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.
IMA in the news  Checkout the article IMA Hosts 2006 BlackwellTapia Conference by Barry Cipra in the January/February 2007 issue of SIAM News.
Opportunities at the IMA  If you are interested in applying for a General Membership for a period of one month to one year in residence at the IMA during the 20072008 thematic program: Mathematics of Molecular and Cellular Biology, please find the application for this membership 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.
11:15a12:15p  Real algebraic geometry tutorial: Quotients of polynomial rings, Hermite's quadratic form and root counting  Kenneth R. Driessel (Iowa State University)  Lind Hall 409  RAG 
1:25p2:25p  IMA/MCIM Industrial problems seminar: Data fusion in a UAV surveillance system  Janet Pavelich Keel (Lockheed Martin Missiles and Space Company, Inc.)  Vincent Hall 1  IPS 
11:15a12:15p  IMA postdoc seminar: Characterization and computation of realradical ideals using semidefinite programming techniques  Philipp Rostalski (Eidgenössische TH ZürichHönggerberg)  Lind 215  PS 
11:15a12:15p  Algebraic geometry and applications seminar: An introduction to algebraic statistics  Serkan Hosten (San Francisco State University)  EE/CS 3180  AGS 
11:15a12:15p  Real algebraic geometry tutorial: Quotients of polynomial rings, Hermite's quadratic form and root counting (continued)  Kenneth R. Driessel (Iowa State University)  Lind Hall 409  RAG 
11:15a12:15p  IMA postdoc seminar: The small Chvátal rank of an integer matrix  Tristram Bogart (University of Washington)  Lind 215  PS 
11:15a12:15p  Algebraic geometry and applications seminar: Statistical formulation of issues associated with multiway contingency tables and the links to algebraic geometry  Stephen E. Fienberg (CarnegieMellon University)  Lind Hall 229  AGS 
11:15a12:15p  Real algebraic geometry tutorial: Quotients of polynomial rings, Hermite's quadratic form and root counting (continued)  Kenneth R. Driessel (Iowa State University)  Lind Hall 409  RAG 
All Day  Presidents' Day. The IMA is open. 
11:15a12:15p  IMA postdoc seminar: Counting rational curves in P^{2} using Kontsevich's formula  Hannah Markwig (University of Minnesota Twin Cities)  Lind 215  PS 
2:30p3:30p  IMA postdoc seminar: Variational partial differential equation(PDE) models with an application to medical imaging  Jungha An (University of Minnesota Twin Cities)  Lind Hall 409  PS 
11:15a12:15p  Algebraic geometry and applications seminar: Rational and algebraic invariants of a group action  Evelyne Hubert (Institut National de Recherche en Informatique Automatique (INRIA))  EE/CS 3180  AGS 
11:15a12:15p  Real algebraic geometry tutorial: Quotients of polynomial rings, Hermite's quadratic form and root counting (continued)  Kenneth R. Driessel (Iowa State University)  Lind Hall 409  RAG 
11:15a12:15p  IMA postdoc seminar: Counting rational curves in P^{2} using tropical geometry  Michael Kerber (Universität Kaiserslautern)  Lind 215  PS 
11:15a12:15p  Algebraic geometry and applications seminar: Moving frames in classical invariant theory and computer vision  Peter J. Olver (University of Minnesota Twin Cities)  EE/CS 3180  AGS 
Tristram Bogart (University of Washington)  IMA postdoc seminar: The small Chvátal rank of an integer matrix 
Abstract: Given an integer matrix A and an integer vector b, we define the small Chvatal rank (SCR) of the system Ax <= b to be the least number of
iterations of an iterated Hilbert basis construction to obtain all facet normals of the integer hull (that is, the convex hull of the set of integer solutions. Our procedure is a variation of the
ChvatalGomory procedure to compute integer hulls of polyhedra. The key difference is that our procedure ignores the righthand side vector b and uses only the matrix A.
We prove that the SCR of Ax <= b is bounded above by the Chvatal rank of Ax <= b and is hence finite. To justify the adjective "small", we show that when n=2, SCR is at most one while Chvatal rank can be arbitrarily high. For a family of examples from combinatorial optimization, we prove that the SCR is one or two while the Chvatal rank is known to be roughly log(n). We next relate SCR to the notion of supernormality of a vector configuration (specifically, the rows of A.) Supernormality is a generalization of unimodularity and we exhibit an infinite family of vector configurations arising from odd cycles that are supernormal but not unimodular. This answers a question of Hosten, Maclagan and Sturmfels. Lastly, we provide lower bounds on SCR. We prove that when n >= 3, SCR can be arbitrarily high and exponentially large in the input size. We also prove that for polytopes contained in the ddimensional unit cube, the SCR can be at least d/2  o(d) which is of the same order as the known lower bounds on Chvatal rank for such systems. Our methods thus provide an alternate way to compute lower bounds on Chvatal rank. This project is joint work with Rekha Thomas. 

