COSE – CULT

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!

2025-2026

In the second semester of this year the topic of the seminar is still "Graph theory". Again, will follow mainly the book by Diestel, by looking at different chapters from the previous semester. Though very much related to the content of the first semester, this seminar can be followed as well by anyone that did not participate in the first semester.

[D] Diestel, "Graph theory" 2nd edition, 2000

DATE	TIME	ROOM	SPEAKER	TITLE	REFERENCES
05/03/2026	11:00-13:00	Sala riunioni	Michele D'Adderio	Topology and graphs	[D] Chapter 4
19/03/2026	11:00-13:00	Sala riunioni	Lorenzo Montana
16/04/2026	11:00-13:00	Sala riunioni	Chiara Lorenzetti
30/04/2026	11:00-13:00	Sala riunioni	Matteo Musumeci
14/05/2026	11:00-13:00	Sala riunioni	Alice Lotti
28/05/2026	11:00-13:00	Sala riunioni	Cristofer Villani

In the first semester of this year the topic of the seminar is "Graph theory". We will follow mainly the book by Diestel.

[D] Diestel, "Graph theory" 2nd edition, 2000

DATE	TIME	ROOM	SPEAKER	TITLE	REFERENCES
01/10/2025	11:00-13:00	Sala riunioni	Michele D'Adderio	Trees, bipartite graphs, and Kőnig's theorem	[D] Chapters 1 and 2
15/10/2025	11:00-13:00	Aula seminari	Giovanni Caiolo	Hall's theorem and Tutte's theorem on 1-factors	[D] Chapter 2
29/10/2025	11:00-13:00	Aula seminari	Pietro Gualdi	Gallai-Milgram theorem and some consequences: Dilworth's theorem, another proof of Hall's theorem and of Kőnig's theorem	[D] Chapter 2
12/11/2025	11:00-13:00	Aula seminari	Christian Nocchi	Characteriation of 2-connected and 3-connected graphs.	[D] Chapter 3
26/11/2025	11:00-13:00	Sala riunioni	Riccardo Biron	Menger's theorem	[D] Chapter 3
10/12/2025	11:00-13:00	Sala riunioni	Gabriel Videtta	Max-flow min-cut theorem	[D] Chapter 6

2024-2025

In the second semester of this year the topic of the seminar is the "Sandpile model". We will take the topics mainly from the book by Corry and Perkinson and from an article of Cori and Le Borgne. Though very much related to the content of the first semester, this seminar can be followed as well by anyone that did not participate in the first semester.

[CP] Divisors and Sandpiles: An Introduction to Chip-Firing, 2010

[CL] Cori, Le Borgne, "The sandpile model and Tutte polynomials", 2003

DATE	TIME	ROOM	SPEAKER	TITLE	REFERENCES
03/03/2025	11:00-13:00	Saletta riunioni	Michele D'Adderio	Introduction to the sandpile model	[CP] Section 6.1
17/03/2025	11:00-13:00	Aula seminari	Alessandro Fenu	Stabilization and Reduced Laplacian	[CP] Sections 6.2-6.4
31/03/2025	11:00-13:00	Aula seminari	Giovanni Interdonato	The sandpile group	[CP] Section 6.5
14/04/2025	11:00-13:00	Aula seminari	Roberto Riccardi	Matrix-tree theorem	[CP] Sections 9.1-9.2
12/05/2025	11:00-13:00	Aula seminari	Alessandro Tedeschi	Dhar's burning algorithm for recurrent configurations	[CP] Section 7
26/05/2025	11:00-13:00	Aula seminari	Lorenzo Noe'	Cori-Le Borgne bijection between spanning trees and recurrent configurations	[CL] Full article

In the first semester of this year the topic of the seminar is the "Dollar game". We will follow mainly the book by Corry and Perkinson.

[CP] Divisors and Sandpiles: An Introduction to Chip-Firing, 2010

DATE	TIME	ROOM	SPEAKER	TITLE	REFERENCES
03/10/2024	11:00-13:00	Aula seminari	Michele D'Adderio	Introduction to the dollar game	[CP] Sections 1.1 and 1.2
17/10/2024	11:00-13:00	Aula seminari	Cristofer Villani	Picard and Jacobian groups. Discrete Laplacian.	[CP] Sections 1.3 and 2.1
31/10/2024	11:00-13:00	Aula seminari	Pietro Gualdi	Reduced Laplacian and structure of Picard group	[CP] Sections 2.2 and 2.4
14/11/2024	11:00-13:00	Aula seminari	Simone Foti	Complete linear systems and a greedy algorithm	[CP] Sections 2.3 and 3.1
28/11/2024	11:00-13:00	Aula seminari	Roberto Maria Tocco	q-reduced divisors and superstable configurations	[CP] Sections 3.2 and 3.3
12/12/2024	11:00-13:00	Aula seminari	Lorenzo Noè	Dhar's burning algorithm and the debt-reduction trick	[CP] Section 3.4

