• January 16th, no seminar.
• January 23rd, no seminar.
• January 30th, David Evans (UEA), Primitive and highly arc transitive digraphs of finite out-valency.
• February 6th, Fred Diamond (King's College), Mod p Langlands correspondences.
• February 13th, Lynne Walling (Bristol), Representations by quadratic forms and Siegel modular forms.
• February 20th, Matt Fayers (Queen Mary), Decomposable Specht modules.
• February 27th, Benedikt Loewe (Amsterdam/INI), TBA.
• March 5th, Rod Gow (University College Dublin), TBA.
• March 12th, Vincenzo Mantova (Oxford), TBA.
• March 19th, Peter Joergensen (Newcastle), TBA.
• March 26th, Vincent Sécherre (Versailles), TBA.
• April 23rd
• May 14th, Robert Marsh (Leeds), TBA.
• May 21st, Toby Gee (Imperial), TBA.

Abstracts

• David Evans: Primitive and highly arc transitive digraphs of finite out-valency
  
  We give a survey of some recent work on directed graphs of finite out-valency and infinite in-valency which have a `large' automorphism group. Suitable notions of largeness here are primitivity, high arc transitivity or descendant homogeneity. The questions of interest are the construction and classification of such digraphs, and the structure of their automorphism groups. Much of what I will talk about is joint work by various subsets of Daniela Amato, John Truss and myself.
   
• Fred Diamond: Mod p Langlands correspondences
  
  The Langlands program  envisions a conjectural framework of compatible correspondences between objects from number theory (such as elliptic curves and Galois representations)
  and objects from representation theory (such as modular forms and automorphic representations). Recent advances (due to Colmez, Emerton, Kisin and others) have come via proving mod p and p-adic versions of these correspondences.  I'll discuss how this works for GL(2) and what some of the obstacles are in trying to generalize the approach to other groups.
   
• Lynne Walling: Representations by quadratic forms and Siegel modular forms
  
  Quadratic forms impose "geometry" on vector spaces, capturing notions of length and orthogonality.  In number theory, we are typically interested in discrete objects; thus we might consider a lattice L equipped with a quadratic form Q.  A classical question is, given an integer t, how many vectors in L have length t?  More generally, given another quadratic form T, on how many sublattices of L does Q restrict to T?  Siegel introduced generalised theta series to encode the answer to this question (for all T), giving us our first examples of Siegel modular forms.  I will give an introduction to this area, then discuss how we can use Siegel Eisenstein series and Hecke operators to find closed-form formulas that answer the latter question posed above.
   
• Matt Fayers: Decomposable Specht modules
  
  The Specht modules are important modules defined for the symmetric group in any characteristic, and a great deal of effort is devoted to finding their structure. It is known that if the underlying characteristic is not 2, then all Specht modules are indecomposable. In characteristic 2 there are decomposable Specht modules, but examples are hard to find. I will report on recent joint work with Craig Dodge, in which we have found new examples of decomposable Specht modules. I will keep this talk elementary and it will be mostly background, with some hands-on calculation.
  
   

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Pure Mathematics seminar archives

The archives of previous years' seminars are here:

http://www.uea.ac.uk/~h008/seminar/pure-seminars-old.shtml