ICERM Semester Program on "Dimension and Dynamics"
(February 1 - May 6, 2016)

Picture

[Photo Credit: Mark A. Wilson]


Introduction

Since its introduction by Felix Hausdorff in 1919, the concept of the Hausdorff dimension of sets and measures has been a versatile and powerful tool in classical analysis, geometry and geometric measure theory, mathematical physics and their numerous applications. However, there has been a particularly important symbiosis between dynamical systems and dimension theory. This connection arises both from application of dimension theory to the classification and geometric analysis of dynamical systems (and their invariant sets and measures), and the fact that many classical objects of study in mathematics arise from (sometimes implicit) dynamical systems, which often play a role in the dimension theory of said objects.

Recently, there has been substantial progress on a number of central problems in dimension theory, and while many old problems remain, many new ones have also presented themselves. These include a deeper understanding of the relationship between dimension, entropy and Lyapunov exponents; the recent strengthenings of the Marstrand projection theorem and its implications for dimensions of sums of Cantor sets and the connections with number theory; multifractal analysis of ergodic averages, particularly the recent advances for multiple ergodic averages; and improved computational methods for obtaining effective bounds on Hausdorff dimension. This proposed program aims to set the stage for further progress on the many open problems in the field.

It is a challenging classical problem to compute numerically dimensions of given fractals. In recent years, computer-aided proofs in mathematical analysis have gained an increasing presence in mathematical research. One reason for this field's growing impact is due to its ability to produce high-quality quantitative information about global, nonlinear problems. As a consequence, solutions to a large class of previously intractable problems are now within reach and recently several long-standing conjectures have been verified using rigorous computations.

During the semester we will focus on three specific aspects of the interaction between these two areas: (i) Ergodic, algebraic and combinatorial methods in dimension theory (ii) Computations in fractal geometry in dynamical systems; and (iii) Fractal geometry and hyperbolic dynamics.

Organizing Committee

  • Dmitry Dolgopyat
    (University of Maryland)
  • Mike Hochman
    (Hebrew University of Jerusalem)
  • Izabella Laba
    (University of British Columbia)
  • Stefano Luzzatto
    (ITCP-Trieste)
  • Yakov Pesin
    (Penn State University)
  • Mark Pollicott
    (Warwick University)
  • Joerg Schmeling
    (Lund University)
  • Boris Solomyak
    (Bar-Ilan University)
  • Warwick Tucker
    (Uppsala University)

Associated Events & Information

Spring 2016 Semester Workshops

DatesTitleOrganizers
February 15-19, 2016Ergodic, algebraic and combinatorial methods in dimension theory Mike Hochman, Izabella Laba, Pablo Shmerkin, Barak Weiss
March 7-11, 2016Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism Lorenzo Diaz, Dmitry Dolgopyat, Maarit Jarvenpaa, Joerg Schmeling, Masato Tsujii, Amie Wilkinson
April 4-8, 2016Computation in Dynamics Denis Gaidashev, Stefano Galatolo, Stefano Luzzatto, Warwick Tucker, Michael Yampolsky

This page will show upcoming seminars that will be scheduled by organizers, speakers, and participants of the Spring 2016 semester program. Walk-ins are welcomed and encouraged for these seminars. Please check back regularly for updates.

We provide an iCal link for those attendees who wish to sync their own devices and/or calendars to our schedule.


Monday February 1, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 4:00Dimension and Dynamics Check-In121 South Main Street (11th Floor)
4:15 - 5:00Informal Coffee/Tea Break11th Floor Collaborative Space

