# Course Descriptions

**Uhlenbeck Lecture Course**: Tropical geometry

Lecturer: Melody Chan, Brown University

Teaching Assistant: Raluca Vlad, Brown University

Tropical geometry is a modern degeneration technique in algebraic geometry. Think of it as a very drastic degeneration in which one associates a limiting object to a family of algebraic varieties that is entirely combinatorial. I will introduce tropical geometry through the beautiful topics of tropical curves, tropical abelian varieties, and their moduli spaces.

**Terng Lecture Course**: Log-concavity and Matroids

Lecturer: Cynthia Vinzant, University of Washington

Teaching Assistant: Tracy Chin, University of Washington

Matroids are combinatorial structures that model independence, such as that of edges in a graph and vectors in a linear space. I will introduce the theory of matroids along with their surprising connection to a class of multivariate polynomials that are log-concave on the positive orthant. Log-concavity is an important feature of many functions and discrete sequences appearing across mathematics, including combinatorics, algebraic geometry, convex analysis, and optimization. We will explore the real and combinatorial geometry underlying log-concavity along with applications to matroids and the mixing times of random walks.

**Prerequisites for the courses**:__Uhlenbeck Course__: Exposure to combinatorics and graph theory, and a semester of algebraic geometry or algebraic topology__Terng Course__: Linear algebra and some exposure to each of algebra, combinatorics, graph theory, and probability