Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall 207 Church Street SE Minneapolis, MN 55455 
20062007 Program
See http://www.ima.umn.edu/20062007 for a full description of the 20062007 program on Applications of Algebraic Geometry.
Opportunities at the IMA  There is still time to apply: If you are interested or know of anyone who is interested in applying for one of the IMA General Membership, New Directions Professorship or Postdoctoral Fellowship positions in connection with the 20072008 thematic program: Mathematics of Molecular and Cellular Biology, the deadline for applying for these positions is January 5, 2007. You can find the applications for these positions at our Applications site.
New Directions Short Course: The IMA is currently accepting applications for the 2007 New Directions Short Course  Compressive Sampling and Frontiers in Signal Processing June 4  15, 2007, taught by Emmanuel Candes, Ron DeVore and Rich Barniuk. This exploding area of research has connections to many areas of mathematics and presents many research opportunities. No prior background in signal processing is expected. Participants will receive full travel and lodging support during the workshop. Participation is by application only. Application deadline: April 1, 2007.
IMA is seeking a new director: The IMA is looking for a new director to begin in summer 2008.
All Day  New Year's Day. The IMA is closed. 
11:15a12:15p  Algebraic geometry and applications seminar: Algorithms in algebraic analysis  Anton Leykin (University of Minnesota Twin Cities)  Lind Hall 409  AGS 
8:00a8:30a  Coffee and Registration  EE/CS 3176  T1.1213.07  
8:30a8:40a  Welcome and opening remarks  Douglas N. Arnold (University of Minnesota Twin Cities)  EE/CS 3180  T1.1213.07 
8:40a9:30a  Gröebner basis methods in integer programming (Lecture Part I)  Edwin O'Shea (University of Kentucky)  EE/CS 3180  T1.1213.07 
9:30a10:00a  Coffee  EE/CS 3176  T1.1213.07  
10:00a10:50a  Hands on exercises assisted by Tristram Bogart (Tutorial Part I)  Edwin O'Shea (University of Kentucky)  Lind Hall 400  T1.1213.07 
11:00a11:50a  Gröebner basis methods in integer programming (Lecture Part II)  Edwin O'Shea (University of Kentucky)  EE/CS 3180  T1.1213.07 
11:50a1:30p  Lunch  T1.1213.07  
1:30p2:20p  Hands on exercises assisted by Tristram Bogart (Tutorial Part II)  Edwin O'Shea (University of Kentucky)  Lind Hall 400  T1.1213.07 
2:20p2:40p  Coffee  EE/CS 3176  T1.1213.07  
2:40p3:30p  Optimization over polynomials with moment matrices and sums of squares
Remarks: (Due to visa problems Monique Laurent was not be able to attend the tutorial.
Jean Bernard Lasserre substituted for Monique Laurent.)
 Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))  EE/CS 3180  T1.1213.07 
3:30p3:50p  Coffee  EE/CS 3176  T1.1213.07  
3:50p4:40p  Optimization over polynomials with moment matrices and sums of squares(continued)  Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))  EE/CS 3180  T1.1213.07 
8:30a9:00a  Coffee  EE/CS 3176  T1.1213.07  
9:00a9:50a  Optimization over polynomials with moment matrices and sums of squares(continued)  Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))  EE/CS 3180  T1.1213.07 
9:50a10:20a  Coffee  EE/CS 3176  T1.1213.07  
10:20a11:10a  Demonstration of software  Hartwig Bosse (Center for Mathematics and Computer Science (CWI))  EE/CS 3180  T1.1213.07 
11:20a12:10p  Generating functions for integer optimization (part I)  Jesus Antonio De Loera (University of California)  EE/CS 3180  T1.1213.07 
12:10p1:30p  Lunch  T1.1213.07  
1:30p2:20p  Generating functions for integer optimization (part I)continued  Jesus Antonio De Loera (University of California)  EE/CS 3180  T1.1213.07 
2:20p2:50p  Coffee  EE/CS 3176  T1.1213.07  
3:00p3:50p  Generating functions for integer optimization (part II)  Jesus Antonio De Loera (University of California)  EE/CS 3180  T1.1213.07 
4:00p5:00p  Demo and introduction to LattE  Jesus Antonio De Loera (University of California)  EE/CS 3180  T1.1213.07 
All Day  Martin Luther King, Jr. holiday (IMA is closed) 
8:30a9:15a  Coffee and Registration  EE/CS 3176  W1.1620.07  
9:15a9:30a  Welcome and Introduction  Douglas N. Arnold (University of Minnesota Twin Cities)  W1.1620.07  
9:30a10:20a  Complexity of multivariate optimization using exact arithmetic  MarieFrancoise Roy (Université de Rennes I)  EE/CS 3180  W1.1620.07 
10:20a11:00a  Coffee  EE/CS 3176  W1.1620.07  
11:00a11:50a  On the Lovasz thetanumber of almost regular graphs with application to ErdosRenyi graphs  Etienne de Klerk (Katholieke Universiteit Brabant (Tilburg University))  EE/CS 3180  W1.1620.07 
11:50a2:00p  Lunch  W1.1620.07  
2:00p2:50p  Optimization of polynomials on the unit sphere  Alexander Barvinok (University of Michigan)  EE/CS 3180  W1.1620.07 
3:00p3:30p  Second Chances  EE/CS 3180  W1.1620.07  
3:40p4:00p  Group photos  W1.1620.07  
4:00p6:30p  IMA Reception and Poster Session  Lind Hall 400  W1.1620.07  
Recent progress in applying semidefinite optimization to the satisfiability problem  Miguel F. Anjos (University of Waterloo)  
Solving polynomial systems via LMIs  Graziano Chesi (University of Hong Kong)  
Computing the best low rank approximation of a matrix  Kenneth R. Driessel (Iowa State University)  
Obstaclesensitive gain scheduling using semidefinite programming  Eric Feron (Georgia Institute of Technology)  
Application of semidefinite programming to eigenvalue problems for elliptic linear partial differential equations  Carlos R. Handy (Texas Southern University)  
Experiments with linear and semidefinite relaxations for solving the minimum graph bisection problem  Christoph Helmberg (Technische Universität ChemnitzZwickau)  
Advances on the BMV trace conjecture  Christopher Hillar (Texas A & M University)  
Graphs of transportation polytopes  Edward D. Kim (University of California)  
SparsePOP and numerical results  Sunyoung Kim (Ewha Womans University)  
Inverse dynamical analysis of gene networks using sparsitypromoting regularization  James Lu (Johann Radon Institute for Computational and Applied Mathematics )  
An exact characterization of bad semidefinite programs  Gabor Pataki (University of North Carolina)  
