Hi, I'm a Gibbs Assistant Professor in the Math Department at Yale.
My field of research is dynamical systems and ergodic theory. In particular:
For a more detailed description, see my research statement. My CV can be found here.
- Entropy and Hausdorff dimension in the quadratic family;
- Random walks on groups, especially the mapping class group;
- Ergodic theory of generalized continued fraction transformations.
I got my Ph.D. from Harvard in 2013, under the supervision of C.T. McMullen.
In my thesis, I develop a connection between families of continued fractions and
the combinatorics of the Mandelbrot set, with applications to entropy.
You can have a look at some of my recent preprints:
Continuity of core entropy of quadratic polynomials,
where I discuss the core entropy, a dynamical invariant associated to complex polynomials
by looking at its action
on a certain invariant tree (the Hubbard tree), and prove it is continuous.
Random walks on weakly hyperbolic groups,
(with J. Maher), where we discuss random walks on groups of isometries
of delta-hyperbolic metric spaces which are not necessarily proper.
Thursdays, 4-6 PM, in 417 DL.
Address: Department of Mathematics,
10 Hillhouse Avenue,
New Haven CT 06511
Office #417 DL
e-mail: giulio DOT tiozzo AT yale DOT edu
"Quando il tetro dromedario giunse dietro al tetraedro alzò gli occhi e disse: « Diamine! Son davanti a una piramide! »" (T. S.)