Stratifications indexed by partitions and combinatorial models for homology
Dmitry Kozlov
Royal Institute of Technology, Stockholm, Sweden
March 2,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

We shall consider several topological spaces equipped with stratifications
indexed by integer partitions. In each case we consider
the problem of studying homology groups of strata. We shall first describe how to
construct various models for computing these groups
and then present the following applications:

Determining the homology of resonancefree orbit arrangements (with the help of
general lexicographic shellability), thereby settling a
conjecture of Bjorner for this special case;
 A combinatorial reproof of Arnol'd theorem regarding the rational homology of the
space of monic complex polynomials with at least q
roots of multiplicity k;
 A counterexample to a conjecture by Sundaram and Welker;
 A computation of the homology groups of the space of hyperbolic polynomials with at
least q roots of multiplicity k.

Speaker's Contact Info: kozlov(atsign)math.kth.se
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