Tuesday February 2, 2016
Time Description Speaker Location Abstracts Slides
9:30 - 10:00ICERM Director WelcomeJill Pipher, ICERM Director11th Floor Lecture Hall
10:00 - 10:45Brief Organizer Introductions and Broad Program OverviewMichael Hochman (Hebrew University of Jerusalem), Izabella Laba (University of British Columbia), Boris Solomyak (Bar-Ilan University), Yakov Pesin (Penn State University)11th Floor Lecture Hall
10:45 - 11:15Coffee/Tea Break11th Floor Collaborative Space
11:15 - 11:205-minute Graduate student introductionsLaura Cladek, University of Wisconsin - Madison11th Floor Lecture Hall
11:20 - 11:255-minute Graduate student introductionsNatalia Jurga, University of Warwick11th Floor Lecture Hall
11:25 - 11:305-minute Graduate student introductionsRoland Molontay, Budapest University11th Floor Lecture Hall
11:30 - 11:355-minute Graduate student introductionsErez Nesharim, Tel Aviv University11th Floor Lecture Hall
11:35 - 11:405-minute Graduate student introductionsVuksan Mijovic, University of St Andrews11th Floor Lecture Hall
11:40 - 11:455-minute Graduate student introductionsSasha Troscheit, University of St. Andrews11th Floor Lecture Hall
11:45 - 11:505-minute Graduate student introductionsJohn Yang, University of Toronto11th Floor Lecture Hall
11:50 - 11:555-minute Graduate student introductionsAgnieszka Zelerowicz, Penn State University11th Floor Lecture Hall
12:00 - 2:30Lunch and Free Time
2:30 - 2:4010-minute Postdoc introductionsMarta Canadell, ICERM Institute Postdoc11th Floor Lecture Hall
2:40 - 2:5010-minute Postdoc introductionsNishant Chandgotia, ICERM Semester Postdoc11th Floor Lecture Hall
2:50 - 3:0010-minute Postdoc introductionsAbel Farkas, ICERM Semester Postdoc11th Floor Lecture Hall
3:00 - 3:1010-minute Postdoc introductionsPeter Hazard, University of Toronto11th Floor Lecture Hall
3:10 - 3:2010-minute Postdoc introductionsZhiqiang Li, ICERM Semester Postdoc11th Floor Lecture Hall
3:30 - 4:30Coffee/Tea Break and Free Time
4:30 - 6:30Welcome Reception11th Floor Collaborative Space

Wednesday February 3, 2016
Time Description Speaker Location Abstracts Slides
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

Thursday February 4, 2016
Time Description Speaker Location Abstracts Slides
11:00 - 11:30IT TutorialBrian Lavall, ICERM Technical Support Coordinator11th Floor Lecture Hall
2:00 - 3:15An example of renormalization in dynamics: rotational attractions of 2D maps.Michael Yampolsky, University of Toronto
3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:15Subadditive topological pressure for nonconformal repeller and it's continuityYongluo Cao, Suzhou University11th Floor Lecture Hall

Friday February 5, 2016
Time Description Speaker Location Abstracts Slides
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

Tuesday February 9, 2016
Time Description Speaker Location Abstracts Slides
1:00 - 2:00Graduate Student/Postdoc Lunch11th Floor Conference Room

Wednesday February 10, 2016
Time Description Speaker Location Abstracts Slides
11:00 - 11:45Mini-course: A class of random Cantor measures, with applicationsPablo Shmerkin, Universidad Torcuato Di Tella11th Floor Lecture Hall
11:45 - 12:15Coffee/Tea Break11th Floor Collaborative Space
12:15 - 1:00Mini-course: A class of random Cantor measures, with applicationsPablo Shmerkin, Universidad Torcuato Di Tella11th Floor Lecture Hall
1:15 - 3:30Break for Lunch/Free Time
3:30 - 4:10Mini-course: Schmidt games and fractals in dynamics and number theory Barak Weiss, Tel Aviv University11th Floor Lecture Hall
4:15 - 4:45Coffee/Tea Break11th Floor Collaborative Space
4:45 - 5:30Mini-course: Schmidt games and fractals in dynamics and number theory Barak Weiss, Tel Aviv University11th Floor Lecture Hall

