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IMA Newsletter #366

April 2007

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.

News and Notes

IMA Postdocs 2007-2008

The IMA is delighted to announce that the IMA Postdocs for 2007-2008 in connection with the upcoming annual program Mathematics of Molecular and Cellular Biology are: Hannah Callendar (Vanderbilt University- 2007), Ludovica Cotta-Ramusino (Ecole Polytecnique Federale de Lausanne (EPFL)-2007), Peter Hinow (Vanderbilt University- 2007), Yeona Kang (Stony Brook University- 2006), Deena Schmidt (Cornell University- 2007), Andrew Stein (University of Michigan- 2007), Erkan Tuzel(University of Minnesota- 2006), Zhian Wang (University of Alberta- 2007). In addition, Olivier Dubois, (McGill - 2007), was appointed to an industrial postdoc position with ExxonMobil.

Former IMA Postdocs receive Sloan Research Fellowships
We are pleased to report that two former IMA postdocs were awarded Sloan Research Fellowships this year: Selim Esedoglu, now at University of Michigan, and Xiantao Li, now at Penn State.

The 2007 IMA Summer Program Classical and Quantum Approaches in Molecular Modeling, July 23-August 3, 2007, is devoted to computational molecular modeling both via classical approaches (emphasized in week 1) and quantum approaches (emphasized in week 2). Both weeks will include talks at the introductory level. The lectures during the first week will be given by Giovanni Ciccotti, Ben Leimkuhler, Robert Skeel, and Mark Tuckerman while the lectures during the second week will be given by Eric Cancès, and Youssef Saad.

PI Summer Program for Graduate Students Applicable Algebraic Geometry will be held at Texas A&M University in College Station, Texas, July 23-August 10, 2007. This program is open only to graduate students from IMA Participating Institutions. In order to participate, students need to fill out the application form and need to be nominated by their department chair by April 15, 2007. The course will concentrate on Applicable Algebraic Geometry. If you know of a graduate student at a Participating Institution who would benefit from the program, please encourage them to contact their department chair.

Mathematical Modeling in Industry Mathematical Modeling in Industry XI - A Workshop for Graduate Students, August 8-17, 2007 offers graduate students and qualified advanced undergraduates first hand experience in industrial research. Teams of up to six students will work under the guidance of a mentor from industry, who will guide the students in the modeling and analysis of real-world industrial problems. This year's mentors are Natalia M. Alexandrov (NASA), Gary B. Green (The Aerospace Corporation) John R. Hoffman (Lockheed Martin), Mark A. Stuff (General Dynamics), and Lisa Zhang (Lucent Technologies, Bell Laboratories). The application deadline is April 15.

IMA is seeking a new director: The IMA is looking for a new director to begin in summer 2008.

Mathematics and Chemistry: The preliminary program for the IMA Thematic year 2008-2009 on Mathematics and Chemistry is now available on line.

IMA Events

IMA Tutorial

What is Algebraic Geometry?

April 13-14, 2007

Organizers: David A. Cox (Amherst College), Bernd Sturmfels (University of California), Bernd Sturmfels (University of California)

IMA Annual Program Year Workshop

Complexity, Coding, and Communications

April 16-20, 2007

Organizers: Peter Bürgisser (Universität-GHS Paderborn), Ketan Mulmuley (University of Chicago), J. Maurice Rojas (Texas A & M University), Joachim Rosenthal (Universität Zürich), Madhu Sudan (Massachusetts Institute of Technology)

Public Lecture

Dr. Jennifer Chayes

April 18, 2007

Schedule

Tuesday, April 3

11:15a-12:15pIMA postdoc seminar: Tropical implicitization and eliminationJosephine Yu (University of California)Lind Hall 215 PS

Wednesday, April 4

11:15a-12:15pOptimal fewnomial bounds from Gale dual polynomial systemsFrank Sottile (Texas A & M University)EE/CS 3-180 AGS

Thursday, April 5

11:15a-12:15pReal algebraic geometry tutorial: The generalized abstract PositivstellensatzKenneth R. Driessel (Iowa State University)Lind Hall 409 RAG

Tuesday, April 10

11:15a-12:15pIMA postdoc seminar: Hilbert functions of standard graded algebrasUwe Nagel (University of Kentucky)Lind Hall 215

Wednesday, April 11

11:15a-12:15pAlgebraic geometry and applications seminar: Combinatorial complexity in o-minimal geometrySaugata Basu (Georgia Institute of Technology)EE/CS 3-180 AGS

Thursday, April 12

11:15a-12:15pReal algebraic geometry tutorial: Applications of the abstract PositivstellensatzKenneth R. Driessel (Iowa State University)Lind Hall 409 RAG

Friday, April 13

8:15a-8:45aCoffee and registrationEE/CS 3-176 T4.13-14.07
8:45a-9:00aWelcome and opening remarksDavid A. Cox (Amherst College)
Bernd Sturmfels (University of California)
EE/CS 3-180 T4.13-14.07
9:00a-10:30aIntersection theoryJessica Sidman (Mount Holyoke College)EE/CS 3-180 T4.13-14.07
10:30a-11:00aCoffeeEE/CS 3-176 T4.13-14.07
11:00a-12:30pCurves and surfacesRagni Piene (University of Oslo)EE/CS 3-180 T4.13-14.07
12:30p-2:00pLunch T4.13-14.07
2:00p-3:30pToric geometryDiane Maclagan (Rutgers University)EE/CS 3-180 T4.13-14.07
3:30p-3:45pCoffeeEE/CS 3-176 T4.13-14.07
3:45p-4:30pSecond chancesEE/CS 3-180 T4.13-14.07
6:30p-8:30pPizza Party and viewing the American premiere of Hauser's "Zeroset" videoLind Hall 400 T4.13-14.07

Saturday, April 14

9:00a-10:30aResolution of singularitiesHerwig Hauser (Leopold-Franzens Universität Innsbruck)EE/CS 3-180 T4.13-14.07
10:30a-11:00aCoffeeEE/CS 3-176 T4.13-14.07
11:00a-12:30pGrassmannians and Schubert varietiesSara Billey (University of Washington)EE/CS 3-180 T4.13-14.07
12:30p-2:00pLunch T4.13-14.07
2:00p-3:30pReal algebraic geometryClaus Scheiderer (Universität Konstanz)EE/CS 3-180 T4.13-14.07
3:30p-3:45pCoffeeEE/CS 3-176 T4.13-14.07
3:45p-4:30pSecond chancesEE/CS 3-180 T4.13-14.07

