Organizer: Hechen Hu
Tropical geometry is a relatively young field. At its heart, it replaces polynomials with piecewise-linear functions, thus turns an algebraic variety into a piecewise-linear polyhedral complex, which is more amenable to direct computation. Its methods can be applied to study real algebraic geometry, enumerative geometry, mirror symmetry, symplectic geometry, etc. For example, in [P] it is shown that the analytification of a quasiprojective variety over a nonarchimedean field is naturally homeomorphic to the inverse limit of the tropicalizations of its quasiprojective embeddings. Gubler applied the tropicalization of subvarieties of Abelian varieties to study the function field analogue of Bogomolov conjecture in [Gub]. Maulik and Ranganathan presented a logarithmic enhancement of GW/DT correspondence in [MR]. When studying boundaries of moduli spaces, i.e. degenerations, log geometry naturally comes into play. It allows one to treat singular objects as if they are smooth. My current plan is to cover tropical enumeration of curves in P^2 and the moduli stack of tropical curves, after that we can explore any topics that is of interest to participants.
If you’d like to sign up for a talk, suggest a topic, or just to be added to the mailing list, please email me at [email protected].
Math 528, Tuesday 16:30-17:30
[CCUW] A moduli stack of tropical curves (Renzo Cavalieri, Melody Chan, Martin Ulirsch, Jonathan Wise)
[Gro] Tropical Geometry and Mirror Symmetry (Mark Gross)
[Mik] Enumerative tropical algebraic geometry in R^2 (Grigory Mikhalkin)
[O] Lectures on Logarithmic Algebraic Geometry (Arthur Ogus)
[MS] Introduction to Tropical Geometry (Diane Maclagan and Bernd Sturmfels)
[P] Analytification is the limit of all tropicalizations (Sam Payne)
[Gub] The Bogomolov conjecture for totally degenerate abelian varieties (Walter Gubler)
[MR] Logarithmic enumerative geometry for curves and sheaves (Davesh Maulik, Dhruv Ranganathan)