Veranstaltungen

I will recall often-used categorical constructions, such as the Yoneda lemma, categorical limits, and adjunctions. Most examples will be algebraic or topological in nature, with more geometric examples coming in the next session. I will also introduce group objects and discrete group objects in a category.

Let k be a field which is finitely generated over the algebraic closure of F_p, L be its perfection and let A be a k-abelian variety. The main goal of this talk is to provide some new result on the structure of the torsion free part of A(L). These results are motivated by their application to the "full" Mordell-Lang conjecture.The main tool is the study of various p-adic incarnation of certain 1-motives attached to L-rational points of A.


https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

I will recall the definition of sheaves and schemes and many of their properties, such as e.g. properness, smoothness, &c. This is all material from Hartshorne, parts II and III, with less of a focus on sheaf cohomology (already treated in the previous reading group, on DT invariants), and making use of the category theory background.

Blowup equations as the functional equations for the Nekrasov partition function of 4-dimensional gauge theory was proposed by Nakajima-Yoshioka in 2003. Certain K-theoretic versions were soon later found by Göttsche, Nakajima and Yoshioka. I will talk about two further generalizations found in recent three years, an elliptic version from the viewpoint of gauge theory and a most general version from the viewpoint of topological string theory on local Calabi-Yau threefolds.