Monday, April 16

8:15a-9:00aRegistration and coffeeEE/CS 3-176 W4.16-20.07
9:00a-9:15aWelcome and introductionDouglas N. Arnold (University of Minnesota Twin Cities)EE/CS 3-180 W4.16-20.07
9:15a-10:05aOn the number of homotopy types of fibres of a definable mapSaugata Basu (Georgia Institute of Technology)EE/CS 3-180 W4.16-20.07
10:05a-10:40aCoffeeEE/CS 3-176 W4.16-20.07
10:40a-11:30aList decoding with optimal data rateVenkat Guruswami (University of Washington)EE/CS 3-180 W4.16-20.07
11:30a-1:30aLunch W4.16-20.07
1:30p-2:20pPseudocodeword connections Judy L. Walker (University of Nebraska)EE/CS 3-180 W4.16-20.07
2:20p-3:00pCoffeeEE/CS 3-176 W4.16-20.07
3:00p-3:30pSecond Chances and Open Problem SessionEE/CS 3-180 W4.16-20.07
3:40p-4:00pGroup PhotosEE/CS 3-180 W4.16-20.07
4:00p-6:00pReception and Poster SessionLind Hall 400 W4.16-20.07
Decoding linear codes via solving systems of polynomial equationsStanislav Bulygin (TU Kaiserslautern)
List decoding BCH codesPhilip Robert Busse (University of Kentucky)
A complexity-reduced interpolation algorithm for soft-decision decoding of Reed-Solomon codesKwankyu Lee (Korea Institute for Advanced Study (KIAS))
NP, coNP and the Nullstellensatz: lower bounds for stable set and graph coloring NullstellensatzeSusan Margulies (University of California)
The word problem for a class of groups with infinite presentation: A mputationally universal problem in the BSS modelKlaus Meer (Syddansk Universitet (University of Southern Denmark))
Descartes rule for complete fields and arbitrary codimensionJ. Maurice Rojas (Texas A & M University)
Metric structure of linear codes Diego Ruano (Universität Kaiserslautern)
Nonextendibility of mutually unbiased basesMeera Sitharam (University of Florida)
New fewnomial upper boundsFrank Sottile (Texas A & M University)
Computing zeta functions of sparse, nondegenerate hypersurfaces John Voight (University of Minnesota Twin Cities)

Tuesday, April 17

8:30a-9:00aCoffeeEE/CS 3-176 W4.16-20.07
9:00a-9:50aThe tangent FFTDaniel J. Bernstein (University of Illinois)EE/CS 3-180 W4.16-20.07
9:50a-10:30aCoffeeEE/CS 3-176 W4.16-20.07
10:30a-11:20aOn Smale's 17th problem: a probabilistic solution in average polynomial timeLuis Miguel Pardo (University of Cantabria)EE/CS 3-180 W4.16-20.07
11:20a-1:30pLunch W4.16-20.07
1:30p-2:20pPolynomial time algorithms to approximate mixed volumes within a simply exponential factorLeonid Gurvits (Los Alamos National Laboratory)EE/CS 3-180 W4.16-20.07
2:20p-3:00pCoffeeEE/CS 3-176 W4.16-20.07
3:00p-3:30pSecond Chances and Open Problem SessionEE/CS 3-180 W4.16-20.07

Wednesday, April 18

8:30a-9:00aCoffeeEE/CS 3-176 W4.16-20.07
9:00a-9:50aStrongly self-orthogonal codes for secure computationIwan Duursma (University of Illinois at Urbana-Champaign)EE/CS 3-180 W4.16-20.07
9:50a-10:30aCoffeeEE/CS 3-176 W4.16-20.07
10:30a-11:20aGeometry and the complexity of matrix multiplicationJoseph M. Landsberg (Texas A & M University)EE/CS 3-180 W4.16-20.07
11:20a-1:30pLunch W4.16-20.07
1:30p-2:20pNew recombination techniques for polynomial factorization algorithms based on Hensel liftingGrégoire Lecerf (Université Versailles/Saint Quentin-en-Yvelines)EE/CS 3-180 W4.16-20.07
2:20p-3:00pCoffeeEE/CS 3-176 W4.16-20.07
3:00p-3:30pSecond Chances and Open Problem SessionEE/CS 3-180 W4.16-20.07
5:00p-6:30pReceptionLind Hall 400 W4.16-20.07
7:00p-8:00pMath matters - IMA public lecture: Epidemics in technological and social networks: The downside of six degrees of separationJennifer Chayes (Microsoft Research)Willey Hall 125 W4.16-20.07

Thursday, April 19

8:30a-9:00aCoffeeEE/CS 3-176 W4.16-20.07
9:00a-9:50aUbiquity of Schubert varietiesV. Lakshmibai (Northeastern University)EE/CS 3-180 W4.16-20.07
9:50a-10:30aCoffeeEE/CS 3-176 W4.16-20.07
10:30a-11:20aDecision versus evaluation in algebraic complexity theoryPascal Koiran (École Normale Supérieure de Lyon)EE/CS 3-180 W4.16-20.07
11:30a-1:30aLunch W4.16-20.07
1:30p-2:20pThe weight adjacency matrix of a convolutional codeHeide Gluesing-Luerssen (University of Kentucky)EE/CS 3-180 W4.16-20.07
2:20p-3:00pCoffeeEE/CS 3-176 W4.16-20.07
3:00p-3:30pSecond Chances and Open Problem SessionEE/CS 3-180 W4.16-20.07
6:30p-8:30pGroup Dinner- Kikugawa at Riverplace43 Main Street SE Minneapolis MN 55414 W4.16-20.07

Friday, April 20

8:30a-9:00aCoffeeEE/CS 3-176 W4.16-20.07
9:00a-9:50a Geometric complexity theory (GCT)Milind Sohoni (Indian Institute of Technology)EE/CS 3-180 W4.16-20.07
9:50a-10:30aCoffeeEE/CS 3-176 W4.16-20.07
10:30a-11:20aThe probability that a slight perturbation of a numerical analysis problem is difficultPeter Bürgisser (Universität-GHS Paderborn)EE/CS 3-180 W4.16-20.07
11:20a-1:30plunch W4.16-20.07
1:30p-2:20pA critical radius for low complexity J. Maurice Rojas (Texas A & M University)EE/CS 3-180 W4.16-20.07
2:30p-3:00pSecond Chances and Closing RemarksEE/CS 3-180 W4.16-20.07

Tuesday, April 24

11:15a-12:15pIMA postdoc seminar: F...?Anton Leykin (University of Minnesota Twin Cities)Lind Hall 215 PS

Wednesday, April 25

11:15a-12:15pAlgebraic geometry and applications seminar: On sparse polynomial systems, mixed volumes and condition numbersGregorio Malajovich (Federal University of Rio de Janeiro)Lind Hall 229 AGS

