Ergodic, Algebraic and Combinatorial Methods in Dimension Theory
(February 15-19, 2016)

Picture
Fractal shapes in nature. Photo credit I. Laba

Description

There are natural interactions between dimension theory, ergodic theory, additive combinatorics, metric number theory and analysis. Each of these fields provides different perspectives on, and complementary approaches to, the hierarchical structures which appear in fractal geometry.

The workshop will focus on recent advances at the interfaces of these fields, including:

  • Classical fractals (self-similar and self-affine sets, random fractals).
  • Dimension theory and additive combinatorics.
  • Diophantine approximation and equidistribution.
  • Schmidt games.
  • Rigidity phenomena.
  • Scenery flow methods.
  • Projection and slice theorems.

Organizing Committee

= speaker   = poster presenter

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 - 9:45Tangents of curves and projection theorem in infinite dimensional spacesMarianna Csörnyei, University of Chicago11th Floor Lecture Hall
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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
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11:30 - 12:15Finite point configurations- a survey of techniques and ideasAlex Iosevich, University of Rochester11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15Measurable equidecompositions and circle squaringAndrás Máthé, University of Warwick11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45An additive energy bound for Ahlfors-regular setsJoshua Zahl, MIT11th Floor Lecture Hall
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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
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:00 - 10:15Poster PresentationMagdalena Nowak11th Floor Collaborative Space
10:30 - 11:15Dimension estimates for spectral measures in DynamicsBoris Solomyak, Bar-Ilan University11th Floor Lecture Hall
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11:30 - 12:15Hausdorff dimension and non-uniquely ergodic interval exchange transformations.Jon Chaika, University of Utah11th Floor Lecture Hall
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12:40 - 2:30Break for Lunch / Free Time
2:30 - 3:15Discrete Analogues in Harmonic Analysis- A Quadratic Carleson TheoremBen Krause, UCLA11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Fractional maximal operators and geometric consequences.Krystal Taylor, The Ohio State University11th 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
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15A Roth type theorem for large subsets of multidimensional Euclidean spacesMalabika Pramanik, University of British Columbia11th Floor Lecture Hall
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11:30 - 12:15Problem Session11th Floor Lecture Hall
12:30 - 2:15Break for Lunch / Free Time
2:15 - 4:30Discussion / Work Time
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space

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
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Dirichlet uniformly well-approximated numbersDong Han Kim, Dongguk University11th Floor Lecture Hall
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11:30 - 12:15Extremality and dynamically defined measuresDavid Simmons, Ohio State University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15New constructions of Kakeya and Besicovitch setsYuval Peres, Microsoft Research11th Floor Lecture Hall
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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
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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
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Fractal percolation is purely a-unrectifiableEsa Järvenpää, University of Oulu11th Floor Lecture Hall
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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
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12:30 - 2:30Break for Lunch / Free Time
12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall
2:30 - 3:15Sections and projections of random fractals and measuresKenneth Falconer, University of St. Andrews11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space