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Forests and Trees: the Formal Semantics of Collective Categorization (ROCKY)


17 April 2018
15:15 - 17:00
Drift 21 room 0.05

The Geometry of Syntax – Matilde Marcolli

The Geometry of Syntax
Matilde Marcolli
California Institute of Technology

Tuesday 17 April at 15.15
Drift 21


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.


The Geometry of Syntax
Codes and complexity
The Geometry of Syntax (Part 2)