Department of Mathematics,
University of California San Diego
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Math 211B - Group Actions Seminar
Luke Jeffreys
University of Bristol
Local dimension in the Lagrange and Markov spectra
Abstract:
Initially studied by Markov around 1880, the Lagrange spectrum, $L$, and the Markov spectrum, $M$, are complicated subsets of the real line that play a crucial role in the study of Diophantine approximation and binary quadratic forms. Perron's 1920s description of the spectra in terms of continued fractions allowed powerful dynamical machinery to come to bear on many problems. In this talk, I will discuss recent work with Harold Erazo and Carlos Gustavo Moreira investigating the function $d_\textrm{loc}(t)$ that determines the local Hausdorff dimension at a point $t$ in $L'$.
Host: Brandon Seward
January 9, 2025
10:00 AM
https://ucsd.zoom.us/j/
Research Areas
Ergodic Theory and Dynamical Systems****************************
