Title	Halfway to Rotaâ s basis conjecture
Creator	Pokrovskiy, Alexey
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-09-03T10:42
Description	In 1989, Rota made the following conjecture. Given $n$ bases $B_1,\ldots, B_n$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint bases of $V$, each containing exactly one element from each $B_i$ (we call such bases transversal bases). Rotaâ s basis conjecture remains open despite its apparent simplicity and the efforts of many researchers (for example, the conjecture was recently the subject of the collaborative â Polymathâ project). In this talk, I will discuss how to find $(0.5 - o(1))n$ disjoint transversal bases, improving the previously best known bound of $n/\log n$. This is joint work with Bucic, Kwan, and Sudakov.
Extent	33.0 minutes
Subject	Mathematics; Combinatorics; Probability theory and stochastic processes
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Birkbeck University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2020-03-02
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0388813
URI	http://hdl.handle.net/2429/73640
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Other
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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