Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall 207 Church Street SE Minneapolis, MN 55455 
The IMA has been awarded a $19.5 million renewal grant by the National Science Foundation for the period 2005‒2010, the largest single research investment in mathematics ever made by NSF and a 77% increase over the IMA's previous level of NSF support. NSF math director William Rundell made the announcement at the IMA on July 20.
Press coverage: U of M (article, press release) · Star Tribune (article, graphic) · MPR · PhysOrg.com
The 2005‒2006 thematic program Imaging opens with the tutorial Radar and Optical Imaging, September 19‒23. The tutorial will consist of two lecture series providing background on imaging techniques for two different regions of the electromagnetic spectrum–the microwave and optical regions. The lectures will provide background on radar imaging, computational optical imaging, and spectroscopy.
The theme of the fall semester is Sensors to Images. Progress in sensor technology is generating new types of data and creating new research areas offering exciting opportunities for mathematicians, including quantum state imaging, nanoscale imaging, and network tomography. Data obtained from wave propagation phenomena will receive special attention, with examples from radar, ultrasound, and seismic prospecting. Another focus will be the emerging area of Integrated Sensing and Processing, i.e. intelligent integration of detection and processing in a systems approach.
There will be three workshops in the fall semester:
IMA New Directions Short Courses are limited to 25 participants, with an application deadline of April 1.
Morning  Posing of problems by the industry mentors.  EE/CS 3180  MM8.110.05  
9:00a9:30a  Coffee and Registration  EE/CS 3176  MM8.110.05  
9:30a9:40a  Welcome and Introduction  Douglas N. Arnold (University of Minnesota) Richard J. Braun (University of Delaware) Fernando Reitich (University of Minnesota) Fadil Santosa (University of Minnesota)  EE/CS 3180  MM8.110.05 
9:40a10:00a  Team 1: Sparse Aperture Imaging  D. Gregory Arnold (Air Force Research Laboratory)  EE/CS 3180  MM8.110.05 
10:00a10:20a  Team 2: Uncertainty Quantification in Geophysical Inverse Problems  Nicholas Bennett (SchlumbergerDoll Research)  EE/CS 3180  MM8.110.05 
10:20a10:40a  Team 3: Contact Algorithms for Dry Granular Flow with Elastic Grains  Petri Fast (Lawrence Livermore National Laboratories)  EE/CS 3180  MM8.110.05 
10:40a11:00a  Break  EE/CS 3176  MM8.110.05  
11:00a11:20a  Team 4: Integrated Circuit Layout Reconstruction  Edward Keyes (Semiconductor Insights)  EE/CS 3180  MM8.110.05 
11:20a11:40a  Team 5: Models of Human Physiology, and Randomized Clinical Trials  David S. Ross (Kaiser Permanente)  EE/CS 3180  MM8.110.05 
11:40a12:00p  Team 6: Algorithms for Digital Halftoning  Chai Wah Wu (IBM Corporation)  EE/CS 3180  MM8.110.05 
12:00p1:00p  Lunch  Orchid Cafe, Thai Cuisine 304 Oak Street Minneapolis Phone: 6123314061  MM8.110.05  
1:30p4:30p  Groups start work on projects. Mentors guide their groups through the modeling process, leading discussion sessions, suggesting references, and assigning work.  EE/CS 3180  MM8.110.05 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05 
Morning  Informal progress reports.  Lind Hall 305  MM8.110.05  
8:15a8:45a  Coffee and registration  EE/CS 3176  W8.56.05  
8:45a10:30a  Session: Probability, Combinatorics, and Statistical Mechanics Organizer:  Russell Lyons (Indiana University)  EE/CS 3180  W8.56.05 
Infinite volume limit of the Abelian sandpile model on Z^{d}  Antal Jarai (Carleton University)  
Simple random surfaces  Richard Kenyon (University of British Columbia)  
Tug of war and the infinity Laplacian  Scott Sheffield (New York University)  
9:30a9:50a  Team 2 Progress Report  Lind Hall 305  MM8.110.05  
9:50a10:10a  Team 4 Progress Report  Lind Hall 305  MM8.110.05  
10:10a10:30a  Team 3 Progress Report  Lind Hall 305  MM8.110.05  
10:30a11:00a  Break  EE/CS 3176  W8.56.05  
10:30a10:50a  Break  Lind Hall 400  MM8.110.05  
10:50a11:10a  Team 6 Progress Report  Lind Hall 305  MM8.110.05  
11:00a12:00p  Invited Lecture: Rough paths: a top down description of controls  Terence Lyons (Oxford University)  EE/CS 3180  W8.56.05 
11:30a12:50p  Team 1 Progress Report  Lind Hall 305  MM8.110.05  
12:00p1:30p  Lunch  W8.56.05  
12:15p2:00p  Picnic  TBA  MM8.110.05  
1:30p2:30p  Medallion Lecture: Recent results and open problems concerning motion in random media  Ofer Zeitouni (University of Minnesota)  EE/CS 3180  W8.56.05 
2:30p2:45p  Break  W8.56.05  
2:45p4:30p  Session: Flows and Random Media Organizer:  Michael Cranston (University of California  Irvine)  EE/CS 3180  W8.56.05 
The pinning transition for a polymer in the presence of a random potential  Ken Alexander (University of Southern California)  
Spectral asymptotics of Laplacians on bondpercolation graphs  Peter Mueller (University of Goettingen)  
Spatial inhomogeneities and large scale behavior of the asymmetric exclusion process  Timo Seppalainen (University of Wisconsin)  
4:30p4:45p  Break  EE/CS 3176  W8.56.05  
4:45p6:00p  Medallion Lecture: The disconnection time of the random walk on a discrete cylinder  Amir Dembo (Stanford University)  EE/CS 3180  W8.56.05 
6:00p8:00p  Reception and poster session  Lind Hall 400  W8.56.05  
A state machine approach to study pattern frequencies in Markovian sequences  Manuel Lladser (University of Colorado)  
Subindependence for stable random variables  Adel Mohammadpour (Universite ParisSud) 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05  
