Discrepancy Theory (October 27-31, 2014)
Organizing Committee
Michael Lacey (Georgia Institute of Technology)
William Chen (Macquarie University)
Dmitriy Bilyk (University of Minnesota)
Aicke Hinrichs (Johannes Kepler Universität Linz)
Mikhail Lifshits (St Petersburg State University)
Friedrich Pillichshammer (Johannes Kepler Universitat Linz)
[Image Credit: Dmitriy Bilyk]
Description
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.
Speaker and Participant List (* = Speaker)
Ali Ahmed (Georgia Institute of Technology)
Christoph Aistleitner* (Technische Universität Graz)
Theresa Anderson (Brown University)
Ulas Ayaz (Rheinische Friedrich-Wilhelms-Universität Bonn)
Nikhil Bansal * (Technische Universiteit Eindhoven)
Kinjal Basu (Stanford University)
Oleksandra Beznosova * (University of Alabama)
Dmitriy Bilyk (University of Minnesota)
Sergiy Borodachov * (Towson State University)
Luca Brandolini (Università di Bergamo)
Emmanuel Candes (Stanford University)
William Chen (Macquarie University)
Yanlai Chen (University of Massachusetts)
Jacqueline Davis (Vanderbilt University)
Josef Dick* (University of New South Wales)
Francesco Di Plinio (Brown University)
Benjamin Doerr* (École Polytechnique)
Carola Doerr* (Max-Planck-Institut für Informatik)
Dinh Dung (Vietnam National University)
Armin Eftekhari (Colorado School of Mines)
Simon Foucart (University of Georgia)
Frank (Fuchang) Gao* (University of Idaho)
Alexander Gilbert (University of New South Wales)
Sigrid Grepstad* (Norwegian University of Science and Technology (NTNU))
Michael Griebel (Institute for Numerical Simulation )
C. Gunturk (Courant Institute of Mathematical Sciences)
Aicke Hinrichs* (Johannes Kepler Universität Linz)
Roswitha Hofer* (Johannes Kepler Universität Linz)
Thang Huynh (Courant Institute of Mathematical Sciences)
Alex Iosevich* (University of Rochester)
Alex Kontorovich * (Rutgers University)
Ben Krause (University of California, Los Angeles)
Frances Kuo (University of New South Wales)
Michael Lacey (Georgia Institute of Technology)
Christiane Lemieux * (University of Waterloo)
Lev Markhasin * (Universität Stuttgart)
Akil Narayan (University of Massachusetts)
Deanna Needell (Claremont McKenna College)
Aleksandar Nikolov * (Microsoft Research (Sillicon Valley))
Dirk Nuyens (KU Leuven)
Yumeng Ou (Brown University)
Andrew Pollington* (National Science Foundation)
James Propp* (University of Massachusetts)
Ed Saff* (Vanderbilt University)
Zhongwei Shen * (University of Kentucky)
Pawel Siedlecki (University of Warsaw)
Maxim Skriganov* (Russian Academy of Sciences)
Craig Spencer* (Kansas State University)
Stefan Steinerberger* (Yale University)
Gowri Suryanarayana (KU Leuven)
Krystal Taylor * (University of Minnesota)
Vladimir Temlyakov (University of South Carolina)
Robert Tichy* (Technische Universität Graz)
Giancarlo Travaglini* (Università di Milano - Bicocca)
Li Wang (University of California, San Diego)
Yingwei Wang (Purdue University)
Rachel Ward (University of Texas at Austin)
Grzegorz Wasilkowski (University of Kentucky)
Houying Zhu (University of New South Wales)
Schedule and Supporting Materials
Monday October 27, 2014 Time Description Speaker Location Abstracts Slides 8:30 - 8:55 Registration: Discrepancy Theory Workshop 11th Floor Collaborative Space 8:55 - 9:00 Welcome ICERM Director 11th Floor Lecture Hall 9:00 - 9:45 Dyadic shift randomization in classical discrepancy theory Maxim Skriganov, Steklov Mathematical Institute, St Petersburg 11th Floor Lecture Hall 10:00 - 10:30 Coffee/Tea Break 11th Floor Collaborative Space 10:30 - 11:15 Factorization Norms and Tusnady's Problem Aleksandar Nikolov, Microsoft Research 11th Floor Lecture Hall 11:30 - 12:15 Directional Discrepancy Craig Spencer, Kansas State University 11th Floor Lecture Hall 12:30 - 2:30 Break for Lunch 2:30 - 3:15 Keynote Lecture- Discrepancy and Homogeneous Dynamics Alex Kontorovich, Rutgers University 11th Floor Lecture Hall 3:30 - 4:00 Coffee/Tea Break 11th Floor Collaborative Space 4:00 - 4:45 Sets of bounded discrepancy for multi-dimensional irrational rotation Sigrid Grepstad, Norwegian University of Science and Technology 11th Floor Lecture Hall 5:00 - 6:30 Welcome Reception 11th Floor Collaborative Space
