Math 390C - Stochastic Tropical Geometry: Theory, Applications and Open Problems

Course description : Tropical geometry is the interface of matroid theory, combinatorial optimization and algebraic geometry. It has found numerous applications in auction theory, mechanism design, game theory, complexity theory, discrete convex analysis. In particular, tropical geometry is a variational version of combinatorial optimization, where it examines the combinatorics and geometry of the entire space of input parameters, as opposed to analyzing the solution of a particular instance. It is an excellent tool for constructing examples and counter-examples in economics, game theory, network optimization, matroid theory and algebraic geometry.

This course aims to take students to the latest open research questions as fast as possible. After a set of introductory lectures, the majority of class time will be spent doing survey papers and literature review of existing research directions and student presentations on progress to open problems.

Lectures: TBA

Instructor: Ngoc Tran (office 11.124 PMA)

Office hours: TBA

Prerequisites: graduate students in mathematics, electrical engineering, or consent of instructor

Grading policy: homework sets and final projects.

Class format: the class breaks up to essentially disjoint topics. On each topic, I will give a set of core lectures, and list a bunch of open problems. Students will choose at least two topics to dwelve further upon. On each of their chosen topics, they need to either write a survey or work on a specific open problem (could be of their own suggestion). Afterwards, they will present progress to the class.

Syllabus and class format

Here is a tentative list of topics to be covered.
  1. The `tropical' origin: tropical semigroup of matrices
  2. Max-plus linear systems and applications: discrete events systems and queueing theory
  3. Tropical combinatorics: linear spaces and oriented matroids.
  4. Tropical varieties, learning tropical manifolds.
  5. Modern applications of tropical mathematics in statistics, max-linear graphical models, phylogenetics, mechanism design, auction theory, game theory, complexity theory

Policies

Add/drop dates

Please take note of the add/drop deadlines here at the university calendar. There are no provisions to adjust scores due to late enrolment.

Make-ups for homeworks

No late homework or final projects will be accepted.
Should you have serious medical problem or genuine emergency, please obtain a written or electronic letter from the Student Emergency Serivces. Under exceptional circumstances, I will give partial grade, provided you have a C average on previous coursework.

Services for students with disabilities

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified stu- dents with disabilities. For more information, contact Services for Students with Disabilities at 471-6259 (voice) or 232-2937 (video phone)

Academic Integrity

By being enrolled in the class, you have agreed to adhere to the student honor code and the university code of conduct. Violations will be treated as required by the university policy.