Inequalities on projected volumes

Add to your list(s) Download to your calendar using vCal

• Zarko Randelovic (University of Cambridge)
• Thursday 30 January 2020, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

Given $2ⁿ – 1$ real numbers $x_A$ indexed by the non-empty subsets $A \subset \{ 1,\ldots,n \}$, is it possible to construct a body $T$ in $Rⁿ$ such that $x_A = \| T_A \|$, where $\| T_A \|$ is the $\| A \|$-dimensional volume of the projection of $T$ onto the subspace spanned by the axes of $A$? As it is more convenient to take logarithms, we denote by $\psi_n$ the set of all vectors $x$ for which there is a body $T$ such that $x_A = \log \| T_A \|$ for all $A$. Bollob\’as and Thomason showed that $\psi_n$ is containd in the polyhedral cone defined by the class of `uniform cover inequalities’. Tao and Zeng conjectured that the convex hull of $\psi_n$ is equal to the cone given by the uniform cover inequalities.

We show that this conjecture is not right, but is `nearly’ right.

Joint work with Imre Leader and Eero Raty.

This talk is part of the Combinatorics Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• Combinatorics Seminar
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.