# Agenda

# The Geometry of Syntax – Matilde Marcolli

The Geometry of Syntax

Matilde Marcolli

California Institute of Technology

Tuesday 17 April at 15.15

Drift 21

Utrecht

**Abstract**

Chomsky’s “Principles and Parameters” model proposes that syntactic

structures can be encoded into a set of binary syntactic parameters. A

main problem in this approach is identifying a good set of independent

variables among these syntactic parameters. Mathematically, this can be

thought of as the question of finding a good set of coordinates on the

“geometry of syntax”. We consider two existing databases of syntactic

structures of world languages, the SSWL database and another independent

set of data recently published by Giuseppe Longobardi. We consider

various mathematical methods to detect computationally the presence of

relations between syntactic parameters. In the talk we focus on three of

these methods: recoverability in sparse distributed memories (Kanerva

networks), error correcting codes and the position in the space of code

parameters, and a heat-kernel method of dimensional reduction of

Belkin–Niyogi. We will illustrate some of the structures that become

visible through these different methods.

This talk can be viewed as a continuation of the mathematics colloquium

talk with the same title, that will take place on April 12, which will

cover other methods applied to the same problem (persistent topology,

phylogenetic algebraic geometry, and spin glass systems). While the two

talks are closely related, they will be self-contained and largely

independent. No advanced mathematics background is required for this talk.

**Handouts**

The Geometry of Syntax

Codes and complexity

The Geometry of Syntax (Part 2)