Distributed optimization in an energyconstrained network  Seid Alireza Razavi Majomard (University of Minnesota Twin Cities)  
Semidefinite characterization and computation of real radical ideals  Philipp Rostalski (Eidgenössische TH ZürichHönggerberg)  
A PARALLEL conic interior point decomposition approach for BLOCK ANGULAR semidefinite programs  Kartik K. Sivaramakrishnan (North Carolina State University)  
Stability region analysis using simulations and sumofsquares programming  Ufuk Topcu (University of California)  
Sensor network localization, Euclidean distance matrix completions, and graph realization  Henry Wolkowicz (University of Waterloo)  
SeDuMi: a package for conic optimization  Yuriy Zinchenko (McMaster University)  
Numerical optimization assisted by noncommutative symbolic algebra  Mauricio de Oliveira (University of California, San Diego) 
9:00a9:30a  Coffee  EE/CS 3176  W1.1620.07  
9:30a10:20a  Complexity aspects of SDP relaxations of polynomial optimization problems  Markus Schweighofer (Universität Konstanz)  EE/CS 3180  W1.1620.07 
10:20a11:00a  Coffee  EE/CS 3176  W1.1620.07  
11:00a11:50a  Coprime factorizations and reduction of linear parametervarying systems  Carolyn Beck (University of Illinois at UrbanaChampaign)  EE/CS 3180  W1.1620.07 
11:50a1:40p  Lunch  W1.1620.07  
1:40p2:30p  Conservative structured noncommutative multidimensional linear systems: realization theory and bounded real lemma  Joseph A. Ball (Virginia Polytechnic Institute and State University)  EE/CS 3180  W1.1620.07 
2:30p3:00p  Coffee  EE/CS 3176  W1.1620.07  
3:00p3:50p  Matrix convexity, matrix inequalities, and beyond  Scott McCullough (University of Florida)  EE/CS 3180  W1.1620.07 
4:00p4:30p  Second Chances  EE/CS 3180  W1.1620.07  
6:30p8:30p  Group Dinner  Kikugawa at Riverplace
(Japanese Restaurant) 43 Main Street SE Minneapolis MN 55414 6123783006 
W1.1620.07 
9:00a9:30a  Coffee  EE/CS 3176  W1.1620.07  
9:30a10:30a  The algebraic degree of semidefinite programming  Bernd Sturmfels (University of California)  EE/CS 3180  W1.1620.07 
10:20a11:00a  Coffee  EE/CS 3176  W1.1620.07  
11:00a11:50a  Sharp thresholds for sparsity recovery in the highdimensional and noisy setting using l_1 relaxations  Martin J. Wainwright (University of California)  EE/CS 3180  W1.1620.07 
11:50a1:40p  Lunch  W1.1620.07  
1:40p2:30p  Sums of squares, gradient ideals, and optimization  Victoria Powers (Emory University)  EE/CS 3180  W1.1620.07 
2:30p3:00p  Coffee  EE/CS 3176  W1.1620.07  
3:00p3:50p  Polynomial optimal control with GloptiPoly 3.0  Didier Henrion (Centre National de la Recherche Scientifique (CNRS))  EE/CS 3180  W1.1620.07 
4:00p4:30p  Second Chances  EE/CS 3180  W1.1620.07  
5:00p6:30p  Reception  Lind Hall 400  W1.1620.07  
7:00p8:00p  Math matters  IMA public lecture: Making sense of a complex world  Christopher J. Budd (University of Bath)  Willey Hall 125  PUB1.18.07 
7:00p8:00p  Math matters  IMA public lecture: Making sense of a complex world  Christopher J. Budd (University of Bath)  Willey Hall 125  W1.1620.07 
9:00a9:30a  Coffee  EE/CS 3176  W1.1620.07  
9:30a10:20a  Estimation of sparse graphical models  Laurent El Ghaoui (University of California)  EE/CS 3180  W1.1620.07 
10:20a11:00a  Coffee  EE/CS 3176  W1.1620.07  
11:00a11:50a  Discrete optimization under moment uncertainty: complexity, persistency and asymptotics  Dimitris Bertsimas (Massachusetts Institute of Technology)  EE/CS 3180  W1.1620.07 
11:50a2:30p  Lunch  W1.1620.07  
2:30p3:20p  LMI representation of convex sets  Victor Vinnikov (Ben Gurion University of the Negev)  EE/CS 3180  W1.1620.07 
3:30p4:00p  Second Chances  EE/CS 3180  W1.1620.07 
9:00a9:30a  Coffee  EE/CS 3176  W1.1620.07  
9:30a10:20a  Sparsity in polynomial optimization  Masakazu Kojima (Tokyo Institute of Technology)  EE/CS 3180  W1.1620.07 
10:20a11:00a  Coffee  EE/CS 3176  W1.1620.07  
11:00a11:50a  Approximation of positive polynomials by sums of squares  Salma Kuhlmann (University of Saskatchewan)  EE/CS 3180  W1.1620.07 
11:50a2:30p  Lunch  W1.1620.07  
2:30p3:20p  Convex sets with lifted semidefinite representation  Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))  EE/CS 3180  W1.1620.07 
3:30p4:00p  Second Chances and closing remarks  EE/CS 3180  W1.1620.07 
11:15a12:15p  IMA postdoc seminar: On the quality bound of low order SOS relaxations  Jiawang Nie (University of Minnesota Twin Cities)  Lind Hall 409  PS 
11:15a12:15p  Algebraic geometry and applications seminar: Moments of positivity  Mihai Putinar (University of California)  Lind Hall 409  AGS 
11:15a12:15p  Real algebraic geometry tutorial: Semialgebraic sets and functions  Kenneth R. Driessel (Iowa State University)  Lind Hall 409  RAG 
1:25p2:25p  IMA/MCIM Industrial problems seminar: A compact high power singlemode microstructured fiber laser  Arash Mafi (Corning)  Vincent Hall 1  IPS 
11:15a12:15p  IMA postdoc seminar: Syzygies of toric varieties  Milena Hering (University of Minnesota Twin Cities)  Lind Hall 409  PS 
11:15a12:05p  Algebraic geometry and applications seminar: "SDP and LPrelaxations in polynomial optimization: The power of real algebraic geometry"  Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))  Lind Hall 229  AGS 
Event Legend: 

AGS  Algebraic Geometry and Applications Seminar 
IPS  Industrial Problems Seminar 
PS  IMA Postdoc Seminar 
PUB1.18.07  Dr. Christopher J. Budd 
RAG  Weekly Tutorial: Real Algebraic Geometry 
T1.1213.07  Algebraic Algorithms in Optimization 
W1.1620.07  Optimization and Control 
Second Chances  
Abstract: No Abstract  
Miguel F. Anjos (University of Waterloo)  Recent progress in applying semidefinite optimization to the satisfiability problem 
Abstract: Extending the work of de Klerk, Warners and van Maaren, we propose new semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. The SDP relaxations are partial liftings motivated by the Lasserre hierarchy of SDP relaxations for 01 optimization problems. Theoretical and computational results show that these relaxations have a number of favourable properties, particularly as a means to prove that a given SAT formula is unsatisfiable, and that this approach compares favourably with existing techniques for SAT.  
