Equations given by Greg Reid.
Arthur Yaghjian (US Air Force Research Laboratory) Plane-wave solutions to frequency-domain and time-domain scattering from negative permittivity and permeability slabs
Abstract: Plane-wave representations are used to formulate the exact solutions to frequency-domain and time-domain sources illuminating a magnetodielectric slab with complex permittivity and permeability. In the special case of a line source at z=0 a distance d2L but also divergent infinite fields in the region 2d2L and divergent in the region 2d
Zhonggang Zeng (Northeastern Illinois University) APAtools: A Maple/Matlab toolbox for approximate polynomial algebra
Abstract: This talk presents a Maple/Matlab toolbox for basic polynomial computations with exact or approximate data. The toolbox includes software for computing the approximate GCD, approximate factorization, dual basis and multiplicity identification, as well as numerical elimination in solving polynomial systems. We shall present the underlying theory of approximate polynomial algebra, the main approach of the algorithms, and computational results.
Visitors in Residence
Jung-Ha An University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Douglas N. Arnold University of Minnesota Twin Cities 7/15/2001 - 8/31/2007
Donald G. Aronson University of Minnesota Twin Cities 9/1/2002 - 8/31/2007
Gang Bao Michigan State University 10/1/2006 - 10/4/2006
Daniel J. Bates University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Gian Mario Besana DePaul University 9/5/2006 - 10/27/2006
Yermal Sujeet Bhat University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Anna M. Bigatti Università di Genova 10/22/2006 - 10/29/2006
Allan Boardman University of Salford 9/30/2006 - 10/4/2006
Yassine Boubendir University of Minnesota Twin Cities 10/2/2006 - 10/4/2006
Rachelle Bouchat University of Kentucky 10/22/2006 - 10/28/2006
Michael P. Brenner Harvard University 10/8/2006 - 10/9/2006
Oscar Bruno California Institute of Technology 10/1/2006 - 10/4/2006
Massimo Caboara Università di Genova 10/22/2006 - 10/27/2006
Maria-Carme T. Calderer University of Minnesota Twin Cities 10/1/2006 - 10/4/2006
John J. Cannon University of Sydney 10/22/2006 - 10/27/2006
Andrew Christlieb University of Michigan 10/1/2006 - 10/4/2006
Ionut Ciocan-Fontanine University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
L. Pamela Cook University of Delaware 10/7/2006 - 10/9/2006
Barry H. Dayton Northeastern Illinois University 10/22/2006 - 10/27/2006
Wolfram Decker Universität des Saarlandes 10/22/2006 - 10/28/2006
Alicia Dickenstein University of Buenos Aires 9/1/2006 - 11/30/2006
Jintai Ding University of Cincinnati 10/22/2006 - 10/28/2006
Sandra Di Rocco Royal Institute of Technology (KTH) 9/1/2006 - 10/20/2006
David C. Dobson University of Utah 10/1/2006 - 10/4/2006
Charles Doering University of Michigan 10/8/2006 - 10/9/2006
Kenneth R. Driessel Iowa State University 9/1/2006 - 5/31/2007
David Eklund Royal Institute of Technology (KTH) 9/14/2006 - 10/15/2006
Nader Engheta University of Pennsylvania 10/3/2006 - 10/4/2006
Makan Fardad University of Minnesota Twin Cities 8/26/2006 - 8/13/2007
Alexander Figotin University of California 10/1/2006 - 10/4/2006
Irene Fonseca Carnegie-Mellon University 10/1/2006 - 10/5/2006
Jake Fontana Kent State University 10/1/2006 - 10/4/2006
Anne Frühbis-Krüger Universität Kaiserslautern 10/22/2006 - 10/27/2006
Shuhong Gao Clemson University 9/5/2006 - 12/20/2006
