Our seminar in applied algebra has been
running since 1997.
The topics of talks have typically been any mixture of algebra
with any other fields: combinatorics, geometry, topology, physics,
etc.
We usually have half a dozen to a dozen people in attendance
at the seminars, and this usually includes several graduate students
and postdocs.
For this reason, we encourage the speakers to devote a portion of
their talk to the suggestion of open problems and the direction of
research in their area.
 note some info, day and time changes in RED
 dates and speaker in ORANGE are special join seminar
AASFields
on Friday

If you are interested in receiving regular announcement
of this seminar then, please send us an email, so that we
can insert you in our mailing list.


Archives  Fall 2008

Michael Lau, University of Windsor


 Title: Forms of Conformal Superalgebras
 Date: Monday, March 30, 2009
 Time: 3:00p.m.
 Place: Room 638 North Ross
Conformal superalgebras describe symmetries of superconformal field theories and come equipped with an infinite family of products.
They also arise as singular parts of the vertex operator superalgebras associated with some wellknown Lie structures
(e.g. affine, Virasoro, NeveuSchwarz).
In joint work with Arturo Pianzola and Victor Kac, we classify forms of conformal superalgebras using a nonabelian Cechlike cohomology set.
As the products in scalar extensions are not given by linear extensions of the products in the base ring,
the usual descent formalism cannot be applied blindly. As a corollary,
we obtain a rigourous proof of the pairwise nonisomorphism of an infinite family of N=4
conformal superalgebras appearing in mathematical physics.


Yun Gao, York University


 Title: Twisted vertex operators and Steinberg unitary Lie algebras
 Date: Monday, March 16, 2009
 Time: 3:00p.m.
 Place: Room 638 North Ross
We will use the twisted Heisenberg Lie algebras to construct a family of vertex operators.
These will provide representations for certain Steinberg unitary Lie algebras coordinatized by quantum tori.
As a byproduct we recover some of affine KacMoody Lie algebras.
This is a joint work with N.Jing and S.Tan.


Nantel Bergeron, York University


 Title: The nonsymmetric operad preLie is free
 Date: Monday, March 09, 2009
 Time: 3:00p.m.
 Place: Room 638 North Ross
I will show that the preLie operad is a free non
symmetric operad.
I will do some recall on the notions of Operads.
This is joint work with M. Livernet


Prasad Senesi, University of Ottawa


 Title: Finitedimensional representation theory of loop algebras
 Date: Monday, March 02, 2009
 Time: 3:00p.m.
 Place: Room 638 North Ross
Let G be a simple complex finitedimensional Lie algebra, and L=L(G)
a Loop algebra corresponding to a diagram automorphism of G. These algebras
occur as the main in a construction of the Affine Lie algebras, and their
representation theory is subject of continuing interest. Some aspects of
the finitedimensional representation theory of the 'twisted' loop algebras
are now well understood. In particular, the universal 'loophighest weight'
Weyl modules have recently been described, has have the blocks of the
corresponding (nonsemisimple) category.
We will discuss these recent classifications, as provide a more geometric
reformulation of the results. We will then discuss possible extensions of
this theory to the multiloop generalizations of L, and beyond.


Francois Descouens, Paris


 Title: Noncommutative LLT polynomials
 Date: Monday, February 23, 2009
 Time: 3:00p.m.
 Place: Room 638 North Ross
In 1990, the LLT polynomials were defined as qanalogs of
products of Schur functions.
In this talk, we define new analogs of LLT polynomials on the noncommutative side.
We give an analog of the quotient map, and we also introduce an
interpretation of these new
polynomials in terms of representations of the Hecke algebra. This noncommutative approach could
give us some ideas for solving some problems on the commutative side.


Anouk BergeronBrlek, York University


 Title: Noncommutative polynomial invariants of finite groups and word relations
 Date: Monday, February 09, 2009
 Time: 3:30p.m.
 Place: Room 638 North Ross
Let V be a vector space over the complex with basis {x1,x2,...,xn} and
G be a finite subgroup of GL(V). Then the tensor algebra T(V) of V
over the complex is isomorphic to the polynomials in the non
commutative variables x1, x2, ..., xn with complex coefficients. We
consider the graded space of invariants in T(V) with respect to the
action of G. More generally, we want to give a combinatorial
interpretation for the decomposition of T(V) into irreducible
representations. For the symmetric and dihedral groups, we have a link
between the representations and a special subalgebra of the group
algebra that gives an interpretation of T(V) in terms of words in the
associated Cayley graph. In particular, we have an interpretation for
the graded dimensions of the invariants in T(V) and we give closed
formulas for those graded dimensions. These examples suggest a general
method to find the decomposition of T(V). To that end, we would need
to find a special set of generators and relations for the group G and
then the decomposition of T(V) would be linked to words in the Cayley
graph of G associated to those generators.


