#### Conference abstracts

Plenary talk

July 11, 11:30 ~ 12:30

## T < 4E

### Karim Adiprasito

### Hebrew University of Jerusalem, Israel - adiprasito@math.huji.ac.il

Descartes proved that a graph embedding into the plane on V vertices and E edges satisfies

\[ E\ <\ 3V\]

Quite disappointingly, no similarly beautiful numerical inequality exists to limit the number of faces of, say, 2-dimensional simplicial complexes embedding in dimension 4, and topological techniques seem to be limited in their reach to provide us with such a result. I will instead use algebra and combinatorics to generalize Descartes' result.