COmbinatorics Seminar for Everyone (COSE)

This is a reading seminar open to everyone, especially bachelor, master and PhD students. The topic changes every year/semester. It includes free coffee breaks.

If you are interested in participating, please send an email to cult-owner@lists.dm.unipi.it, bring your coffee cup/mug/water bottle, and be ready to give a talk!

In the second semester of this year the topic of the seminar is “Hyperplane arrangements”. We will follow mainly the lecture notes by Richard Stanley: 

[Stanley] Stanley, “An introduction fo Hyperplane arrangements”, 2006

DATETIMEROOMSPEAKERTITLEREFERENCES
28/02/202411:00-13:00Saletta riunioniMichele D’AdderioIntroduction to hyperplane arrangements[Stanley] Lecture 1
13/03/202411:00-13:00Sala riunioniGiulia CodenottiCharacteristic polynomial and Moebius function[Stanley] Lecture 1
27/03/202411:00-13:00Sala riunioniSabrina BotticchioCrosscut theorem, Whitney’s theorem, deletion-restriction of the characteristic polynomial of an arrangement[Stanley] Lecture 2, Section 2.1
10/04/202411:00-13:00Sala riunioniAlessio SgubinZaslavsky theorem via deletion restriction and via Euler characteristic[Stanley] Lecture 2, Section 2.2
30/04/202411:00-13:00Sala riunioniAlessandro Tedeschi
15/05/202411:00-13:00Sala riunioniDavide Chionna

In the first semester of this year the topic of the seminar is “Matroids”. We will follow mainly the lecture notes by Vic Reiner: 

[Reiner] Reiner, “Lectures on matroids and oriented matroids”, 2005

DateTimeRoomSpeakerTitleReferences
04/10/202311:00-13:00Aula seminariMichele D’AdderioIntroduction to matroids[Reiner] Lecture 1
18/10/202311:00-13:00Aula seminariAlessandro TedeschiBirkhoff theorem on the poset of flats of a matroid[Reiner] Lecture 1
25/10/202311:00-13:00Aula seminariAlessio SgubinIntroduction to oriented matroids[Reiner] Lecture 1
15/11/202311:00-13:00Aula seminariLuca VantaggioMatroids, greedy algorithm, direct sum, deletion and contraction[Reiner] Lectures 1 and 2
29/11/202311:00-13:00Aula seminariGiovanni InterdonatoDuality and representability of matroids[Reiner] Lecture 2
13/12/202311:00-13:00Aula seminariRoberto RiccardiRealizability of oriented matroids and zonotopes[Reiner] Lecture 2

This year the topic of the seminar is “Combinatorial reciprocity theorems”. We will be reading the beautiful book by Beck and Sanyal:

[BS] Beck, Sanyal “Combinatorial reciprocity theorems: An invitation to enumerative geometric combinatorics”, AMS, 2018

DateTimeRoomSpeakerTitle References
04/10/202211:00-13:00Aula seminariMichele D’AdderioIntroduction to COSE 2022-2023[BS] Chapter 1
25/10/202211:00-13:00Aula seminariMatteo PolettoIntroduction to posets. First reciprocity theorem.[BS] Chapter 2
08/11/202211:00-13:00Aula seminariMatteo MiglioriniIntroduction to polytopal geometry.[BS] Chapter 3,
Sections 3.1, 3.2, 3.3.
22/11/202211:00-13:00Aula seminariAlessandro TedeschiFace poset and Euler characteristic.[BS] Chapter 3,
Sections 3.3, 3.4.
06/12/202211:00-13:00Aula seminariAlessio SgubinMoebius functions and Zaslavsky’s theorem[BS] Chapter 3,
Sections 3.5, 3.6.
09/03/202211:00-13:00Aula riunioniMatteo PalmieriThe Brianchon-Gram Relation[BS] Chapter 3,
Section 3.7.
23/03/202211:00-13:00Aula riunioniPhilippe NadeauCombinatorial reciprocity for chromatic polynomialshttps://arxiv.org/abs/1904.01262
06/04/202211:00-13:00Aula riunioniGiovanni InterdonatoGenerating functions and quasipolynomials[BS] Chapter 4,
Sections 4.1-4.5.
20/04/202211:00-13:00Aula riunioniDavide ChionnaReciprocity for rational simplices[BS] Chapter 4,
Sections 4.6-4.7.
04/05/202211:00-13:00Aula riunioniFederico LazzeriReciprocity for simplicial cones[BS] Chapter 4,
Section 4.8.
18/05/202211:00-13:00Aula riunioniRoberto RiccardiChain partitions and recirpocity[BS] Chapter 4,
Section 4.9.
25/05/202211:00-13:00Aula riunioniLucio TanziniSubdivisions and Ehrhart-Macdonald reciprocity[BS] Chapter 5,
Sections 5.1-5.2.