Events at The University of Manchester
  • University home
  • Events
  • Home
  • Exhibitions
  • Conferences
  • Lectures and seminars
  • Performances
  • Events for prospective students
  • Family events
  • All Events

Logic Seminar - Dugald Macpherson (Leeds)

Dates:11 May 2022
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Adults, Alumni, Current University students
See travel and contact information
Add to your calendar

More information

  • Department of Mathematics

Other events

  • In category "Seminar"
  • In group "(Maths) Maths seminar series"
  • In group "(Maths) Logic"
  • By Department of Mathematics

Title: Uniform families of definable sets in finite structures

Abstract: A theorem of Chatzidakis, van den Dries and Macintyre, stemming ultimately from the Lang-Weil estimates, asserts, roughly, that if \phi(x,y) is a formula in the language of rings (where x,y are tuples) then the size of the solution set of \phi(x,a) in any finite field F_q (where a is a parameter tuple from F_q) takes one of finitely many dimension-measure pairs as F_q and a vary: for a finite set E of pairs (\mu,d) (\mu rational, d integer) dependent on \phi, any set \phi(F_q,a) has size roughly \mu.q^d for some (\mu,d) \in E. This led in work of Elwes, Steinhorn and myself to the notion of `asymptotic class’ of finite structures (a class satisfying essentially the conclusion of Chatzidakis-van den Dries-Macintyre). As an example, by a theorem of Ryten, any family of finite simple groups of fixed Lie type forms an asymptotic class. There is a corresponding notion for infinite structures of `measurable structure’ (e.g. a pseudofinite field, by the Chatzidakis- van den Dries-Macintyre theorem, or certain pseudofinite difference fields). I will discuss a body of work with Sylvy Anscombe, Charles Steinhorn and Daniel Wolf which generalises this, incorporating a richer range of examples with fewer model-theoretic constraints; for example, the corresponding infinite `generalised measurable’ structures, for which the definable sets are assigned values in some ordered semiring, need no longer have simple theory. I will also discuss a variant in which sizes of definable sets in finite structures are given exactly rather than asymptotically.

Travel and Contact Information

Find event

Frank Adams 1 (and zoom, link in email)
Alan Turing Building
Manchester

 

Share / follow event

Contact us

  • +44 (0) 161 306 6000

Find us

The University of Manchester
Oxford Rd
Manchester
M13 9PL
UK

Connect with the University

  • Facebook page for The University of Manchester
  • Twitter page for The University of Manchester
  • YouTube page for The University of Manchester
  • Google+ page for The University of Manchester
  • Pinterest page for The University of Manchester

  • Privacy /
  • Copyright notice /
  • Accessibility /
  • Freedom of information /
  • Charitable status /
  • Royal Charter Number: RC000797
  • Close menu
  • Home
    • Featured events
    • Today's events
    • The Whitworth events
    • Manchester Museum events
    • Jodrell Bank Discovery Centre events
    • Martin Harris Centre events
    • The John Rylands Library events
    • Exhibitions
    • Conferences
    • Lectures and seminars
    • Performances
    • Events for prospective students
    • Family events
    • All events