# Curl Summer 2019

This summer there are two students participating in CURL, each doing a project in applied algebraic geometry.

We will meet from Monday, May 13th through Friday, June 28th on weekdays from 9:00 to 12:00.

**Students:** Jacob Weiker, Jacob Zoromski

**Mentors:** Jose Israel Rodriguez, Colin Crowley

### Computing Mixed Nash Equilibria

**Student:** Jacob Weiker

Problems in economics are often modeled as multiplayer games. In a model where each player chooses between multiple strategies according to a probability distribution, of interest are the so called Mixed Nash Equilibria: situations where no player can benefit by changing their probability of using a particular strategy. In this project we will cover background material on solving polynomial systems, and then study the polynomial formulation of various Mixed Nash Equilibria problems.

### Computational algebraic geometry for Algebraic Kinematics

**Student:** Jacob Zoromski

Various problems in Kinematics lead to polynomial systems. We will cover background on solving these systems, and then compute examples involving exceptional mechanisms and transitional mechanisms.

In both projects we will focus on using software to compute many examples, and forming observations and conjectures about the real solutions. With remaining time we aim to prove theoretical results or develop implementations.