Curl Summer 2019: Difference between revisions
No edit summary |
|||
| Line 5: | Line 5: | ||
'''Mentors:''' [https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez], Colin Crowley | '''Mentors:''' [https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez], Colin Crowley | ||
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 | 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 === | ===Computational algebraic geometry for Algebraic Kinematics === | ||
| Line 11: | Line 11: | ||
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. | 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. | |||
Revision as of 16:51, 16 May 2019
This summer there are two students participating in CURL, each doing a project in applied algebraic geometry.
Computing Mixed Nash Equilibria
Student: Jacob Weiker Mentors: Jose Israel Rodriguez, Colin Crowley
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 Mentors: Jose Israel Rodriguez, Colin Crowley
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.