##### Department of Mathematics,

University of California San Diego

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### Colloquium

## Prof. Fay Dowker

#### Imperial College London

## Combinatorial Geometry: a tale of two signatures

##### Abstract:

Can a purely combinatorial object be approximated by a continuum geometry? I will describe evidence that the answer is "yes'' if that object is a transitive directed acyclic graph, otherwise known as a discrete order, otherwise known as a causal set. In which case, the approximating continuum geometry must be pseudo-Riemannian with a "Lorentzian'' signature of $(-, +, +, \ldots, +)$. I will, along the way, explain the crucial difference between Riemannian and Lorentzian geometry: in the former case the geometry is local and in the latter the geometry is, if not actually nonlocal then teetering on the edge of being nonlocal. If there is time I will describe a model of random orders called Transitive Percolation, which is the Lorentzian analogue of the Erdős-Renyi random graph and is an interesting toy model for a physical dynamics of discrete space-time.

Host: David Meyer

### February 14, 2024

### 4:00 PM

APM 6402

Research Areas

Mathematical Physics****************************