Algebra Research Group

Algebraic research at York covers a wide spectrum of interests, from pure group theory, representation theory and semigroup theory to applications of algebraic techniques in geometry, quantum physics and biology. The department is a fertile breeding ground for research, with regular organized seminars and study groups complemented by plenty of opportunities for informal discussion. We are also always on the lookout for strong PhD students in all areas of algebra; please see the Pure PhD projects page for some project ideas, and please also feel free to get in touch with any member of staff if you want to find out more. For details of individual members' interests, please click here.

Seminars and Study Groups

We run a weekly Algebra Study Group during term time. Please contact Michael Bate for details of the current topic, or to be included on the email list for this group.

External speakers in the area of Algebra are usually invited to give a talk in the Algebra Seminar, which is also a forum for internal research seminars. The next talk is shown below.

Categorification of Lie algebra representations.


Series: 
Algebra Seminar
Date and time: 
April 28, 2014, 16:15
Speaker: 
Antonio Sartori (York)
Room: 
G/109

Categorification of Lie algebras and their representations has been a very interesting and productive subject in the last years. After a general introduction to the topic, I will present a construction of tensor product categorifications for the general linear Lie algebra using the BGG category O.

Submitted on 18 Apr 2014 - 16:57 by bje1

The York Semigroup meets every week in term time and is a mixture of informal sessions, led by York Semigroup PhD students, and more formal presentations.

 

Other Algebraic Events

Leeds York Lie Theory (LYLT):  The most recent LYLT meeting took place on the 13th November in York, with talks by Alison Parker and Emilie Dufresne. Please see the webpage for the event for more details. 

Algebra and Representation Theory in the North (ARTIN):  York is part of the ARTIN network, which holds regular meetings around the north of the UK. For details of the next event and a list of past meetings click here.

North British Geometric Group Theory (NBGGT):  The NBGGT meetings are collaborative seminars held regularly across the north of Britain. For more details click here.

North British Semigroups and Applications Network (NBSAN):  The NBSAN meets regularly, with events all over the north of Britain. For more details, please visit the NBSAN page.

Members and Research Interests

Below is an alphabetical list of members of the Algebra Group, with brief descriptions of their (algebraic) research interests. Clicking on the name of a particular member of staff will direct you to their homepage.

  • Dr Martina Balagovic  Quantum groups, Cherednik algebras, algebraic representation theory
  • Dr Michael Bate  Subgroup structure and representation theory of linear algebraic groups; spherical buildings; geometric invariant theory
  • Dr Gustav Delius  Boundary affine algebras and twisted Yangians
  • Professor Stephen Donkin  Algebra; representation theory; algebraic groups
  • Dr Brent Everitt  (Co)homology of sheaves over categories; combinatorics and representations of Coxeter groups
  • Professor John Fountain  Semigroup Theory and Group Theory
  • Dr Haralampos Geranios  Representations of algebraic groups and invariant theory
  • Professor Victoria Gould  Semigroup theory: structure theory for non-regular semigroups; endomorphism monoids of certain universal algebras; semigroups of quotients; S-sets over a monoid S
  • Dr Miklos Hartmann Structure theory for orthodox semigroups and theory of S-acts
  • Dr Eli Hawkins Noncommutative deformations, Lie groupoids and algebroids, geometric models of noncommutative algebras, C*-algebras, Hochschild and cyclic (co)homology
  • Dr Niall MacKay  Yangians, quantum affine algebras and their representations and realizations in physics; generalizations of Brauer and symmetric-group centralizer algebras to exceptional Lie algebras, and their diagrammatic representations
  • Professor Maxim Nazarov  Representations of affine quantum groups and affine Hecke algebras
  • Professor Reidun Twarock  Affine extensions of noncrystallographic Coxeter groups with applications in virology