Thursday February 11, 2016
Time Description Speaker Location Abstracts Slides
11:00 - 11:45Mini-course: Schmidt games and fractals in dynamics and number theoryDmitry Kleinbock, Brandeis University11th Floor Lecture Hall
11:45 - 12:15Coffee/Tea Break11th Floor Collaborative Space
12:15 - 1:00Mini-course: Schmidt games and fractals in dynamics and number theoryDmitry Kleinbock, Brandeis University11th Floor Lecture Hall
1:15 - 3:30Break for Lunch/Free Time
3:30 - 4:15Mini-course: Equidistribution and dimension via additive combinatoricsElon Lindenstrauss, The Hebrew University of Jerusalem11th Floor Lecture Hall
4:15 - 4:45Coffee/Tea Break11th Floor Collaborative Space
4:45 - 5:30Mini-course: Equidistribution and dimension via additive combinatoricsElon Lindenstrauss, The Hebrew University of Jerusalem11th Floor Lecture Hall
5:30 - 6:30Light Reception11th Floor Collaborative Space

Friday February 12, 2016
Time Description Speaker Location Abstracts Slides
11:00 - 11:45Mini-course: A class of random Cantor measures, with applicationsPablo Shmerkin, Universidad Torcuato Di Tella11th Floor Lecture Hall
11:45 - 12:15Coffee/Tea Break11th Floor Collaborative Space
12:15 - 1:00Mini-course: A class of random Cantor measures, with applicationsPablo Shmerkin, Universidad Torcuato Di Tella11th Floor Lecture Hall
1:15 - 3:30Break for Lunch/Free Time
3:30 - 4:15Mini-course: Equidistribution and dimension via additive combinatoricsElon Lindenstrauss, The Hebrew University of Jerusalem11th Floor Lecture Hall
4:15 - 4:45Coffee/Tea Break11th Floor Collaborative Space
4:45 - 5:30Mini-course: Equidistribution and dimension via additive combinatoricsElon Lindenstrauss, The Hebrew University of Jerusalem11th Floor Lecture Hall

Monday February 15, 2016
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45TBDMarianna Csörnyei, University of Chicago11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Ledrappier-Young formula and exact dimensionality of self-affine measuresBalázs Bárány , University of Warwick11th Floor Lecture Hall
11:30 - 12:15TBDAlex Iosevich, University of Rochester11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15TBDAndrás Máthé , University of Warwick11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Some questions in discretized additive combinatoricsJoshua Zahl, MIT11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday February 16, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Dimensions of projected sets and measures on self-affine setsDe-Jun Feng, The Chinese University of Hong Kong11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Dimension estimates for spectral measures in DynamicsBoris Solomyak, Bar-Ilan University11th Floor Lecture Hall
11:30 - 12:15Hausdorff dimension and non-uniquely ergodic interval exchange transformations.Jon Chaika, University of Utah11th Floor Lecture Hall
12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall
12:40 - 2:30Break for Lunch / Free Time
2:30 - 3:15TBDBen Krause, UCLA11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Fractional maximal operators and geometric consequences.Krystal Taylor, University of Minnesota11th Floor Lecture Hall

Wednesday February 17, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Polynomial configurations in fractal sets.Izaballa Laba, University of British Columbia11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Fourier decay and restriction properties of certain fractalsXianghong Chen, U Wisconsin - Milwaukee11th Floor Lecture Hall
11:30 - 12:15A Roth type theorem for large subsets of multidimensional Euclidean spacesMalabika Pramanik, University of British Columbia11th Floor Lecture Hall
12:30 - 2:15Break for Lunch / Free Time
2:15 - 3:00Problem Session
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:15Problem Session

Thursday February 18, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Hausdorff dimension of singular vectorsYitwah Cheung, San Francisco State University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15A new complexity function of repetition and irrationality exponentsDong Han Kim, Dongguk University11th Floor Lecture Hall
11:30 - 12:15Extremality and dynamically defined measuresDavid Simmons, Ohio State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15New constructions of Kakeya and Besicovitch setsYuval Peres, Microsoft Research11th Floor Lecture Hall
3:15 - 3:30On-line Exit Survey Reminder 11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Self affine sets with a fibered tangent structureHenna Koivusalo, University of York11th Floor Lecture Hall

Friday February 19, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Dimension of Furstenberg measure of SL_2(R) random matrix productsMichael Hochman, Hebrew University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Fractal percolation is purely $\alpha$-unrectifiableEsa Järvenpää, University of Oulu11th Floor Lecture Hall
11:30 - 12:15On the dimension of diagonally affine self-affine sets and overlaps.Karoly Simon, Budapest University of Technology and Economics11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15Sections and projections of random fractals and measuresKenneth Falconer, University of St. Andrews11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

= speaker

Please register if you are planning to attend any mini courses.

