## 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), Geometry of rational curves on some varieties with a group action
• 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), Giving an algebraic description of the support scattering diagram
• April 16, (ARTS 2.02), Joint Pure and Applied Seminar, Mr Iain Dorrington (Cardiff University), The biggest bangs since the big one: How to detect Gravitational Waves
• April 23, (ARTS 2.02), Ms Jenny August (University of Edinburgh), The Derived Equivalence Class of Contraction Algebras.
• April 30, (Queens 1.03), Stacey Law (University of Cambridge), On permutation characters and Sylow p-subgroups of the symmetric groups

### Abstracts

Iain Dorrington: In February 2016, LIGO (the Laser Interferometer Gravitational-wave Observatory) announced the first ever direct detection of gravitational-waves. The source of the gravitational-waves was two black holes, each approximately 30 solar masses, crashing together at about 60% of the speed of light. At it’s peak, this system was emitting more energy per second than every light source in the universe combined. Despite the enormous amount of energy released, gravitational-waves have very weak effects. Detecting this signal involved measuring distances to a precision of less than 0.002fm, less than 1% the diameter of a proton. This is not just a huge technological challenge, but a data analysis problem too: How can we be sure we really have detected gravitational-waves? In this seminar I will give an overview of gravitational-wave astronomy. I will cover the basics of gravitational-wave theory, the instruments used to make the detections, and my own work into the data analysis techniques we use.

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.

Clelia Pech: In this talk I will describe a family of algebraic varieties with actions of Lie groups which are closely related to homogeneous spaces (which for instance include projective spaces, quadrics, Grassmannians). After describing the geometry and the orbit structure of these varieties, I will explain how to understand rational curves on these varieties, as well as an algebraic structure encoding the intersection theory of these curves, called the quantum cohomology ring. This is joint work with R. Gonzales, N. Perrin, and A. Samokhin.

Hipolito Treffinger: Cluster scattering diagrams were introduced by Gross, Hacking, Keel and Kontsevich in order to tackle the phenomenon of mirror symmetry, resulting, at the same time, in proofs for several conjectures in the theory of cluster algebras. Later, Bridgeland defined scattering diagrams for quivers with potential and he showed that both notions of scattering diagrams coincide under some technical condition on the potential. In this talk, following Bridgeland's methods, we study the wall and chamber structure of an algebra using the \tau-tilting theory introduced by Adachi, Iyama and Reiten. In particular we show how \tau-rigid pairs induce stability conditions \theta, as defined by King, and we give an explicit description of the category of \theta-semistable modules. As a corollary we show how \tau-tilting pairs induce chambers in the wall and chamber structure of the algebra. This includes all reachable chambers. Time permitting, we will talk about c-vectors for every finite dimensional algebra and their categorical meaning.

Jenny August : Contraction algebras are a class of finite dimensional, symmetric algebras introduced by Donovan and Wemyss as a tool to study the minimal model program in geometry.  In this talk, I will give an introduction to these algebras, before then going on to describe how an associated hyperplane arrangement (a simple picture) controls something that, for a general algebra, is considered extremely complicated; namely, the entire derived equivalence class of such an algebra.

Stacey Law: Let p be an odd prime and n a natural number. We determine the irreducible constituents of the permutation module induced by the action of the symmetric group S_n on the cosets of a Sylow p-subgroup P_n. Before describing some consequences of this result, we will give an overview of the background and recent related results in the area. This is joint work with E. Giannelli.

## 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.