SPRING 2018 SEMINARS AND ABSTRACTS SPRING 2018 SEMINARS AND ABSTRACTS

Seminars take place on Monday afternoons 14:00 - 15:00. Everyone is welcome.

Talks

  • January 22, (Queens 1.03), Michael Livesey (University of Manchester), Towards Donovan's conjecture for abelian defect groups
  • January 29, (JSC 2.03), Clelia Pech (University of Kent)
  • February 5, (JSC 2.03), Joseph Karmanzyn (University of Sheffield), Noncommutative algebras and classifications of threefold flops 
  • February 12, (ARTS 2.02), Hipolito Treffinger (University of Leicester)
  • February 26, (Queens 1.03), Stephane Launois (University of Kent)
  • March 12, (JSC 1.01), PhD Student Talks - Joint Pure and Applied Seminar
  • April 30, (Queens 1.03), Stacey Law (University of Cambridge)

Abstracts

Joseph Karmanzyn: Many aspects of the minimal model program in algebraic geometry can be interpreted and understood via noncommutative algebra.

I will give an introduction to some results in this area. In particular, I will talk about a classification of simple threefold flops in algebraic geometry which Curto and Morrison conjectured could be understood explicitly via matrix factorisations.

I aim to explain how their ideas can be translated into noncommutative algebra where their conjecture can be confirmed.

Michael Livesey: We introduce a new invariant for a p-block, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for blocks with abelian 2-groups of rank at most 4 as defect groups. We also apply these methods to completely classify all blocks with defect group C2n×C2×C2 up to Morita equivalence. This is all joint work with Charles Eaton.

 

Autumn 2017 Seminars and Abstracts Autumn 2017 Seminars and Abstracts

Seminars take place on Monday afternoons 14:00 - 15:00. Everyone is welcome.

Talks

  • 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

Abstracts

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.