Assistant Professor of Mathematics
University of Toronto
My field of research is dynamical systems and ergodic theory, with applications to
complex analysis, probability, and geometric group theory. In particular:
For a more detailed description, see my research statement (from 2015).
- 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.
Lecture notes for the Summer School in Teichmueller Dynamics, August 2018:
Random walks on weakly hyperbolic groups
Here are some slides related to my recent work:
My research is partially supported by NSERC and the Sloan Foundation.
St George campus: BA 6206
Office hours Fall 2018: Mon 4.30-5.30 PM
Scarborough campus: IC 495
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.)