8:45a10:30a  Session:Stochastic Integration Organizer:  Terence Lyons (Oxford University)  EE/CS 3180  W8.56.05 
Anticipating stochastic calculus via good rough path sequences  Peter Friz (Courant Institute)  
Applications of rough paths to speech recognition  Anastasia Papavasiliou (Princeton University)  
Stochastic integrals for processes with longtime memory  Zhongmin Qian (Oxford University)  
10:30a11:00a  Break  EE/CS 3176  W8.56.05  
11:00a12:00p  Invited Lecture: Unimodularity and stochastic processes  Russell Lyons (Indiana University)  EE/CS 3180  W8.56.05 
12:00p1:30p  Lunch  W8.56.05  
1:30p3:15p  Session:Random Walk in Random Environment Organizer:  Ofer Zeitouni (University of Minnesota)  EE/CS 3180  W8.56.05 
Random walk in random scenery  Nina Gantert (Universitaet Karlsruhe)  
Growth in dynamic random environment  Vladas Sidoravicius (IMPA, Brazil)  
On some selfinteracting random walks in random environment  Martin Zerner (University of Tuebingen)  
3:15p3:45p  Break  EE/CS 3176  W8.56.05  
3:45p5:30p  Session:Stochastic Partial Differential Equations Organizer:  Jonathan C. Mattingly (Duke University)  EE/CS 3180  W8.56.05 
Stochastic modulation equations  Martin Hairer (University of Warwick)  
On the foundation of the L_{p}theory of SPDEs  Nicolai Krylov (University of Minnesota)  
Ergodicity of the degenerately forced stochastic fluid equations  Jonathan C. Mattingly (Duke University) 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.110.05 
Morning  Final presentations and submission of written reports.  EE/CS 3180  MM8.110.05  
9:00a9:30a  Team 6 Final Report  EE/CS 3180  MM8.110.05  
9:30a10:00a  Team 3 Final Report  EE/CS 3180  MM8.110.05  
10:00a10:30a  Team 4 Final Report  MM8.110.05  
10:30a11:00a  Break  EE/CS 3180  MM8.110.05  
11:00a11:30a  Team 1 Final Report  EE/CS 3180  MM8.110.05  
11:30a12:00p  Team 5 Final Report  EE/CS 3180  MM8.110.05  
12:00p12:30p  Team 2 Final Report  EE/CS 3180  MM8.110.05  
12:30p2:00p  Pizza party  Lind Hall 400  MM8.110.05 
8:30a10:00a  Lecture: Introduction, quantum states, operations, etc.  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: Overview  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05  
2:30p3:00p  Group Photo  ND8.1526.05  
3:00p4:00p  Reception  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Teleportation, superdense coding, introduction to quantum error correcting codes  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: The toric code and its variations  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Algorithms  periodicity  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: Spin Hamiltonians, ground states and excitations  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Algorithms  Grover's algorithm and quantum walk algorithms  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: Lattice models based on discrete groups  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Measures of entanglement  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: Quantum computation with S_3 anyons  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Quantum channel capacities  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture:The honeycomb lattice model  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Channel capacities and additivity  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: Algebraic theory of anyons  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
11:30a1:00p  Lunch  ND8.1526.05  
1:30p2:30p  Guest Lecturer, Topic: TBA  John Watrous (University of Calgary)  Lind Hall 409  ND8.1526.05 
2:30p3:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Quantum error correcting codes  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: Algebraic theory of anyons, cont.  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: Quantum fault tolerance  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture:Computation with Fibonacci anyons  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05 
8:30a10:00a  Lecture: TBA  Peter W. Shor (Massachusetts Institute of Technology)  Lind Hall 409  ND8.1526.05 
10:00a10:30a  Break  Lind Hall 400  ND8.1526.05  
10:30a12:00p  Lecture: More models and the physical perspective  Alexei Kitaev (California Institute of Technology)  Lind Hall 409  ND8.1526.05 
12:00p1:30p  Lunch  ND8.1526.05  
1:30p2:30p  Problem Solving and Brain Storming Session  Lind Hall 409  ND8.1526.05  
2:30p2:45p  Wrap up  Lind Hall 409  ND8.1526.05 
Event Legend: 

MM8.110.05  Mathematical Modeling in Industry IX  A Workshop for Graduate Students 
ND8.1526.05  Quantum Computation 
W8.56.05  New Directions in Probability Theory 
Ken Alexander (University of Southern California)  The pinning transition for a polymer in the presence of a random potential 
Abstract: We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. We assume the probability of an excursion of length n from 0, in the absence of the potential, decays like n^{c} for some c>1. Disorder is introduced by, having the interaction vary from one monomer to another, as a constant u plus i.i.d. mean0 randomness. There is a critical value of u above which the polymer is pinned, placing a positive fraction, called the contact fraction, of its monomers at 0 with high probability. We obtain bounds for the contact fraction near the critical point and examine the effect of the disorder on the specific heat exponent, which describes the approach to 0 of the contact fraction at the critical point. Our results are consistent with predictions in the physics literature that the effect of disorder is quite different in the cases c<3/2 and c>3/2.  
