Dynamical Systems and Analysis Seminar - Steven Robertson
| Dates: | 14 October 2024 |
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| Times: | 14:00 - 15:00 |
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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: Steven Robertson (University of Manchester)
Title: Low Discrepancy Digital Hybrid Sequences and the t-adic Littlewood Conjecture
Abstract: The discrepancy of a sequence measures how quickly it approaches a uniform distribution. Given a natural number d, any collection of one-dimensional so-called low discrepancy sequences {S_i : 1 ? i ? d} can be concatenated to create a d-dimensional hybrid sequence (S_1, . . . , S_d). Since their introduction by Spanier in 1995, many connections between the discrepancy of a hybrid sequence and the discrepancy of its component sequences have been discovered. However, a proof that a hybrid sequence is capable of being low discrepancy has remained elusive. In this talk, an explicit connection between Diophantine approximation over function fields and two dimensional low discrepancy hybrid sequences is provided.
Specifically, it is shown that any counterexample to the so-called t-adic Littlewood Conjecture (t-LC) can be used to create a low discrepancy digital Kronecker-Van der Corput sequence. Such counterexamples to t-LC are known explicitly over a number of finite fields by, on the one hand, Adiceam, Nesharim and Lunnon, and on the other, by Garrett and the Robertson. All necessary concepts will be defined in the talk.
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
