Curl Summer 2019: Difference between revisions
No edit summary |
|||
| (5 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
This summer there are two students participating in CURL, each doing a project in applied algebraic geometry. | 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:''' [https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez], Colin Crowley | |||
===Computing Mixed Nash Equilibria=== | ===Computing Mixed Nash Equilibria=== | ||
'''Student:''' Jacob Weiker | '''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. | |||
Latest revision as of 16:56, 16 May 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.