Organizing Committee
Abstract

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

Fractal shapes in nature. Photo credit I. Laba

Confirmed Speakers & Participants

Workshop Schedule

Monday, February 15, 2016
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Tangents of curves and projection theorem in infinite dimensional spaces - Marianna 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 measures - Balázs Bárány, University of Warwick11th Floor Lecture Hall
11:30 - 12:15Finite point configurations- a survey of techniques and ideas - Alex Iosevich, University of Rochester11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Measurable equidecompositions and circle squaring - András Máthé, University of Warwick11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45An additive energy bound for Ahlfors-regular sets - Joshua Zahl, MIT11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, February 16, 2016
TimeEventLocationMaterials
9:00 - 9:45Dimensions of projected sets and measures on self-affine sets - De-Jun Feng, The Chinese University of Hong Kong11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:00 - 10:15Poster Presentation - Magdalena Nowak11th Floor Collaborative Space 
10:30 - 11:15Dimension estimates for spectral measures in Dynamics - Boris 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
12:40 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Discrete Analogues in Harmonic Analysis- A Quadratic Carleson Theorem - Ben 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, The Ohio State University11th Floor Lecture Hall 
Wednesday, February 17, 2016
TimeEventLocationMaterials
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 - 11:15A Roth type theorem for large subsets of multidimensional Euclidean spaces - Malabika Pramanik, University of British Columbia11th Floor Lecture Hall
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
TimeEventLocationMaterials
9:00 - 9:45Hausdorff dimension of singular vectors - Yitwah Cheung, San Francisco State University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Dirichlet uniformly well-approximated numbers - Dong Han Kim, Dongguk University11th Floor Lecture Hall
11:30 - 12:15Extremality and dynamically defined measures - David Simmons, Ohio State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15New constructions of Kakeya and Besicovitch sets - Yuval 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 structure - Henna Koivusalo, University of York11th Floor Lecture Hall
Friday, February 19, 2016
TimeEventLocationMaterials
9:00 - 9:45Dimension of Furstenberg measure of SL_2(R) random matrix products - Michael Hochman, Hebrew University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Fractal percolation is purely a-unrectifiable - Esa 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  
12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall 
2:30 - 3:15Sections and projections of random fractals and measures - Kenneth Falconer, University of St. Andrews11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

Dimension and Dynamics
Computation in Dynamics

Lecture Videos