2023-2024

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

DATE	TIME	ROOM	SPEAKER	TITLE	REFERENCES
28/02/2024	11:00-13:00	Saletta riunioni	Michele D'Adderio	Introduction to hyperplane arrangements	[Stanley] Lecture 1
13/03/2024	11:00-13:00	Sala riunioni	Giulia Codenotti	Characteristic polynomial and Moebius function	[Stanley] Lecture 1
27/03/2024	11:00-13:00	Sala riunioni	Sabrina Botticchio	Crosscut theorem, Whitney's theorem, deletion-restriction of the characteristic polynomial of an arrangement	[Stanley] Lecture 2, Section 2.1
10/04/2024	11:00-13:00	Sala riunioni	Alessio Sgubin	Zaslavsky theorem via deletion restriction and via Euler characteristic	[Stanley] Lecture 2, Section 2.2
30/04/2024	11:00-13:00	Sala riunioni	Alessandro Tedeschi	Graphic arrangements	[Stanley] Lecture 2, Section 2.3
15/05/2024	11:00-13:00	Sala riunioni	Lorenzo Noé	Matroids, Tutte polynomial and arrangements	[Stanley] Lecture 3

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

Date	Time	Room	Speaker	Title	References
04/10/2023	11:00-13:00	Aula seminari	Michele D'Adderio	Introduction to matroids	[Reiner] Lecture 1
18/10/2023	11:00-13:00	Aula seminari	Alessandro Tedeschi	Birkhoff theorem on the poset of flats of a matroid	[Reiner] Lecture 1
25/10/2023	11:00-13:00	Aula seminari	Alessio Sgubin	Introduction to oriented matroids	[Reiner] Lecture 1
15/11/2023	11:00-13:00	Aula seminari	Luca Vantaggio	Matroids, greedy algorithm, direct sum, deletion and contraction	[Reiner] Lectures 1 and 2
29/11/2023	11:00-13:00	Aula seminari	Giovanni Interdonato	Duality and representability of matroids	[Reiner] Lecture 2
13/12/2023	11:00-13:00	Aula seminari	Roberto Riccardi	Realizability of oriented matroids and zonotopes	[Reiner] Lecture 2

2022-2023

Date	Time	Room	Speaker	Title	References
04/10/2022	11:00-13:00	Aula seminari	Michele D'Adderio	Introduction to COSE 2022-2023	[BS] Chapter 1
25/10/2022	11:00-13:00	Aula seminari	Matteo Poletto	Introduction to posets. First reciprocity theorem.	[BS] Chapter 2
08/11/2022	11:00-13:00	Aula seminari	Matteo Migliorini	Introduction to polytopal geometry.	[BS] Chapter 3, Sections 3.1, 3.2, 3.3.
22/11/2022	11:00-13:00	Aula seminari	Alessandro Tedeschi	Face poset and Euler characteristic.	[BS] Chapter 3, Sections 3.3, 3.4.
06/12/2022	11:00-13:00	Aula seminari	Alessio Sgubin	Moebius functions and Zaslavsky's theorem	[BS] Chapter 3, Sections 3.5, 3.6.
09/03/2022	11:00-13:00	Aula riunioni	Matteo Palmieri	The Brianchon-Gram Relation	[BS] Chapter 3, Section 3.7.
23/03/2022	11:00-13:00	Aula riunioni	Philippe Nadeau	Combinatorial reciprocity for chromatic polynomials	https://arxiv.org/abs/1904.01262
06/04/2022	11:00-13:00	Aula riunioni	Giovanni Interdonato	Generating functions and quasipolynomials	[BS] Chapter 4, Sections 4.1-4.5.
20/04/2022	11:00-13:00	Aula riunioni	Davide Chionna	Reciprocity for rational simplices	[BS] Chapter 4, Sections 4.6-4.7.
04/05/2022	11:00-13:00	Aula riunioni	Federico Lazzeri	Reciprocity for simplicial cones	[BS] Chapter 4, Section 4.8.
18/05/2022	11:00-13:00	Aula riunioni	Roberto Riccardi	Chain partitions and recirpocity	[BS] Chapter 4, Section 4.9.
25/05/2022	11:00-13:00	Aula riunioni	Lucio Tanzini	Subdivisions and Ehrhart-Macdonald reciprocity	[BS] Chapter 5, Sections 5.1-5.2.

COmbinatorics Seminar for Everyone (COSE)​

COmbinatorics Seminar for Everyone (COSE)