**Speaker:** Dr. Luo Ye from Xiamen University

**Date and Time:** Friday, February 11, 2022, 9:00-10:00 via Zoom. Please contact Will Brian to obtain the Zoom link.

**Title:** Tropical convexity analysis and some applications

**Abstract:** The tropical semiring is an idempotent semiring where the usual operations of addition and multiplication are replaced by operations of minimum/maximum and addition respectively. Tropical geometry is a theory of geometry over the tropical semiring which has rich combinatorial features and can be described as a degenerated version of algebraic geometry over the field of complex numbers under Maslov dequantization or over a non-archimedean field under the valuation map. The features of “linear combinations” in tropical geometry can be captured by the notion of tropical convexity. In this talk, I will introduce a general theory of tropical convexity analysis based on the so-called “B-pseudonorms” on tropical projective spaces, and show some subsequent results, e.g., a tropical version of Mazur’s Theorem on closed tropical convex hulls and a fixed point theorem for tropical projections. Two applications will also be presented. The first is to establish a connection between tropical projections and reduced divisors on (metric) graphs, and the second is to construct min-max-plus neural networks, a new type of artificial neural networks.