Tropical and nonArchimedean geometry (2)
Martin Ulirsch  SFBTransregio45Seminar zur Algebraischen Geometrie
What 


When 
Dec 08, 2015 from 02:00 pm to 04:00 pm 
Where  Bonn, Raum 0.011, MathematikZentrum, Endenicher Allee 60 
Contact Name  Sachinidis 
Add event to calendar 
vCal iCal 
Logarithmic structures and the tropical geometry of moduli spaces While $\overline{M}_{0,n}$ admits a wellunderstood embedding into a toric variety, this is not true for the DeligneKnudsenMumford moduli stacks $\overline{\mathcal{M}}_{g,n}$ of higher genus curves. In this talk I will explain how logarithmic geometry in the sense of K. Kato provides us with a much more general framework for tropicalization that naturally applies to these moduli spaces. The final goal will be a theorem of AbramovichCaporasoPayne which gives a modular interpretation for the tropicalization of the algebraic moduli spaces. Given time I will also talk about ongoing work with R. Cavalieri, M. Chan, and J. Wise, where we propose a stacktheoretic generalization of this result.