Mike Zabrocki, York University


 Title: q,tcounting Dyck paths below a staircase
 Date: Monday, February 02, 2009
 Time: 3:00p.m.
 Place: Room 638 North Ross
I will present recent joint work with Jim Haglund and Jennifer
Morse about the action of the operator nabla on HallLittlewood
symmetric functions. The combinatorics of Dyck paths leads us
to very surprising symmetric function identities relating
HallLittlewood symmetric functions indexed by compositions.


Carolina Benedetti, U. of Comlombia, South America


 Title: Volumes of matroid polytopes
 Date: Monday, January 26, 2009
 Time: 3:00p.m.
 Place: Fields Institute, Room 210
Given a matroid M we can associate with it its matroid
polytope
$P_M$ as well as its independent set polytope I_M. In this talk I
will show an explicit way to decompose these polytopes as a signed
Minkowski sum of simplices. Using this decomposition, which
involves a lot of information of M such as its beta invariant, I
will give a nice formula to calculate the volumes of P_M and I_M,
offering a geometric point of view for beta (M). Finally, we will
see analogous results in the case of a nice class of flag
matroids, namely the cascading flag matroids. In this case the
role of beta (M) will be done by the gamma invariant.
This is
joint work with Federico Ardila (San Francisco State University)
and Jeffrey Doker (UC Berkeley).


Amel Kaouche, University du Québec à Montréal (UQAM)
Please note that this talk will take place at Fields Institute !


 Title: Imperfect gases and graph invariants
 Date: Monday, November 24, 2008
 Time: 3:00p.m.
 Place: Fields Institute, Room 210
The Mayer and ReeHoover theories for the virial expansions in the context of a nonideal gas
reveal certain invariants (weights) associated to graphs.
We give a special attention to the case of the hardcore continuum gas in one dimension.
We present the method of graph homomorphisms that we apply to compute the Mayer and ReeHoover weights of various classes of graphs.




Joel Kamnitzer, University of Toronto,
This talk took place at Fields Institute !


 Title: MV polytopes and components of quiver varieties
 Date: Monday, November 17, 2008
 Time: 3:00p.m.
 Place: Fields Institute, Room 210
A number of interesting bases exist for the upper half of the universal envelopping algebra of a semisimple Lie algebra.
One such basis is Lusztig's semicanonical basis which is indexed by components of quiver varieties.
Another interesting basis is indexed by MirkovicVilonen cycles which lead to the combinatorics of MV polytopes.
In this talk, I will explain a natural bijection between the components of quiver varieties and the MV polytopes.
This is joint work with Pierre Baumann.


Hugh Thomas, University of New Brunswick,
This talk took take place at Fields Institute !


 Title: Antichains in the poset of positive roots, Catalan phenomena, and some conjectures of Panyushev
 Date: Monday, November 10, 2008
 Time: 3:00p.m.
 Place: Fields Institute, Room 210


Philippe Choquette, York University 

 Title: Hyperoctahedral species
 Date: Monday, November 3, 2008
 Time: 3:00p.m.
 Place: Room 638 North Ross
We introduce a new definition for species of type B,
called Hspecies, analog to the classical species (of type A),
but on which we consider the action of the groups Bn of signed permutations.
Classical species are modules of the symmetric group and Hspecies are modules of
the hyperoctahedral group.
We are interested in algebraic structure on these Hspecies and give examples of Hopf monoids.
Many functors allow us to obtain Hspecies from species,
and one functor is particularly interesting as it sends the regular representation of Sn to the regular
representation of Bn.
With this functor and the natural way to get a graded vector space from a species, we give a link between the
classical species of set composition and the combinatorial Hopf algebra DQSym.


JeanLouis Loday, Université
de Strasbourg  France 

 Title: Combinatorial Hopf algebras
 Date: Monday, October 27, 2008
 Time: 3:00p.m.
 Place: Room 638 North Ross
Many recent papers are devoted to some infinite dimensional Hopf algebras called collectively "combinatorial Hopf algebras".
Among the examples we find the Faa di Bruno algebra, the ConnesKreimer algebra and the MalvenutoReutenauer algebra.
We give a precise definition of such an object and we provide a classification.
We show that the notion of preLie algebra and of brace algebra play a key role.



 

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