A class of random Cantor measures, with applications
Speaker: Pablo Shmerkin, Universidad Torcuato Di Tella

  • Wednesday, February 10, 2016 from 11:00 am – 1:00 pm
  • Friday, February 12, 2016 from 11:00 am – 1:00 pm
Schmidt games and fractals in dynamics and number theory
Speakers: Dmitry Kleinbock*, Brandeis University, and Barak Weiss**, Tel Aviv University
  • Wednesday, February 10, 2016 ** from 3:30 pm – 5:30 pm
  • Thursday, February 11, 2016 * from 11:00 am – 1:00 pm
Equidistribution and dimension via additive combinatorics
Speaker: Elon Lindenstrauss, The Hebrew University of Jerusalem
  • Thursday, February 11, 2016 from 3:30 pm – 5:30 pm
  • Friday, February 12, 2016 from 3:30 pm – 5:30 pm


Schedule For Mini-Courses:

Wednesday, February 10th

11:00 - 11:45 Mini-course: A class of random Cantor measures, with applications Pablo Shmerkin, Universidad Torcuato Di Tella 11th Floor Lecture Hall
11:45 - 12:15 Coffee Break 11th Floor Collaborative Space
12:15 - 1:00 Mini-course: A class of random Cantor measures, with applications Pablo Shmerkin, Universidad Torcuato Di Tella 11th Floor Lecture Hall
1:15 - 3:30 Break for Lunch
3:30 - 4:15 Mini-course: Schmidt games and fractals in dynamics and number theory Barak Weiss, Tel Aviv University 11th Floor Lecture Hall
4:15 - 4:45 Coffee Break 11th Floor Collaborative Space
4:45 - 5:30 Mini-course: Schmidt games and fractals in dynamics and number theory Barak Weiss, Tel Aviv University 11th Floor Lecture Hall

Thursday, February 11th

11:00 - 11:45 Mini-course: Schmidt games and fractals in dynamics and number theory Dmitry Kleinbock, Brandeis University 11th Floor Lecture Hall
11:45 - 12:15 Coffee Break 11th Floor Collaborative Space
12:15 - 1:00 Mini-course: Schmidt games and fractals in dynamics and number theory Dmitry Kleinbock, Brandeis University 11th Floor Lecture Hall
1:15 - 3:30 Break for Lunch
3:30 - 4:15 Mini-course: Equidistribution and dimension via additive combinatorics Elon Lindenstrauss, The Hebrew University of Jerusalem 11th Floor Lecture Hall
4:15 - 4:45 Coffee Break 11th Floor Collaborative Space
4:45 - 5:30 Mini-course: Equidistribution and dimension via additive combinatorics Elon Lindenstrauss, The Hebrew University of Jerusalem 11th Floor Lecture Hall

Friday, February 12th

11:00 - 11:45 Mini-course: A class of random Cantor measures, with applications Pablo Shmerkin, Universidad Torcuato Di Tella 11th Floor Lecture Hall
11:45 - 12:15 Coffee Break 11th Floor Collaborative Space
12:15 - 1:00 Mini-course: A class of random Cantor measures, with applications Pablo Shmerkin, Universidad Torcuato Di Tella 11th Floor Lecture Hall
1:15 - 3:30 Break for Lunch
3:30 - 4:15 Mini-course: Equidistribution and dimension via additive combinatorics Elon Lindenstrauss, The Hebrew University of Jerusalem 11th Floor Lecture Hall
4:15 - 4:45 Coffee Break 11th Floor Collaborative Space
4:45 - 5:30 Mini-course: Equidistribution and dimension via additive combinatorics Elon Lindenstrauss, The Hebrew University of Jerusalem 11th Floor Lecture Hall