D. Gregory Arnold (Air Force Research Laboratory)  Team 1: Sparse Aperture Imaging 
Abstract: Standard 2D SAR image formation techniques require data samples that have been collected on a regular rectangular grid (with respect to the viewpoint). A target that happened to move through the imaged scene will be displaced and smeared across the final image. Imaging a moving target is equivalent to collecting data that is not on a regular grid (although more generally this generates data in a cube, rather than data in a square). Surprisingly little is understood about how to form an image in this more general case. This topic encompasses a myriad of research areas. One starting point would be to use standard scattering center models to predict the scattering at new locations. This approach requires the ability to extract viewpoint stable features from the measured data. Filtering, tracking, and dynamic programming are key elements to this approach. Alternately, knowing the final product is a 3D image, it may be possible produce the end result without requiring explicit feature extraction. Data will be available to test newly developed approaches.  
Nicholas Bennett (SchlumbergerDoll Research)  (Team 2) Uncertainty Quantification in Geophysical Inverse Problems 
Abstract: Solving an inverse problem means determining the parameters of a model given a set of measurements. In solving many practical inverse problems, accounting for the uncertainty of the solution is very important to aid in decisionmaking. A standard approach to do this begins by choosing a model parametrization and then using a Bayesian approach to make inferences on the model parameters from measurement data. However, this quantified uncertainty is a function of the model parametrization and for many inverse problems, there are many model parametrizations that account for the data equally well. A well known approach to accounting for model uncertainty is Bayesian Model Averaging where many model parametrizations are considered. Wavelet model updates provide an efficient means of sifting through a family of model parametrizations given by decimated wavelet bases. By decimated wavelet basis we mean a subset of the model's coordinates in a wavelet basis. When working with measurement data sets which are particularly noisy or large in terms of their data storage size, it is natural to consider denoising or compressing the data also using a decimated wavelet representation. Kalman filters can be used to update the solution (including its uncertainty) when denoising or locally changing the resolution of the measurement data by changing the decimation. We shall explore how to compute likely representations of both model and measurements in the context of solving a few model geophysical inverse problems.  
Amir Dembo (Stanford University)  Medallion Lecture: The disconnection time of the random walk on a discrete cylinder 
Abstract: Consider the simple random walk on the discrete cylinder whose base is the ddimnesional torus with sidelength N, and whose height is the set of all integers. When d>1, the time the walk needs to disconnect the discrete cylinder is very roughly of order N to the power 2d, and comparable to the cover time of the slice of height 0. Further, by the time disconnection occurs, a massive "clogging'' takes place in the truncated cylinders of height N to power d' for any d'  
Petri Fast (Lawrence Livermore National Laboratories)  (Team 3) Contact Algorithms for Dry Granular Flow with Elastic Grains 
Abstract: Consider the dynamics of interacting elastic disks in the plane. This is an experimentally realizable 2d model of dry granular flow where the stresses can be visualized using the photoelastic effect. As the elastic disks move in a vacuum they interact through collisions with each other and with the surrounding geometry. Because of the finite propagation speed of deformations inside each grain it can be difficult to capture computationally even simple experiments involving just a few interacting grains. The goal of this project is to improve our ability to simulate dense granular flow in complex geometry. Some project ideas: (A) Pursue full numerical simulations of of the interacting elastic disks driven by contact mechanics. (B) Develop simplified discrete element models for tracking the center of mass of each disk using classical mechanics including heuristics for the delay arising from the finite propagation speed of elastic deformations in each disk. (C) Compare with experimental data.  
Peter Friz (Courant Institute)  Anticipating stochastic calculus via good rough path sequences 
Abstract: We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semimartingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the stochastic process, the unique solution of the above SDE understoof in the rough path sense is actually a Stratonovich solution. This condition is satisfied by Brownian motion and fractional Brownian motion with Hurst parameter greater than 1/4.  
Nina Gantert (Universitaet Karlsruhe)  Random walk in random scenery 
Abstract: Let (Z_n)_{n in N_0} be a ddimensional random walk in random scenery, i.e., Z_n=sum_{k=0}^{n1}Y(S_k) with (S_k)_{k in N_0} a random walk in Z^d and (Y(z))_{z in Z^d} an i.i.d. scenery, independent of the walk. The walker's steps have mean zero and finite variance. We identify the speed and the rate of the logarithmic decay of P(1/n Z_n > b_n) for various choices of sequences (b_n)_n in [1,infty). Depending on (b_n)_n and the upper tails of the scenery, we identify different regimes for the speed of decay and different variational formulas for the rate functions. In contrast to recent work by A.~Asselah and F.~Castell, we consider sceneries unbounded to infinity. It turns out that there are interesting connections to large deviation properties of selfintersections of the walk, which have been studied recently by X. Chen. The talk is based on joint work with Wolfgang Koenig, Remco van der Hofstad and Zhan Shi.  
Martin Hairer (University of Warwick)  Stochastic modulation equations 
Abstract: We consider the stochastic SwiftHohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic GinzburgLandau equation. Unlike in the deterministic case, this approximation holds for all times and extends to the respective invariant measures.  
Antal Jarai (Carleton University)  Infinite volume limit of the Abelian sandpile model on Z^{d} 
Abstract: The Abelian 'sandpile' model was introduced by physicists as a basic example of selforganized criticality (SOC). Roughly speaking, SOC arises when a stochastic dynamics drives a system towards a stationary state characterized by power laws. We study existence of the infinite volume limit for the model, and properties of this limit, giving insight into the asymptotic behaviour of large 'sandpiles'. Most progress can be made above the upper critical dimension d > 4. We discuss some open problems related to extending these results to lower dimensions.  