Thursday, April 26

10:15a-11:10aAlgebraic geometry and applications seminar: Random polynomial systems and balanced metrics on toric varietiesJ. Maurice Rojas (Texas A & M University)EE/CS 3-180 AGS
11:15a-12:15pReal algebraic geometry tutorial: Real and complex varieties: comparisons, contrasts and examplesJoel Roberts (University of Minnesota Twin Cities)Lind Hall 409 RAG

Friday, April 27

1:25p-2:25pIMA/MCIM Industrial problems seminar: Tensor decompositions, the MATLAB tensor toolbox, and applications to data analysisTamara Gibson Kolda (Sandia National Laboratories)Vincent Hall 1 IPS
Abstracts
Second Chances and Closing Remarks
Abstract: No Abstract
Saugata Basu (Georgia Institute of Technology) On the number of homotopy types of fibres of a definable map
Abstract: I will describe some results giving a single exponential upper bound on the number of possible homotopy types of the fibres of a Pfaffian map, in terms of the format of its graph. In particular, we show that if a semi-algebraic set S ⊂ ℝm+n is defined by a Boolean formula with s polynomials of degrees less than d, and π: (R)m+n → (R)n is the projection on a subspace, then the number of different homotopy types of fibres of π does not exceed (2m snd)O(nm). All previously known bounds were doubly exponential. As applications of our main results we prove single exponential bounds on the number of homotopy types of semi-algebraic sets defined by polynomials having a fixed number of monomials in their support (we need to fix only the number of monomials, not the support set itself), as well as by polynomials with bounded additive complexity. We also prove single exponential upper bounds on the radii of balls guaranteeing local contractibility for semi-algebraic sets defined by polynomials with integer coefficients. (Joint work with N. Vorobjov).
Daniel J. Bernstein (University of Illinois) The tangent FFT
Abstract: My goal in this talk is to advertise an algorithm found by James Van Buskirk, the first improvement in more than thirty years in the exact complexity of the discrete Fourier transform over the reals. The previous speed record was held by the split-radix FFT, announced by Yavne in 1968 and widely understood since the early 1980s. The split-radix FFT uses 4n\lg n-6n+8 operations over the reals for a size-n complex DFT when n is a large power of 2, and therefore (12+o(1))n\lg n operations for a complex cyclic convolution of length n. Bruun's real-factor FFT also uses (12+o(1))n\lg n operations. An analysis by Johnson and Frigo shows that Van Buskirk's new algorithm uses only (34/3+o(1))n\lg n operations.
Sara Billey (University of Washington) Grassmannians and Schubert varieties
Abstract: The study of Schubert varieties has grown out questions in enumerate geometry from the 19th century. This field has flourished over the past fifty years and now has applications in algebraic geometry, representation theory, combinatorics, physics, computer graphics, and economics. We will define Schubert varieties in the context of Grassmannians and flag varieties. These varieties have many interesting properties determined by combinatorial data like partitions, permutations, posets, and graphs. We present five fun facts on Schubert varieties and some open problems in the field.
Stanislav Bulygin (TU Kaiserslautern) Decoding linear codes via solving systems of polynomial equations
Abstract: This is a joint work of the presenter and Ruud Pellikaan (Technical University of Eindhoven, Netherlands). We investigate a question of decoding linear codes, in particular up to half the minimum distance. We propose a method based on solving systems of polynomial equations over a finite field. Such a method was already quite successfully applied for cyclic codes earlier, we move on to the general case. We concentrate on solving the systems that emerge with the use of Groebner bases. The poster reflects a theoretical framework, the main result (the system we want to solve has a unique solution, etc.), and also some results on complexity estimation and experimental results.
Philip Robert Busse (University of Kentucky) List decoding BCH codes
Abstract: List decoding Reed-Solomon codes via an interpolation and root-finding algorithm was pioneered by Madhu Sudan in the mid to late 1990's. In 2006, Kwankyu Lee and Michael O'Sullivan developed a Gröbner basis based implementation of the interpolation algorithm, which they showed was an efficient generalization of the Berlekamp-Massey Algorithm. We propose to apply these ideas to list decoding BCH codes by presenting BCH codes as subfield subcodes of generalized Reed-Solomon codes and to explore the resulting algorithm. In particular, we seek ways to optimize the new algorithm and to compare it with the Berlekamp-Massey algorithm.
Peter Bürgisser (Universität-GHS Paderborn) The probability that a slight perturbation of a numerical analysis problem is difficult
Abstract: The running time of many iterative numerical algorithms is dominated by the condition number of the input, a quantity measuring the sensitivity of the solution with regard to small perturbations of the input. Examples are iterative methods of linear algebra, interior-point methods of linear and convex optimization, as well as homotopy methods for solving systems of polynomial equations. Spielman and Teng introduced in 2001 the seminal concept of smoothed analysis, which arguably blends the best of both worst-case and average-case analysis of algorithms. This led to a much better understanding of the success of the simplex method in practice. We present a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs. Several applications to linear and polynomial equation solving show that the estimates obtained in this way are easy to derive and quite accurate. The main theorem is based on a volume estimate of ε-tubular neighborhoods around a real algebraic subvariety of a sphere, intersected with a disk of radius σ. Besides ε and σ, this bound depends only the dimension of the sphere and on the degree of the defining equations. This is joint work with Felipe Cucker and Martin Lotz.
Jennifer Chayes (Microsoft Research) Math matters - IMA public lecture: Epidemics in technological and social networks: The downside of six degrees of separation
Abstract: During the past decade, complex networks have become increasingly important in communication and information technology. Vast, self-engineered networks, like the Internet, the World Wide Web, and Instant Messaging Networks, have facilitated the flow of information, and served as media for social and economic interaction. In social networks, the ease of information flow goes by many names: the "small world" phenomenon, the "Kevin Bacon phenomenon," and "six degrees of separation"—the claim that any two people on earth can be connected through a chain of acquaintances with at most five intermediaries. Unfortunately, many of the properties that facilitate information transmission also facilitate the spread of viruses in both technological and social networks. Dr. Chayes uses simple mathematical models to explain these epidemics and to examine strategies for their containment.