Tangan Gao California State University 10/22/2006 - 10/27/2006
Carlos Garcia-Cervera University of California 10/1/2006 - 10/4/2006
Jürgen Gerhard Maplesoft 10/26/2006 - 10/29/2006
Rachel S. Goldman University of Michigan 10/1/2006 - 10/4/2006
Dmitry Golovaty University of Akron 10/1/2006 - 10/4/2006
Anand Gopinath University of Minnesota Twin Cities 10/1/2006 - 10/4/2006
Jason E. Gower University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Lawrence Gray University of Minnesota Twin Cities 10/9/2006 - 10/9/2006
Daniel R. Grayson University of Illinois at Urbana-Champaign 10/22/2006 - 10/27/2006
Anthony Grbic University of Michigan 10/1/2006 - 10/4/2006
Leslie F. Greengard New York University 10/1/2006 - 10/4/2006
Yun Guan University of Illinois 10/22/2006 - 10/27/2006
Tatsuyoshi Hamada Fukuoka University 10/23/2006 - 10/28/2006
Gloria Haro Ortega University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Jonathan Hauenstein University of Notre Dame 10/1/2006 - 10/28/2006
Raymond Hemmecke Otto-von-Guericke-Universität Magdeburg 10/21/2006 - 10/27/2006
Milena Hering University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Benjamin J. Howard University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Zhaoran Rena Huang Rensselaer Polytechnic Institute 10/1/2006 - 10/4/2006
Evelyne Hubert Institut National de Recherche en Informatique Automatique (INRIA) 9/1/2006 - 6/30/2007
Zubin Jacob Princeton University 10/1/2006 - 10/4/2006
Farhad Jafari University of Wyoming 9/1/2006 - 6/30/2007
Abdul Salam Jarrah Virginia Polytechnic Institute and State University 10/23/2006 - 10/28/2006
Anders Nedergaard Jensen Aarhus University 9/6/2006 - 6/30/2007
Gabriela Jeronimo University of Buenos Aires 9/4/2006 - 10/31/2006
Clayton Kerce Georgia Institute of Technology 10/1/2006 - 10/3/2006
Mercedeh Khajavikhan University of Minnesota Twin Cities 10/2/2006 - 10/4/2006
Jaewon Kim University of Minnesota Twin Cities 10/2/2006 - 10/4/2006
Robert V. Kohn New York University 10/8/2006 - 10/9/2006
Robert V. Kohn New York University 10/1/2006 - 10/5/2006
Masakazu Kojima Tokyo Institute of Technology 10/21/2006 - 10/28/2006
Thomas Koschny Iowa State University 10/1/2006 - 10/4/2006
Teresa Krick University of Buenos Aires 9/1/2006 - 10/15/2006
Song-Hwa Kwon University of Minnesota Twin Cities 8/30/2005 - 8/31/2007
Akhlesh Lakhtakia Pennsylvania State University 10/1/2006 - 10/3/2006
Niels Lauritzen Aarhus University 8/28/2006 - 6/30/2007
Grégoire Lecerf Université Versailles/Saint Quentin-en-Yvelines 10/21/2006 - 10/28/2006
Charles Y-C Lee US Air Force Research Laboratory 10/1/2006 - 10/4/2006
Jae Lew Eaton Corporation 10/20/2006 - 10/20/2006
Anton Leykin University of Minnesota Twin Cities 8/16/2006 - 8/15/2007
Jichun Li University of Nevada 10/1/2006 - 10/5/2006
Peijun Li University of Michigan 10/1/2006 - 10/4/2006
Tien-Yien Li Michigan State University 10/22/2006 - 10/27/2006
Hstau Liao University of Minnesota Twin Cities 9/2/2005 - 8/31/2007
Robert P. Lipton Louisiana State University 10/1/2006 - 10/5/2006
Natalia Litchinitser University of Michigan 10/2/2006 - 10/4/2006
Di Liu Michigan State University 10/1/2006 - 10/5/2006
Laura Lurati University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Gennady Lyubeznik University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Diane Maclagan Rutgers University 9/5/2006 - 11/30/2006
Arash Mafi Corning 10/1/2006 - 10/5/2006
