##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Janos Pach

#### Renyi Institute and EPFL

## The blessing of low dimensionality

##### Abstract:

We discuss some notoriously hard combinatorial problems for large classes of graphs and hypergraphs arising in geometric, algebraic, and practical applications. These structures escape the â€œcurse of dimensionalityâ€: 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 dimensionality? I will suggest a few possible answers to this question, and illustrate them on classical examples.

Host: Andrew Suk

### March 21, 2019

### 4:00 PM

### AP&M 2402

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