I'm currently a EPSRC research fellow at the University of Sheffield. I moved here from the University of Bath in October 2016.
My recent research interests have been in the study of resolutions and deformations of singularities,
particularly working with non-commutative algebras to study derived categories in geometry. I'm also interested moduli space constructions in these situations.
Noncommutative algebras and classifications of threefold flops.
Pure Mathematics Seminar, University of East Anglia
Noncommutative algebras and equivalences of singularity categories.
London Algebra Seminar, City University
Matrix factorisations, noncommutative algebras, and the length classifications of threefold flops.
Algebra Seminar, The University of York
The length classification of simple threefold flops, matrix factorisations, and noncommutative algebras.
Geometry Seminar, The University of Hong Kong
Threefold flops, matrix factorisations, and noncommutative algebras.
Algebra seminar, University of Leeds
Knorrer periodicity for cyclic quotient surface singularities.
Matrix factorisations and related topics, ICMS Edinburgh
Noncommutative algebras and universal flops.
Linking noncommutative rings and algebraic geometry, ICMS Edinburgh
Universal flops and noncommutative algebras.
AG seminar, Oxford
November 2016 -
Simultaneous Resolutions and Noncommutative Algebras.
3C in G/EMG conference, Warwick
October 2016 -
Rational curves and noncommutative algebra
Algebraic Geometry Seminar, Sheffield
August 2016 -
Singularity categories of cyclic quotient
Homological Methods in Algebra and Geometry, AIMS Ghana
May 2016 -
Resolving rational surface singularities via noncommutative algebra.
ICTP mathematics seminar, ICTP
April 2016 -
Nakayama's lemma and the generation of derived categories.
DeCaDe 2016 , Edinburgh
March 2016 -
Total spaces of line bundles and deformations of surface singularities.
Workshop on Weighted Projective Spaces and Representation Theory , Hefei
December 2015 - Knörrer periodicity and equivalences of singularity categories.
Algebra / Algebraic Geometry seminar , Sheffield
October 2015 - Noncommutative Knörrer periodicity.
Edge Seminar , Edinburgh
April 2015 -
Realising moduli spaces from derived equivalences.
COW meeting , BMC Cambridge
March 2015 -
Moduli spaces and the minimal model program.
Geometry Seminar , Bath
March 2015 -
Moduli, McKay, and Minimal Models.
EDGE Seminar , Edinburgh
Nov 2014 - Constructing Moduli spaces of Quiver Representations.
Gears Seminar , Edinburgh and Glasgow student seminar
Nov 2014 - Quiver GIT for Reconstruction Algebras.
Algebra Seminar , Glasgow
Sept 2014 - Quiver GIT and Resolving Rational Surface Singularities.
McKay Correspondence, Orbifolds, Quivers , EPSRC Symposium, Warwick
March 2014 - Cyclic Quotient Surface Singularities.
Geometry Club, Edinburgh
February 2014 -
Deformations of the Reconstruction Algebras.
Nagoya-Warwick Workshop on McKay, Warwick
November 2013 - Deformed Reconstruction Algebras.
Algebraic Geometry Seminar, Nagoya
November 2013 - Algebras Defined By Superpotentials.
PG Applicants Open Day, Edinburgh
October 2013 - Quiver GIT and Tilting.
Geometry Club, Edinburgh
August 2013 - Deformed Reconstruction Algebras.
Kent Algebra Days, Kent
May 2013 - Deformations of the Reconstruction Algebras.
36th Artin meeting, Glasgow
May 2013 - Quivers with Superpotentials
and their Deformations. PG Seminar , Newcastle
March 2013 -
Resolutions, Deformations, and Non-Commutative Algebras. Geometry Club, Edinburgh
Nov 2012 - Superpotentials, Calabi-Yau Algebras and PBW deformations. Maximals seminar, Edinburgh
Ringel duality for certain strongly quasi-hereditary algebras (Joint with Martin Kalck);
The length classification of threefold flops via noncommutative algebras ;
arXiv:1709.02720 (Some associated Magma code )
Noncommutative Knorrer type equivalences via noncommutative resolutions of singularities (Joint with Martin Kalck);
arXiv:1707.02836 (Slightly updated version)
Multigraded linear series and recollement (Joint with Alastair Craw and Yukari Ito);
Math. Zeit. (arXiv:1701.01679)
Deformations of Algebras Defined by Tilting Bundles ;
Quiver GIT for Varieties with Tilting Bundles ;
Superpotentials, Calabi-Yau algebras, and PBW deformations;
Journal of Algebra (arXiv:1210.1341)
2011-2015 - Tutor in Edinburgh;
Tutor for Linear algebra and Calculus (First year course). 2011-2015
Tutor for Geometry (Second year course). 2014
Tutor for Group theory (Third year course). 2014
Tutor for Jewels of Algebra (Forth year course). 2012-2014
Hirzebruch-Jung fraction calculator.