• SYMMETRY IN NEWCASTLE
  • Location: (Online Campus)
  • Dates: Mon, 23rd Nov 2020 - Mon, 23rd Nov 2020
  • Schedule (Zoom):

    18.30-19.30: William Hautekiet
    19.30-20.00: Break
    20.00-21.00: Florian Breuer


  • Speaker: Dr William Hautekiet, Facult√© des Sciences, Universit√© libre de Bruxelles
  • Title: Automorphism groups of transcendental field extensions
  • Abstract for Automorphism groups of transcendental field extensions:
         It is well-known that the Galois group of an (infinite) algebraic field extension is a profinite group. When the extension is transcendental, the automorphism group is no longer compact, but has a totally disconnected locally compact structure (TDLC for short). The study of TDLC groups was initiated by van Dantzig in 1936 and then restarted by Willis in 1994. In this talk some of Willis' concepts, such as tidy subgroups, the scale function, flat subgroups and directions are introduced and applied to examples of automorphism groups of transcendental field extensions. It remains unknown whether there exist conditions that a TDLC group must satisfy to be a Galois group. A suggestion of such a condition is made.

  • Speaker: Prof. Florian Breuer, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Realising general linear groups as Galois groups
  • Abstract for Realising general linear groups as Galois groups:
         I will show how to construct field extensions with Galois groups isomorphic to general linear groups (with entries in various rings and fields) from the torsion of elliptic curves and Drinfeld modules. No prior knowledge of these structures is assumed.
  • Abstract for Automorphism groups of transcendental field extensions:

    It is well-known that the Galois group of an (infinite) algebraic field extension is a profinite group. When the extension is transcendental, the automorphism group is no longer compact, but has a totally disconnected locally compact structure (TDLC for short). The study of TDLC groups was initiated by van Dantzig in 1936 and then restarted by Willis in 1994. In this talk some of Willis' concepts, such as tidy subgroups, the scale function, flat subgroups and directions are introduced and applied to examples of automorphism groups of transcendental field extensions. It remains unknown whether there exist conditions that a TDLC group must satisfy to be a Galois group. A suggestion of such a condition is made.

  • Abstract for Realising general linear groups as Galois groups:

    I will show how to construct field extensions with Galois groups isomorphic to general linear groups (with entries in various rings and fields) from the torsion of elliptic curves and Drinfeld modules. No prior knowledge of these structures is assumed.

  • [Permanent link]



  • CARMA COLLOQUIUM
  • Speaker: Prof. Florian Breuer, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: The Parallel Worlds of Number Theory
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 10th May 2018
  • Abstract:

    There is an intriguing analogy between number fields and function fields. If we view classical Number Theory as the study of the ring of integers and its extensions, then function field arithmetic is the study of the ring of polynomials over a finite field and its extensions. According to this analogy, most constructions and phenomena in classical Number Theory, ranging from the elementary theorems of Euler, Fermat and Wilson, to the Riemann Hypothesis, Elliptic curves, class field theory and modular forms all have their function field analogues. I will give a panoramic tour of some of these constructions and highlight their similarities and differences to their classical counterparts.

    This lecture should be accessible to advanced undergraduate students.

  • [Permanent link]