Dr Jason Semeraro

Lecturer in Mathematics

Programme Director of BSc and MMath Mathematics

jpgs1@leicester.ac.uk

Tel: +44 (0)116 252 3892

Office: College House, 202;

Office hours: Wednesday 10am-11am (please let me know if you plan to stop by).

About me

I completed undergraduate and masters degrees in music and mathematics at the University of Birmingham between 2005 and 2009 and music remains a large part of my life. I completed my DPhil in 2013 at the University of Oxford under the supervision of David Craven and Michael Collins. From 2013-2019 I was a Heilbronn Fellow, first at the University of Bristol and then at the University of Leicester. My Erdős number is 2.

Research

I am interested in interactions between algebraic topology, group theory, representation theory and combinatorics. Currently, I am interested in using homotopy theory to develop a modular representation theory for spetses and related structures. Here is a paper I wrote with Radha Kessar and Gunter Malle on that subject.

With Chris Parker I have written some code to compute with and classify fusion systems.

I organised a conference on topological methods in group representation theory with Frank Neumann in November 2019

Selected recent publications:

The principal block of a $\ZZ_\ell$-spets and Yokonuma type algebras arXiv: 2106.14499 (joint with Radha Kessar and Gunter Malle) (submitted)

Weight conjectures for $\ell$-compact groups and spetses arXiv: 2008.07213 (joint with Radha Kessar and Gunter Malle) (submitted)

Weights in a Benson--Solomon block arXiv: 1712.02826 (joint with Justin Lynd) (submitted)

A $2$-compact group as a spets Exper. Math. (2021), 1-16

Algorithms for fusion systems with applications to $p$ -groups of small order (joint with Chris Parker) J. Math. Comp. (2021)

Weight conjectures for fusion systems Adv. Math. 357 (2019), 1-40 (joint with Radha Kessar, Markus Linckelmann and Justin Lynd)

Fusion systems on maximal class $3$-groups of rank two revisited, Proc. Amer. Math. Soc. 147 (2019), 3773-3786 (joint with Chris Parker)

Fusion systems over a Sylow $p$-subgroup of $G_2(p)$ Math. Z. 289 (2018), 629-662 (joint with Chris Parker)

The cycle polynomial of a permutation group Electron. J. Comb, Volume 25, Issue 1 (2018) (joint with Peter Cameron)

Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: II Adv. Math 322 (2017), 201-268 (joint with David Craven and Bob Oliver)

Conway’s groupoid and its relatives Contemporary Mathematics Volume 694, 2017 in honour of John H. Conway (joint with Nick Gill, Neil Gillespie and Cheryl Praeger)

Tournaments, 4-uniform hypergraphs, and an exact extremal result J. Comb. Theory, Series B, 126 (2017) 114-136 (joint with Karen Gunderson)

Travel

Groups, representations and applications: new perspectives, INI, Cambridge, May 22- Jun 11 2022

Workshop on Homotopy Theory and Group Theory (IRP Higher Homotopical Structures), CRM Workshop, Barcelona, July 05-09 2021

CanaDAM 2021, Online, May 25-28 2021

Groups, representations and applications: new perspectives, INI, Cambridge, March 01-14 2020

Groups and Geometries, BIRS, Banff, August 25-30 2019

Classifying spaces of finite groups of Lie type, Copenhagen, July 2019

Representations of Finite Groups, Oberwolfach, March 2019

Group representation theory and applications, MSRI, Berkeley, March 2018

Teaching 21/22

Semester One: MA1114 Linear Algebra; MA2510 Investigations in Mathematics

Semester Two: MA1114 Linear Algebra; MA3412 Representation Theory; MA3511 Communicating Mathematics

Please see relevant Blackboard pages for up-to-date information.

Fun stuff

Noughts and Crosses
Conway's Cosmological Theorem
M(13) demonstration
Finite simple group of order two
Quiver mutations in Java