Richard Kenyon (University of British Columbia)  Simple random surfaces 
Abstract: This is joint work with David Brydges and Jessica Young. We study a model of random surfaces coming with an immersion into an arbitrary twocomplex. Certain probabilistic quantities can be computed using the Green's function for the Laplacian on 1forms.  
Edward Keyes (Semiconductor Insights)  (Team 4) Integrated Circuit Layout Reconstruction 
Abstract: Integrated Circuits are designed
using a polygon representations of the wiring and transistors layers known as
"layout". Layout must conform to strict design rules. Typically the design rules
describes the minimum width of any polygon, minimum spacing between adjacent
polygons, directionality (normally only vertical or horizontal runs are allowed)
and corner angles (normally only 90 degrees). Multiple wiring layers are common,
with modern ICs having as many as ten wiring levels. Different wiring layers
are connected through a contact or "via" level. The via levels must also obey
their own set of design rules on size and spacing.
The process of analyzing the design of an integrated circuit involves imaging the various layers and then using image processing to reconstruct the layout of the different layers. Builtin biases, both in the manufacturing process and the analysis process prevent the reconstructed layout from being a faithful representation of the original layout. For example, sharp corners become rounded, line widths may either expand or contract and straight lines become roughened with many false vertices. Typical extracted layout is shown in figure 1. Our problem is, given the raw polygon data from image processing, how can we as faithfully as possible recreate the original layout? There are a number of potential errors that must be avoided in any reconstruction scheme including: creation of shorts between adjacent polygons, creation of a break or "open" in an existing polygon, creation of self intersecting polygons, creation of "via opens" (a break in the connection to an upper or lower layer). The ideal algorithm should also significantly compaction the layout data by eliminating spurious vertices. The layout reconstruction problem has significant overlap with the general problem of line simplification which has been extensively studied for Geographic Information Systems (GIS). One of the first and most effective methods for line simplification is the algorithm proposed by Douglas and Peucker[1] in 1973. A straightforward implementation of the algorithm runs in time O(k2) for a chain of size k; Hershberger and Snoeyink[2] show how to improve this to O(k log k). This algorithm is very efficient, however it is a general line simplification solution and not optimized to the highly specific characteristics of IC layout. Unique features of our problem are the strict design rules governing permissible polygon shapes as well as the constraints imposed by the via points.  [1] DOUGLAS, D. H., AND PEUCKER, T. K. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer 10 (1973), 112122. [2] HERSHBERGER, J., AND SNOEYINK, J. Speeding up the DouglasPeucker line simplification algorithm. Proc. 5th Internat. Sympos. Spatial Data Handling (1992), pp. 134143. 

Nicolai Krylov (University of Minnesota)  On the foundation of the L_{p}theory of SPDEs 
Abstract: We discuss a detailed proof of a generalization of the LittlewoodPaley inequality upon which the Lptheory of SPDEs is based.  
Manuel Lladser (University of Colorado)  A state machine approach to study pattern frequencies in Markovian sequences 
Abstract: We present a general method to compute the distribution of the number of occurrences of various patterns in a random string produced by a Markov process in a finite size alphabet. The key idea to the method is the observation that the probability of occurrence of a single pattern in a random string of length N corresponds to the probability that a random walk on a state machine (also known as automaton) visits a terminal state within N steps. Through a synchronization argument the method can be extended to study the occurrence of none, some, or all of a list of patterns in a random string generated by a homogeneous Markov Process with a bounded amount of memory. Within this framework the use of generating functions and matrix methods are readily available to determine explicitly or asymptotically the probability of simultaneous occurrence of various patterns in a random string of arbitrary length.  
Russell Lyons (Indiana University)  Invited Lecture: Unimodularity and stochastic processes 
Abstract: Stochastic processes on vertextransitive graphs, especially Cayley graphs of groups, have been studied for 50 years (not counting the special case of integer lattices, which goes back hundreds of years). The assumption of invariance under graph automorphisms plays a key role, but investigations of the last 15 years have shown that an additional assumption is also extremely useful. This newer assumption is the property of unimodularity, which is equivalent to the MassTransport Principle. We shall review some wellknown applications and also discuss recent work with David Aldous.  
Terence Lyons (Oxford University)  Invited Lecture: Rough paths: a top down description of controls 
Abstract: The theory of rough paths as developed by the Author (and several others including those speaking at this workshop as well as others such as Hambly, Ledoux, Coutin, ..) aims to study the differential equations used to model the situation where a system responds to external control or forcing. The theory describes a robust approach to these equations that allows the forcing to be far from differentiable. The methodology permits the main probabilistic classes as well as many new types of stochastic forcing that do not fit into the classical semimartingale setting directly. The key to this theory is to answer the question  when do two controls produce similar responses. This is also a core question for the problem for multiscale analysis where one needs to summarise small scale behaviour in a way that large scale responses can be predicted from the summarised information. The question can be translated into one asking that one characterises the continuity properties of the It? map. This is indeed possible and the Universal Limit theorem proves the (uniform) continuity of the map taking the forcing control to response for a wide class of metrics on smooth paths  and the completions of the space under these metrics give the so called rough paths  giving insight into the control problem. The approach is quite structured, and allows one to give a top down analysis of a control in terms of a sequence of algebraic coefficients we call the signature of the control (which have similarity to a child's pr?cis of a complicated text by a simpler one and are a noncommutative analogue of Fourier coefficients) with refinements giving more accurate information about the control. Hambly and Lyons recently proved that this "signature" of a control completely characterises the control up to the appropriate null sets. The talk will summarise some of this work.  
