Mathematics Dept.
  Events
Kornelia Hera
Eotvos Lorand University, Budapest
Fri 19 Jan 2018, 2:00pm
Harmonic Analysis Seminar
MATH 126
Furstenberg-type estimates for unions of affine subspaces
MATH 126
Fri 19 Jan 2018, 2:00pm-3:00pm

Abstract

A plane set is called a t-Furstenberg set for some t in (0,1), if it has an at least t-dimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension).  Classical results are that every t-Furstenberg set has dimension at least 2t, and at least t + 1/2.

We generalize these estimates for families of affine subspaces. As a result, we prove that the union of any s-dimensional family of k-dimensional affine subspaces is at least k + s/(k+1) -dimensional, and is exactly k + s -dimensional if s is at most 1.

Based on joint work with Tamas Keleti and Andras Mathe.
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