Posts

Symmetry in Newcastle, 1 July 2022

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Symmetry in Newcastle seminar is here again! If you like groups acting trees, then this Friday is your lucky day because the confirmed speakers for this Friday are Claudio Bravo, University of Chile, Matt Conder, University of Auckland, and George Willis, University of Newcastle. We will be meeting in room W202 on Callaghan campus, but fear not – you can still join us via zoom! Feel free to grab a beverage appropriate for your respective timezone and join us for a friendly chat during the morning tea!

The zoom link is https://uonewcastle.zoom.us/j/82596235512.

For more information and schedule see the AustMS events page.

Symmetry in Newcastle seminar – Monday 24th May 2021

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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

Abstract:
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

Abstract:
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)

See the website for Zoom details.

Symmetry in Newcastle – 19th April 2021

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Symmetry in Newcastle seminar is here again! The confirmed speakers for next Monday are Zoe Chatzidakis, CNRS – ENS, and Laura Ciobanu, Herriot-Watt University. Feel free to grab a beverage appropriate for your respective timezone 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) Zoe Chatzidakis

17:30 – 18:00 AEST (07:30 – 08:00  UTC) Break and chat

18:00 – 19:00 AEST (08:00 – 09:00  UTC) Laura Ciobanu

Speaker: Zoe Chatzidakis (CNRS – ENS)
Title: A new invariant for difference fields
Abstract: 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)

Speaker: Laura Ciobanu
Title: Free group homomorphisms and the Post Correspondence Problem
Abstract: The Post Correspondence Problem (PCP) is a classical problem in computer science that can be stated as: is it decidable whether given two morphisms g and h between two free semigroups A and B, there is any nontrivial x in A such that g(x)=h(x)? This question can be phrased in terms of equalisers, asked in the context of free groups, and expanded: if the `equaliser’ of g and h is defined to be the subgroup consisting of all x where g(x)=h(x), it is natural to wonder not only whether the equaliser is trivial, but what its rank or basis might be.

While the PCP for semigroups is famously insoluble and acts as a source of undecidability in many areas of computer science, the PCP for free groups is open, as are the related questions about rank, basis, or further generalisations. However, in this talk we will show that there are links and surprising equivalences between these problems in free groups, and classes of maps for which we can give complete answers. This is joint work with Alan Logan.