[Facets-of-complexity] Invitation to Monday's Lecture May 23

[Günter Rote <rote@inf.fu-berlin.de>]

Our next Monday's Lecture will take place on May 23,
in attendance, at 14:15 at FU Berlin.

*_Location_*

*Room 005 - Ground Floor*
Freie Universität Berlin
Takustr. 9
14195 Berlin

*_Time_: **Monday, May 23 - 14:15*

*_Lecture_: Katharina Jochemko (KTH Stockholm)

*_Title_: The Eulerian transformation

*_Abstract_:*

Many polynomials arising in combinatorics are known or conjectured
to have only real roots. One approach to these questions is to study
transformations that preserve the real-rootedness property.
This talk is centered around the Eulerian transformation which is
the linear transformation that sends the i-th standard monomial to
the i-th Eulerian polynomial. Eulerian polynomials appear in various
guises in enumerative and geometric combinatorics and have many
favorable properties, in particular, they are real-rooted and symmetric.
We discuss how these properties carry over to the Eulerian
transformation. In particular, we disprove a conjecture by Brenti (1989)
concerning the preservation of real roots, extend recent results on
binomial Eulerian polynomials and provide enumerative and geometric
interpretations.
This is joint work with Petter Brändén.


There will be no zoom link, no Coffee & Tea Break, and
no colloquium, but there will be a grill party after the lecture.