Jonathan C. Mattingly (Duke University)  Ergodicity of the degenerately forced stochastic fluid equations 
Abstract: I will present a theory which allows one to prove the uniqueness of the stationary measure for a large class of SPDEs with additive noise. To do so, I will discuss Malliavin Calculus in the SPDE setting and a generalization of Hormander's hypoelliptic theory to the SPDEs. I will also discuss a new generalization of the strong Feller property which seems to be use full in infinite dimensions.  
Peter Mueller (University of Goettingen)  Spectral asymptotics of Laplacians on bondpercolation graphs 
Abstract: Bondpercolation graphs are random subgraphs of the ddimensional integer lattice generated by a standard Bernoulli bondpercolation process. The associated graph Laplacians, subject to Dirichlet or Neumann conditions at cluster boundaries, represent bounded, selfadjoint, ergodic random operators. They possess almost surely the nonrandom spectrum [0,4d] and a selfaveraging integrated density of states. This integrated density of states is shown to exhibit Lifshits tails at both spectral edges in the nonpercolating phase. Depending on the boundary condition and on the spectral edge, the Lifshits tail discriminates between different cluster geometries (linear clusters versus cubelike clusters) which contribute the dominating eigenvalues. Lifshits tails arising from cubelike clusters continue to show up above the percolation threshold. In contrast, the other type of Lifshits tails cannot be observed in the percolating phase any more because they are hidden by van Hove singularities from the percolating cluster.  
Anastasia Papavasiliou (Princeton University)  Applications of rough paths to speech recognition 
Abstract: It is a well known fact that when someone speaks, the signal reaching the human ear is the original signal produced by the speaker and several delays. We think of this as a multidimensional rough path. Using tools coming from the theory of rough paths, I will construct much simpler rough paths (piecewise linear) approximating the one containing the speech signal and its delays, which still cause a similar response. Thus, the constructed rough paths contain all the information relevant to the response. If we think of the "meaning" of the speech signal as the response, the constructed rough paths will contain the "meaning" in a much more robust way than the signal itself, and thus can be used to construct a likelihood function for each word.  
Zhongmin Qian (Oxford University)  Stochastic integrals for processes with longtime memory 
Abstract: Stochastic processes with longtime memory have been used extensively in modelling random phenomena. In this talk I will discuss the theory of rough paths and its application to a class of stochastic dynamical systems driven by such longtime memory.  
David S. Ross (Kaiser Permanente)  (Team 5) Models of Human Physiology, and Randomized Clinical Trials 
Abstract: Randomized clinical trials are the central feature of modern medical methodology. In an RCT, two or more populations of patients who are statistically identical on the relevant dimensions are given different medical treatments. The results are then recorded, and are used to establish medical practice. The Archimedes Project of Kaiser Permanente has undertaken the development of a mathematical model of human physiology that will complement RCTs. The purpose of the model is to integrate data from various RCTs, then to predict health outcomes for populations not specifically considered in any particular RCT, perhaps for treatments not specifically considered in any particular RCT. What sort of model(s) of human physiology are appropriate for this purpose? References: Eddy, D., and Schlessinger, L.,Diabetes Care 26:31023110, 2003 Eddy, D., and Schlessinger, L.,Diabetes Care 26:30933101, 2003  
Timo Seppalainen (University of Wisconsin)  Spatial inhomogeneities and large scale behavior of the asymmetric exclusion process 
Abstract: This talk describes some results and open problems for the onedimensional asymmetric exclusion process in situations where spatial inhomogeneities, either deterministic or random, are added to the model.  
Scott Sheffield (New York University)  Tug of war and the infinity Laplacian 
Abstract: The infinity Laplacian (informally, the "second derivative in the gradient direction") is a simple yet mysterious operator with many applications. "Tug of war" is a two player random turn game played as follows: SETUP: Assign each player one of two disjoint target sets T_1 and T_2 in the plane, and fix a starting position x and a constant epsilon. Place the game token at x. GAME PLAY: Toss a fair coin and allow the player who wins the coin toss to move the game token up to epsilon units in the direction of his or her choice. Repeat the above until the token reaches a target set T_i. The ith player is then declared the winner. Given parameters epsilon and x, write u_epsilon(x) for the probability that player one wins when both players play optimally. We show that as epsilon tends to zero, the functions u_epsilon(x) converge to the infinity harmonic function with boundary conditions 1 on T_1 and 0 on T_2. Our strategic analysis of tug of war leads to new formulations and significant generalizations of several classical results about infinity laplacians. The game theoretic arguments are simpler and more elementary than the original proofs. This talk is based on joint work with Yuval Peres, Oded Schramm, and David Wilson.  
Vladas Sidoravicius (IMPA, Brazil)  Growth in dynamic random environment 
Abstract: We consider the following model for the spread of an infection: There is a "gas" of socalled Aparticles, each of which performs a continuous time simple random walk on Z^d, with jumprate D_A. We assume that initially the number of Aparticles at x is independent, mean mu_A Poisson distribution. In addition, there are Bparticles which perform continuous time simple random walks with jumprate D_B. Initially we start with only one Bparticle in the system, located at the origin. The Bparticles move independently of each other, and the only interaction is that when a Bparticle and an Aparticle coincide, the latter instantaneously turns into a Bparticle. For different values of the parameters D_A and D_B one obtains several interesting evolutions, raging from stochastic sandpile type dynamics (activated random walkers) to contact process like evolution and DLAtype growth. The difficult aspect of all these models is the absence of useful subadditive quantities. I briefly discuss these models before going to our main results: Consider the set C(t):= {x in Z^d: a Bparticle visits x during [0,t]}. If D_A=D_B, then B(t) := C(t) + [ 1/2, 1/2]^d grows linearly in time with an asymptotic shape, i.e., there exists a nonrandom set B_0 such that (1/t)B(t) \to B_0, in a sense which will be made precise. Moreover, if the "recuperation'' transition form A to B occurs at the rate lambda>0, for each particle independently, then we show that there is a phase transition between survival and extiction of B particles. I also briefly present the key ideas of the proof. The talk is based on joint works with H. Kesten.  