Joseph A. Ball (Virginia Polytechnic Institute and State University)  Conservative structured noncommutative multidimensional linear systems: realization theory and bounded real lemma 
Abstract: By a noncommutative multidimensional linear system we mean a linear discretetime input/state/output system with evolution along a finitely generated free semigroup. A formal Ztransform of the inputoutput map results in a transfer function equal to a formal power series in noncommuting indeterminates with operator (or matrix) coefficients. If one imposes energybalance inequalities and additional structure to the system equations, the resulting transfer function is a formal power series with the additional structure of interest for analyzing the robust control problem for a plant with linearfractionalmodeled timevarying structured uncertainty. The Bounded Real Lemma for such systems is closely connected with work of Paganini on the robust control of such systems. An abelianization of the system equations leads to systems with evolution along a multidimensional integer lattice with transfer function equal to a linearfractional expression in several commuting variables of GivonRoesser, FornasiniMarchesini or other structured types. Connections with the automata theory of Schuetzenberger, Fliess, Eilenberg and others from the 1960s will also be discussed. This talk reports on joint work of the speaker with Tanit Malakorn (Naresuan University, Thailand) and Gilbert Groenewald (North West University, South Africa).  
Alexander Barvinok (University of Michigan)  Optimization of polynomials on the unit sphere 
Abstract: We consider the problem of computing the maximum absolute value of a real multivariate polynomial on the unit sphere. We identify a class of polynomials for which the problem admits a randomized polynomial time approximation algorithm consisting in computing the maximum absolute value of the restriction of the polynomial onto a random subspace of logarithmic dimension and scaling the result. The characteristic feature of polynomials admitting such an algorithm is that they are "focused": the ratio of their maximum absolute value and the L^{2} norm is large.  
Carolyn Beck (University of Illinois at UrbanaChampaign)  Coprime factorizations and reduction of linear parametervarying systems 
Abstract: We present a complete derivation of coprime factorizations for a class of multidimensional systems containing linear parametervarying and uncertain systems. A generalization of coprime factors model reduction using a balanced truncation approach is then given, with error bounds on the factorized mapping in the l2induced norm. The proposed reduction method is thus applicable to linear parametervarying and uncertain systems that do not satisfy the usual l2induced stability constraint required by the standard nonfactored truncation methods.  
Dimitris Bertsimas (Massachusetts Institute of Technology)  Discrete optimization under moment uncertainty: complexity, persistency and asymptotics 
Abstract: We address the problem of evaluating the expected optimal objective value of a discrete optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distributional information for the objective coefficients in the form of moments. We show that for a fairly general class of marginal information, a tight upper (lower) bound on the expected optimal objective value of a discrete maximization (minimization) problem can be computed in polynomial time if the corresponding deterministic discrete optimization problem is solvable in polynomial time. We provide an efficiently solvable semidefinite programming formulation to compute this tight bound. We use the insights from this analysis to: a) understand the percistency of a decision variable, i.e., the probability that it is part of an optimal solution; for instance, in project scheduling, when the task activity times are random, the challenge is to determine a set of critical activities that will potentially lie on the longest path; b) to analyze the asymptotic behavior of a general class of combinatorial problems that includes the linear assignment, spanning tree and traveling salesman problems, under knowledge of complete marginal distributions, with and without independence. We calculate the limiting constants exactly. (joint work with Karthik Natarajan and Chung Piaw Teo)  
Hartwig Bosse (Center for Mathematics and Computer Science (CWI))  Demonstration of software 
Abstract: No Abstract  
Christopher J. Budd (University of Bath)  Math matters  IMA public lecture: Making sense of a complex world 
Abstract: The world around us often seems terribly complex, chaotic and difficult to understand. We encounter this every day: in the weather, social networks, sophisticated machinery, the internet. Frequently this complexity arises from the interaction of widely diverse scales in time and space. For example, the weather can turn in minutes, while the climate persists for many many years. Can math and science help us to make sense of all this complexity, or is it a study doomed from the start? Illustrating with many examples, Professor Budd will show that all is not lost. He will explain how simple properties often emerge from seemingly very complex systems, and how we can use these properties to gain understanding.  
Graziano Chesi (University of Hong Kong)  Solving polynomial systems via LMIs 
Abstract: Joint work with Y.S. Hung. The problem of computing the solution of systems of polynomial equalities and inequalities is considered. First, it is shown that the solutions of these systems can be found by looking for vectors with polynomial structure in linear spaces obtained via a convex LMI optimization. Then, it is shown that an upper bound to the dimension of the linear spaces where the sought solutions are looked for can be imposed in a nonconservative way by imposing suitable linear matricial constraints. This allows one to obtain the linear spaces with the smallest dimension, which is important because the solutions can be extracted only if the dimension of the linear spaces is smaller than a certain threshold. Moreover, the proposed approach allows one to improve the numerical accuracy of the extraction mechanism.  
Jesus Antonio De Loera (University of California)  Demo and introduction to LattE 
Abstract: No Abstract  
Kenneth R. Driessel (Iowa State University)  Computing the best low rank approximation of a matrix 
Abstract: Consider the following Problem: Given an mbyn real matrix A and a positive integer k, find the mbyn matrix with rank k that is closest to A. (I use the Frobenius inner product.) I shall present a rankpreserving differential equation (d.e.) in the space of mbyn real matrices which solves this problem. In particular, I shall show that if X(t) is a solution of this d.e. then the distance between X(t) and A decreases; in other words, this distance function is a Lyapunov function for the d.e. I shall also show that (generically) this d.e. converges to a unique stable equilibrium point. This point is the solution of the given problem.  
Laurent El Ghaoui (University of California)  Estimation of sparse graphical models 
Abstract: The graphical model formalism allows to describe multivariate probability distributions using a graph where random variables are represented by nodes, and the absence of an edge corresponds to conditional independence. While this formalism is very general, the corresponding maximumlikelihood problem is often challenging numerically. In addition, one often needs to obtain a graph that is sparse, in order to enhance interpretability of the result. In this talk, we examine the problem where loglikelihood function is penalized by an lone norm term to encourage sparsity, in two special cases,first for Gaussian then for Boolean variables. In the Gaussian case, we discuss firstorder methods and a block coordinate descent algorithm. For Boolean random variables, the problem is NPhard, due to an exponential number of terms in the loglikelihood function. We discuss two approximations, one based on Wainwright and Jordan's log determinant approximation (2005), and another based on lifting and rank relaxation.  
Eric Feron (Georgia Institute of Technology)  Obstaclesensitive gain scheduling using semidefinite programming 
Abstract: Joint work with Mazen Farhood. We present an application of semidefinite programming techniques to the regulation of vehicle trajectories in the vicinity of obstacles. We design control laws, together with Lyapunov functions that guarantee closedloop stability and performance of the vehicle's regulation loop. These control laws are easy to implement and automatically "relax the system's gains" when away from the obstacles, while tightening them when obstacle proximity is detected.  
