Lecture on the Geometry of Syntax by Matilde Marcolli
NEW TIME AND PLACE!
On April 17, Matilde Marcolli, professor of Mathematics at the California Institute of Technology, will give a talk on The Geometry of Syntax.
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.