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Discrepancy Theory (October 27-31, 2014)


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Review of applications will begin on July 15, 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.


  • Ali Ahmed
    (Georgia Institute of Technology)
  • Christoph Aistleitner*
    (Technische Universität Graz)
  • 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))
  • 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)
  • 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)
MondayOctober 27, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration: Discrepancy Theory Workshop11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45Dyadic shift randomization in classical discrepancy theoryMaxim Skriganov, Steklov Mathematical Institute, St Petersburg11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Factorization Norms and Tusnady's ProblemAleksandar Nikolov, Microsoft Research11th Floor Lecture Hall
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11:30 - 12:15Directional DiscrepancyCraig Spencer, Kansas State University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:15Keynote Lecture- Discrepancy and Homogeneous DynamicsAlex Kontorovich, Rutgers University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Sets of bounded discrepancy for multi-dimensional irrational rotationSigrid Grepstad, Norwegian University of Science and Technology11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

TuesdayOctober 28, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Distribution of simplexes in thin subsets of Euclidean space and Riemannian manifoldsAlex Iosevich, University of Rochester11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15TBAKrystal Taylor, IMA, University of Minnesota11th Floor Lecture Hall
11:30 - 12:15Quasi-random numbers for copula modelsChristiane Lemieux, University of Waterloo11th Floor Lecture Hall
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12:30 - 1:45Break for Lunch
1:45 - 2:30Algorithmic aspects of discrepancyNikhil Bansal, Technische Universiteit Eindhoven11th Floor Lecture Hall
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2:45 - 3:15Coffee/Tea Break11th Floor Collaborative Space
3:15 - 4:00Discrepancy of random pointsBenjamin Doerr, École Polytechnique11th Floor Lecture Hall
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4:15 - 5:00Constructing Low Star Discrepancy Point Sets with Genetic AlgorithmsConstructing Low Star Discrepancy Point Sets with Genetic AlgorithmsCarola Doerr, Max-Planck-Institut für Informatik11th Floor Lecture Hall
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WednesdayOctober 29, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Diversions from the Koksma-Hlawka inequalityGiancarlo Travaglini, Università di Milano - Bicocca11th Floor Lecture Hall
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10:00 - 10:20Coffee/Tea Break11th Floor Collaborative Space
10:20 - 11:05Distribution of points on compact Lie Groups and applications.Andy Pollington, National Science Foundation11th Floor Lecture Hall
11:20 - 12:05Circumventing Schmidt's bound on discrepancy using tapered estimatorsJames Propp, University of Massachusetts at Lowell11th Floor Lecture Hall
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12:20 - 12:30Group Photo 11th Floor Lecture Hall
12:30 - 2:00Break for Lunch
2:00 - 2:45Continuity of halo functions associated to homothecy invariant dencity bases.Oleksandra Beznosova, University of Alabama11th Floor Lecture Hall
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3:00 - 3:45Problem Session11th Floor Lecture Hall
3:45 - 5:45Poster Session / Coffee/Tea Break11th Floor Collaborative Space

ThursdayOctober 30, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Low-discrepancy sequences for non-uniform measuresChristoph Aistleitner, Technische Universität Graz11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Vandermonde Nets and SequencesRoswitha Hofer, Johannes Kepler Universität Linz11th Floor Lecture Hall
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11:30 - 12:15Limit theorems for discrepanciesRobert Tichy, Technische Universität Graz11th Floor Lecture Hall
12:30 - 1:45Break for Lunch
1:45 - 2:30Optimal point sets for quasi-Monte Carlo integration of bivariate periodic functionsAicke Hinrichs, Johannes Kepler Universität Linz11th Floor Lecture Hall
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2:45 - 3:15Coffee/Tea Break11th Floor Collaborative Space
3:15 - 4:00BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimensioLev Makhasin, Universität Stuttgart11th Floor Lecture Hall
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4:15 - 5:00Explicit constructions of point sets and sequences with low discrepancyJosef Dick, University of New South Wales11th Floor Lecture Hall
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FridayOctober 31, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45An Application of the Erdos-Turan-Koksma Inequality in Almost-Periodic HomogenizationZhongwei Shen, Universoity of Kentucky11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:00 - 10:00Please take a moment to complete the survey that was distributed by email.
10:30 - 11:15TBAEd Saff, Vanderbilt University11th Floor Lecture Hall
11:30 - 12:15Asymptotic Results on the Discrete Riesz Minimal Energy and Polarization when the Power of the Potential Equals the Dimension of the SetSergiy Borodachov, Towson University11th Floor Lecture Hall
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12:30 - 2:00Break for Lunch
2:00 - 2:45Bracketing entropy of high dimensional distributionsFrank Gao, University of Idaho11th Floor Lecture Hall
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3:00 - 3:45(Quasi) Monte Carlo and Partial Differential Equations- what can be doneStefan Steinerberger, Yale University11th Floor Lecture Hall
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4:00 - 4:30Coffee/Tea Break11th Floor Collaborative Space