# Jerusalem Mathematics Colloquium

Thursday, 8th November 2007, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Sefi Ladkani

(Hebrew University)

"Posets, sheaves and their derived representations"

** Abstract: **

Since their invention a few decades ago, derived categories have been proved
to be a powerful tool in relating objects arising from different areas of
mathematics, such as coherent sheaves over algebraic varieties on the one
hand and modules over algebras on the other hand.
In recent years, inspired by applications to physics such as the Homological
mirror symmetry conjecture, the question of equivalence of two derived
categories arising from objects of the same nature has also attracted a
growing interest.

We investigate a similar question for finite partially ordered sets
(posets). To a given poset, one can attach a category of representations,
which shares common features with both sheaves and modules. We say that two
posets are derived equivalent if the derived categories of their
representations are equivalent. This leads to an equivalence relation
between posets, which is coarser than isomorphism, but is nevertheless
non-trivial, as for example there is no known algorithm that determines for
two posets whether they are derived equivalent or not.

In the talk, I will explain the above notions and present several new
explicit constructions of posets derived equivalent to given ones, whose
common theme is the structured reversal of order relations. I will also
outline a recent combinatorial application to posets of tilting objects
related to cluster algebras.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2007-08

Archive of talks