Dynamical Systems and Analysis Seminar - Sean Prendiville
| Dates: | 10 February 2025 |
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| Times: | 14:00 - 14:00 |
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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, Current University students |
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Speaker: Sean Prendiville (University of Lancaster)
Title: An inverse theorem for the Gowers U^3 norm relative to quadratic level sets
Abstract: The Gowers uniformity norms have become well-used tools in additive combinatorics, ergodic theory and analytic number theory. We discuss the utility of these objects and their associated inverse theorems. We report on a recent effective version of the inverse theorem for the Gowers U^3-norm for functions supported on high-rank quadratic level sets in finite vector spaces. This enables one to run so-called "density increment arguments" with respect to quadratic level sets, which are analogues of Bohr sets in the context of quadratic Fourier analysis on finite vector spaces. For instance, one can use such an approach to derive an exponential bound on the Ramsey number of three-term progressions which are the same colour as their common difference ("Brauer quadruples"), a result it seems difficult to obtain by other means.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
