# Joseph Karmazyn

Email: J.H.Karmazyn@Sheffield.ac.uk
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.

### Talks

** 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 *

### Papers

** 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)

# Teaching

### ** 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.