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Vorträge 2022

Imre Bárány (Rényi Institute, Budapest): Cells in the box and a hyperplane

It is well known that a line can intersect at most 2 n −1 cells of the  n × n chessboard. What happens in higher dimensions: how many cells of the  d -dimensional [0, n ]^ d box can a hyperplane intersect? We answer this question asymptotically. We also prove the integer analogue of the following fact. If  K,L are convex bodies in  R ^d and  K ⊂ L , then the surface area  K is smaller than that of  L . This is joint work with Péter Frankl.

Ort: Chemistry building Arnimallee 22 14195 Berlin Hörsaal A

30.05.2022 | 16:00 s.t.

János Pach (Rényi Institute, Budapest): Facets of Simplicity

We discuss some notoriously hard combinatorial problems for large classes of graphs and hypergraphs arising in geometric, algebraic, and practical applications. These structures are of bounded complexity: they can be embedded in a bounded-dimensional space, or have small VC-dimension, or a short algebraic description. What are the advantages of low complexity? I will suggest a few possible answers to this question, and illustrate them with classical examples.

Ort: Chemistry building Arnimallee 22 14195 Berlin Hörsaal A

30.05.2022 | 14:15