Chai Wah Wu (IBM Corporation)  (Team 6) Algorithms for Digital Halftoning 
Abstract: If you have ever looked closely at an image in a magazine or a newspaper, you will see that the image, which looks like it has many shades and colors, is actually composed of dots of ink of only a handful of colors. Digital halftoning is the art of representing a full color picture with only a few colors and is necessary in all digital printers. Halftoning is possible due to the lowpass frequency characteristic of the human visual system. Several types of algorithms exist in modern digital printers with usually a tradeoff between speed and quality. This tradeoff is important since digital printers can operate at speeds of a few pages a minute (an inkjet printer for home use) to thousands of pages a minute (a production class digital printer). This project studies some questions regarding the stability and efficiency of algorithms used to perform digital halftoning. One of the goals of this project is to design an algorithm which has superior output quality, yet operates at speeds close to speedier algorithms. The type of mathematics used include linear algebra, dynamical systems theory, convex analysis, and mathematical programming.  
Ofer Zeitouni (University of Minnesota)  Medallion Lecture: Recent results and open problems concerning motion in random media 
Abstract: The talk will describe the current knowledge and some of the challenges in the study of motion in random environment, focusing on the model of random walk in random environment and the related model of diffusions in random environments. For the latter, I will describe a CLT in the case where the environment is a small perturbation of the constant environment. 
Henry DeGraft Acquah  University of Gottingen  8/4/2005  8/6/2005 
Ken Alexander  University of Southern California  8/4/2005  8/6/2005 
Ismail Ali  Kuwait University  8/4/2005  8/6/2005 
Mina Aminghafari  Universite ParisSud  8/4/2005  8/6/2005 
D. Gregory Arnold  Air Force Research Laboratory  7/31/2005  8/10/2005 
Douglas N. Arnold  University of Minnesota  7/15/2001  8/31/2006 
Donald G. Aronson  University of Minnesota  9/1/2002  8/31/2005 
Gerard Awanou  University of Minnesota  9/2/2003  8/31/2005 
Marton Balazs  University of Wisconsin–Madison  8/4/2005  8/6/2005 
Antar Bandyopadhyay  Chalmers University of Technology–Sweden  8/1/2005  8/6/2005 
Katherine Bartley  University of Nebraska–Lincoln  7/31/2005  8/10/2005 
John Baxter  University of Minnesota  8/14/2005  8/26/2005 
Christian Benes  Tufts University  8/4/2005  8/6/2005 
Nicholas Bennett  SchlumbergerDoll Research  7/31/2005  8/10/2005 
Noam Berger  California Institute of Technology  8/4/2005  8/6/2005 
Ian Besse  University of Iowa  7/31/2005  8/10/2005 
Sagar Bhatt  Rice University  7/31/2005  8/10/2005 
Debasis Bhattacharya  VisvaBharati University  8/4/2005  8/6/2005 
Animikh Biswas  University of North Carolina–Charlotte  8/14/2005  8/26/2005 
Henry A. Boateng  University of Michigan  7/31/2005  8/10/2005 
Petra BonfertTaylor  Wesleyan University  8/14/2005  8/26/2005 
Maury Bramson  University of Minnesota  8/5/2005  8/6/2005 
Richard J. Braun  University of Delaware  7/31/2005  8/10/2005 
Wlodzimierz Bryc  University of Cincinnati  8/4/2005  8/7/2005 
Patrick R. Campbell  Los Alamos National Laboratory  7/31/2005  8/11/2005 
Suneal K. Chaudhary  University of Utah  8/14/2005  8/25/2005 
Pengwen Chen  University of Florida  7/31/2005  8/11/2005 
Qianyong Chen  University of Minnesota  9/1/2004  8/31/2006 
William W. Chen  Internal Revenue Service  8/4/2005  8/6/2005 
TsungLin Cheng  National Changhua University of Education  8/4/2005  8/6/2005 
Zhiyi Chi  University of Chicago  8/4/2005  8/6/2005 
Julianne Chung  Emory University  7/31/2005  8/10/2005 
Keith Crank  National Science Foundation  8/4/2005  8/6/2005 
Michael Cranston  University of California–Irvine  8/4/2005  8/6/2005 
Shilpa Das Gupta  Mississippi State University  7/31/2005  8/10/2005 
Amir Dembo  Stanford University  8/4/2005  8/6/2005 
Lee Dicker  University of Pennsylvania  8/4/2005  8/6/2005 
Brian DiDonna  University of Minnesota  9/1/2004  8/31/2006 
Jintai Ding  University of Cincinnati  8/14/2005  8/26/2005 
John Rhodes Dixon  Florida State University  8/14/2005  8/26/2005 
John Dodson  American Express Financial Advisors  8/4/2005  8/6/2005 
Hongjie Dong  University of Minnesota  8/4/2005  8/6/2005 
