Dynamical Systems and Analysis Seminar - Rhiannon Dougall
| Dates: | 23 November 2026 |
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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: Rhiannon Dougall (Durham University)
Title: Relative tau, Expanders, and decay of correlations for certain expanding maps
Abstract: Expander graphs are characterized as being "highly connected". Another way think about this is: a sequence of k-regular expander graphs have fast mixing for the simple random walk. We see this phenomena in other places: the "geodesic flow" dynamics associated to certain congruence covers of $\mathbb{H}^2/PSL(2,Z)$ have exponential decay of correlations (uniform in the covers), and this can be seen as being related to the expander property for the associated Cayley graphs.
The previous two examples one has some nice structures: self-adjoint operators and representation theory. Does one still expect good mixing behaviour for analogous extensions of maps with “hyperbolic” behaviour? I will consider this problem for dynamics driven by 1. A subshift of finite type, or 2. An expanding interval map.
The problem is (surely?) interesting but the arguments are also nice for how they gather adjacent concepts mathematics.
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
