| Mar. 10, 2010 |
Jean-Louis Loday
|
Dendriform structures
|
14:15-15:15 |
HG G 19.1 |
| Abstract: |
A dendriform algebra is an associative algebra whose product is the sum of two binary operations making the algebra a bimodule over itself. This algebraic structure is related to many objects: Stasheff polytope, integration by parts, combinatorial Hopf algebras, renormalization, divided powers, algebraic K-theory. |
| Speakers: |
Jean-Louis Loday
(CNRS / Université de Strasbourg)
|
|
| Mar. 17, 2010 |
Benjamin Audoux
|
A geometrical viewpoint on singular link Floer homology
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
Link Floer homology is a link invariant which categorifies the Alexander polynomial. I gave an extension, combinatorial in nature, of this invariant to singular links in S3, which satisfies some "Vassiliev theory"-like properties. In this talk, I give a geometric viewpoint on this construction which enables us to extend it to singular links in other 3-manifolds. Moreover, it provides a simple proof of the annulation of this invariant on singular connected sums of links. Finally, I will discuss some possible "finite type" properties. |
| Speakers: |
|
|
| Mar. 24, 2010 |
Roman Sauer
|
The limit of characteristic p Betti numbers of a tower of finite covers with amenable fundamental groups
|
14:00-15:00 |
HG G 19.1 |
|
|
| Mar. 31, 2010 |
Paul-Olivier Dehaye
|
Integer partitions and moments of derivatives of characteristic polynomials
|
14:00-15:00 |
HG G 19.1 |
| Speakers: |
Dr. Paul-Olivier Dehaye
(ETH Zürich, Switzerland)
E-Mail:
|
|
| Apr. 7, 2010 |
|
No seminar (Easter break)
|
|
|
|
|
| Apr. 12, 2010 |
Laurent Demonet
|
Introductory talk: Total positivity, cluster algebras and categorification
|
15:15-16:15 |
HG G 19.2 |
| Abstract: |
This talk is an introductory talk, to prepare for the talk in the Algebra-Topology seminar on April 14.
Abstract:
Let $G$ be the group of unipotent upertriangular $n \times n$
matrices. For a matrix of this group, being totally positive means
to have all its non-trivial minors positive (those which are non-vanishing in $\mathbb{C}[G]$). From an algorithmic point of view, it is interesting to find a subset of the set of the minors, seen as elements of $\mathbb{C}[G]$, which fully characterizes the total positivity. Such subsets, with only $\left( \begin{matrix} n \\ 2 \end{matrix} \right)$ minors, exist. For example, if
$$M = \left( \begin{matrix}
1 & x & y \\
0 & 1 & z \\
0 & 0 & 1 \end{matrix} \right)$$
then, the positivity of the minors
$$\left| \begin{matrix} x & y \\ 1 & z \end{matrix} \right| \quad
\text{et} \quad x \quad \text{et} \quad y $$
is enough to obtain the positivity of all minors. In the first part of this talk, we will see how to pass from such a positivity criterium to others and to create a familly of such criteria. This processus is encoded by a "cluster algebra". After that, we will see how to attach certain categories to these cluster algebras, which permits to prove, through the representation theory, results which are inaccessible by the combinatoric.
