# Seminars & Colloquia Calendar

## An asymptotic for the growth of Markoff-Hurwitz tuples

#### Ryan Ronan (CUNY)

Location: ** Hill 525**

Date & time: Tuesday, 27 February 2018 at 2:00PM - 3:00PM

The Markoff equation is a Diophantine equation in 3 variables first stud- ied in Markoff’s celebrated work on indefinite binary quadratic forms. An asymptotic formula to count the number of positive integral solutions to this equation below a given height was obtained by Zagier in 1982. In this talk, we establish an asymptotic formula for the growth of solutions to an n variable generalization of this equation, which we refer to as the Markoff- Hurwitz equation. The previous best result for n > 3 is due to Baragar in 1998 who established an exponential rate of growth with an exponent which is not, in general, an integer. We use methods from symbolic dynamics to improve this asymptotic count, and which yield a new interpretation of this exponent as the unique parameter for which there exists a certain conformal measure on projective space.

Joint work with Alex Gamburd and Michael Magee.

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Hong Chen Seminar webpage

Brian Pinsky, Rashmika Goswami website

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

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