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Seminar

RAS - Postdoc Seminar: Fried's Conjecture and Salem Number Stretch Factors November 19, 2020 (09:00 AM PST - 10:30 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Joshua Pankau (The University of Iowa)
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Fried's Conjecture And Salem Number Stretch Factors

Abstract/Media

To attend this seminar, please register here: https://www.msri.org/seminars/25205

Abstract: Associated to every pseudo-Anosov mapping class is a real number known as its stretch factor. Every stretch factor is a particular type of algebraic integer known as a bi-Perron unit, and it was conjectured by Fried that every bi-Perron unit has a power that is a stretch factor. This remains an open question, but in this talk I will discuss some of my recent work on resolving this conjecture. I will give an overview of a construction of pseudo-Anosov maps due to Thurston, I will describe a way of constructing surfaces from positive integer matrices, and I will discuss how I used these tools to show that Fried's conjecture holds for the class of Salem numbers.

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Fried's Conjecture And Salem Number Stretch Factors

H.264 Video 25257_28815_8642_Fried's_Conjecture_and_Salem_Number_Stretch_Factors.mp4