Kenneth R. Driessel (Iowa State University)  Real algebraic geometry tutorial: Quotients of polynomial rings, Hermite's quadratic form and root counting (continued) 
Abstract: I shall mainly follow the material in the section "Zerodimensional systems" in the book by Basu, Pollack and Roy.  
Stephen E. Fienberg (CarnegieMellon University)  Algebraic geometry and applications seminar: Statistical formulation of issues associated with multiway contingency tables and the links to algebraic geometry 
Abstract: Many statistical problems arising in the context of multidimensional tables of nonnegative counts (known as contingency tables) have natural representations in algebraic and polyhedral geometry. I will introduce some of these problems in the context of actual examples of large sparse tables and talk about how we have treated them and why. For example, our work on bounds for contingency table entries has been motivated by problems arising in the context of the protection of confidential statistical data results on decompositions related to graphical model representations have explicit algebraic geometry formulations. Similarly, results on the existence of maximum likelihood estimates for loglinear models are tied to polyhedral representations. It turns out that there are close linkages that I will describe.  
Serkan Hosten (San Francisco State University)  Algebraic geometry and applications seminar: An introduction to algebraic statistics 
Abstract: This will be a gentle introduction to the applications of algebraic geometry to statistics. The main goal of the talk is to present statistical models, i.e. sets of probability distributions (defined parametrically most of the time), as algebraic varieties. I will give examples where defining equations of such statistical model varieties have been successfully computed: various graphical models and models for DNA sequence evolution. I will also talk about the algebraic degree of maximum likelihood estimation with old and new examples.  
Evelyne Hubert (Institut National de Recherche en Informatique Automatique (INRIA))  Algebraic geometry and applications seminar: Rational and algebraic invariants of a group action 
Abstract: We consider a rational group action on the affine space and propose a construction of a finite set of rational invariants and a simple algorithm to rewrite any rational invariant in terms of those generators. The construction can be extended to provide algebraic foundations to Cartan's moving frame method, as revised in [Fels & Olver 1999]. This is joint work with Irina Kogan, North Carolina State University.  
Janet Pavelich Keel (Lockheed Martin Missiles and Space Company, Inc.)  IMA/MCIM Industrial problems seminar: Data fusion in a UAV surveillance system 
Abstract: This talk will be about a recent Lockheed Martin project, the implementation of a data fusion method in the surveillance system of an Unmanned Aerial Vehicle (UAV). In this context data fusion is the problem of sequentially estimating the state of a dynamic system  ships at sea  given a sequence of noisy and incomplete measurements from the sensor suite on the UAV: radar, an ElectroOptical/Infrared (EO/IR) camera, and an Automatic Identification System (AIS) receiver. We will present the basic algorithms used in this project, and will then discuss their limitations and possible improvements.  
Michael Kerber (Universität Kaiserslautern)  IMA postdoc seminar: Counting rational curves in P^{2} using tropical geometry 
Abstract: Tropical geometry is a rapidly developing field of algebraic geometry with important applications in quite distinct areas of pure and applied mathematics. In this talk, we give a short introduction to the theory of tropical curves and discuss its applications to the enumerative geometry of plane curves, with a focus on computing the Kontsevich number N_{d} of rational plane curves of fixed degree d interpolating an appropriate number of given points in general position.  
Hannah Markwig (University of Minnesota Twin Cities)  IMA postdoc seminar: Counting rational curves in P^{2} using Kontsevich's formula 
Abstract: The numbers N_{d} of rational plane curves has for a long time only been known for small d. In 1990, Kontsevich came up with a recursive formula. In this talk, we will give some basic ideas and an example how Kontsevich's formula can be derived.  