Iwan Duursma (University of Illinois at Urbana-Champaign) Strongly self-orthogonal codes for secure computation
Abstract: The well-known Shamir secret sharing scheme uses polynomial interpolation to recover a shared secret. The scheme and its application to secure computation generalizes to algebraic curve based schemes (Chen-Cramer 2006). For secure computation against an active adversary a scheme needs to be strongly multiplicative. We show that this can be achieved by using what we call strongly self-orthogonal codes. (Joint work with various authors)
Heide Gluesing-Luerssen (University of Kentucky) The weight adjacency matrix of a convolutional code
Abstract: Convolutional codes can be described by linear input-state-output systems. This gives rise to a state transition graph and an associated weight adjacency matrix. The latter counts in a detailed way the weights occurring in the code. After discussing some uniqueness issues we will present a MacWilliams identity theorem for convolutional codes and their duals in terms of the weight adjacency matrix. Furthermore, we will discuss isometries for convolutional codes and their effect on the weight adjacency matrix. It will be shown that for a particular class of codes the weight adjacency matrix forms a complete invariant under monomial equivalence, that is, under permutation and rescaling of the codeword coordinates.
Venkat Guruswami (University of Washington) List decoding with optimal data rate
Abstract: The fundamental trade-off in coding theory is the one between the rate of the code (a measure of amount of redundancy introduced) and the amount of errors that can be corrected. In this talk, I will describe an explicit construction of codes that achieves the optimal trade-off between these parameters, for a worst-case noise model where the channel can corrrupt the codeword arbitrarily subject to a bound on the total number of errors. Formally, for every 0 < R < 1 and eps > 0, we present an explicit construction of codes of rate R (which encode R.n symbols into n symbols) that can be list decoded in polynomial time from up to a fraction (1-R-eps) of errors. Clearly, one needs at least Rn correct symbols in the received word to have any hope of identifying the Rn message symbols, so recovering from (R+eps)n correct symbols is information-theoretically best possible. Our codes are simple to describe: they are certain *folded* Reed-Solomon codes, which are just Reed-Solomon codes, but viewed as a code over a larger alphabet by a careful bundling of codeword symbols. The talk will introduce the problem of list decoding, and then give a peek into the algebraic ideas and constructions that lead to the above result. Time permitting, I will also describe some challenging questions concerning algebraic-geometric codes that, if resolved, could improve the decoding complexity as one approaches the optimal trade-off. Based on joint work with Atri Rudra (UW).
Leonid Gurvits (Los Alamos National Laboratory) Polynomial time algorithms to approximate mixed volumes within a simply exponential factor
Abstract: Let K =(K1…Kn) be a n-tuple of convex compact subsets in the Euclidean space Rn, and let V (·) be the Euclidean volume in Rn . The Minkowski polynomial VK is defined as VK(x1, …, xn)= V (λ1K1 +…+λnKn) and the mixed volume V(K1,…,Kn) as
V(K1…Kn) = ∂n / ∂λ1…∂λn VK1K1 +…λnKn).
The mixed volume is one of the backbones of convexity theory. After BKH theorem, the mixed volume( and its generalizations) had become crucially important in computational algebraic geometry. We present in this talk randomized and deterministic algorithms to approximate the mixed volume of well-presented convex compact sets. Our main result is a poly-time randomized algorithm which approximates V (K1,…, Kn) with multiplicative error en and with better rates if the affine dimensions of most of the sets Ki are small. Because of the famous Barany-Furedi lower bound, even such rate is not achievable by a poly-time deterministic oracle algorithm. Our approach is based on the particular, geometric programming, convex relaxation of log(V (K1,…, Kn)). We prove the mixed volume analogues of the Van der Waerden and the Schrijver/Valiant conjectures on the permanent. These results, interesting on their own, allow to "justify" the above mentioned convex relaxation, which is solved using the ellipsoid method and a randomized poly-time time algorithm for the approximation of the volume of a convex set.
Herwig Hauser (Leopold-Franzens Universität Innsbruck) Resolution of singularities
Abstract: This is a spectacular subject, both by its many applications and its intricate proof. We describe in the talk the main ideas (after Zariski, Hironaka, Abhyankar and various other people) how to use blowups for the resolution of singular varieties, and how to build up an induction procedure to choose at each step of the resoluton process the center of the next blowup and to show that the singularities have improved after blowup. The key constructions and phenomena are illustrated by visualizations of surface singularities. As the talk will give mostly the intuitive ideas, we would like to refer the interested reader for details to three notes we have written on the subject. There, also quite complete lists of other references can be found. The three references to my talk are on my web-site www.hh.hauser.cc
Pascal Koiran (École Normale Supérieure de Lyon) Decision versus evaluation in algebraic complexity theory
Abstract: wo main categories of problems are studied in algebraic complexity theory: evaluation problems and decision problems. A typical example of an evaluation problem is the evaluation of the permanent of a matrix. Such problems can be studied within Valiant's framework. Deciding whether a multivariate polynomial has a real root is a typical example of a decision problem. This problem is NP-complete in the Blum-Shub-Smale model of computation over the real numbers. In this talk I will present a transfer theorem which shows that if certain evaluation problems are easy, then other decision problems (including the above-mentioned NP-complete problem) are easy too. Therefore, to show that that P is different from NP over the set of real numbers, one should first be able show that certain evaluation problems are hard.
Tamara Gibson Kolda (Sandia National Laboratories) IMA/MCIM Industrial problems seminar: Tensor decompositions, the MATLAB tensor toolbox, and applications to data analysis
Abstract: Tensors (also known as multidimensional arrays or N-way arrays) provide powerful tools for data representation and analysis. Consequently, they have been used in a variety of sciences ranging from chemometrics to psychometrics and most recently to data mining. In this talk, I'll provide a brief tutorial on tensors and their decompositions, assuming only a background in linear algebra. I will then describe the MATLAB Tensor Toolbox for working with dense, sparse, and structured tensors. I'll conclude with examples from several data mining contexts including web mining and cross-language information retrieval. This is joint work with Brett Bader, Sandia National Labs.
V. Lakshmibai (Northeastern University) Ubiquity of Schubert varieties
