Date
 Speaker
 Title (click on titles to show/hide abstracts)

Sept. 12 (C) 
Emine Yildirim (Queen's University) 
Generalized Associahedra and Newton polytopes of Fpolynomials.
Abstract:
Generalized associahedron is a polytope whose outer normal fan is the gvector fan. Considerable attention has been given to combinatorics of such polytopes since their relation to cluster algebra. In this talk, we will discuss constructing generalized associahedra based on quiver representations for simply laced Dynkin quivers. Our inspiration comes from a paper by ArkaniHamed, Bai, He, Yan (2017) on scattering forms on the kinematic space in physics. Their construction can be viewed as giving an associahedron associated to the linearly oriented type A quiver. Our approach generalizes this associahedron to all simplylaced Dynkin types. Furthermore, we show that our construction can also be used to realize the Newton polytopes of the Fpolynomials associated to the cluster variables. This is a joint work with Véronique BazierMatte, Guillaume Douville, Kaveh Mousavand, Hugh Thomas.

Sept. 19 (C) 
Kaveh Mousavand (UQAM) 
Representation Theory of Special Biserial Algebras.
Abstract:
Due to the seminal work of P. Gabriel in 1970’s, if k is an algebraically closed field, each finite dimensional kalgebra A has a presentation of the form kQ/I, where Q is a finite directed graph and I is an ideal in the path algebra kQ. Although classification of all indecomposable modules over A is, a priori, a hard problem, assuming some combinatorial constraints on Q and I results in the description of indecomposable Amodules and their homological interaction in terms of some concrete diagrams.
In this talk, after reviewing the rudiments of representation theory of quivers, we focus on an interesting family of finite dimensional algebras, called special biserial. We observe that this family of algebras is closed under quotient and we use this to reduce the study of τtilting finiteness of special biserial algebras to that of a tractable subfamily, called minimal representationinfinite algebras. Using this subfamily, we show that τtilting theory, introduced by Adachi, Iyama and Reiten in 2014, can be studied via the classical concept of tilting theory and we obtain new criteria for τtilting finiteness of special biserial algebras.

Sept. 27 (O) 
Boris Kunyavski (BarIlan University) 
Bracket width of simple Lie algebras.
Abstract:
For an element of a group G representable as a product of commutators,
one can define its commutator length as the smallest number of commutators
needed for such a representation, by definition the other elements
are of infinite length. The commutator width of G is defined
as supremum of the lengths of its elements. Recently it was proven
that all finite simple groups have commutator width one. On the other hand,
there are examples of infinite simple groups of arbitrary finite width
and of infinite width.
In a similar manner, one can define the bracket width of a Lie algebra.
It is known that all finitedimensional simple Lie algebras over an
algebraically closed field have bracket width one. Our goal is to present
first examples of simple Lie algebras of bracket width greater than one.
The simplest example relies on a recent work by Yu. Billig and V. Futorny
on Lie algebras of vector fields on smooth affine varieties.
This talk is based on a work in progress, joint with A. Regeta.

Oct. 3 (C) 
Amir Nasr (UNB/Carleton) 
Del Pezzo orders with no worse than canonical singularities.
Abstract:
We classify del Pezzo noncommutative surfaces that are finite over their centres with terminal and canonical singularities. Using the minimal model program, we introduce the minimal model of such surfaces. We first classify the minimal models and then give the classification of these surfaces in general. This presents a complementary result and method to the classification given by Chan and Kulkarni in 2003.

Oct. 16 (C) 
Adèle Bourgeois (Ottawa) 
Restricting Supercuspidal Representations to the Derived Subgroup
Abstract:
The representation theory of reductive groups over padic fields reduces to the study of
supercuspidal representations. In 2001, J.K. Yu described a construction that allows us to
obtain supercuspidal representations of any positive depth. It was later proved by Kim (2007)
that these constructions exhaust all supercuspidal representations for large enough p.
To construct a supercuspidal representation of a reductive group G over a padic field F, J.K.
Yu uses what he calls a Gdatum. In this talk, we will be interested in the derived subgroup
of G, which we will denote by G _{der}. We will discuss how we can obtain various G _{der}data from
a Gdatum. We will then explore the relationships between the supercuspidal arising from the
Gdatum and the supercuspidals arising from the various G _{der}data. In particular, we would like
to know how the supercuspidals arising from the G _{der}data appear in the restriction to G _{der} of
the supercuspidal arising from the Gdatum.

Oct. 31 (C) 
Owen Patashnik (?) 

Nov. 7 (O) 
WanYu Tsai (Ottawa) 

Nov. 14 (O) 
Michael Reeks (Ottawa) 

Nov. 21 (O) 
Emily Cliff (Illinois) 

Nov. 28 (O) 
Erhard Neher (Ottawa) 

Dec. 5 (C) 
Özgür Esentepe (Toronto) 
