From radin@macs.biu.ac.il Sun Nov 5 11:12:47 2006 Date: Sun, 5 Nov 2006 11:12:40 +0200 (IST) From: Adin Ron To: Combinatorics Seminar: ; Subject: Bar-Ilan Combinatorics Seminar ============================== Bar-Ilan Combinatorics Seminar ============================== The next meeting of the seminar will take place, IYH, on (when) Tuesday, 16 Marcheshvan (Nov. 7) refreshments at 11:45, talk at 12:00 noon (where) Room 331 (Math Dept Seminar Room), Math and CS Building (216), Bar-Ilan University (who) Sefi Ladkani (Hebrew University) will talk about (what) "On Derived Equivalences of Categories of Sheaves over Finite Posets" Abstract: --------- A finite poset $X$ can be naturally endowed with a structure of a topological space. This gives, for a fixed field $k$, an identification of the following algebraic objects: 1. Sheaves of $k$-vector spaces over $X$. 2. Diagrams of $k$-vector spaces (over the Hasse diagram of $X$). 3. Right modules over the incidence algebra of $X$. Given a poset $X$, we can attach to it an algebraic object which is the derived category of the category of objects 1-3 above. Roughly speaking, the derived category of a category $A$ encompasses all the homological information in $A$. We say that two posets are derived equivalent if their attached derived categories are equivalent. This gives an equivalence relation between finite posets, which is coarser than isomorphism of posets, but still fine enough to be interesting. However, there is no known algorithm that determines for two posets $X, Y$ whether they are derived equivalent or not. In the talk, I will explain all the above notions, survey some known results and present a new construction that gives many derived equivalences and generalizes some well known examples. This construction uses algebraic and combinatorial techniques. Forthcoming Events ================== * 23 Marcheshvan (Nov. 14) Tamar Seeman (Bar-ilan university): TBA ************************************************************************* You are all invited ! (Graduate students especially welcome) If you want to give a talk at the seminar, or know a prospective speaker, please contact Ron Adin . Seminar's homepage: *************************************************************************