[Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Nov.22 !

["I.Brunke" <i.brunke@fu-berlin.de>]

Dear all,

next Monday's Lecture and Colloquium will take place November 22 at TU Berlin.
You all are cordially invited!


Please note Corona restrictions !  - See rules in detail below !

Location:

Room MA 041 - Ground Floor
Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin

Monday's Lecture: Markus Brill (Technische Universität Berlin)

Time: Monday, November 22 - 14:15 h

Title: Approval-Based Apportionment

Abstract:

In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters cast approval ballots over parties, such that each voter can support multiple parties. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates. Using techniques from both apportionment and multiwinner elections, we identify rules that generalize the D'Hondt apportionment method and that satisfy strong axioms which are generalizations of properties commonly studied in the apportionment literature. In fact, the rules we discuss provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we demonstrate that extended justified representation is compatible with committee monotonicity (also known as house monotonicity). Second, we show that core-stable committees are guaranteed to exist and can be found in polynomial time.

Joint work with Paul Gölz, Dominik Peters, Ulrike Schmidt-Kraepelin, and Kai Wilker.

Coffee Break

Monday's Colloquium: Jonathan Leake (Technische Universität Berlin)

Time: Monday, November 22 - 16:00 h s.t.

Title: Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture

Abstract:

About 5 years ago, the Heron-Rota-Welsh conjecture (log-concavity of the coefficients of the characteristic polynomial of a matroid) was proven by Adiprasito, Huh, and Katz via the exciting development of a new combinatorial Hodge theory for matroids. In very recent work with Petter Brändén, we have given a new short "polynomial proof" of the Heron-Rota-Welsh conjecture. Our proof uses an extension of the theory of Lorentzian polynomials to convex cones. In this talk, I will briefly discuss the basics of Lorentzian (aka completely log-concave) polynomials, and then I will give an overview of our new proof of the Heron-Rota-Welsh conjecture.


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Corona access rules accordingly:

Please observe the current Corona safety constraints:

3G access rule - a medical or FFP2 mask must be worn!
See https://www.fu-berlin.de/en/sites/coronavirus/faq/studium/3g/

Please bring a proof of your vaccination status or test by a certified unit, as well as a photo-ID.

For tracking the contacts in case of an infection, we use a.nwesen.de.
See https://anwesende.imp.fu-berlin.de/

There is a QR-code at every place, which you can scan with your smartphone.


You all are cordially invited!

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