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# Geometry MMA Seminar: Correlation theorem and Hitchin representations

Mar 20, 2023, 10:30 - 11:30 AM

**Speaker: **Giuseppe Martone, Yale University

**Title: ** Correlation theorem and Hitchin representations

**Abstract: ** Given distinct hyperbolic structures m and m' on a closed orientable surface, how many closed curves have m- and m'-length roughly equal to x, as x gets large? Schwartz and Sharp's correlation theorem answers this question. Their explicit asymptotic formula involves a term exp(Mx) and 0<M<1 is the correlation number of the hyperbolic structures m and m'.

In this talk, we will show that the correlation number can decay to zero as we vary m and m', answering a question of Schwartz and Sharp. Then, we extend the correlation theorem to Hitchin representations and find diverging sequences of SL(3,R)-Hitchin representations along which the correlation number stays uniformly bounded away from zero.

This talk is based on joint work with Xian Dai.

**Time:** Monday, March 20, 2023 - 10:30am-11:30am

**Place:** Exploratory Hall, Room 4106