For linear algebra lovers: Carathéodory's theorem and its relatives

Start: 09/09/2015 - 4:15pm
End  : 09/09/2015 - 5:15pm


Jesus De Loera (UC Davis)


Are you someone that found linear algebra the most awesome and beautiful subject in the universe?  Do linear equations and vectors make you smile? Then I have the theorem for you; Carath\'eodory’s theorem! It states that any vector in the convex hull of a subset $X$ of $R^d$ can be expressed as a linear convex combination of at most $d+1$ vectors of the set $X$.  It is a variation on the basic fact that vectors in $R^d$ can be expressed as linear combination of a basis (with $d$ vectors). This talk will consider the lovely Carath\'eodory’s theorem, and its many relatives and variations. I will show the many applications (e.g., in economics, logistics, and signal processing) and how this theorem touches in the inner depths of the mathematician's soul. I will offer many open questions for people young solve, so come prepared to fall in love with $Ax=b$.


Argue Auditorium, Millikan, Pomona College