Carlos R. Handy (Texas Southern University)  Application of semidefinite programming to eigenvalue problems for elliptic linear partial differential equations 
Abstract: The calculation of eigenvalues for stiff elliptic linear
partial differential equations (LPDEs) can be plagued with
significant inaccuracies depending on the "estimation" methods
used (i.e. variational, finite differencing, asymptotic
analysis, perturbative, Galerkin, etc.). A preferred approach
is to be able to generate tight, converging lower and upper
bounds to the eigenvalues, thereby removing any uncertainties
in the reliability of the generated results. Twenty years ago
one such method was developed by Handy, Bessis, and coworkers
[13]. This general approach is referred to as the Eigenvalue
Moment Method (EMM) and involves a Semidefinite Programming
formalism coupled with a Linear Programming based “Cutting
Algorithm.” It makes use of well known nonnegativity properties
of SturmLiouville type systems combined with important
theorems from the classic Moment Problem. The EMM procedure has
been used to solve a variety of LPDEs on various support spaces
(i.e. unbounded, semibounded, bounded, periodic, discrete).
Equivalent gradient search variational reformulations,
exploiting higher levels of convexity, have also been developed
leading to the Volcano Function representation [4]. It is also
possible to extend EMM to certain nonhermitian systems of
importance in forefront areas in mathematical physics. Here
too, the EMM approach can yield converging lower and upper
bounds to the real and imaginary parts of the complex
eigenvalues (or other physical parameters) [5]. More recently
EMM was broadened (exploiting certain quasiconvexity
properties and the generalized eigenvlaue problem) in order to
convexify a multiextrema plagued procedure in mathematical
physics [6]. We outline the important EMM results achieved over
the last two decades.
1. C. R. Handy and D. Bessis, "Rapidly Convergent Lower Bounds
for the Schrodinger Equation Ground State Energy," Phys. Rev.
Lett. 55, 931 (1985).
2. C. R. Handy, D. Bessis, and T. R. Morley, "Generating Quantum Energy Bounds by the Moment Method: A Linear Programming Approach," Phys. Rev. A 37, 4557 (1988). 3. C. R. Handy, D. Bessis, G. Sigismondi, and T. D. Morley, "Rapidly Converging Bounds for the Ground State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields," Phys. Rev. Lett. 60, 253 (1988). 4. C. R. Handy, K. Appiah, and D. Bessis "MomentProblem Formulation of a Minimax Quantization Procedure", Phys. Rev. A 50, 988 (1994). 5. C. R. Handy, "Generating Converging Bounds to the (Complex) Discrete States of the P^{2} + iX^{3} + iaX Hamiltonian," J. Phys. A: Math. Gen. 34, 5065 (2001). 6. C. R. Handy “(Quasi)convexification of Barta’s (multiextrema) bounding theorem," J. Phys. A: Math. Gen. 39, 3425 (2006) 

Christoph Helmberg (Technische Universität ChemnitzZwickau)  Experiments with linear and semidefinite relaxations for solving the minimum graph bisection problem 
Abstract: Given a graph with node weights, the convex hull of the incidence vectors of all cuts satisfying a weight restricition on each side is called the bisection cut polytope. We study the facial structure of this polytope which shows up in many graph partitioning problems with applications in VLSIdesign or frequency assignment. We give necessary and in some cases sufficient conditions for the knapsack tree inequalities introduced in Ferreira et al. 1996 to be facetdefining. We extend these inequalities to a richer class by exploiting that each cut intersects each cycle in an even number of edges. Furthermore, we present a new class of inequalities that are based on nonconnected substructures yielding nonlinear righthand sides. We show that the supporting hyperplanes of the convex envelope of this nonlinear function correspond to the faces of the socalled cluster weight polytope, for which we give a complete description under certain conditions. Finally, we incorporate cutting planes algorithms based on the presened inequalities in a branchandcut framework and discuss their interaction with the linear and semidefinite relaxation.  
Didier Henrion (Centre National de la Recherche Scientifique (CNRS))  Polynomial optimal control with GloptiPoly 3.0 
Abstract: Joint work by JeanBernard Lasserre, Johan Löfberg, Christophe Prieur and Emmanuel Trélat. The new release 3.0 of the Matlab package GloptiPoly is introduced through an application to a class of nonlinear optimal control problems for which the data (differential equations, state and control constraints, cost) are multivariate polynomials. GloptiPoly 3.0 is aimed at solving generalized moment problems. It allows to manipulate several measures and define linear decision problems on their moments. The problems can then be solved numerically with any semidefinite programming solver interfaced with YALMIP.  
Milena Hering (University of Minnesota Twin Cities)  IMA postdoc seminar: Syzygies of toric varieties 
Abstract: Understanding the equations defining algebraic varieties and the relations, or syzygies, between them is a classical problem in algebraic geometry. Green showed that sufficient powers of ample line bundles induce a projectively normal embedding that is cut out by quadratic equations and whose first q syzygies are linear. In this talk I will present numerical criteria for line bundles on toric varieties to satisfy this property. I will also discuss criteria for the coordinate ring of such an embedding to be Koszul.  
Christopher Hillar (Texas A & M University)  Advances on the BMV trace conjecture 
Abstract: We discuss some progress on a longstanding conjecture in
mathematical physics due to Bessis, Moussa, and Villani (1975). The
statement is enticingly simple (thanks to a reformulation by Elliot Lieb
and Robert Seiringer): For every positive integer m and every pair of
positive semidefinite matrices A and B, the polynomial
p(t) = Tr[(A+tB)^{m}] has nonnegative coefficients. Our approach allows for several reductions to this difficult conjecture. For instance, it would be enough to show that a nonzero (matrix) coefficient (A+tB)^{m} has at least 1 positive eigenvalue. Additionally, if the conjecture is true for infinitely many m, then it is true for all m. Finally, two challenges to the SOS community are proposed: Prove the conjecture in dimension 3 for m = 6 (known) and m = 7 (unknown). 

Edward D. Kim (University of California)  Graphs of transportation polytopes 
Abstract: Joint work with Jesus A. de Loera (University of California, Davis). Transportation polytopes are wellknown objects in operations reseach and mathematical programming. These polytopes have very quick tests for feasiblity, coordinates of a vertex can be quickly determined, and they have nice embedding properties: every polytope can be viewed as a certain kind of transportation polytope. Using the notion of chamber complex, Gale diagrams, and the theory of secondary polytopes we are able to exhaustively and systematically enumerate all combinatorial types of nondegenerate transportation polytopes of small sizes. These generic polytopes (those of maximal dimension whose vertices are simple) will have the largest graph diameters and vertex counts in their class. Using our exhaustive lists, we give results on some of the conjectures of Yemelichev, Kovalev, and Kratsov. In particular, this poster focuses on questions related to the 1skeleton graph of these polyhedra. The study of 1skeleta of these polytopes are fundamental in attempting to consider the complexity of the simplex method of linear programming.  
