Symmetry in Newcastle seminar is here again! The confirmed speakers for next Monday are Libor Barto, Charles University in Prague, and Zoe Chatzidakis, CNRS–ENS. Feel free to grab a beverage appropriate for your respective timezone (we won’t judge) and join us for a friendly chat during the break!
The talks will be recorded and made available on our YouTube channel https://tinyurl.com/zerodimensionalgroup and our website https://zerodimensional.group/. The running times of the talks, titles and abstracts are as follows:
16:30–17:30 AEST (06:30–07:30 UTC) Libor Barto
17:30–18:00 AEST (07:30–08:00 UTC) Break and chat
18:00–19:00 AEST (08:00–90:00 UTC) Zoe Chatzidakis
Speaker: Libor Barto (Charles University in Prague)
Title: CSPs and Symmetries
How difficult is to solve a given computational problem? In a large class of computational problems, including the fixed-template Constraint Satisfaction Problems (CSPs), this fundamental question has a simple and beautiful answer: the more symmetrical the problem is, the easier is to solve it. The tight connection between the complexity of a CSP and a certain concept that captures its symmetry has fueled much of the progress in the area in the last 20 years. I will talk about this connection and some of the many tools that have been used to analyze the symmetries. The tools involve rather diverse areas of mathematics including algebra, analysis, combinatorics, logic, probability, and topology.
Speaker: Zoe Chatzidakis (CNRS–ENS)
Title: A new invariant for difference fields
If (K, f ) is a difference field, and a is a finite tuple in some difference field extending K, and such that f (a) in K(a)alg, then we define dd(a/K)=lim[K( f k(a),a):K(a)]1/k, the distant degree of a over K. This is an invariant of the difference field extension K(a)alg/K. We show that there is some b in the difference field generated by a over K, which is equi-algebraic with a over K, and such that dd(a/K)=[K( f (b),b):K(b)], i.e.: for every k>0, f(b) in K(b, f k(b)).
Viewing Aut(K(a)alg/K) as a locally compact group, this result is connected to results of Goerge Willis on scales of automorphisms of locally compact totally disconnected groups. I will explicit the correspondence between the two sets of results.
(Joint with E. Hrushovski)
The zoom link is https://uonewcastle.zoom.us/j/82596235512.
Hope to see some of you on Monday!