|
| Speakers: |
Laurent Demonet
(MPI Bonn)
Invited by: FIM
E-Mail:
|
|
| Apr. 14, 2010 |
Laurent Demonet
|
Categorification of skew-symmetrizable cluster algebras and application to Kac-Moody groups
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
We introduce an abstract framework to categorify some antisymetrizable cluster algebras by using actions of finite groups on stably $2$-Calabi-Yau exact categories. We introduce the notion of the equivariant category and we construct some examples of such categorifications. For example, if we let $\mathbb{Z}/2\mathbb{Z}$ act on the category of representations of the preprojective algebra of type $A_{2n-1}$ via the only non trivial action on the diagram, we obtain the cluster structure on the coordinate ring of the maximal unipotent subgroup of the semi-simple Lie group of type $B_n$. More generally, we get categorifications for an important family of finite-dimensional subgroups of the unipotent subgroups of Kac-Moody groups. We also prove by similar methods as in [Fu Keller] a conjecture of Fomin and Zelevinsky stating that the cluster monomials are linearly independent. |
| Speakers: |
Laurent Demonet
(MPI Bonn)
|
|
| Apr. 21, 2010 |
Dusko Bogdanic
|
Graded Brauer Tree Algebras
(CANCELLED)
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
We introduce the idea of transfer of gradings via derived equivalences and we apply it to construct non-negative gradings on a basic Brauer tree algebra $A_{\Gamma}$ corresponding to an arbitrary Brauer tree $\Gamma$ of type $(m,e)$. We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra $A_S$, whose tree is a star with the exceptional vertex in the middle, to $A_{\Gamma}$. The grading on $A_S$ comes from the tight grading given by the radical filtration. To transfer gradings via derived equivalence we use tilting complexes constructed by taking Green's walk around $\Gamma$. We also prove that there is unique grading on $A_{\Gamma}$ up to graded Morita equivalence and rescaling. |
| Speakers: |
Dusko Bogdanic
(Oxford)
E-Mail:
|
|
| Apr. 28, 2010 |
|
No seminar
|
|
HG G 19.1 |
|
|
| May. 5, 2010 |
Michelle Bucher-Karlsson
|
Milnor-Wood inequalities and affine manifolds
(CANCELLED)
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
A classical inequality of Milnor says that the Euler number of flat oriented vector bundles over surfaces (different from the sphere) are at most one half the Euler characteristic of the surfaces. I will discuss generalizations of this seminal inequality and applications to affine manifolds, in particular to a conjecture of Chern saying that an affine manifold has vanishing Euler characteristic. This is joint work with Tsachik Gelander. |
| Speakers: |
|
|
| May. 12, 2010 |
Alain Jeanneret
|
Spaces with noetherian cohomology
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
In this talk we consider the cohomology of spaces with twisted
coefficients by the action of the fundamental group. We generalize the
Evens-Venkov Theorem ( a result in group cohomology) to the case of
$p$-compact groups, an homotopical version of the Lie groups. |
| Speakers: |
Alain Jeanneret
(Universität Bern)
E-Mail:
|
|
| May. 19, 2010 |
Ruth Charney
|
Length functions of free groups and right angled Artin groups
|
14:00-15:00 |
HG G 19.1 |
| Speakers: |
Ruth Charney
(Brandeis University, Waltham, USA)
|
|
| May. 26, 2010 |
Sebastian Baader
|
Knots, cobordisms and stable genus
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
Knots can be added, but not subtracted. A simple relation suggested by
cobordism theory makes the subtraction possible. The resulting group is
well-studied and carries a semi-norm called stable genus. We will
describe the unit ball of the stable genus, with a special emphasis on
the subgroup generated by torus links. |
| Speakers: |
Dr. Sebastian Baader
(ETH Zürich, Switzerland)
E-Mail:
|
|
| Jun. 1, 2010 |
Dusko Bogdanic
|
Introductory talk: Path algebras of quivers
|
12:00-12:30 |
HG G43 |
| Abstract: |
We introduce path algebras of
quivers and show how to construct radical layers of projective
indecomposable modules. |
| Speakers: |
Dusko Bogdanic
(Oxford)
E-Mail:
|
|
| Jun. 2, 2010 |
Dusko Bogdanic
|
Graded Brauer Tree Algebras
|
14:00-15:00 |
HG G 19.1 |
| Abstract: |
We introduce the idea of transfer of gradings via derived equivalences and we apply it to construct non-negative gradings on a basic Brauer tree algebra $A_{\Gamma}$ corresponding to an arbitrary Brauer tree $\Gamma$ of type $(m,e)$. We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra $A_S$, whose tree is a star with the exceptional vertex in the middle, to $A_{\Gamma}$. The grading on $A_S$ comes from the tight grading given by the radical filtration. To transfer gradings via derived equivalence we use tilting complexes constructed by taking Green's walk around $\Gamma$. We also prove that there is unique grading on $A_{\Gamma}$ up to graded Morita equivalence and rescaling. |
| Speakers: |
Dusko Bogdanic
(Oxford)
E-Mail:
|
|
