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.

- Weeks 1-3: the `tropical' origin: tropical semigroup of matrices, max-plus linear systems and applications in queueing theory
- Weeks 4-8: Tropical combinatorics: linear spaces, oriented matroids, tropical varieties, learning tropical manifolds.
- Weeks 9-10: Discrete optimization and tropical geometry
- Weeks 11-12: student presentations

- Synchronization and Linearity: An Algebra for Discrete Event Systems, Francois Baccelli, Guy Cohen, Geert Jan Olsder and Jean-Pierre Quadrat
- Max-linear Systems: Theory and Algorithms, Peter Butkovic
- Large deviations and idempotent probability, Anatolli Puhalskii
- Idempotent Analysis and Its Applications, Vassili N. Kolokoltsov and Victor P. Maslov
- Introduction to Tropical Geometry, Diane Maclagan and Bernd Sturmfels
- Essentials of Tropical Combinatorics, Michael Joswig
- Discrete convex analysis, Kazuo Murota

- Methods and Applications of (max,+) Linear Algebra, Marianne Akian, Guy Cohen, Stephane Gaubert, Jean-Pierre Quadrat and Michel Viot
- M. Akian, S. Gaubert, and A. Guterman. Tropical polyhedra are equivalent to mean payoff games
- X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig, Log-barrier interior point methods are not strongly polynomial
- X. Allamigeon, U. Fahrenberg, S. Gaubert, R. Katz and A. Legay, Tropical Fourier-Motzkin elimination, with an application to real-time verification
- J. Depersin, S. Gaubert, and M. Joswig. A tropical isoperimetric inequality
- Develin, Mike, and Bernd Sturmfels. Tropical convexity.
- Tropical hyperplane arrangements and oriented matroids Federico Ardila, Mike Develin
- A Topological Representation Theorem for tropical oriented matroids, S Horn
- Valuations for matroid polytope subdivisions, F Ardila, A Fink, F Rincon
- Stiefel tropical linear spaces, A Fink, F Rincon
- Monomial tropical cones for multicriteria optimization Michael Joswig, Georg Loho
- Algorithms for tight spans and tropical linear spaces, Simon Hampe, MichaelJoswig, Benjamin Schroeter
- Tropical linear spaces, David Speyer
- Tropical and ordinary convexity combined, M Joswig, K Kulas
- Enumerating polytropes, N M Tran
- HodgeRank Is the Limit of Perron Rank, N M Tran
- Tropical Principal Component Analysis and its Application to Phylogenetics, Ruriko Yoshida, Leon Zhang, Xu Zhang
- Tropical Gaussians: A brief survey, Ngoc Tran
- Tropical geometry and mechanism design, R Crowell and N Tran
- Product-Mix Auctions and Tropical Geometry, Ngoc Mai Tran, Josephine Yu
- Split probabilities and species tree inference under the multispecies coalescent model, E.S. Allman, J.H. Degnan and J.A. Rhodes
- L. Zhang, G. Naitzat, and L.-H. Lim, "Tropical geometry of deep neural networks"
- Bayesian Networks for Max-linear Models, Claudia Klueppelberg, Steffen Lauritzen
- Maximum Likelihood Estimation for Totally Positive Log-Concave Densities Elina Robeva, Bernd Sturmfels, Ngoc Tran, Caroline Uhler
- Tropical matrix duality and Green's D relation Christopher Hollings, Mark Kambites
- Identities in Upper Triangular Tropical Matrix Semigroups and the Bicyclic Monoid, Laure Daviaud, Marianne Johnson, Mark Kambites
- Geometry and algorithms for upper triangular tropical matrix identities, Marianne Johnson, Ngoc Mai Tran
- Performance Evaluation of (max,+) Automata, Stephane Gaubert
- Valuated matroids, Andreas W.M Dress, Walter Wenzel
- Valuated matroids: a new look at the greedy algorithm, Andreas W.M.Dress, Walter Wenzel

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.