Hi, I am an Assistant Professor in the Math Department.

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.

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Office:

St George campus: PG 101B

Scarborough campus: IC 495

Office hours - Winter 2017

Tue 3-4 PM

Thu 2-3 PM

e-mail: tiozzo AT math DOT utoronto DOT ca

*"Quando il tetro dromedario giunse dietro al tetraedro alzò gli occhi e disse: « Diamine! Son davanti a una piramide! »" (T. S.)*