Seminars take place on Monday afternoons 14:00 - 15:00. Everyone is welcome.
- October 23, (Queens 1.03), Ben Fairbarn (Birbeck), Invertible Generating Graphs
- October 30, (EFry 01.10), Gareth Jones (Manchester), Pfaffian functions and elliptic functions
- November 6, (TPSC 0.1), Xiaoting Zhang (Uppsala)
- November 13, (TPSC 0.1), Anton Cox (City, University of London), Paths and the graded representation theory of cyclotomic Hecke algebras.
- November 20, (C.Hall 0.17), Daniel Skodlerack, Cuspidal representations of p-adic classical groups and semisimple characters
- December 4, (Lecture Theatre 4), Vincenzo Mantova (University of Leeds), About the Dual Schanuel Conjecture
- December 11, (EFry 1.01), Behrang Noohi (QMUL), Enhanced HRS-tilting
Ben Fairbarn: Let G be a group. The generating graph of G is defined as follows: the vertices are the non-trivial elements of G with two vertices being adjoined by an edge if the corresponding pair of elements generate the group. This much-studied object is known to encode a number of generational properties of the group. In this talk we will discuss a variant recently introduced by the speaker.
Gareth Jones: I will discuss work with Harry Schmidt in which we give a definition of Weierstrass elliptic functions in terms of pfaffian functions, refining a result due to Macintyre. I'll also mention an application in which we give an effective version of a result of Corvaja, Masser and Zannier on a sharpening of the Manin-Mumford conjecture for non-split extensions of elliptic curves by the additive group.
Anton Cox: By considering certain diagrammatic Cherednik algebras introduced by Webster, we will show how a theory of paths can be used to investigate the modular representation theory of cyclotomic Hecke algebras. This gives new results even in the classical type A case.
Daniel Skodlerack: To give the full classification of complex cuspidal irreducible representations of quaternionic inner forms of classical groups (p odd) we generalize semisimple characters to the quaternionic case. These characters play an important role in the explicit description of the Jacquet-Langlands correspondence and the Local Langlands correspondence for classical groups.
Vincenzo Mantova: Schanuel's conjecture predicts a lower bound for the transcendence degree of the values of the complex exponential function. A lesser known "dual" conjecture, formulated independently by Schanuel and by Zilber, is the following: the graph of the exponential function must intersect generically all "free rotund" algebraic varieties. This would have strong consequences (i.e., quasi-minimality) for the model theory of complex exponentiation.
Behrang Noohi: Happel-Reiten-Smalo tilting associates to a torsion pair (T,F) in an abelian category A a new category B with a new torsion pari (T',F'). This is done via `tilting' the standard t-structure on the derived category D(A) using the torsion pair. In this talk we give an alternative explicit construction of B, of the DG structure on the category of chains Ch(B), and the derived category D(B). This is achieved using a new notion which we call a `decorated complex' that may (or may not!) be of independent interest.