Title: A Strongly Polynomial Label-Correcting Algorithm for Linear Systems with Two Variables per InequalitySpeaker: Cedric Koh Affiliation: London School of Economics and Political Science Zoom: Contact Sharat Ibrahimpur
In this talk, I will present a strongly polynomial label-correcting algorithm for solving the feasibility of linear systems with two variables per inequality. The algorithm is based on the Newton–Dinkelbach method for fractional combinatorial optimization, and extends previous work of Madani (2002).
Title: Matroids, tropical geometry, and positivitySpeaker: Lauren K. Williams Affiliation: Harvard University & Radcliffe Institute Zoom: Please email Emma Watson.
The theory of matroids -- a class of combinatorial objects which simultaneously generalize graphs as well as vectors in a vector space -- was pioneered by William Tutte in his 1948 PhD thesis. Matroids are also closely connected to the Grassmannian and the tropical Grassmannian. In recent years, mathematicians and physicists have been exploring positive notions of all of these objects, finding applications to scattering amplitudes and shallow water waves. In my talk I will give an introduction to matroids, tropical geometry, and positivity, and survey some of the beautiful results and applications.