Abstract: Hodge gave basis for the homogeneous co-ordinate rings of the Grassmannian and its Schubert varieties in terms of "standard monomials" in the Plucker co-ordinates. This clasical work of Hodge was extended to the generalized flag variety and its Schubert varieties by Lakshmibai-Littelmann-Musili-Seshadri. We shall give a survey talk on this generalization and will also relate many important algebraic varieties to Schubert varieties.
Joseph M. Landsberg (Texas A & M University) Geometry and the complexity of matrix multiplication
Abstract: I'll give geometric formulations and interpretations of some of the main results regarding the complexity of matrix multiplication. I'll also explain the relevance of this geometry for areas such as algebraic statistics and quantum computing.
Grégoire Lecerf (Université Versailles/Saint Quentin-en-Yvelines) New recombination techniques for polynomial factorization algorithms based on Hensel lifting
Abstract: I will present new deterministic and probabilistic recombination algorithms to compute the irreducible factorization of bivariate polynomials via the classical Hensel lifting technique, and for the dense representation model. In bi-degree (dx, dy) with dy ≤ dx, and whatever the characteristic of the base field is, these algorithms only require the precision of the lifting to be dx+1. The cost of the deterministic recombination algorithm is sub-quadratic in dx dy, and the probabilistic version is faster by a factor of dy. At the end, I will explain how these algorithms can be adapted to the computation of the absolute factorization, and how they extend to more than 2 variables.
Kwankyu Lee (Korea Institute for Advanced Study (KIAS)) A complexity-reduced interpolation algorithm for soft-decision decoding of Reed-Solomon codes
Abstract: Soon after Lee and O'Sullivan proposed a new interpolation algorithm for algebraic soft-decision decoding of Reed-Solomon codes, there have been some attempts to apply a coordinate transformation technique to the new algorithm, with a remarkable complexity reducing effect. We propose a conceptually simple way of applying the transformation technique to the interpolation algorithm.
Anton Leykin (University of Minnesota Twin Cities) IMA postdoc seminar: F...?
Abstract: Algorithms for computing Groebner bases are in the core of all computer algebra systems. One of the fastest installations of a Groebner method is F4 produced by Faugere and makes use of fast linear algebra. Its modification, F5, has been claimed to crack certain examples intractable by other methods. But what is behind F4 and F5?
Diane Maclagan (Rutgers University) Toric geometry
Abstract: This talk gives a brief introduction to the theory of toric varieties. In the first half of the talk I give seven different definitions of a toric variety and compare them briefly. In the second half I describe some of the uses of toric varieties. The first of these is as a testing ground for algebraic geometric conjectures, as many geometric questions about toric varieties can be turned into combinatorial questions. A second use is as a good ambient variety in which to embed and study other varieties, using the fact that smooth toric varieties are natural generalizations of projective space.
Gregorio Malajovich (Federal University of Rio de Janeiro) Algebraic geometry and applications seminar: On sparse polynomial systems, mixed volumes and condition numbers
Abstract: Abstract is a pdf file format and is posted at http://www.ima.umn.edu/2006-2007/seminars/malajovich/talk-ima.pdf.
Susan Margulies (University of California) NP, coNP and the Nullstellensatz: lower bounds for stable set and graph coloring Nullstellensatze
Abstract: Systems of polynomial equations over the complex numbers can be used to characterize NP-Complete graph-theoretic decision problems. From the point of view of computer algebra and symbolic computation, these are interesting polynomial systems because they are provably hard: solving them is as hard as solving the underlying NP-Complete problem. Furthermore, unless NP = coNP, there must exist infinite instances of these infeasible systems whose Hilbert Nullstellensatz certificates grow with respect to the underlying graphs.
Klaus Meer (Syddansk Universitet (University of Southern Denmark)) The word problem for a class of groups with infinite presentation: A mputationally universal problem in the BSS model
Abstract: Joint work with Martin Ziegler. The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real extension of the word problem for a certain class of groups which are presented as quotient groups of a free group and a normal subgroup. The main result establishes the word problem for such groups to be computationally equivalent to the Halting Problem for BSS machines over the reals. It thus provides the first non-trivial example of a concrete problem that is computationally universal for the BSS model.
Uwe Nagel (University of Kentucky) IMA postdoc seminar: Hilbert functions of standard graded algebras
Abstract: Hilbert functions have been introduced more than 100 years ago and they have been intensely studied ever since. Indeed, they continue to attract a lot of interest because numerous problems in various areas of mathematics can be reinterpreted as questions about Hilbert functions. In this talk we will discuss some of the fundamental results about Hilbert functions as well as several open problems.The minimum number of set-theoretic defining equations of algebraic varieties.
Luis Miguel Pardo (University of Cantabria) On Smale's 17th problem: a probabilistic solution in average polynomial time
Abstract: In this talk I will discuss several conceptual aspects leading a a probabilistic positive solution to the following problem proposed by S. Smale: "Can a zero of n complex polynomial equations in n unknowns be found approximately on the average, in polynomial time with a uniform algorithm?"
Ragni Piene (University of Oslo) Curves and surfaces
Abstract: This talk is intended as a brief introduction to certain aspects of the theory of algebraic curves and surfaces. To a projective algebraic variety one associates its arithmetic genus, using the constant term of the Hilbert polynomial. Since a complex projective algebraic curve can be viewed as a compact Riemann surface, it also has a topological genus, equal to the number of holes in the Riemann surface. Hirzebruch's Riemann-Roch theorem says that the topological genus is equal to the arithmetic genus. I sketch a proof of this fundamental result, using algebra, geometry, and topology. For algebraic surfaces there is a corresponding result, Noether's formula, expressing the arithmetic genus in terms of topological invariants, which can be proved in a similar way. The last part of the talk discusses the theory of curves on surfaces, in particular the links to classical enumerative geometry and to modern string theory in theoretical physics.
Joel Roberts (University of Minnesota Twin Cities) Real algebraic geometry tutorial: Real and complex varieties: comparisons, contrasts and examples