Sunyoung Kim (Ewha Womans University)  SparsePOP and numerical results 
Abstract: SparesPOP is MATLAB implementation of a sparse semidefinite programming (SDP) relaxation method proposed for polynomial optimization problems (POPs) in the recent paper by Waki, Kim, Kojima and Muramatsu. The sparse SDP relaxation is based on "a hierarchy of LMI relaxations of increasing dimensions" by Lasserre, and exploits a sparsity structure of polynomials in POPs. The efficiency of SparsePOP to compute bounds for optimal values of POPs is increased and larger scale POPs can be handled. Numerical results are shown to illustrate the perfomance of SparsePOP.  
Masakazu Kojima (Tokyo Institute of Technology)  Sparsity in polynomial optimization 
Abstract: A polynomial optimization problem (POP) is a problem of minimizing a polynomial objective function subject to polynomial equalities and inequalities. It is getting popular to apply the sum of squares (SOS) relaxation to compute global minimum solutions of a POP. The SOS relaxation problem is reduced to a semidefinite programming problem (SDP), which we can solve by applying the primaldual interiorpoint method. In this process, exploiting sparsity is essential in solving a largescale POP. We present "correlative sparsity," a certain structured sparsity of a POP which is characterized as a sparse Cholesky factorization of an aggregated sparsity pattern matrix of the POP. With this correlative sparsity, we can apply the sparse SOS relaxation to a largescale POP, and we can solve the resulting SDP efficiently by the primaldual interiorpoint method. We also discuss some applications.  
Salma Kuhlmann (University of Saskatchewan)  Approximation of positive polynomials by sums of squares 
Abstract: Approximation of positive polynomials by sums of squares has important applications to polynomial optimisation. In this talk, I will survey the main recent results achieved on that topic: I will consider positive (respectively, nonnegative) polynomials on compact (respectively, unbounded) semialgebraic sets. I will discuss representations in the associated preorderings (respectively, linear representations in the associated quadratic module). The representation often depends on the dimension of the semialgebraic set; I will present stronger results in the low dimensional case. I will also highlight special representations when the positive polynomials under consideration are sparse (that is, satisfy some separation and overlap conditions on the variables appearing in the monomials).  
Jean Bernard Lasserre (Centre National de la Recherche Scientifique (CNRS))  Algebraic geometry and applications seminar: "SDP and LPrelaxations in polynomial optimization: The power of real algebraic geometry" 
Abstract: Summary: In this seminar we consider the general polynomial optimization problem: that is, finding the GLOBAL minimum of a polynomial over a compact basic semialgebraic set, a NPhard problem. We will describe how powerful representation results in real algebraic geometry are exploited to build up a hierarchy of linear or semidefinite programming (LP or SDP) relaxations, whose monotone sequence of optimal values converges to the desired value. A comparison with the usual KuhnTucker local optimality conditions is also discussed.  
Anton Leykin (University of Minnesota Twin Cities)  Algebraic geometry and applications seminar: Algorithms in algebraic analysis 
Abstract: In the first part of this talk I will give an introduction to the algorithmic theory of Dmodules. This would include the description of the properties of the rings of differential operators, in particular, the ones that allow for computation of Gröbner bases. The second part will show the applications of Dmodules to the computation of local cohomology of a polynomial ring at a given ideal. The nonvanishing of the local cohomology module of a certain degree may answer the question about the minimal number of generators for the ideal. The presentation is going to be accompanied by the demonstration of the relevant computations in the Dmodules for Macaulay 2 package.  
James Lu (Johann Radon Institute for Computational and Applied Mathematics )  Inverse dynamical analysis of gene networks using sparsitypromoting regularization 
Abstract: Given an ODE model for a biological system, the forward problem consists of
determining its solution behavior. However, many biological questions are of
the inverse type: what are the possible dynamics that can arise out of the
model? how is the control mechanism encoded in the topology of the regulatory
network?
We propose inverse dynamical analysis as a methodology for addressing various
questions that arise in studying biological systems, from the initial
modelling to the proposal of new experiments. In addition, once a
satisfactory model has been developed, the method can be used to design
various bifurcation phenotypes that exhibit certain dynamical properties. To
summarize, the proposed methodology consists of the following two inverse
analyses:


Arash Mafi (Corning)  IMA/MCIM Industrial problems seminar: A compact high power singlemode microstructured fiber laser 
Abstract: We will discuss the design and fabrication of a compact, high power, singlemode, microstructured (photonic crystal) fiber laser. A low index core (antiguiding) assisted by the geometry of the microstructure is used to maximize the core size while maintaining the number of propagating modes. Beam quality factor (M^{2}) is studied for these fibers and is successfully used as a design tool. Some design concepts for scaling up the power using singlesupermode multicore microstructure fibers will also be discussed.  
Scott McCullough (University of Florida)  Matrix convexity, matrix inequalities, and beyond 
Abstract: Many ideas from convex analysis and real algebraic geometry extend canonically to the operator space setting giving rise to the notions of matrix (noncommutative) convex sets and functions. These notions also model matrix inequalities which are scalable in the sense that they do not explicitly depend upon the size of the matrices involved. This talk will survey matrix convexity emphasizing the rigid nature of convexity in the noncommutative semialgebraic setting. It may aslo include a discussion of characterizing factorizations of a noncommutative polynomial in terms of the signature of its Hessian.  
Edwin O'Shea (University of Kentucky)  Hands on exercises assisted by Tristram Bogart (Tutorial Part II) 
Abstract: No Abstract  
Gabor Pataki (University of North Carolina)  An exact characterization of bad semidefinite programs 
Abstract: SDP's duality theory has been somewhat less well studied than its algorithmic aspects. Strong duality, — expected in linear programming fails in many cases, and the variety of how things can go wrong is bewildering: one can have nonattainment in either one of the primal and the dual problems, attainment on both sides, but a finite duality gap, etc. The main result we present in this talk is a surprisingly simple, exact, "excluded minor" type characterization of all semidefinite systems that have a badly behaved dual for some objective function. The characterization is based on some new, fundamental results in convex analysis on the closedness of the linear image of a closed convex cone. In particular, our result is a necessary condition for the closedness of the linear image — as opposed to the usual sufficient conditions, such as the existence of a Slaterpoint, or polyhedrality. Our conditions are necessary and sufficient, when the cone belongs to a large class, called nice cones.  
Victoria Powers (Emory University)  Sums of squares, gradient ideals, and optimization 
Abstract: We discuss algorithms for optimizing polynomials on semialgebraic sets using representation theorems from real algebraic geometry for positive polynomials. In the case of compact semialgebraic sets, the method of Lasserre generates a sequence of SDP relaxations which converge to the solution, however this method does not always work in the noncompact case. We will discuss work of Demmel, Nie, and Sturmfels in the global case and joint work with Demmel and Nie in the case of noncompact semialgebraic sets.  
