TAGSS V - TROPICAL GEOMETRY AND RELATED TOPICS
The school will feature courses by:
Margarida
Melo - Università Roma
Tre
Tropical moduli spaces of curves and
Jacobians
In algebraic geometry, the existence of
moduli spaces to parametrize certain classes of objects is of
central importance. Moreover, since these moduli spaces are often
not compact, the construction of modular compactifications for
theses spaces is very useful, as one can study them by using tools
that are only available for proper spaces. In the last few years,
it has been understood that often these compactifications depend
on combinatorial data that can be given a tropical modular
interpretation. When this is the case, one can study many
properties of the original space by looking at its tropical
counterpart, generating many interesting relations between the two
worlds. I will try to explain this phenomenon by looking at the
guiding examples of the moduli space of curves and its
Deligne-Mumford compactification, and the moduli space of
(universal) Jacobians and its different compactifications.
and
Marta Panizzut - Max
Planck Institute for Mathematics in the Sciences, Leipzig
Computing in
tropical geometry
Many exciting research topics lie at the
interface between combinatorics and algebraic geometry creating
fruitful grounds for new computational methods. Tropical geometry
has recently fueled these interactions, providing a systematic
framework to study degenerations of algebraic varieties. In the
course I will introduce computational tools to tropicalize
varieties defined over valued fields. We will consider a wide
range of examples on polyhedral computations at the core of the
study of curves and surfaces through tropical lenses. Towards the
end of the course we will also briefly present recent exciting
connections of tropical geometry to applied area, such as
statistics and physics.