Abstract: Properties of a complex variety often can be illustrated by a picture of its real locus. Conversely, we can often understand a real variety by studying the corresponding complex variety. At the same time, there are cases where the properties of real varieties and complex varieties are quite different. This can include basic properties like connectedness, compactness, and local dimension near singular points. In this talk we will exhibit pictures of some curves and surfaces, that illustrate some of these similarities and differences. These figures will include several types of surfaces in R3. Many of the surface pictures are interactive, in that they are posted on a webpage, where the viewer – using nothing more than a Java-enabled browser – can rotate the figure continuously by dragging it with the mouse.
J. Maurice Rojas (Texas A & M University) Algebraic geometry and applications seminar: Random polynomial systems and balanced metrics on toric varieties
Abstract: Suppose c0,...,cd are independent identically distributed real Gaussians with mean 0 and variance 1. Around the 1940s, Kac and Rice proved that the expected number of real roots of the polynomial c0 + c1 x + ... + cd xdi, then the expected number of real roots is EXACTLY the square root of d. Aside from the cute square root phenomenon, Kostlan also observed that the distribution function of the real roots is constant with respect to the usual metric on the real projective line. The question of what a "natural" probability measure for general multivariate polynomials then arises. We exhibit two (equivalent) combinatorial constructions that conjecturally yield such a measure. We show how our conjecture is true in certain interesting special cases, thus recovering earlier work of Shub, Smale, and McLennan. We also relate our conjecture to earlier asymptotic results of Shiffman and Zelditch on random sections of holomorphic line bundles. This talk will deal concretely with polynomials and Newton polytopes, so no background on probability or algebraic geometry is assumed.
Diego Ruano (Universität Kaiserslautern) Metric structure of linear codes
Abstract: We use the study of bilinear forms over a finite field to give a decomposition of the linear codes similar to the one in [D. Ruano: On the structure of generalized toric codes, arXiv:cs.IT/0611010, 2006] for generalized toric codes. Such decomposition, called geometric decomposition of a linear code and which can be obtained in a constructive way, allows to express easily the dual of a linear code and gives a new paradigm for linear codes. The proofs for characteristic 2 are different, but they will be developed parallel.
Claus Scheiderer (Universität Konstanz) Real algebraic geometry
Abstract: While algebraic geometry is traditionally done over the complex field, most problems from real life are modelled on real numbers and ask for real, not for complex, solutions. Thus real algebraic geometry --- the study of algebraic varieties defined over the real numbers, and of their real points — is important. While most standard techniques from general algebraic geometry remain important in the real setting, there are some key concepts that are fundamental to real algebraic geometry and have no counterpart in complex algebraic geometry. In its first part, this talk gives an informal introduction to a few such key concepts, like real root counting, orderings of fields, or semi-algebraic sets and Tarski-Seidenberg elimination. We also sketch typical applications. In the second part, relations between positivity of polynomials and sums of squares are discussed, as one example for a currently active and expanding direction. Such questions have already been among the historic roots of the field. New techniques and ideas have much advanced the understanding in recent years. Besides, these ideas are now successfully applied to polynomial optimization.
Jessica Sidman (Mount Holyoke College) Intersection theory
Abstract: Intersection theory is a big subject that has played an important role in algebraic geometry, and any attempt at a comprehensive introduction in 90 minutes would surely fail. With this in mind, I have decided instead to attempt to convey some of the beauty and flavor of intersection theory by way of discussing a few concrete classical examples of intersection theory on surfaces. The material in the talk is covered in almost any text in algebraic geometry. There are many approaches to finding 27 lines on a cubic surface. If one wishes to see a more rigorous version of the presentation given in this talk, then please see Hartshorne's treatment in Chapter V.4 of the book cited in the refereces. Chapter V of Hartshorne's book is a very nice introduction to intersection theory on surfaces. For a more general orientation in the subject with good historical context, one might wish to read Fulton's "Introduction to intersection theory in algebraic geometry." Fulton's other book cited in the references is the standard in the subject, and the other texts listed offer additional points of view.
Meera Sitharam (University of Florida) Nonextendibility of mutually unbiased bases
Abstract: Two orthonormal bases of a finite dimensional Hilbert space are mutually unbiased if for every pair of vectors one from each basis, the modulus of the standard inner product is the same. The problem of determining bounds on the maximum number of such bases (MUBs) for a fixed dimension is an important open problem of 20 years that has been shown to arise in different guises in many areas of mathematics. The most common application of MUBs is found in quantum cryptography where MUBs are the quantum states used in many protocols. Here we consider 2 questions and provide preliminary results and conjectures:
  1. When is a given set of MUBs non-extendible? I.e., characterize mutually unbiased sets M1,M2,..,Mk of for which there is no basis M unbiased to M1,..,Mk?
  2. Characterize families of bases where non-extendibility of a set of MUBs imply maximality, and are there natural families of bases with this property. I.e, within such a family of bases, a greedy method for constructing MUBs would guarantee a maximal cardinality MUB collection.
This is joint work with Oscar Boykin and Mohamad Tarifi at the University of Florida.
Milind Sohoni (Indian Institute of Technology) Geometric complexity theory (GCT)
Abstract: We will outline a possible approach to outstanding computational complexity theory (CCT) questions. The approach relies on a faithful mapping of these questions to questions in geometric invariant (GIT) theory and representation theory. We begin with a construction of Valiant and show its connection to the Orbit Closure and Membership problems in GIT. Proofs of non-existence of algorithms translate to the existence of obstructions. This immediately leads to the important notion of stability in invariant theory. For stable points, we show that obstructions are easily constructed. We then outline proofs of the stability of forms such as the determinant and the permanent, which are important in CCT. We next define our notion of partially stable points. We pose our problems as (i) to understand the orbit closure for stable points with distinctive stabilizers, and (ii) extension of these results to partially stable points. We finish with an outline of our current attempts at these teo, and also relate it to the wrok of other researchers. This is joint work with Ketan Mulmuley.
