Dear all,

Our next ETDS seminar will be this Thursday. The details are
Speaker: Alexia Yavicoli (St. Andrews)
Title: On the dimension of sets that avoid approximate arithmetic progressions
Date and time: 23rd April 2pm 
Online link: https://bluejeans.com/729781245

Abstract: I will present quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid epsilon-approximations of arithmetic progressions. These estimates improve considerably the bounds given by Fraser, Saito and Yu (IMRN, 2019), in particular answering a question left open in that paper. I will also show that for this problem, Hausdorff dimension is equivalent to box or Assouad dimension. Joint work with J. Fraser and P. Shmerkin.

Best wishes,

Thomas


PS: In addition the analysis and geometry seminar after the talk may be of interest

The next Analysis & Geometry seminar will be on Thursday 23rd April by 
Jens Marklof from here at Bristol, at 3:15pm.  The title is "Kinetic 
theory for the low-density Lorentz gas" (abstract below).

You can join the meeting via web browser by the following link:
https://bluejeans.com/938671656/6461
The meeting ID, passcode, and alternative ways to connect are given 
below after the abstract.

We will open the meeting around ten minutes early to give people a 
chance to join, and keep it open afterwards for discussion for a little 
while.

Best regards,

Asma, John, Kevin, Michiel


Abstract:

The Lorentz gas is one of the simplest and most widely-studied models 
for particle transport in matter. It describes a cloud of
non-interacting gas particles in an infinitely extended array of 
identical spherical scatterers, whose radii are small compared to their 
mean separation. The model was introduced by Lorentz in 1905 who, 
following the pioneering ideas of Maxwell and Boltzmann, postulated that 
its macroscopic transport properties should be governed by a linear 
Boltzmann equation. A rigorous derivation of the linear Boltzmann 
equation from the underlying particle dynamics was given, for random 
scatterer configurations, in three seminal papers by Gallavotti, Spohn 
and Boldrighini-Bunimovich-Sinai. The objective of this lecture is to 
develop an approach for a large class of deterministic scatterer 
configurations, including various types of quasicrystals. We prove the 
convergence of the particle dynamics to transport processes that are in 
general (depending on the scatterer configuration) not described by the 
linear Boltzmann equation. This was previously understood only in the 
case of the periodic Lorentz gas through work of Caglioti-Golse and 
Marklof-Strombergsson. Our results extend beyond the classical Lorentz 
gas with hard sphere scatterers, and in particular hold for general 
classes of spherically symmetric finite-range potentials. We employ a 
rescaling technique that randomises the point configuration given by the 
scatterers' centers. The limiting transport process is then expressed in 
terms of a point process that arises as the limit of the randomised 
point configuration under a certain volume-preserving one-parameter 
linear group action. Based on joint work with Andreas Strombergsson.
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