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Workshop

Tropical Positivity and Symmetric Low Rank Matrices

Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

In 2003, Speyer and Williams introduced two definitions for positive tropicalizations of algebraic varieties over complex Puiseux series and proved their equivalence for Grassmannians. The two corresponding notions of positive tropical generators were studied by Brandenburg, Loho, and Sinn in 2022. In this talk, I will provide a brief introduction to tropical geometry and then present a combinatorial description of the tropicalization of the space of symmetric rank two matrices, along with their real and positive parts. We will compare the two notions of tropical positivity for rank 2 or corank 1 symmetric matrices. The results are based on joint works with Abeer Al Ahmadieh, May Cai, and Kisun Lee.

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

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