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Research seminar in Discrete Mathematics
Asymptotically-tight packing and covering with transversal bases in Rota’s basis conjecture
Asymptotically-tight packing and covering with transversal bases in Rota’s basis conjecture
组织者
马杰
, 本杰明·苏达科夫
演讲者
Lisa Sauermann
时间
2026年03月03日 17:05 至 18:15
地点
Online
线上
Zoom 787 662 9899
(BIMSA)
摘要
Rota’s basis conjecture from 1989 asserts that, given any n bases $B_1,...,B_n$ of a vector space of dimension n (or, more generally, a matroid of rank $n$), one can find a collection of n disjoint transversal bases. In other words, this means that the union
$B_1 \cup ... \cup B_n$ can be decomposed into n new bases of the vector space (or matroid), each consisting of exactly one element from each of the original bases $B_1,...,B_n$. In this talk, we discuss some progress towards this famous conjecture, showing that the union $B_1 \cup ... \cup B_n$ contains $(1-o(1))n$ disjoint transversal bases, and also that the union $B_1 \cup ... \cup B_n$ can be covered by $(1+o(1))n$ transversal bases. Joint work with Richard Montgomery.
$B_1 \cup ... \cup B_n$ can be decomposed into n new bases of the vector space (or matroid), each consisting of exactly one element from each of the original bases $B_1,...,B_n$. In this talk, we discuss some progress towards this famous conjecture, showing that the union $B_1 \cup ... \cup B_n$ contains $(1-o(1))n$ disjoint transversal bases, and also that the union $B_1 \cup ... \cup B_n$ can be covered by $(1+o(1))n$ transversal bases. Joint work with Richard Montgomery.
演讲者介绍
Lisa Sauermann is a Professor at the University of Bonn. She received her PhD in mathematics from Stanford University in 2019 under the supervision of Jacob Fox. She then held post-doctoral positions at Stanford University and the Institute for Advanced Study (IAS), and spent two years as an Assistant Professor at Massachusetts Institute of Technology (MIT), before joining the University of Bonn in summer 2023. She received the Richard-Rado-Prize in 2020, the European Prize in Combinatorics in 2021, a Sloan Fellowship in 2022, and the von Kaven Award in 2023.