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Department of Mathematical Sciences


This week's seminars

Pure Maths Colloquium: Uniform spectral gap in number theory

Presented by Michael Magee, Durham

20 November 2017 16:00 in CM221

I'll begin by discussing Selberg's eigenvalue conjecture. This is an analog of the Riemann hypothesis for a special family of Riemann surfaces that feature heavily in number theory, for example in Wiles' proof of the Taniyama-Shimura conjecture. I'll explain how in the last 10-15 years, number theorists have had to turn to Anosov dynamics to obtain the approximations to Selberg's conjecture that became relevant to emerging 'thin groups' questions about Apollonian circle packings and continued fractions. I will explain the spectral gap results I worked on in this area. Then if I have time, I'll explain how I am now looking for analogs of the Selberg conjecture in the setting of Teichm├╝ller dynamics with yet more interesting number theory questions in mind.

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Research Seminars by Series

The research groups in the Department of Mathematical Sciences hold several seminar series in term time. Information on date, time and location are available here.

For information on previous years' seminars please see the seminar archives pages.