Efthymios Sofos (Glasgow) - Multivariate Gaussian distribution for integral points
| Dates: | 24 September 2019 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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| Speaker: | Efthymios Sofos |
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Join us for this research seminar, part of the Number Theory Seminar Series.
Abstract : Given a Diophantine equation with "many" integer solutions, one may ask what is known about the prime factorisation of the coordinates of the integer solutions. For example, are there solutions where every coordinate is prime? We study the typical factorisation of the coordinates of the integer solutions. It turns out that the factorisation is characterised by a multivariate Gaussian distribution, which is in line with the classical Erd?s–Kac theorem.
What is unexpected is that the covariance matrix has an explicit expression via certain geometric invariants associated to the variety defined by the Diophantine equation. Joint work with Daniel El-Baz and Dan Loughran.
Speaker
Efthymios Sofos
Organisation: Glasgow University
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