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:

- 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. Slides for the School in Bedlewo, April 2019:

An introduction to core entropy

Lecture notes for the Summer School in Teichmueller Dynamics, August 2018:

Random walks on weakly hyperbolic groups

Here are some of my recent preprints:

- Shannon's theorem for locally compact groups, with B. Forghani.
- Entropy and drift for Gibbs measures on geometrically finite manifolds, with I. Gekhtman.

- The core entropy of polynomials of higher degree,

in memoriam of Tan Lei (Angers, Oct 2017) -
Counting loxodromics for group actions

(Warwick, Dec 2017)

Boundaries of random walks and applications at Bowdoin College, June 4-6, 2019.

Please register if you are interested in joining.

My profile by Universities Canada.

My research is partially supported by NSERC and the Sloan Foundation.

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Office:

St George campus: BA 6206

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.)*