School of Mathematics and Statistics
Newcastle upon Tyne NE1 7RU
office phone: +44 (0)191 222 5370
fax: +44 (0)191 222 8020
- Noncommutative geometry
- Resolutions of singularities
- Geometric invariant theory
- Representation theory of quivers
- Calabi Yau Manifolds and Algebras
- Applications of quivers in theoretical physics and topology
Publications of Raf Bocklandt
Smooth quiver representation spaces.
J. Algebra 253 (2002), no. 2, 296--313.
Adriaenssens, Jan; Bocklandt, Raf; Van de Weyer, Geert;
Smooth character varieties for torus knot groups.
Comm. Algebra 30 (2002), no. 6, 3045--3061.
Bocklandt, Raf; Le Bruyn, Lieven;
Necklace Lie algebras and noncommutative symplectic geometry.
Math. Z. 240 (2002), no. 1, 141--167.
Bocklandt, Raf; Le Bruyn, Lieven; Van de Weyer, Geert;
Smooth order singularities.
J. Algebra Appl. 2 (2003), no. 4, 365--395.
Bocklandt, Raf; Le Bruyn, Lieven; Symens, Stijn;
Isolated singularities, smooth orders, and Auslander regularity.
Comm. Algebra 31 (2003), no. 12, 6019--6036.
Symmetric quiver settings with a regular ring of invariants.
Special issue on linear algebra methods in representation theory.
Linear Algebra and its Appl. 365 (2003), 25--43.
Quiver quotient varieties and complete intersections.
Algebras and Representation Theory, 8 (2005), no. 1, 127 -- 145.
Bocklandt, Raf; Van de Weyer, Geert; Symens, Stijn;
The flat locus of Brauer Severi fibrations of smooth orders.
Journal of Algebra, 297 (2006), no. 1, 101--124.
Bocklandt, Raf; Symens, Stijn;
The local structure of graded representations.
Communications in algebra, 34 (2006), no. 12, 4401-4426.
Graded Calabi Yau algebras of dimension 3.
Journal of Pure and Applied Algebra
212 (2008), no. 1, 14--32.
Bocklandt, Raf; Van de Weyer, Geert;
Cofree quiver settings. Journal of Algebra 319 (2008), no. 5, 2082-2105.
Bocklandt, Raf; Van de Weyer, Geert;
The power of slicing in non-commutative geometry.
Bulletin of the Belgian Math. Soc.,vol. 15 (2008), no. 2, 303-310
Bocklandt, Raf; Graded 3-dimensional Calabi Yau algebras. Extended
Abstract for the workshop on
Interactions between Algebraic Geometry and Noncommutative Algebra.
Oberwolfach Report Volume 3, Issue 2, 2006.
Peeters, Gino; Bocklandt, Raf; Van Houdt, Benny;
Multiple Access Algorithms without Feedback using Combinatorial Designs.
IEEE Transactions on Communications 57 (2009), no. 9, 2724-2733.
Bocklandt, Raf; Schedler, Travis; Wemyss Michael;
Superpotentials and Higher Order Derivations.
Journal of Pure and Applied Algebra 214 (2010), no. 9, 1502-1522.
A Slice Theorem for Quivers with an Involution.
Journal of Algebra and its Applications 9 2010, no. 3, 339-363.
The Local structure of Calabi Yau Algebras.
Calabi Yau algebras and Quiver Polyhedra
Consistency Conditions for dimer models.
Generating toric noncommutative crepant resolutions
The geometry of quotient Varieties of
Overview of my research
My main research area is the representation theory of noncommutative algebras and its connections to various other parts of mathematics, such as
Algebraic geometry, Non-commutative geometry, algebraic topology, Knot theory and theoretical physics.
I started out studying the geometry of quotient varieties of quivers, classifying all quivers and dimension vectors such that the
quotient space classifying all isomorphism classes of semi-simple representations is a smooth variety.
Together with Lieven Le Bruyn, Geert Van de Weyer, Jan Adriaensens and Stijn Symens I extended these methods to investigate singularities that can occur in these varieties, the properties of the fibers of the quotient map and other geometric objects associated to noncommutative algebras like character varieties, moduli spaces, graded representation spaces and Brauer-Severi varieties.
Together with Lieven Le Bruyn also studied the connection between noncommutative symplectic geometry, preprojective algebras and a type of infinite dimensional Lie algebras called Necklace Lie Algebras.
I also have been investigating Calabi-Yau algebras. These algebras appear in the homological study of 3-dimensional gorenstein singularities and
also in the study of superstring theory on calabi yau manifolds. I showed that graded 3-dimensional Calabi-Yau algebras derive from superpotentials and together with Michael Wemyss and Travis Schedler we extended the superpotential method to arbitrary dimensions in the case that the algebra is Koszul.
In the case of toric singularities I proved that noncommutative toric crepant resolutions in dimension 3 alway come from dimer models and
I studied the connection between the different different consistency conditions for dimer models.
Recently I have been working on a program that can construct all possible dimer models for a given 3-dimensional Gorenstein singularity.
This program can be tried out here
Here is a list of my talks.
Here are some lecture notes for undergraduate and graduate courses that I taught.
Differential Geometry II
Advanced Master Course on Kleinian Singularities
Coding theory and Cryptography
Capita Selecta on noncommutative resolutions of singularities