Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Sums of two Cantor sets and Palis conjecture

Yuki Takahashi
Monday, May 16, 2016
4:00 pm - 4:50 pm
RH340P

Talk Abstract:

Sums of two Cantor sets arise naturally in homoclinic bifurcations, Markov and Lagrange dynamical spectra, and the spectrum of the square Fibonacci Hamiltonian. In the 1970s Palis conjectured that for generic pairs of regular Cantor sets either the sum has zero Lebesgue measure or else it contains an interval. This problem is known to be extremely difficult, and is still open for affine Cantor sets. In this talk, we will discuss the history of sums of two Cantor sets, and also introduce my recent results about sums of two homogeneous Cantor sets.

About the Speaker:

Yuki is a 4th year Ph.D. student at UC Irvine. He received a Bachelor's degree in Mathematics from the University of Tokyo, and now he is working on Dynamical Systems and Mathematical Physics under the guidance of Professor A. Gorodetski. In his free time, Yuki enjoys juggling, swimming, and practicing yoga.

Refreshments:

Pizza will be served after the talk.