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

Image for "Ergodic, Algebraic and Combinatorial Methods in Dimension Theory"
Fractal shapes in nature. Photo credit I. Laba

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, February 15, 2016
TimeEventLocationMaterials
8:30 - 8:55am ESTRegistration11th Floor Collaborative Space 
8:55 - 9:00am ESTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am ESTTangents of curves and projection theorem in infinite dimensional spaces - Marianna Csörnyei, University of Chicago11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTLedrappier-Young formula and exact dimensionality of self-affine measures - Balázs Bárány, University of Warwick11th Floor Lecture Hall
11:30 - 12:15pm ESTFinite point configurations- a survey of techniques and ideas - Alex Iosevich, University of Rochester11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTMeasurable equidecompositions and circle squaring - András Máthé, University of Warwick11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTSome questions in discretized additive combinatorics - Joshua Zahl, MIT11th Floor Lecture Hall 
5:00 - 6:30pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, February 16, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTDimensions of projected sets and measures on self-affine sets - De-Jun Feng, The Chinese University of Hong Kong11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:00 - 10:15am ESTPoster Presentation - Magdalena Nowak11th Floor Collaborative Space 
10:30 - 11:15am ESTDimension estimates for spectral measures in Dynamics - Boris Solomyak, Bar-Ilan University11th Floor Lecture Hall
11:30 - 12:15pm ESTHausdorff dimension and non-uniquely ergodic interval exchange transformations. - Jon Chaika, University of Utah11th Floor Lecture Hall
12:40 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTDiscrete Analogues in Harmonic Analysis- A Quadratic Carleson Theorem - Ben Krause, UCLA11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTFractional maximal operators and geometric consequences. - Krystal Taylor, The Ohio State University11th Floor Lecture Hall 
Wednesday, February 17, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTPolynomial configurations in fractal sets. - Izaballa Laba, University of British Columbia11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTA Roth type theorem for large subsets of multidimensional Euclidean spaces - Malabika Pramanik, University of British Columbia11th Floor Lecture Hall
11:30 - 12:15pm ESTProblem Session11th Floor Lecture Hall 
12:30 - 2:15pm ESTBreak for Lunch / Free Time  
2:15 - 4:30pm ESTDiscussion / Work Time  
3:00 - 3:30pm ESTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, February 18, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTHausdorff dimension of singular vectors - Yitwah Cheung, San Francisco State University11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTA new complexity function of repetition and irrationality exponents - Dong Han Kim, Dongguk University11th Floor Lecture Hall 
11:30 - 12:15pm ESTExtremality and dynamically defined measures - David Simmons, Ohio State University11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTNew constructions of Kakeya and Besicovitch sets - Yuval Peres, Microsoft Research11th Floor Lecture Hall
3:15 - 3:30pm ESTOn-line Exit Survey Reminder - 11th Floor Lecture Hall 
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTSelf affine sets with a fibered tangent structure - Henna Koivusalo, University of York11th Floor Lecture Hall
Friday, February 19, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTDimension of Furstenberg measure of SL_2(R) random matrix products - Michael Hochman, Hebrew University11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTFractal percolation is purely a-unrectifiable - Esa Järvenpää, University of Oulu11th Floor Lecture Hall
11:30 - 12:15pm ESTOn the dimension of diagonally affine self-affine sets and overlaps. - Karoly Simon, Budapest University of Technology and Economics11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
12:30 - 12:40pm ESTGroup Photo in Lecture Hall11th Floor Lecture Hall 
2:30 - 3:15pm ESTSections and projections of random fractals and measures - Kenneth Falconer, University of St. Andrews11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

Dimension and Dynamics
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Computation in Dynamics
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Lecture Videos