Each year the Sofia Kovalevskaya lecture takes place at the Faculty of Mathematics at Bielefeld University. It is in honour of the Russian female mathematician with that name, and is given by a successful or promising female mathematician, who is chosen by a jury.
Lisa Sauermann is working in probabilistic combinatorics. Her doctoral thesis was awarded the Richard Rado Prize of the Interest Group for Discrete Mathematics of the German Mathematical Society (DMV) in 2020. In 2021 she received the European Prize in Combinatorics, and in 2023 the German Research Foundation (DFG) honoured her with the von Kaven Prize.
Abstract: Given some large positive integer N, what is the largest possible size of a subset of {1,...,N} which does not contain a three-term arithmetic progression (i.e. without three distinct elements x,y,z satisfying x+z=2y)? Similarly, given a prime p and a large positive integer n, what is the largest possible size of a subset of the vector space Fpn which does not contain a three-term arithmetic progression (i.e. without three distinct vectors x,y,z satisfying x+z=2y)? These are long-standing problems in additive combinatorics. This talk will explain the known bounds for these problems, give an overview of some of the proof techniques, and discuss additional applications of these techniques to other additive combinatorics problems.