Oluwole Daniel Makinde University of Limpopo 10/31/2006 - 11/5/2006
Peter Nicholas Malkin Université Catholique de Louvain 10/21/2006 - 10/28/2006
Samuel P. Marin General Motors Corporation 10/8/2006 - 10/9/2006
Hannah Markwig University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Thomas Markwig Universität Kaiserslautern 9/1/2006 - 6/30/2007
Andrew A. McLennan University of Minnesota Twin Cities 10/22/2006 - 10/27/2006
Roberto D. Merlin University of Michigan 10/1/2006 - 10/4/2006
R. Alexander Milowski NONE 10/22/2006 - 10/27/2006
Graeme Milton University of Utah 10/1/2006 - 10/4/2006
Richard Moeckel University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Bernard Mourrain Institut National de Recherche en Informatique Automatique (INRIA) 10/22/2006 - 10/27/2006
Ziad H. Musslimani Florida State University 10/1/2006 - 10/5/2006
Arje Nachman US Air Force Research Laboratory 10/1/2006 - 10/4/2006
Uwe Nagel University of Kentucky 9/1/2006 - 6/1/2007
Evgenii Narimanov Princeton University 10/1/2006 - 10/4/2006
Jeremy Neal Kent State University 10/1/2006 - 10/4/2006
Sia Nemat-Nasser University of California, San Diego 9/30/2006 - 10/4/2006
Jiawang Nie University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Sang- Hyun Oh University of Minnesota Twin Cities 10/2/2006 - 10/4/2006
Michael E. O'Sullivan San Diego State University 9/15/2006 - 10/26/2006
Peter Palffy-Muhoray Kent State University 10/1/2006 - 10/5/2006
Antonis Papachristodoulou California Institute of Technology 10/22/2006 - 10/27/2006
George C. Papanicolaou Stanford University 10/1/2006 - 10/4/2006
Pablo A. Parrilo Massachusetts Institute of Technology 10/22/2006 - 10/27/2006
Chris Peterson Colorado State University 9/1/2006 - 12/31/2006
Sonja Petrovic University of Kentucky 10/22/2006 - 10/27/2006
Arlie O. Petters Duke University 10/8/2006 - 10/9/2006
Kathy Wei Piret University of Illinois 10/22/2006 - 10/27/2006
Viktor Podolskiy Oregon State University 10/1/2006 - 10/4/2006
Craig T. Poling Lockheed Martin Missiles and Space Company, Inc. 10/8/2006 - 10/10/2006
Sorin Popescu Stony Brook University 9/1/2006 - 12/31/2006
Jianliang Qian Wichita State University 10/1/2006 - 10/5/2006
Omar Ramahi University of Waterloo 10/1/2006 - 10/4/2006
Greg Reid University of Western Ontario 9/6/2006 - 12/1/2006
Victor Reiner University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Fernando Reitich University of Minnesota Twin Cities 10/1/2006 - 10/4/2006
Kui Ren Columbia University 10/1/2006 - 10/5/2006
Donald Richards Pennsylvania State University 10/7/2006 - 10/9/2006
Joel Roberts University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Fabrice Rouillier Institut National de Recherche en Informatique Automatique (INRIA) 10/22/2006 - 10/27/2006
Bjarke Hammersholt Roune Aarhus University 9/12/2006 - 6/30/2007
Olivier Ruatta Université de Limoges 10/22/2006 - 10/27/2006
Jacob Rubinstein Indiana University 10/1/2006 - 10/4/2006
David Rusin Northern Illinois University 9/1/2006 - 12/31/2006
Fadil Santosa University of Minnesota Twin Cities 10/1/2006 - 10/4/2006
Arnd Scheel University of Minnesota Twin Cities 7/15/2004 - 8/31/2007
Hans Schoenemann Universität Kaiserslautern 10/21/2006 - 10/27/2006
Eric Schost École Polytechnique 10/22/2006 - 10/27/2006
Frank-Olaf Schreyer Universität des Saarlandes 9/5/2006 - 10/15/2006
Mathias Schulze Purdue University 10/22/2006 - 10/27/2006
Pierre Seppecher Université de Toulon et du Var 9/30/2006 - 10/4/2006
