Seminari Al@Bicocca: Martino Garonzi

Lunedì 19 Gennaio 2026 alle ore 11:30, nel quadro del ciclo di seminari Al@Bicocca, Martino Garonzi (Università degli Studi di Ferrara) terrà il seguente intervento

Titolo: The Herzog-Schönheim Conjecture for finite simple groups

Abstract: In the 1950’s Davenport, Mirsky, Newman and Rado proved that if the integers are partitioned by a finite set of arithmetic progressions, then the largest difference must appear more than once. In other words, if g₁,..., g_n and a₁ ≤ a₂ ≤ ... ≤ a_n are integers such that {g_i + a_iZ}ⁿ_i=1 is a partition of Z then a_n−1 = a_n. This confirmed a conjecture of Erdos and opened a broad area of research (see Covering systems of Paul Erdös. Past, present and future, Paul Erdös and his mathematics, I (Budapest, 1999), Bolyai Soc. Math. Stud., vol. 11, pp. 581- 627. Janos Bolyai Math. Soc., Budapest (2002) for a detailed bibliography). The Herzog–Schönheim Conjecture (1974) states that, if a group G is partitioned into cosets H₁x₁,..., H_nx_n, then the indices |G : H_i |, i = 1,..., n, cannot be pairwise distinct. It is known that, in order to prove this conjecture in general, it is enough to prove it for finite groups. The conjecture holds for finite groups having a Sylow tower (Berger et al. 1987), so in particular for supersolvable groups. In this talk, I will present a proof of this conjecture for all finite simple groups and symmetric groups. This is a joint work with Leo Margolis (Universidad Autónoma de Madrid). A preprint of the paper is available at the following ArXiv link: https://arxiv.org/abs/2509.25118

Informazioni per partecipare

Il seminario si terrà in Aula U9-11 (Edificio U9 | Viale dell'Innovazione 10, Milano) e sarà possibile partecipare anche online da questo link.

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