Mihai Putinar (University of California)  Algebraic geometry and applications seminar: Moments of positivity 
Abstract: The seminar will offer an unifying overview of the
theory
of positive functionals, the spectral theorem, moment
problems and
polynomial optimization. We will treat only the commutative
case, in the
following order:
1. The integral
2. Positive definite quadratic forms and the spectral
theorem
3. Orhtogonal polynomials and Jacobi matrices
4. Moment problems and continued fractions
5. Polynomial optimization
6. Open questions
We encourage the participants to have a look at Stieltjes'
classical memoir on continued fractions, available at:


Seid Alireza Razavi Majomard (University of Minnesota Twin Cities)  Distributed optimization in an energyconstrained network 
Abstract: We consider a distributed optimization problem whereby two nodes S1 and S2 wish to jointly minimize a common convex quadratic cost function f(x1; x2), subject to separate local constraints on x1 and x2, respectively. Suppose that node S1 has control of variable x1 only and node S2 has control of variable x2 only. The two nodes locally update their respective variables and periodically exchange their values over a noisy channel. Previous studies of this problem have mainly focused on the convergence issue and the analysis of convergence rate. In this work, we focus on the communication energy and study its impact on convergence. In particular, we consider a class of distributed stochastic gradient type algorithms implemented using certain linear analog messaging schemes. We study the minimum amount of communication energy required for the two nodes to compute an epsilonminimizer of f(x1; x2) in the mean square sense. Our analysis shows that the communication energy must grow at least at the rate of (1/epsilon). We also derive specific designs, which attain this minimum energy bound, and provide simulation results that confirm our theoretical analysis. Extension to the multiple node case is described.  
Philipp Rostalski (Eidgenössische TH ZürichHönggerberg)  Semidefinite characterization and computation of real radical ideals 
Abstract: Joint work with J.B. Lasserre and M. Laurent. For an ideal given by a set of generators, h_1...h_m \in R[x] a new semidefinite characterization of its real radical ideal I(V_R(I))is presented, provided it is zerodimensional (even if I is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety V_R=V(I) \subset R^n as well as generators of the real radical ideal. The latter are obtained in the form of border or Gröbner bases. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.  
MarieFrancoise Roy (Université de Rennes I)  Complexity of multivariate optimization using exact arithmetic 
Abstract: Global optimization of polynomial functions under polynomial constraints will be related to general algorithmic problems in real algebraic geometry and the current existing complexity results discussed. The results in the special case of quadratic polynomials will be described. Main reference for the talk: S. Basu, R. Pollack, M.F. Roy: Algorithms in real algebraic geometry, Springer, second edition (2006)  
Markus Schweighofer (Universität Konstanz)  Complexity aspects of SDP relaxations of polynomial optimization problems 
Abstract: We discuss complexity aspects of Lasserre's sequence
of SDP relaxations of a given
polynomial optimization problem. As a special example where a
lot is known, we
consider the MAXCUT problem. The following topics should be
covered:  the moment problem and convergence to unique minimizers,  speed of convergence to the optimal value,  Scheiderers result on stability and the moment problem,  the approximability result of Goemans and Williamson for MAXCUT, and  the inapproximability result of Khot, Kindler, Mossel and O'Donnell for MAXCUT. 

Kartik K. Sivaramakrishnan (North Carolina State University)  A PARALLEL conic interior point decomposition approach for BLOCK ANGULAR semidefinite programs 
Abstract: Semidefinite programs (SDPs) with a BLOCKANGULAR structure occur routinely in practice. In some cases, it is also possible to exploit the SPARSITY and SYMMETRY in an unstructured SDP, and preprocess it into an equivalent SDP with a blockangular structure. We present a PARALLEL CONIC INTERIOR POINT DECOMPOSITION approach to solve blockangular SDPs. Our aim is to solve such a SDP in an iterative fashion between a master problem (a quadratic conic program); and decomposed and distributed subproblems (smaller SDPs) in a parallel computing environment. We present our computational results with the algorithm on several test instances; our computations were performed on the distributed HENRY2 cluster at North Carolina State University.  
Bernd Sturmfels (University of California)  The algebraic degree of semidefinite programming 
Abstract: Given a semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices. We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes. This is a joint paper with Jiawang Nie and Kristian Ranestad, posted at rxiv.org/abs/math.OC/0611562.  
Ufuk Topcu (University of California)  Stability region analysis using simulations and sumofsquares programming 
Abstract: The problem of computing bounds on the regionofattraction for systems with polynomial vector fields is considered. Invariant subsets of the regionofattraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates are assessed solving linear sumofsquares optimization problems. Qualified candidates are used to compute invariant subsets of the regionofattraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on several small examples from the literature and a controlled aircraft dynamics problem.  
Victor Vinnikov (Ben Gurion University of the Negev)  LMI representation of convex sets 
Abstract: I will discuss the characterization of convex sets in ^{m} which can be represented by Linear Matrix Inequalities, i.e., as feasible sets of semidefinite programmes. There is a simple necessary condition, called rigid convexity, which has been shown to be sufficient for sets in the plane and is conjectured to be sufficient (in a somewhat weakened sense) for any m. This should be contrasted with the situation for matrix convex sets that will feature in the talk of Scott McCullough, where all the available evidence suggests that any matrix convex set with noncommutative algebraic boundary admits an LMI representation. This is a joint work with Bill Helton.  
Martin J. Wainwright (University of California)  Sharp thresholds for sparsity recovery in the highdimensional and noisy setting using l_1 relaxations 
Abstract: The problem of recovering the sparsity pattern of an unknown signal arises in various domains, including graphical model selection, signal denoising, constructive approximation, compressive sensing, and subset selection in regression. The standard optimizationtheoretic formulation of sparsity recovery involves l_0constraints, and typically leads to computationally intractable optimization problems. This difficulty motivates the development and analysis of approximate methods; in particular, a great deal of work over the past decade has focused on the use of convex l_1relaxations for sparsity recovery. In this work, we analyze the performance of l_1constrained quadratic programming for recovering an unknown signal in p dimensions with at most s nonzero entries based on a set of n noisy observations. Of interest is the number of observations n that are required, as a function of the model dimension p and sparsity index s, for exact sparsity recovery. We analyze this question in the highdimensional setting, in which both the model dimension p and number of observations n tend to infinity. Our main result is to establish, for a broad class of Gaussian measurement ensembles, precise threshold results on the required growth rate for successful recovery using the computationally tractable l_1 relaxation.  
