## Speaker:

Christos Saroglou

## Institution:

University of Ioannina

## Time:

Thursday, December 1, 2022 - 10:00am

## Location:

Zoom ID: 99342387189

Let $k\geq 2$ be an integer. In the spirit of Kolesnikov-Werner, for each $j\in\{2,\ldots,k\}$, we conjecture a sharp Santaló type inequality (we call it $j$-Santal\'{o} conjecture)  for many sets (or more generally for many functions), which we are able to confirm in some cases, including the case $j=k$ and the unconditional case. Interestingly, the extremals of this family of inequalities are tuples of the $l_j^n$-ball.
Our results also strengthen one of the main results of Kolesnikov-Werner, which corresponds to the case $j=2$. All members of the family of our conjectured inequalities can be interpreted as generalizations of the classical Blaschke-Santaló inequality.
Related, we discuss an analogue of a conjecture due to K. Ball in the multi-entry setting and establish a connection to the $j$-Santaló conjecture.