Publications in Algebra

Submitted

In Press

[Anonymous].  In Press.  Every group is a maximal subgroup of a naturally . Semigroup Forum.
Everitt B.  In Press.  The Combinatorial Topology of Groups. Springer Verlag (book, to appear). Abstract
Everitt B, Turner P.  In Press.  The homotopy theory of Khovanov homology. Algebraic and Geometric Topology (to appear). Abstract

2014

2013

Everitt B, Fountain J.  2013.  Partial mirror symmetry, lattice presentations and algebraic monoids. Proceedings of the London Mathematical Society. 107(2):414-450. Abstract

2012

Tange R.  2012.  A bideterminant basis for a reductive monoid. Journal of Pure and Applied Algebra. 216(5):1207-1221.
Shaheen L.  2012.  Axiomatisability of S-Acts, Revisited. Semigroup Forum. 85(2):337-360. Download: AxiomatisabilityofSacts05-05-10.pdf (217.7 KB)
Gould V, Wang Y.  2012.  Beyond orthodox semigroups. Journal of Algebra. 368:209–230. Download: Beyond_orthodox_semigroupsrevisedsubmission.pdf (259.62 KB)

Algebra Seminar

The seminar takes place on Mondays from 16:15 in Room G/109 in the James College Nucleus. The typical length of the talks is about 1 hour. The seminar organisers are currently Stephen Donkin and Brent Everitt.

Next Seminar

Categorification of Lie algebra representations.


Series: 
Algebra Seminar
Date and time: 
April 28, 2014, 16:15
Speaker: 
Antonio Sartori (York)
Room: 
G/109

Categorification of Lie algebras and their representations has been a very interesting and productive subject in the last years. After a general introduction to the topic, I will present a construction of tensor product categorifications for the general linear Lie algebra using the BGG category O.

Submitted on 18 Apr 2014 - 16:57 by bje1

Programme for this term

Date and timesort icon Title Speaker Room
January 6, 2014, 16:00 Coarse Equivalences of Euclidean Buildings Jeroen Schillewaert (Imperial) G/109
January 20, 2014, 16:00 Symplectic Permutation Modules John Murray (Maynooth) G/109
January 27, 2014, 16:15 - 17:15 Noncommutative differential calculus Ulrich Kraehmer (Glasgow) G/109
February 10, 2014, 16:15 - 17:15 From the deformed Virasoro algebra to Temperley-Lieb algebras Azat Gainutdinov (Hamburg) G/109
February 17, 2014, 16:15 Quasi-isometry for right-angled Coxeter groups Anne Thomas (Glasgow) G/109
February 24, 2014, 16:15 Sheets and finite W-algebras Lewis Topley (UEA) G/109
March 3, 2014, 16:00 Modular representation theory of the partition algebra Maud De Visscher (City, London) G/109
March 10, 2014, 16:15 - 17:15 Torsion homology of arithmetic lattices and K2 of imaginary fields Vincent Emery (EPFL, Lausanne) G/109
April 28, 2014, 16:15 Categorification of Lie algebra representations. Antonio Sartori (York) G/109


See also the full list of Algebra Seminars.

iCal feed for this seminar

York Semigroup

The York Semigroup meets every week in term time on Wednesdays at 11.15. It consists of a mixture of informal sessions, led by York Semigroup PhD students and staff, and more formal presentations, including external speakers. The formal sessions are usually advertised well in advance - if you wish to be included on the mailing list please e-mail Vicky Gould.

Programme for this term

Date and timesort icon Title Speaker Room
January 15, 2014, 11:30 - 12:30 Automorphisms of tropical polytopes Marianne Johnson G/002
February 4, 2014, 11:00 Computing with finite semigroups James Mitchell P/T/006
February 12, 2014, 11:30 - 12:30 THE FINITE BASIS PROBLEM FOR UNARY MATRIX SEMIGROUPS Professor Igor Dolinka G/002

See also the full list of York Semigroup talks.

iCal feed for this seminar

Other Semigroup Events:

North British Semigroups and Applications Network (NBSAN): The next NBSAN meeting in York will be held 21th November 2012.