Henry Wolkowicz (University of Waterloo)  Sensor network localization, Euclidean distance matrix completions, and graph realization 
Abstract: We study Semidefinite Programming, SDP, relaxations for Sensor Network Localization, SNL, with anchors and with noisy distance information. The main point of the paper is to view SNL as a (nearest) Euclidean Distance Matrix, EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular SDP relaxation is equivalent to known relaxations in the literature for EDM completions. The existence of anchors in the problem is not special. The set of anchors simply corresponds to a given fixed clique for the graph of the EDM problem. We next propose a method of projection when a large clique or a dense subgraph is identified in the underlying graph. This projection reduces the size, and improves the stability, of the relaxation. In addition, viewing the problem as an EDM completion problem yields better low rank approximations for the low dimensional realizations. And, the projection/reduction procedure can be repeated for other given cliques of sensors or for sets of sensors, where many distances are known. Thus, further size reduction can be obtained. Optimality/duality conditions and a primaldual interiorexterior path following algorithm are derived for the SDP relaxations We discuss the relative stability and strength of two formulations and the corresponding algorithms that are used. In particular, we show that the quadratic formulation arising from the SDP relaxation is better conditioned than the linearized form, that is used in the literature and that arises from applying a Schur complement.  
Yuriy Zinchenko (McMaster University)  SeDuMi: a package for conic optimization 
Abstract: No Abstract  
Etienne de Klerk (Katholieke Universiteit Brabant (Tilburg University))  On the Lovasz thetanumber of almost regular graphs with application to ErdosRenyi graphs 
Abstract: We consider kregular graphs with loops, and study the Lovasz thetanumbers and Schrijver theta'numbers of the graphs that result when the loop edges are removed. We show that the thetanumber dominates a recent eigenvalue upper bound on the stability number due to Godsil and Newman [C.D. Godsil and M.W. Newman. Eigenvalue bounds for independent sets. Journal of Combinatorial Theory B, to appear]. As an application we compute the theta and theta' numbers of certain instances of ErdosRenyi graphs. This computation exploits the graph symmetry using the methodology introduced in [E. de Klerk, D.V. Pasechnik and A. Schrijver. Reduction of symmetric semidefinite programs using the regular *representation. Mathematical Programming B, to appear]. The computed values are strictly better than the GodsilNewman eigenvalue bounds. (Joint work with Mike Newman, Dima Pasechnik, and Renata Sotirov.)  
Mauricio de Oliveira (University of California, San Diego)  Numerical optimization assisted by noncommutative symbolic algebra 
Abstract: We describe how a symbolic computer algebra tool (NCAlgebra) that can handle symbolic matrix (noncommutative) products is used to numerically solve systems and control problems. Our current focus is on semidefinite programs arising from control theory, where matrix variables appear naturally. Our tools keep matrix variables aggregated at all steps of a primaldual interiorpoint algorithm. Symbolic matrix expressions are automatically generated and used on iterative numerical procedures for the determination of search directions, showing promising results. 
Cheonghee Ahn  Yonsei University  1/4/2007  1/23/2007 
Suliman AlHomidan  King Fahd University of Petroleum & Minerals  1/16/2007  1/20/2007 
Elizabeth Allman  University of Alaska  1/7/2007  4/7/2007 
Jungha An  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Miguel F. Anjos  University of Waterloo  1/15/2007  1/20/2007 
D. Gregory Arnold  US Air Force Research Laboratory  1/17/2007  1/19/2007 
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 
Michel Baes  Katholieke Universiteit Leuven  1/15/2007  1/22/2007 
Joseph A. Ball  Virginia Polytechnic Institute and State University  1/15/2007  1/21/2007 
Chunsheng Ban  Ohio State University  1/15/2007  1/20/2007 
Alexander Barvinok  University of Michigan  1/15/2007  1/18/2007 
Saugata Basu  Georgia Institute of Technology  1/15/2007  1/20/2007 
Daniel J. Bates  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Carolyn Beck  University of Illinois at UrbanaChampaign  1/15/2007  1/18/2007 
Dimitris Bertsimas  Massachusetts Institute of Technology  1/15/2007  1/19/2007 
Yermal Sujeet Bhat  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Víctor Blanco Izquierdo  University of Sevilla  1/11/2007  4/21/2007 
Cristiano Bocci  Università di Milano  1/10/2007  3/10/2007 
Tristram Bogart  University of Washington  1/8/2007  3/25/2007 
Hartwig Bosse  Center for Mathematics and Computer Science (CWI)  1/11/2007  1/21/2007 
Christopher J. Budd  University of Bath  1/16/2007  1/21/2007 
Constantine M. Caramanis  University of Texas  1/15/2007  1/20/2007 
Enrico Carlini  Politecnico di Torino  1/10/2007  2/16/2007 
Dong Eui Chang  University of Waterloo  1/15/2007  1/21/2007 
Graziano Chesi  University of Hong Kong  1/15/2007  1/19/2007 
Hi Jun Choe  Yonsei University  1/5/2007  1/20/2007 
Ionut CiocanFontanine  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Raul Curto  University of Iowa  1/15/2007  1/20/2007 
Etienne de Klerk  Katholieke Universiteit Brabant (Tilburg University)  1/13/2007  1/20/2007 
Jesus Antonio De Loera  University of California  1/11/2007  1/20/2007 
Mauricio de Oliveira  University of California, San Diego  1/15/2007  1/19/2007 
Xuan Vinh Doan  Massachusetts Institute of Technology  1/11/2007  1/21/2007 
John C. Doyle  California Institute of Technology  1/18/2007  1/21/2007 
Kenneth R. Driessel  Iowa State University  9/1/2006  6/29/2007 
Michael Dritschel  University of Newcastle upon Tyne  1/15/2007  1/20/2007 
Mathias Drton  University of Chicago  1/8/2007  3/30/2007 
Laurent El Ghaoui  University of California  1/18/2007  1/19/2007 
Richard Falk  Rutgers University  1/7/2007  1/12/2007 
Lingling Fan  Midwest ISO  1/12/2007  1/13/2007 
Lingling Fan  Midwest ISO  1/16/2007  1/20/2007 
Makan Fardad  University of Minnesota Twin Cities  8/26/2006  8/13/2007 
Maryam Fazel  California Institute of Technology  1/14/2007  1/21/2007 
Eric Feron  Georgia Institute of Technology  1/15/2007  1/20/2007 
Lawrence A. Fialkow  SUNY at New Paltz  1/15/2007  1/20/2007 
Stephen E. Fienberg  CarnegieMellon University  1/1/2007  3/31/2007 
Pedro Forero  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Ioannis Fotiou  Eidgenössische TH ZürichHönggerberg  1/10/2007  2/16/2007 
Dennice Gayme  California Institute of Technology  1/15/2007  1/21/2007 
Tryphon T. Georgiou  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Sonja Glavaski  Honeywell Systems and Research Center  1/16/2007  1/20/2007 