Tuesday October 28, 2014 Time Description Speaker Location Abstracts Slides 9:00 - 9:45 Distribution of simplexes in thin subsets of Euclidean space and Riemannian manifolds Alex Iosevich, University of Rochester 11th Floor Lecture Hall 10:00 - 10:30 Coffee/Tea Break 11th Floor Collaborative Space 10:30 - 11:15 Convolution operators, measures of polynomial growth, and finite point configurations. Krystal Taylor, IMA, University of Minnesota 11th Floor Lecture Hall 11:30 - 12:15 Quasi-random numbers for copula models Christiane Lemieux, University of Waterloo 11th Floor Lecture Hall 12:30 - 1:45 Break for Lunch 1:45 - 2:30 Algorithmic aspects of discrepancy Nikhil Bansal, Technische Universiteit Eindhoven 11th Floor Lecture Hall 2:45 - 3:15 Coffee/Tea Break 11th Floor Collaborative Space 3:15 - 4:00 Discrepancy of random points Benjamin Doerr, École Polytechnique 11th Floor Lecture Hall 4:15 - 5:00 Constructing Low Star Discrepancy Point Sets with Genetic Algorithms Carola Doerr, Max-Planck-Institut für Informatik 11th Floor Lecture Hall
Wednesday October 29, 2014 Time Description Speaker Location Abstracts Slides 9:00 - 9:45 Diversions from the Koksma-Hlawka inequality Giancarlo Travaglini, Università di Milano - Bicocca 11th Floor Lecture Hall 10:00 - 10:20 Coffee/Tea Break 11th Floor Collaborative Space 10:20 - 11:05 Some 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 Foundation 11th Floor Lecture Hall 11:20 - 12:05 Circumventing Schmidt's bound on discrepancy using tapered estimators James Propp, University of Massachusetts at Lowell 11th Floor Lecture Hall 12:20 - 12:30 Group Photo 11th Floor Lecture Hall 12:30 - 2:00 Break for Lunch 2:00 - 2:45 Continuity of halo functions associated to homothecy invariant dencity bases. Oleksandra Beznosova, University of Alabama 11th Floor Lecture Hall 3:00 - 3:45 Problem Session 11th Floor Lecture Hall 3:45 - 4:00 Coffee Break 11th Floor Collaborative Space 4:00 - 5:00 Poster Session and Short Talks 11th Floor Collaborative Space and Lecture Hall 5:00 - 5:45 Collaboration and discussion 11th Floor Collaborative Space and Lecture Hall
Thursday October 30, 2014 Time Description Speaker Location Abstracts Slides 9:00 - 9:45 Low-discrepancy sequences for non-uniform measures Christoph Aistleitner, Technische Universität Graz 11th Floor Lecture Hall 10:00 - 10:30 Coffee/Tea Break 11th Floor Collaborative Space 10:30 - 11:15 Vandermonde Nets and Sequences Roswitha Hofer, Johannes Kepler Universität Linz 11th Floor Lecture Hall 11:30 - 12:15 Limit theorems for discrepancies Robert Tichy, Technische Universität Graz 11th Floor Lecture Hall 12:30 - 1:45 Break for Lunch 1:45 - 2:30 Optimal point sets for quasi-Monte Carlo integration of bivariate periodic functions Aicke Hinrichs, Johannes Kepler Universität Linz 11th Floor Lecture Hall 2:45 - 3:15 Coffee/Tea Break 11th Floor Collaborative Space 3:15 - 4:00 Explicit constructions of point sets and sequences with low discrepancy Josef Dick, University of New South Wales 11th Floor Lecture Hall 4:15 - 5:00 BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimensio Lev Makhasin, Universität Stuttgart 11th Floor Lecture Hall
Friday October 31, 2014 Time Description Speaker Location Abstracts Slides 9:00 - 9:45 An Application of the Erdos-Turan-Koksma Inequality in Almost-Periodic Homogenization Zhongwei Shen, Universoity of Kentucky 11th Floor Lecture Hall 10:00 - 10:30 Coffee/Tea Break 11th Floor Collaborative Space 10:00 - 10:00 Please take a moment to complete the survey that was distributed by email. 10:30 - 11:15 TBA Ed Saff, Vanderbilt University 11th Floor Lecture Hall 11:30 - 12:15 Asymptotic Results on the Discrete Riesz Minimal Energy and Polarization when the Power of the Potential Equals the Dimension of the Set Sergiy Borodachov, Towson University 11th Floor Lecture Hall 12:30 - 2:00 Break for Lunch 2:00 - 2:45 Bracketing entropy of high dimensional distributions Frank Gao, University of Idaho 11th Floor Lecture Hall 3:00 - 3:45 (Quasi) Monte Carlo and Partial Differential Equations- what can be done Stefan Steinerberger, Yale University 11th Floor Lecture Hall 4:00 - 4:30 Coffee/Tea Break 11th Floor Collaborative Space