Guest seminar summer 2017

Guest seminar "Arithmetic Geometry"

Time: Thursdays, 2pm-4pm

Place: New!! Arnimallee 14 (Physik), room T1 (1.3.21)


April 20


Johannes Nicaise (Imperial college)

Title: A motivic Fubini theorem for the tropicalization map

This talk is based on joint work with Sam Payne. I will explain the formulation and proof of a motivic Fubini theorem for the tropicalization map in the context of Hrushovski and Kazhdan's theory of motivic integration. Denef and Loeser's motivic nearby fiber has a natural interpretation in this setting. As an application, I will present a very short and conceptual proof of the integral identity conjecture of Kontsevich and Soibelman, one of the cornerstones of their theory of motivic Donaldson-Thomas invariants. This conjecture was previously solved by Le Quy Thuong by means of a related but more involved method.

May 11


Thomas Oliver (Bristol)

Title: tba

June 7


Michael Groechenig (Berlin)

Infinity categories I (Minicourse)

June 8


Javier Fresán (Zurich)

Title: tba

 June 9


Michael Groechenig (Berlin)

Infinity categories II (Minicourse)

 June 22


Alan Thompson (Warwick)

Title: Mirror symmetry for lattice polarized del Pezzo surfaces

Mirror symmetry for lattice polarized K3 surfaces is a well-established correspondence, first studied in the work of Dolgachev and Nikulin. I will discuss the possibility of extending this theory to log Calabi-Yau surfaces, and in particular to weak del Pezzo surfaces. I will describe how to endow a weak del Pezzo surface with a lattice polarization and how to define the mirror notion of a lattice polarized Landau-Ginzburg model. Finally, I will discuss how this notion of mirror symmetry should be compatible with Dolgachev-Nikulin mirror symmetry for lattice polarized K3's.

June 29


Raju Krishnamoorthy (Berlin)

Title: "On Analogs of the Hasse Invariant"

We'll use formal properties of "correspondences with a core" to give "conceptual" (i.e. non-computational) proofs of statements like the following.
1. Any two supersingular elliptic curves over \bar{F_p} are related by an l-primary isogeny for any l\neq p.2. A Hecke correspondence of compactified modular curves is always ramified at at least one cusp.3. There is no canonical lift of supersingular points on a (projective) Shimura curve. (In particular, this provides yet another conceptual reason why there is not a canonical lift of supersingular elliptic curves.) 
To do this, we'll introduce the concepts of "invariant line bundles" and of "invariant sections" on a correspondence without a core. We'll end with several open questions.