Jason E. Gower  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Carlos R. Handy  Texas Southern University  1/15/2007  1/20/2007 
Bernard Hanzon  National University of Ireland, University College Cork  1/16/2007  1/21/2007 
Gloria Haro Ortega  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Christoph Helmberg  Technische Universität ChemnitzZwickau  1/15/2007  1/21/2007 
J. William Helton  University of California, San Diego  1/14/2007  1/26/2007 
Didier Henrion  Centre National de la Recherche Scientifique (CNRS)  1/15/2007  1/21/2007 
Milena Hering  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Christopher Hillar  Texas A & M University  1/15/2007  1/21/2007 
JeanBaptiste HiriartUrruty  Université de Toulouse III (Paul Sabatier)  1/15/2007  1/21/2007 
SungPil Hong  Seoul National University  1/16/2007  2/1/2007 
Serkan Hosten  San Francisco State University  1/2/2007  2/16/2007 
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 
Farhad Jafari  University of Wyoming  9/1/2006  6/30/2007 
Amin Jafarian  University of Texas  1/12/2007  1/20/2007 
Anders Nedergaard Jensen  Aarhus University  9/6/2006  6/30/2007 
Steve Kaliszewski  Arizona State University  1/7/2007  6/30/2007 
Tapan Kumar Kar  Yokohama National University  1/15/2007  1/20/2007 
Mordechai Katzman  University of Sheffield  1/10/2007  5/15/2007 
Edward D. Kim  University of California  1/11/2007  1/20/2007 
SiJo Kim  Andong National University  1/12/2007  1/13/2007 
SiJo Kim  Andong National University  1/16/2007  1/20/2007 
Sunyoung Kim  Ewha Womans University  1/14/2007  1/20/2007 
Henry C. King  University of Maryland  1/11/2007  1/21/2007 
Masakazu Kojima  Tokyo Institute of Technology  1/14/2007  1/20/2007 
Salma Kuhlmann  University of Saskatchewan  1/13/2007  1/20/2007 
Nuri Kundak  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
SongHwa Kwon  University of Minnesota Twin Cities  8/30/2005  8/31/2007 
Sanjay Lall  Stanford University  1/19/2007  1/20/2007 
Andrew Lamperski  California Institute of Technology  1/15/2007  1/21/2007 
Jean Bernard Lasserre  Centre National de la Recherche Scientifique (CNRS)  1/7/2007  2/3/2007 
Niels Lauritzen  Aarhus University  8/28/2006  7/10/2007 
Anton Leykin  University of Minnesota Twin Cities  8/16/2006  8/15/2007 
Hstau Liao  University of Minnesota Twin Cities  9/2/2005  8/31/2007 
James Lu  Johann Radon Institute for Computational and Applied Mathematics  1/15/2007  1/21/2007 
Tom Luo  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
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 
Arash Mafi  Corning  1/25/2007  1/27/2007 
Hannah Markwig  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Thomas Markwig  Universität Kaiserslautern  9/1/2006  6/30/2007 
Scott McCullough  University of Florida  1/15/2007  1/20/2007 
Alexandre Megretski  Massachusetts Institute of Technology  1/15/2007  1/21/2007 
Lisa A. Miller  University of Minnesota Twin Cities  1/12/2007  1/13/2007 
Lisa A. Miller  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Richard Moeckel  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Uwe Nagel  University of Kentucky  9/1/2006  6/1/2007 
Kristen Nairn  St. John's University  1/11/2007  1/13/2007 
Jiawang Nie  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Edwin O'Shea  University of Kentucky  1/11/2007  1/15/2007 
Antonis Papachristodoulou  University of Oxford  1/17/2007  1/21/2007 
Pablo A. Parrilo  Massachusetts Institute of Technology  1/11/2007  1/21/2007 
Gabor Pataki  University of North Carolina  1/14/2007  1/20/2007 
Helfried Peyrl  Automatic Control Laboratory  1/15/2007  2/3/2007 
Victoria Powers  Emory University  1/15/2007  1/20/2007 
Mihai Putinar  University of California  1/7/2007  3/24/2007 
Jacob Quant  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Bharath Rangarajan  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Bharath Rangarajan  University of Minnesota Twin Cities  1/12/2007  1/13/2007 
Seid Alireza Razavi Majomard  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Ben Recht  California Institute of Technology  1/15/2007  1/20/2007 
Victor Reiner  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Franz Rendl  Universität Klagenfurt  1/16/2007  1/21/2007 
James Renegar  Cornell University  1/15/2007  1/20/2007 
John A. Rhodes  University of Alaska  1/7/2007  4/7/2007 
Jakayla Robbins  University of Kentucky  1/11/2007  1/14/2007 
Joel Roberts  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Marie Rognes  University of Oslo  1/10/2007  6/30/2007 
Philipp Rostalski  Eidgenössische TH ZürichHönggerberg  1/2/2007  2/19/2007 
Bjarke Hammersholt Roune  Aarhus University  9/12/2006  6/30/2007 
MarieFrancoise Roy  Université de Rennes I  1/15/2007  1/21/2007 
Christopher Ryan  University of British Columbia  1/11/2007  1/20/2007 
Arnd Scheel  University of Minnesota Twin Cities  7/15/2004  8/31/2007 
Markus Schweighofer  Universität Konstanz  1/15/2007  1/21/2007 
Parikshit Shah  Massachusetts Institute of Technology  1/11/2007  1/20/2007 
Chehrzad Shakiban  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Kartik K. Sivaramakrishnan  North Carolina State University  1/15/2007  1/20/2007 
Aleksandra Slavkovic  Pennsylvania State University  1/31/2007  3/31/2007 
Steven Sperber  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Dumitru Stamate  University of Minnesota Twin Cities  1/12/2007  1/13/2007 
Dumitru Stamate  University of Minnesota Twin Cities  1/16/2007  1/20/2007 
Bernd Sturmfels  University of California  1/17/2007  1/20/2007 
Jie Sun  National University of Singapore  1/15/2007  1/20/2007 
Bridget Eileen Tenner  Massachusetts Institute of Technology  1/17/2007  1/20/2007 
Tamas Terlaky  McMaster University  1/15/2007  1/20/2007 
Rekha R. Thomas  University of Washington  1/1/2007  3/31/2007 
Carl Toews  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Ufuk Topcu  University of California  1/15/2007  1/20/2007 
Levent Tuncel  University of Waterloo  1/15/2007  1/20/2007 
Victor Vinnikov  Ben Gurion University of the Negev  1/15/2007  1/26/2007 
John Voight  University of Minnesota Twin Cities  8/15/2006  8/31/2007 
Martin J. Wainwright  University of California  1/16/2007  1/19/2007 
Tiyu Wang  University of California  1/11/2007  1/13/2007 
Angelika Wiegele  Universität Klagenfurt  1/15/2007  1/21/2007 
Ragnar Winther  University of Oslo  1/7/2007  1/12/2007 
Henry Wolkowicz  University of Waterloo  1/14/2007  1/20/2007 
Gregory Emmanuel Yawson  Lawrence Technological University  1/11/2007  1/20/2007 
Josephine Yu  University of California  1/9/2007  6/30/2007 
Hongchao Zhang  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Lihong Zhi  Chinese Academy of Sciences  1/11/2007  3/4/2007 
Yuriy Zinchenko  McMaster University  1/16/2007  1/19/2007 