Giulio Tiozzo

I'm currently a fourth-year grad student in Mathematics at Harvard, under the supervision of Prof. C. McMullen.
My field of research is dynamical systems and ergodic theory. My CV can be found here.

Papers

  1. A canonical thickening of Q and the entropy of alpha-continued fraction transformations (with C. Carminati),
    to appear in Ergodic Theory and Dynamical Systems.
  2. The entropy of alpha-continued fractions: numerical results (with C. Carminati, S. Marmi, A. Profeti),
    Nonlinearity 23 (2010), 2429-2456.
  3. Dynamics of continued fractions and kneading sequences of unimodal maps (with C. Bonanno, C. Carminati, S. Isola),
    to appear in Discrete and Continuous Dynamical Systems, Series A.
  4. The entropy of alpha-continued fractions: analytical results, submitted.
  5. The bifurcation locus for numbers of bounded type (with C. Carminati).
  6. Tuning and plateaux for the entropy of alpha-continued fractions (with C. Carminati), submitted.

Teaching

Fall 2011: MATH 1a "Introduction to calculus"
Fall 2010: MATH 1a "Introduction to calculus"
Fall 2009: MATH 99r tutorial "Dynamics of analytic maps and small divisor problems"

Other math

Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set, slides from my talk in Warwick, April 2012.
A poster on alpha-continued fractions and renormalization.
Slides from my talk on "Dynamics of continued fractions and kneading sequences of unimodal maps", and a slightly different presentation.
Differentiable structures on the 7-sphere. This is my minor thesis at Harvard.
Dynamics of continued fractions and central limit theorem (in Italian). My senior thesis.
The convex hull associated to a cubic number field.

Address: Dept of Mathematics, 1 Oxford St 02138 Cambridge MA
Office #532 SC
e-mail: tiozzo AT math DOT harvard DOT edu

RA 19h34m52.91 +38 25'17.5''