Chehrzad Shakiban University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Vladimir Shalaev Purdue University 10/1/2006 - 10/4/2006
Haiping Shen New York University 10/1/2006 - 10/4/2006
Stephen Shipman Louisiana State University 10/1/2006 - 10/4/2006
Gennady Shvets University of Texas 10/1/2006 - 10/3/2006
Lyubima Simeonova University of Utah 10/1/2006 - 10/4/2006
Andrew Sommese University of Notre Dame 9/1/2006 - 12/31/2006
Steven Sperber University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Dumitru Stamate University of Minnesota Twin Cities 10/23/2006 - 10/27/2006
William Stein University of Washington 10/22/2006 - 10/27/2006
Brandy Stigler Mathematical Biosciences Institute 10/22/2006 - 10/27/2006
Michael E. Stillman Cornell University 10/22/2006 - 10/27/2006
Erik Stokes University of Kentucky 10/22/2006 - 10/28/2006
Bernd Sturmfels University of California 10/23/2006 - 10/25/2006
Bernd Sturmfels University of California 10/8/2006 - 10/11/2006
Eitan Tadmor University of Maryland 10/8/2006 - 10/9/2006
Bahman Taheri AlphaMicron 10/2/2006 - 10/4/2006
Nobuki Takayama Kobe University 10/22/2006 - 10/28/2006
Akiko Takeda Kobe University 10/22/2006 - 10/27/2006
Amelia Taylor Colorado College 10/22/2006 - 10/27/2006
Rekha R. Thomas University of Washington 10/22/2006 - 10/27/2006
Enrique Augusto Tobis University of Buenos Aires 10/15/2006 - 11/11/2006
Carl Toews University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Philippe Trebuchet Université de Paris VI (Pierre et Marie Curie) 10/22/2006 - 10/27/2006
Elias P. Tsigaridas National University of Athens 10/19/2006 - 10/28/2006
Igor Tsukerman University of Akron 9/30/2006 - 10/4/2006
Catalin Turc California Institute of Technology 10/1/2006 - 10/4/2006
Theodore L. Turocy Texas A & M University 10/22/2006 - 10/27/2006
Arun Verma Cornell University 10/12/2006 - 10/15/2006
Bogdan M. Vernescu Worcester Polytechnic Institute 10/1/2006 - 10/4/2006
Jan Verschelde University of Illinois 9/6/2006 - 11/30/2006
Victor Veselago Russian Academy of Sciences 10/1/2006 - 10/4/2006
Michael Vogelius Rutgers University 10/1/2006 - 10/4/2006
John Voight University of Minnesota Twin Cities 8/15/2006 - 8/31/2007
Darko Volkov Worcester Polytechnic Institute 10/1/2006 - 10/4/2006
Charles W. Wampler General Motors Corporation 9/14/2006 - 10/27/2006
Mingsheng Wang Chinese Academy of Sciences 9/15/2006 - 11/15/2006
Stephen M. Watt University of Western Ontario 10/22/2006 - 10/27/2006
Ruth J. Williams University of California, San Diego 10/7/2006 - 10/9/2006
Gershon Wolansky Technion-Israel Institute of Technology 10/2/2006 - 10/4/2006
Thomas Wolf Brock University 10/21/2006 - 10/28/2006
Margaret H. Wright New York University 10/7/2006 - 10/10/2006
Wenyuan Wu University of Western Ontario 9/6/2006 - 12/1/2006
Arthur Yaghjian US Air Force Research Laboratory 10/1/2006 - 10/5/2006
Ruriko Yoshida University of Kentucky 10/22/2006 - 10/27/2006
Zhonggang Zeng Northeastern Illinois University 9/18/2006 - 10/27/2006
Hongchao Zhang University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Ailing Zhao University of Illinois 10/22/2006 - 10/27/2006
Yan Zhuang University of Illinois 9/1/2006 - 12/1/2006
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
3M, Boeing, Carnegie-Mellon University, Consiglio Nazionale delle Ricerche (CNR), Corning, ExxonMobil, Ford, General Electric, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Johnson & Johnson, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute