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:

- 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:

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.

(with J. Maher), where we discuss random walks on groups of isometries

of delta-hyperbolic metric spaces which are not necessarily proper.

## Papers |
## Teaching |
## Slides |
## Gallery |

Office hours:

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.)*