Peter J. Olver (University of Minnesota Twin Cities)  Algebraic geometry and applications seminar: Moving frames in classical invariant theory and computer vision 
Abstract: Classical invariant theory was inspired by the basic problems of equivalence and symmetry of polynomials (or forms) under the projective group. In this talk, I will explain how a powerful new approach to the Cartan method of moving frames can be applied to classify algebraic and differential invariants for very general group actions, leading, among many other applications, to new solutions to the equivalence and symmetry problems arising in both invariant theory, differential geometry, and object recognition in computer vision.  
Philipp Rostalski (Eidgenössische TH ZürichHönggerberg)  IMA postdoc seminar: Characterization and computation of realradical ideals using semidefinite programming techniques 
Abstract: In this talk I will discuss a method (joined work with M. Laurent and J.B. Lasserre) for computing all real points on a zerodimensional semialgebraic set described by polynomial equalities and inequalities as well as some "nice" polynomial generators for the corresponding vanishing ideal, namely border resp. Gröbner basis for the real radical ideal. In contrast to exact computational algebraic methods, the method we propose uses numerical linear algebra and semidefinite optimization techniques to compute approximate solutions and generator polynomials. The method is realalgebraic in nature and prevents the computation of any complex solution. The proposed methods fits well into a relatively new branch of mathematics called "Numerical Polynomial Algebra." 
Elizabeth 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 
Hélène Barcelo  Arizona State University  2/3/2007  3/31/2007 
Daniel J. Bates  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Arend Bayer  University of Utah  2/19/2007  2/19/2007 
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 
Enrico Carlini  Politecnico di Torino  1/10/2007  2/16/2007 
Ionut CiocanFontanine  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Alicia Dickenstein  University of Buenos Aires  2/15/2007  3/14/2007 
Kenneth R. Driessel  Iowa State University  9/1/2006  6/29/2007 
Mathias Drton  University of Chicago  1/8/2007  3/30/2007 
Nicholas Eriksson  Stanford University  2/14/2007  3/16/2007 
Makan Fardad  University of Minnesota Twin Cities  8/26/2006  8/13/2007 
Stephen E. Fienberg  CarnegieMellon University  1/1/2007  3/31/2007 
Ioannis Fotiou  Eidgenössische TH ZürichHönggerberg  1/10/2007  2/16/2007 
Jason E. Gower  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Gloria Haro Ortega  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Milena Hering  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Patricia Hersh  Indiana University  2/15/2007  5/15/2007 
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 
Anders Nedergaard Jensen  Aarhus University  9/6/2006  6/30/2007 
Steve Kaliszewski  Arizona State University  1/7/2007  6/30/2007 
Mordechai Katzman  University of Sheffield  1/10/2007  5/15/2007 
Janet Pavelich Keel  Lockheed Martin Missiles and Space Company, Inc.  2/2/2007  2/2/2007 
Michael Kerber  Universität Kaiserslautern  2/19/2007  5/11/2007 
SongHwa Kwon  University of Minnesota Twin Cities  8/30/2005  8/31/2007 
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 
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 
Hannah Markwig  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Thomas Markwig  Universität Kaiserslautern  9/1/2006  6/30/2007 
Richard Moeckel  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Uwe Nagel  University of Kentucky  9/1/2006  6/1/2007 
Jiawang Nie  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Peter J. Olver  University of Minnesota Twin Cities  2/28/2007  2/28/2007 
Michael E. O'Sullivan  San Diego State University  2/21/2007  3/24/2007 
Lior Pachter  University of California  2/28/2007  3/10/2007 
Helfried Peyrl  Automatic Control Laboratory  1/15/2007  2/3/2007 
Mihai Putinar  University of California  1/7/2007  3/24/2007 
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 
Amos Ron  University of Wisconsin  2/14/2007  2/14/2007 
Philipp Rostalski  Eidgenössische TH ZürichHönggerberg  1/2/2007  2/19/2007 
Bjarke Hammersholt Roune  Aarhus University  9/12/2006  6/30/2007 
Arnd Scheel  University of Minnesota Twin Cities  7/15/2004  8/31/2007 
Chehrzad Shakiban  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Aleksandra Slavkovic  Pennsylvania State University  1/31/2007  3/31/2007 
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 
Andrew Stein  University of Michigan  2/6/2007  2/8/2007 
Seth Sullivant  Harvard University  2/19/2007  3/30/2007 
Rebecca Swanson  Indiana University  2/22/2007  3/31/2007 
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 
John Voight  University of Minnesota Twin Cities  8/15/2006  8/31/2007 
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 
Yi Zhou  CarnegieMellon University  2/28/2007  3/16/2007 