Lines and Curves in the Tropics

Abstract: Tropical Geometry has been the subject of a great amount of recent activity over the last decade. Loosely speaking, it can be described as a piecewise-linear version of algebraic geometry. It is based on tropical algebra, where the sum of two numbers is their maximum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of geometric information about their classical counterparts. In particular, tropical curves become metric graphs and lines yield metric trees.

In this talk, I will give a gentle introduction to the subject and will illustrate this powerful technique through a concrete example from classical algebraic geometry: the 28 bitangent lines to smooth plane quartics. This is based on joint work with Hannah Markwig.

commutative algebraalgebraic geometrygeneral mathematicsnumber theoryrings and algebras

Audience: undergraduates

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PRiME: Pomona Research in Mathematics Experience

Series comments: PRiME is hosting a series of talks which will take place on Fridays in July. All are welcome to join us either in person at Pomona College or virtually over Zoom. There will be two types of series.

PROFESSIONAL DEVELOPMENT WORKSHOPS

We will have a series of 2-hour workshops geared for undergraduate students, graduate students, and faculty. The Morning Sessions will take place from 10:00 AM - 12:00 PM Pacific, while the Afternoon Sessions will take place from 2:00 PM - 4:00 PM Pacific. The Student Professional Development Series (geared for undergraduates) will meet at Pomona College in Estella 1051 (Argue Auditorium); while the Faculty Professional Development Series (geared for graduate students and junior faculty) will meet in Estella 1021 (Noether Auditorium).

COLLOQUIUM SERIES

We will have outside speakers to visit with us on Fridays from 4:30 PM - 6:00 PM Pacific. We will meet in person at Pomona College in Estella 1051 (Argue Auditorium).

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