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Research

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We have been working on a number of problems in tropical geometry and algebra.

Research Topics

Factoring Tropical Polynomials

Nathan Grigg has been working on topics related to Factoring Tropical Polynomials. Among other things, he has written an elementary proof of the Fundamental Theorem of Tropical Algebra. He has also written an honors thesis entitled Factorization of Tropical Polynomials in One and Several Variables.

• Nathan's Honors Thesis: Factorization of Tropical Polynomials
• Preprint of "An elementary proof of the Fundamental Theorem of Tropical Algebra"
• Presentation on Tropical Factorization, given at Nathan's thesis defense.
• Nathan's Poster on Tropical Factorization

Tropical Bézout's Theorem

Gretchen Rimmasch is working on her proof of the Tropical Bézout's Theorem.

Projective duality

Julian Tay has proved several results about Tropical Projective duality.

• Julian's Honors thesis on Projective duality
• Julian's poster on Projective duality

Classification of tropical plane conics

Amanda Ellis did work classifying conics in the tropical projective plane. Her masters thesis, Classification of Conics in the Tropical Projective Plane, is a very useful introduction and resource.

• Amanda's Thesis on classifying conics

Correspondence between weighted graphs and tropical polynomials

Natalie Wilde is writing up a proof of the correspondence between weighted balanced graphs and tropical polynomials. Her algorithm that produces a polynomial from a weighted balanced graph will help us to better understand tropical varieties.

• Natalie's poster on recovering polynomials from weighted graphs

Other topics

• Sheaves of regular functions on tropical varieties
• Intersection theory and singularities in tropical geometry

More details and results will be posted here as they become available.

Presentations

We have presented our research in a number of places, including the following:

• BYU College of Physical and Mathematical Sciences' Spring Research Conference.
• MAA Intermountain Section Meetings
• Young Mathematicians' Conference (Ohio State University)
• AMS/MAA/SIAM Annual Joint Meetings