Vanja Dukic  University of Chicago  8/4/2005  8/6/2005 
Valjean Elander  University of Nevada–Las Vegas  7/31/2005  8/10/2005 
Malena Espanol  Tufts University  7/31/2005  8/10/2005 
Qirong Fang  Purdue University  7/31/2005  8/10/2005 
Lara Faoro  Rutgers University  8/14/2005  8/26/2005 
Petri Fast  Lawrence Livermore National Laboratories  7/31/2005  8/10/2005 
Harshini Fernando  Texas Tech University  7/31/2005  8/10/2005 
Bert Fristedt  University of Minnesota  8/4/2005  8/6/2005 
Peter Friz  Courant Institute  8/4/2005  8/6/2005 
Nina Gantert  Universitaet Karlsruhe  8/2/2005  8/8/2005 
Ryan Gantner  University of Minnesota  8/4/2005  8/6/2005 
Tim Garoni  University of Minnesota  8/25/2003  8/31/2005 
Tim Garoni  University of Minnesota  8/4/2005  8/6/2005 
Paul Garrett  University of Minnesota  8/14/2005  8/26/2005 
Armenak Gasparyan  Program Systems Institute of RAS  8/4/2005  8/6/2005 
Jason Gower  University of Cincinnati  8/14/2005  8/26/2005 
Lawrence Gray  University of Minnesota  8/4/2005  8/6/2005 
Arindam Gupta  University of Calcutta  8/4/2005  8/6/2005 
Jooyoung Hahn  KAIST  8/15/2005  7/31/2006 
Martin Hairer  University of Warwick  8/4/2005  8/6/2005 
Sean Han  University of Minnesota  8/4/2005  8/6/2005 
Michael Hardy  University of Minnesota  8/4/2005  8/6/2005 
John Harlim  University of Maryland  7/31/2005  8/10/2005 
James Hegeman  University of Wisconsin  8/2/2005  8/6/2005 
Alfa Heryudono  University of Delaware  7/31/2005  8/10/2005 
Wenming Hong  Beijing Normal University  8/4/2005  8/6/2005 
Mark Huber  Duke University  8/4/2005  8/6/2005 
Lucky Igbinosun  University of Benin  8/4/2005  8/6/2005 
Mark Iwen  University of Michigan  7/31/2005  8/10/2005 
Naresh Jain  University of Minnesota  8/4/2005  8/6/2005 
Antal Jarai  Carleton University  8/4/2005  8/6/2005 
Jan Jelinek  Honeywell  8/4/2005  8/6/2005 
Lijian Jiang  Texas A & M University  7/31/2005  8/11/2005 
Chao Jin  University of Colorado–Boulder  7/31/2005  8/11/2005 
Yasong Jin  University of Kansas  8/4/2005  8/6/2005 
Sookyung Joo  University of Minnesota  9/1/2004  8/31/2006 
Palle E. T. Jorgensen  University of Iowa  8/14/2005  8/26/2005 
Hye Won Kang  University of Wisconsin  8/4/2005  8/6/2005 
Soyoung Kang  Purdue University  8/4/2005  8/6/2005 
Chiu Yen Kao  University of Minnesota  9/1/2004  8/31/2006 
Belaide Karima  Abderahmane Mira University  8/4/2005  8/6/2005 
Richard Kenyon  University of British Columbia  8/4/2005  8/6/2005 
Edward Keyes  Semiconductor Insights  7/31/2005  8/10/2005 
Mercedeh Khajavikhan  University of Minnesota  8/4/2005  8/6/2005 
Asha Khanna  Indian Institute of Forest Management  8/4/2005  8/6/2005 
JongMin Kim  University of Minnesota–Morris  8/4/2005  8/6/2005 
KyeongHun Kim  University of Utah  8/4/2005  8/6/2005 
Alexei Kitaev  California Institute of Technology  8/14/2005  8/26/2005 
Richard Kollar  University of Minnesota  9/1/2004  8/31/2005 
George Kordzakhia  University of California–Berkeley  8/4/2005  8/6/2005 
Elena Kosygina  Baruch College–The City University of New York  8/4/2005  8/6/2005 
Nicolai Krylov  University of Minnesota  8/4/2005  8/6/2005 
Saji Kumar  University of Kerala  8/4/2005  8/6/2005 
Thomas G. Kurtz  University of Wisconsin  8/4/2005  8/6/2005 
Matthias Kurzke  University of Minnesota  9/1/2004  8/31/2006 
SongHwa Kwon  University of Minnesota  8/30/2005  8/31/2007 
Soumendra Nath Lahiri  Iowa State University  8/14/2005  8/26/2005 
Chang Hyeong Lee  University of Minnesota  8/4/2005  8/6/2005 
ChangOck Lee  KAIST  8/1/2005  7/31/2006 
Frederic Legoll  University of Minnesota  9/3/2004  8/1/2005 
Melvin Leok  University of Michigan  8/14/2005  8/26/2005 
Joel Lepak  University of Michigan  7/31/2005  8/10/2005 
Debra Lewis  University of Minnesota  7/15/2004  8/31/2006 
Xiantao Li  University of Minnesota  8/3/2004  8/14/2005 
Yan Li  Texas A & M University  7/31/2005  8/11/2005 
Hstau Liao  University of Minnesota  8/30/2005  8/31/2007 
Chjan Chin Lim  Rensselaer Polytechnic Institute  8/14/2005  8/26/2005 
Enbing Lin  University of Toledo  8/14/2005  8/26/2005 
Manuel Lladser  University of Colorado  8/4/2005  8/6/2005 
Russell Lyons  Indiana University  8/4/2005  8/7/2005 
Terence Lyons  Oxford University  8/2/2005  8/7/2005 
Jonathan C. Mattingly  Duke University  8/4/2005  8/6/2005 
Elebeoba E. May  Sandia National Laboratories  8/14/2005  8/26/2005 