Frank Sottile (Texas A & M University) New fewnomial upper bounds
Abstract: In 1980, Askold Khovanskii established his fewnomial bound for the number of real solutions to a system of polynomials, showing that the complexity of the set of real solutions to a system of polynomials depends upon the number of monomials and not on the degree. This fundamental finiteness result in real algebraic geometry is believed to be unrealistically large. I will Describe joint work with Frederic Bihan on a new fewnomial bound which is substantially lower than Khovanskii's bound and asymptotically optimal. This bound is obtained by first reducing a given system to a Gale system, and then bounding the number of solutions to a Gale system. Like Khovanskii's bound, this bound is the product of an exponential function and a polynomial in the dimension, with the exponents in both terms depending upon the number of monomials. In our bound, the exponents are smaller than in Khovanskii's.
John Voight (University of Minnesota Twin Cities) Computing zeta functions of sparse, nondegenerate hypersurfaces
Abstract: We discuss the efficient computation of the zeta function of a hypersurface X defined over a finite field k. The zeta function Z(X,T) of X is the exponential generating series for the number of points on X defined over k and its finite extensions; Z(X,T) is a rational function in T. Zeta functions arise naturally in coding theory, arithmetic geometry, complexity theory, and many other areas. We consider the situation when X is affine, toric, or projective, when its defining equation f is nondegenerate (a condition which implies that X is smooth and which holds outside of a codimension 1 subset), and when f is sparse (consisting of few monomials). In this situation, one can use Dwork cohomology to give a very efficient method of computing Z(X,T). We exhibit this method and provide several examples.
Judy L. Walker (University of Nebraska) Pseudocodeword connections
Abstract: The term "pseudocodeword" is used in relationship to decoding linear block codes in at least three different ways. In linear programming decoding (introduced by Feldman), any vertex of the fundamental polytope is called a pseudocodeword. In a rigorous formulation (as first proposed by Wiberg) of min-sum or sum-product decoding, any valid configuration of any computation tree is called a pseudocodeword. And, using a more intuitive interpretation of iterative message-passing decoding, any valid configuration on any finite cover of the Tanner graph corresponds to a pseudocodeword (this is made precise through Graph Cover Decoding, proposed by Vontobel and Koetter). Though some justification of the triple-use of the term has been given, these three notions of pseudocodeword are indeed distinct. In this talk, we will describe the connections and disconnections involved.
Josephine Yu (University of California) IMA postdoc seminar: Tropical implicitization and elimination
Abstract: Implicitization is the problem of computing the defining ideal of the image of a polynomial map, and elimination is the problem of computing the defining ideal of the projection of an algebraic variety. In this talk, I will show how to apply tropical methods to these problems. For generic cases, we can use polyhedral computations to construct the tropical varieties of the unknown ideals without computing the ideal.
Visitors in Residence
Nicolas Addington University of Wisconsin 4/12/2007 - 4/15/2007
Silvia Adduci University of Texas 4/12/2007 - 4/15/2007
Eric Allender Rutgers University 4/16/2007 - 4/20/2007
Elizabeth S. Allman University of Alaska 1/7/2007 - 4/7/2007
Jungha 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
Kapila Rohan Attele Chicago State University 4/12/2007 - 4/15/2007
Saugata Basu Georgia Institute of Technology 4/4/2007 - 6/30/2007
Daniel J. Bates University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Daniel J. Bernstein University of Illinois 4/15/2007 - 4/20/2007
Yermal Sujeet Bhat University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Sara Billey University of Washington 4/13/2007 - 4/14/2007
Víctor Blanco Izquierdo University of Sevilla 1/11/2007 - 4/21/2007
Markus Bläser Universität des Saarlandes 4/15/2007 - 4/21/2007
Stanislav Bulygin TU Kaiserslautern 4/15/2007 - 4/21/2007
Peter Bürgisser Universität-GHS Paderborn 4/11/2007 - 5/18/2007
Philip Robert Busse University of Kentucky 4/15/2007 - 4/20/2007
Eimear Byrne University College Dublin 4/15/2007 - 4/21/2007
Jennifer Chayes Microsoft Research 4/17/2007 - 4/19/2007
Ionut Ciocan-Fontanine University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Aaron Cohen University of Minnesota Twin Cities 4/19/2007 - 4/20/2007
Gerard Cohen École Nationale Supérieure de Télécommunications (ENST) 4/15/2007 - 4/20/2007
David A. Cox Amherst College 4/12/2007 - 4/15/2007
Ruchira Datta University of California 4/15/2007 - 4/21/2007
Rafael Del Valle-Vega University of Puerto Rico 4/15/2007 - 4/21/2007
Giovanni Di Crescenzo Telcordia 4/16/2007 - 4/20/2007
Sandra Di Rocco Royal Institute of Technology (KTH) 4/4/2007 - 6/4/2007
Kenneth R. Driessel Iowa State University 9/1/2006 - 6/29/2007
Vanja Dukic University of Chicago 4/13/2007 - 4/14/2007
Iwan Duursma University of Illinois at Urbana-Champaign 4/15/2007 - 4/20/2007
Jinwoo Eo University of Minnesota Twin Cities 4/14/2007 - 4/20/2007
Makan Fardad University of Minnesota Twin Cities 8/26/2006 - 8/13/2007
Jeffrey Farr Department of Defense 4/16/2007 - 4/20/2007
Ignacio Fernandez Rua University of Oviedo 4/12/2007 - 4/21/2007
Andrei Gabrielov Purdue University 4/15/2007 - 4/21/2007
Jayantha Gan Hewage Oakland University 4/12/2007 - 4/21/2007
Hans Olav Geil Aalborg University 4/14/2007 - 4/21/2007
Tryphon T. Georgiou University of Minnesota Twin Cities 4/17/2007 - 4/17/2007
Marc Giusti École Polytechnique 4/13/2007 - 4/20/2007
Heide Gluesing-Luerssen University of Kentucky 4/15/2007 - 4/21/2007
Leah Gold Cleveland State University 4/15/2007 - 4/20/2007
Elisa Gorla Universität Zürich 4/13/2007 - 4/21/2007
Jason E. Gower University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Venkat Guruswami University of Washington 4/15/2007 - 4/19/2007
Leonid Gurvits Los Alamos National Laboratory 4/15/2007 - 4/20/2007
Michael Hardy University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Ananthnarayan Hariharan University of Kansas 4/12/2007 - 4/15/2007
Gloria Haro Ortega University of Minnesota Twin Cities 9/1/2005 - 4/9/2007
Herwig Hauser Leopold-Franzens Universität Innsbruck 4/12/2007 - 4/15/2007
David Haws University of California 4/12/2007 - 4/14/2007
Milena Hering University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Patricia Hersh Indiana University 2/15/2007 - 5/15/2007
Tom Hoeholdt Technical University of Denmark 4/14/2007 - 4/21/2007
Benjamin J. Howard University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Evelyne Hubert Institut National de Recherche en Informatique Automatique (INRIA) 9/1/2006 - 6/30/2007
Carmelo Interlando San Diego State University 4/14/2007 - 4/21/2007
Farhad Jafari University of Wyoming 9/1/2006 - 6/30/2007
