Joseph Karmazyn


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.


February 2018- Noncommutative algebras and classifications of threefold flops. Pure Mathematics Seminar, University of East Anglia

February 2018- Noncommutative algebras and equivalences of singularity categories. London Algebra Seminar, City University

January 2018- Matrix factorisations, noncommutative algebras, and the length classifications of threefold flops. Algebra Seminar, The University of York

December 2017- The length classification of simple threefold flops, matrix factorisations, and noncommutative algebras. Geometry Seminar, The University of Hong Kong

November 2017- Threefold flops, matrix factorisations, and noncommutative algebras. Algebra seminar, University of Leeds

July 2017- Knorrer periodicity for cyclic quotient surface singularities. Matrix factorisations and related topics, ICMS Edinburgh

June 2017- Noncommutative algebras and universal flops. Linking noncommutative rings and algebraic geometry, ICMS Edinburgh

Older talks

Jan 2017- 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 surface singularities. 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); arXiv:1711.00416

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 ; arXiv:1505.04049

Quiver GIT for Varieties with Tilting Bundles ; Manuscripta (arXiv:1407.5005)

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.