David Meintrup  University of the Federal Arms Munich  8/14/2005  8/27/2005 
Michael J. Minardi  Air Force Research Laboratory  7/31/2005  8/1/2005 
Oana Mocioalca  Kent State University  8/4/2005  8/7/2005 
Adel Mohammadpour  Universite ParisSud  8/3/2005  8/6/2005 
Peter Mueller  University of Goettingen  8/4/2005  8/6/2005 
Abdallah Muwanga  Swaziland Government  8/4/2005  8/6/2005 
Kiran Naidu  Air Force Research Laboratory  7/31/2005  8/2/2005 
Jayoung Nam  Indiana University  7/31/2005  8/10/2005 
Subhrangshu Nandi  University of Massachusetts–Amherst  8/4/2005  8/6/2005 
Claudia Neuhauser  University of Minnesota  8/4/2005  8/6/2005 
Mahdi Nezafat  University of Minnesota  8/4/2005  8/6/2005 
Kwadwo Agyei Nyantakyi  8/4/2005  8/6/2005  
Frank Oduro  Graphic Communications Group Limited  8/4/2005  8/6/2005 
Tamer Oraby  University of Cincinnati  8/4/2005  8/7/2005 
Anastasia Papavasiliou  Princeton University  8/4/2005  8/6/2005 
Jonathon Peterson  University of Minnesota  8/4/2005  8/6/2005 
Peter Philip  University of Minnesota  8/22/2004  8/31/2006 
Oleg Pikhurko  Carnegie Mellon University  8/14/2005  8/25/2005 
Lea Popovic  University of Minnesota  9/2/2003  8/19/2005 
Lea Popovic  University of Minnesota  8/4/2005  8/6/2005 
Karel L. Prikry  University of Minnesota  8/14/2005  8/26/2005 
Zhongmin Qian  Oxford University  8/4/2005  8/6/2005 
Maurice Rahe  Texas A & M University  8/14/2005  8/26/2005 
Jorge M. Ramirez  Oregon State University  7/31/2005  8/11/2005 
Gregory Jason Randall  Universidad de la Republica  8/10/2005  7/31/2006 
Arni SR Srinivasa Rao  University of Guelph  8/4/2005  8/6/2005 
Firas RassoulAgha  Ohio State University  8/4/2005  8/6/2005 
S. S. Ravindran  University of Alabama–Huntsville  8/14/2005  8/26/2005 
Fernando Reitich  University of Minnesota  8/1/2005  8/10/2005 
Alexander Roitershtein  University of British Columbia  8/4/2005  8/6/2005 
Robert Ronkese  University of Delaware  7/31/2005  8/11/2005 
David S. Ross  Kaiser Permanente  7/31/2005  8/10/2005 
John Sabino  Rice University  7/31/2005  8/10/2005 
Rina Santos  University of Nevada–Las Vegas  7/31/2005  8/10/2005 
Fadil Santosa  University of Minnesota  8/1/2005  8/10/2005 
Arnd Scheel  University of Minnesota  7/15/2004  8/31/2006 
Clyde Schoolfield  University of Florida  8/4/2005  8/6/2005 
Timo Seppalainen  University of Wisconsin  8/2/2005  8/6/2005 
Lee Seung  Ohio State University  8/4/2005  8/6/2005 
QiMan Shao  Hong Kong University of Science and Technology  8/4/2005  8/6/2005 
Tanush Shaska  University of Idaho  8/14/2005  8/26/2005 
Scott Sheffield  New York University  8/4/2005  8/6/2005 
Peter W. Shor  Massachusetts Institute of Technology  8/14/2005  8/26/2005 
Vladas Sidoravicius  IMPA, Brazil  8/4/2005  8/6/2005 
Warren Sinnott  Ohio State University  8/14/2005  8/26/2005 
KaiSheng Song  Florida State University  8/14/2005  8/26/2005 
Qingshuo Song  Wayne State University  7/31/2005  8/10/2005 
Skyler Speakman  University of Kentucky  7/31/2005  8/11/2005 
David Steinsaltz  Queen's University  8/4/2005  8/6/2005 
David St John  University of Illinois–Chicago  7/31/2005  8/10/2005 
Jason Swanson  University of Wisconsin  8/4/2005  8/6/2005 
TzyhJong Tarn  Washington University  8/14/2005  8/26/2005 
David Tello  Arizona State University  7/31/2005  8/10/2005 
Pham Huu Tiep  University of Florida  8/14/2005  8/26/2005 
Igor Tsukerman  University of Akron  8/15/2005  8/26/2005 
Imre Tuba  Virginia Tech  8/15/2005  8/26/2005 
Abolfazl Vaghefi  Iran University of Science & Technology  8/4/2005  8/6/2005 
Paula Andrea Vasquez  University of Delaware  7/31/2005  8/10/2005 
John Verzani  College of Staten Island–The City University of New York  8/4/2005  8/6/2005 
Andrew Vizcarra  Purdue University  8/4/2005  8/6/2005 
Shuyan Wan  Ohio State University  8/4/2005  8/6/2005 
Lei Wang  University of Michigan  7/31/2005  8/10/2005 
Thomas Williams  Mississippi State University  7/31/2005  8/11/2005 
Doug Wright  University of Minnesota  2/15/2005  8/31/2005 
Chai Wah Wu  IBM Corporation  7/31/2005  8/10/2005 
Chuan Xue  University of Minnesota  7/31/2005  8/10/2005 
Emmanuel Yomba  University of NgaoundÃ©rÃ©  10/6/2004  8/31/2005 
Ofer Zeitouni  University of Minnesota  8/4/2005  8/6/2005 
Yong Zeng  University of Missouri–Kansas City  8/4/2005  8/6/2005 
Martin Zerner  University of Tuebingen  8/4/2005  8/6/2005 