Graduate Student Seminar | Haochen Cheng (Northwestern University)

Title: Newton Polygons

Abstract: Newton Polygons, introduced as early as 1671 by Isaac Newton to approximate the roots of polynomials with polynomial coefficients, were later rediscovered by Victor Puiseux in 1850 and became known as the Newton-Puiseux theorem. In this talk, I will briefly talk about how this approximation by Newton polygons works and the analogue over p-adic fields. Finally, I will introduce their modern significance in arithmetic geometry, particularly in the study of abelian varieties and their moduli spaces over finite fields.

Note: The talk will start at 4:10 pm

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