# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, October 03, 2019, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Stefan Glock

## High-girth Steiner triple systems and a Turán problem of Brown, Erdős and Sós

A Steiner triple system of order n is a set of triples in an n-set such that every pair is covered by exactly one triple. Kirkman characterised in 1847 for which n these exist. Erdős conjectured in 1973 that for fixed g and any sufficiently large admissible order n, there exists a Steiner triple system of order n with girth at least g, meaning that there are no j points which span at least j-2 triples for any 3 < j < g. We prove this conjecture asymptotically by analysing a random process. In this talk, we will discuss this result and also briefly discuss connections to a Turán problem of Brown, Erdős and Sós. partly joined with Daniela Kühn, Allan Lo and Deryk Osthus

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