The main problem in phylogenetics is to reconstruct evolutionary relationships between collections of species, typically represented by a phylogenetic tree. In the statistical approach to phylogenetics, a probabilistic model of mutation is used to reconstruct the tree that best explains the data (the data consisting of DNA sequences from homologous genes of the extant species). In algebraic statistics, we interpret these statistical models of evolution as geometric objects in a high-dimensional probability simplex. This connection arises because the functions that parametrize these models are polynomials, and hence we can consider statistical models as algebraic varieties. The goal of the talk is to introduce this connection and explain how the algebraic perspective leads to new theoretical advances in phylogenetics, and also provides new research directions in algebraic geometry. The talk material will be kept at an introductory level, with background on phylogenetics and algebraic geometry. Bio: Seth Sullivant received his PhD in 2005 from the University of California, Berkeley. After a Junior Fellowship in Harvard's Society of Fellows, he joined the department of mathematics at North Carolina State University in 2008 as an assistant professor. He was promoted to full professor in 2014 and distinguished professor in 2018. Sullivant's work has been honored with a Packard Foundation Fellowship and an NSF CAREER award and he was selected as a Fellow of the American Mathematical Society. He helped to found the SIAM activity group in Algebraic Geometry where he has served as both secretary and chair. Sullivant's current research interests include algebraic statistics, mathematical phylogenetics, applied algebraic geometry, and combinatorics.