Heeralal Janwa University of Puerto Rico 4/13/2007 - 4/21/2007
Anders Nedergaard Jensen Aarhus University 9/6/2006 - 6/30/2007
Gabriela Jeronimo University of Buenos Aires 4/15/2007 - 6/9/2007
Ben Jordan University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
David Joyner U.S. Naval Academy 4/15/2007 - 4/20/2007
Steve Kaliszewski Arizona State University 1/7/2007 - 6/30/2007
Mordechai Katzman University of Sheffield 1/10/2007 - 5/15/2007
Christine A Kelley Ohio State University 4/15/2007 - 4/21/2007
Michael Kerber Universität Kaiserslautern 2/19/2007 - 5/11/2007
Michael Kettner Georgia Institute of Technology 4/10/2007 - 4/24/2007
Si-Jo Kim Andong National University 4/13/2007 - 4/14/2007
Pascal Koiran École Normale Supérieure de Lyon 4/15/2007 - 4/20/2007
Tamara Gibson Kolda Sandia National Laboratories 4/27/2007 - 4/28/2007
Teresa Krick University of Buenos Aires 4/13/2007 - 4/20/2007
Song-Hwa Kwon University of Minnesota Twin Cities 8/30/2005 - 8/31/2007
V. Lakshmibai Northeastern University 4/15/2007 - 4/20/2007
Joseph M. Landsberg Texas A & M University 4/15/2007 - 4/20/2007
Tanja Lange Technische Universiteit Eindhoven 4/15/2007 - 4/20/2007
Niels Lauritzen Aarhus University 8/28/2006 - 7/10/2007
Grégoire Lecerf Université Versailles/Saint Quentin-en-Yvelines 4/13/2007 - 4/20/2007
Kwankyu Lee Korea Institute for Advanced Study (KIAS) 4/12/2007 - 4/26/2007
Anton Leykin University of Minnesota Twin Cities 8/16/2006 - 8/15/2007
Hstau Y Liao University of Minnesota Twin Cities 9/2/2005 - 8/31/2007
Sergio Lopez-Permouth Ohio University 4/15/2007 - 4/20/2007
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 4/11/2007 - 4/13/2007
Gearoid P. MacSithigh University of Missouri 4/11/2007 - 4/14/2007
Gregorio Malajovich Federal University of Rio de Janeiro 4/15/2007 - 4/27/2007
Guillermo Mantilla Soler University of Wisconsin 4/12/2007 - 4/14/2007
Susan Margulies University of California 4/12/2007 - 4/20/2007
Hannah Markwig University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Thomas Markwig Universität Kaiserslautern 9/1/2006 - 6/30/2007
Klaus Meer Syddansk Universitet (University of Southern Denmark) 4/14/2007 - 4/20/2007
Martin Mereb University of Texas 4/12/2007 - 4/15/2007
Lisa A. Miller University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Abigail Mitchell University of Notre Dame 4/16/2007 - 4/20/2007
Michal Mlejnek Corning 4/12/2007 - 4/15/2007
Richard B. Moeckel University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Jason Morton University of California 4/16/2007 - 4/20/2007
James Murdock Iowa State University 4/12/2007 - 4/15/2007
Dinkar Mylaraswamy Honeywell Systems and Research Center 4/13/2007 - 4/14/2007
Uwe Nagel University of Kentucky 9/1/2006 - 6/1/2007
Jiawang Nie University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Andrew M. Odlyzko University of Minnesota Twin Cities 4/17/2007 - 4/17/2007
Luke Oeding Texas A & M University 4/15/2007 - 4/20/2007
Michael E. O'Sullivan San Diego State University 4/12/2007 - 5/11/2007
Roger Oyono University of Waterloo 4/15/2007 - 4/20/2007
Ekin Ozman University of Wisconsin 4/12/2007 - 4/14/2007
Casian Pantea University of Wisconsin 4/12/2007 - 4/14/2007
Luis Miguel Pardo University of Cantabria 4/15/2007 - 4/22/2007
Ragni Piene University of Oslo 4/11/2007 - 4/15/2007
Fernando Piñero University of Puerto Rico 4/14/2007 - 4/21/2007
Nikki Pitcher University of Illinois 4/15/2007 - 4/21/2007
Vera S. Pless University of Illinois 4/15/2007 - 4/20/2007
Bjorn Poonen University of California 4/15/2007 - 4/21/2007
Bharath Rangarajan University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Patrick Rault University of Wisconsin 4/12/2007 - 4/14/2007
Victor Reiner University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
John A. Rhodes University of Alaska 1/7/2007 - 4/7/2007
Joel Roberts University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Daniel Robertz RWTH Aachen 2/18/2007 - 4/1/2007
Marie Rognes University of Oslo 1/10/2007 - 6/30/2007
J. Maurice Rojas Texas A & M University 4/11/2007 - 6/3/2007
Tim Römer Universität Osnabrück 3/24/2007 - 4/7/2007
Joachim Rosenthal Universität Zürich 4/13/2007 - 4/20/2007
Bjarke Hammersholt Roune Aarhus University 9/12/2006 - 6/30/2007
Diego Ruano Universität Kaiserslautern 4/14/2007 - 4/21/2007
Rakinawasan Sanjeewa Oakland University 4/12/2007 - 4/15/2007
Vishal Saraswat University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Vishal Saraswat University of Minnesota Twin Cities 4/16/2007 - 4/20/2007
Arnd Scheel University of Minnesota Twin Cities 7/15/2004 - 8/31/2007
Claus Scheiderer Universität Konstanz 4/10/2007 - 4/15/2007
Renate Scheidler University of Calgary 4/15/2007 - 4/20/2007
Karl Schmedders Northwestern University 4/12/2007 - 4/14/2007
Chehrzad Shakiban University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Amir Shpilka Technion-Israel Institute of Technology 4/12/2007 - 4/20/2007
Jessica Sidman Mount Holyoke College 4/12/2007 - 4/14/2007
Delphene Simpson University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Donald H. Singley 3M 4/13/2007 - 4/14/2007
Meera Sitharam University of Florida 4/12/2007 - 4/20/2007
Roxana Smarandache San Diego State University 4/15/2007 - 4/22/2007
Milind Sohoni Indian Institute of Technology 4/13/2007 - 5/18/2007
Martin Sombra University of Barcelona 4/15/2007 - 4/22/2007
Frank Sottile Texas A & M University 2/26/2007 - 6/30/2007
Steven Sperber University of Minnesota Twin Cities 9/1/2006 - 6/30/2007
Dumitru Stamate University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Dumitru Stamate University of Minnesota Twin Cities 4/16/2007 - 4/20/2007
Ileana Streinu Smith College 4/12/2007 - 4/20/2007
Bernd Sturmfels University of California 4/13/2007 - 4/17/2007
Madhu Sudan Massachusetts Institute of Technology 4/17/2007 - 4/21/2007
Kathleen Iwancio Thompson North Carolina State University 4/12/2007 - 4/15/2007
Carl Toews University of Minnesota Twin Cities 9/1/2005 - 8/31/2007
Cindy Traub St. Mary's College of Maryland 4/12/2007 - 4/14/2007
Ya-Lun Tsai University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Seyfi Turkelli University of Wisconsin 4/12/2007 - 4/14/2007
John Voight University of Minnesota Twin Cities 8/15/2006 - 8/31/2007
Pascal Olivier Vontobel Hewlett-Packard Laboratories 4/14/2007 - 4/18/2007
Joachim von zur Gathen Rheinische Friedrich-Wilhelms-Universität Bonn 4/15/2007 - 4/21/2007
Nicolai Vorobjov University of Bath 4/15/2007 - 4/21/2007
Judy L. Walker University of Nebraska 4/15/2007 - 4/20/2007
Galbodayage Sujeeva Wijesiri Oakland University 4/12/2007 - 4/14/2007
Troels Windfeldt University of Copenhagen 4/12/2007 - 4/14/2007
Fei Yang University of Minnesota Twin Cities 4/13/2007 - 4/14/2007
Fei Yang University of Minnesota Twin Cities 4/16/2007 - 4/20/2007
Josephine Yu University of California 1/9/2007 - 6/30/2007
Fabrizio Zanello University of Notre Dame 4/12/2007 - 4/15/2007
Hongchao Zhang University of Minnesota Twin Cities 9/1/2006 - 8/31/2007
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
3M, Boeing, Carnegie-Mellon University, 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, Schlumberger-Doll Research, 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