Organizing Committee
Abstract

Discrepancy theory deals with the problem of distributing points uniformly over some geometric object and evaluating the inevitably arising errors. The theory was ignited by such famous early results as Herman Weyl's equidistribution theorem and Klaus Roth's theorem on the irregularities of point distributions.

The subject has now grown into a broad field with deep connections tomany areas such as number theory, combinatorics, approximation theory, harmonic analysis, and probability theory, in particular empirical and Gaussian processes. The computational aspects of the subject include searching for well-distributed sets and numerical integration rules. Despite years of research, many fundamental questions, especially in high dimensions, remain wide open, although several important advances have been achieved recently.

The participants of this workshop will share a wide range of views on topics related to discrepancy with an eye towards the recent developments in the subject. The workshop will bring together different communities working on various aspects of discrepancy theory. The exchange of ideas and approaches, the cross-fertilization of viewpoints, sharing the visions of near and far term goals of the field will be the highlight of the conference.

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Image Credit: Dmitriy Bilyk

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, October 27, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration: Discrepancy Theory Workshop11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTDyadic shift randomization in classical discrepancy theory - Maxim Skriganov, Steklov Mathematical Institute, St Petersburg11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTFactorization Norms and Tusnady's Problem - Aleksandar Nikolov, Microsoft Research11th Floor Lecture Hall
11:30 - 12:15pm EDTDirectional Discrepancy - Craig Spencer, Kansas State University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch   
2:30 - 3:15pm EDTKeynote Lecture- Discrepancy and Homogeneous Dynamics - Alex Kontorovich, Rutgers University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTSets of bounded discrepancy for multi-dimensional irrational rotation - Sigrid Grepstad, Norwegian University of Science and Technology11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, October 28, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTDistribution of simplexes in thin subsets of Euclidean space and Riemannian manifolds - Alex Iosevich, University of Rochester11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTConvolution operators, measures of polynomial growth, and finite point configurations. - Krystal Taylor, IMA, University of Minnesota11th Floor Lecture Hall 
11:30 - 12:15pm EDTQuasi-random numbers for copula models - Christiane Lemieux, University of Waterloo11th Floor Lecture Hall
12:30 - 1:45pm EDTBreak for Lunch   
1:45 - 2:30pm EDTAlgorithmic aspects of discrepancy - Nikhil Bansal, Technische Universiteit Eindhoven11th Floor Lecture Hall
2:45 - 3:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:00pm EDTDiscrepancy of random points - Benjamin Doerr, École Polytechnique11th Floor Lecture Hall
4:15 - 5:00pm EDTConstructing Low Star Discrepancy Point Sets with Genetic Algorithms - Carola Doerr, Max-Planck-Institut für Informatik11th Floor Lecture Hall 
Wednesday, October 29, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTDiversions from the Koksma-Hlawka inequality - Giancarlo Travaglini, Università di Milano - Bicocca11th Floor Lecture Hall
10:00 - 10:20am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:05am EDTSome work of Antonia J Jones - The gamma test and a recently discovered manuscript of a book on the traveling salesman question. - Andy Pollington, National Science Foundation11th Floor Lecture Hall 
11:20 - 12:05pm EDTCircumventing Schmidt's bound on discrepancy using tapered estimators - James Propp, University of Massachusetts at Lowell11th Floor Lecture Hall
12:20 - 12:30pm EDTGroup Photo 11th Floor Lecture Hall 
12:30 - 2:00pm EDTBreak for Lunch   
2:00 - 2:45pm EDTContinuity of halo functions associated to homothecy invariant dencity bases - Oleksandra Beznosova, University of Alabama11th Floor Lecture Hall
3:00 - 3:45pm EDTProblem Session11th Floor Lecture Hall 
3:45 - 4:00pm EDTCoffee Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTPoster Session and Short Talks11th Floor Collaborative Space and Lecture Hall 
5:00 - 5:45pm EDTCollaboration and discussion11th Floor Collaborative Space and Lecture Hall 
Thursday, October 30, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTLow-discrepancy sequences for non-uniform measures - Christoph Aistleitner, Technische Universität Graz11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTVandermonde Nets and Sequences - Roswitha Hofer, Johannes Kepler Universität Linz11th Floor Lecture Hall
11:30 - 12:15pm EDTLimit theorems for discrepancies - Robert Tichy, Technische Universität Graz11th Floor Lecture Hall 
12:30 - 1:45pm EDTBreak for Lunch   
1:45 - 2:30pm EDTOptimal point sets for quasi-Monte Carlo integration of bivariate periodic functions - Aicke Hinrichs, Johannes Kepler Universität Linz11th Floor Lecture Hall
2:45 - 3:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:00pm EDTExplicit constructions of point sets and sequences with low discrepancy - Josef Dick, University of New South Wales11th Floor Lecture Hall
4:15 - 5:00pm EDTBMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimensio - Lev Makhasin, Universität Stuttgart11th Floor Lecture Hall 
Friday, October 31, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTAn Application of the Erdos-Turan-Koksma Inequality in Almost-Periodic Homogenization - Zhongwei Shen, Universoity of Kentucky11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:00 - 10:00am EDTPlease take a moment to complete the survey that was distributed by email.  
10:30 - 11:15am EDTTBA - Ed Saff, Vanderbilt University11th Floor Lecture Hall 
11:30 - 12:15pm EDTAsymptotic Results on the Discrete Riesz Minimal Energy and Polarization when the Power of the Potential Equals the Dimension of the Set - Sergiy Borodachov, Towson University11th Floor Lecture Hall
12:30 - 2:00pm EDTBreak for Lunch   
2:00 - 2:45pm EDTBracketing entropy of high dimensional distributions - Frank Gao, University of Idaho11th Floor Lecture Hall
3:00 - 3:45pm EDT(Quasi) Monte Carlo and Partial Differential Equations- what can be done - Stefan Steinerberger, Yale University11th Floor Lecture Hall
4:00 - 4:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

High-dimensional Approximation
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Approximation, Integration, and Optimization
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Research Cluster

Lecture Videos

Bracketing entropy of high dimensional distributions

Frank Gao
University of Idaho
October 31, 2014

Limit theorems for discrepancies

Robert Tichy
Technische Universität Graz
October 30, 2014

Circumventing Schmidt's bound on discrepancy using tapered estimators

James Propp
University of Massachusetts at Lowell
October 29, 2014

Diversions from the Koksma-Hlawka inequality

Giancarlo Travaglini
Universitá di Milano - Bicocca
October 29, 2014

Quasi-random numbers for copula models

Christiane Lemieux
University of Waterloo
October 28, 2014

Sets of bounded discrepancy for multi-dimensional irrational rotation

Sigrid Grepstad
Norwegian University of Science and Technology
October 27, 2014

Directional Discrepancy

Craig Spencer
Kansas State University
October 27, 2014

Factorization Norms and Tusnady's Problem

Aleksandar Nikolov
Microsoft Research
October 27, 2014