About the speaker:
Thomas Lam is a combinatorialist working at the interface with algebraic geometry, representation theory, and physics. Lam received his B.Sc. from the University of New South Wales in Sydney, Australia. He received his Ph.D. in 2005 under the guidance of Richard Stanley from the Massachusetts Institute of Technology in Cambridge, USA. After a Benjamin Peirce Assistant Professorship at Harvard University, Lam joined the University of Michigan in 2009 where he has been since.
Lam received a Sloan Fellowship in 2009, a Simons Fellowship in 2015 and 2024, and a Von Neumann Fellowship in 2018.
Abstract:
Tropical Grassmannians Trop Gr(k,n) were introduced by Speyer and Sturmfels, and in the case of 2-planes, the tropical Grassmannian can be identified with the space of phylogenetic trees. Besides the applications to mathematical biology, in recent years the tropical Grassmannian has seen new connections to scattering amplitudes in physics.
Despite its importance, the construction of a combinatorial model for higher tropical Grassmannians has remained an open problem for many years. In this work, we propose such a combinatorial model, and discuss connections with tropical linear spaces, buildings, webs, noncrossing tableaux, and matroid decompositions. This is based on joint work with Nick Early.
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