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RUMA Lectures

The classification of Delzant polygons

Joseph Palmer, Rutgers University

Location:  Hill 425
Date & time: Thursday, 01 March 2018 at 7:00PM - 8:00PM

Abstract:  In this talk we present a novel proof to a classical result. Delzant polygons are a special class of convex polygons in \(\mathbb{R}^2\) which arise in the study of certain physical systems with symmetries (and smooth toric surfaces from algebraic geometry). To classify these polygons we describe an operation known as a corner chop and show that any Delzant polygon can be obtained from a short list of so-called emph{minimal models} by performing a sequence of corner chops. The main interest of the talk is the proof, which proceeds by rephrasing the question several times: we translate the question about polygons to one about integer vectors, which in turn becomes a question about matrices in SL\(_2(\mathbb{Z})\), which finally we change into a question about certain lists of integers. We conclude the proof by classifying these lists of integers. This talk should be accessible to any undergraduate math major.

This work is joint with Kane-Pelayo.

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

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