Kiumars Kaveh has recently been funded by the US National Science Foundation (award DMS 2101843) for the proposal “Collaborative Research: Toric Geometry, Tropical Geometry, and Buildings” for the period of September 1, 2021 – August 31, 2024. This project involves research at the intersection of algebraic geometry and combinatorics. Algebraic geometry is the study of solution sets of polynomial equations called algebraic varieties. It has applications in many fields as diverse as high energy physics, coding, cryptography, and mathematical biology. Understanding how the shape of the solution set changes as the coefficients are varied is one of the oldest and central questions in the field. Such continuous deformations, which appear in all branches of algebraic geometry and its applications, are called algebraic families. An important example is the geometric Langlands program, which is concerned with understanding principal bundles on curves, a very special class of families. Bundles are also main players in gauge theory in high energy physics. Algebraic families are the central focus of this project. The research aims to introduce new methods to classify and compute with algebraic families