Hi all,

This is a reminder that GradSWANTAG VII will be held this Sunday, December 10th. 

All talks will be held in APM 6402. See below for the (provisional) schedule and abstracts.

9:30-10 Light breakfast
10-11 Iacopo
11-12 Zonglin
1-2 Roman
2-3 François

Iacopo Brivio
Title: DIP VS CBF

Abstract: A famous theorem by Y.T. Siu states that the plurigenera $P_m(X)$ of a complex projective manifold $X$ are invariant under smooth deformations. The proof however uses heavily analytic techniques and an algebro-geometric proof is known only when $X$ is of general type. In general, extension of sections is regulated by a coherent algebraic/analytic sheaf of ideals $\mathcal{I}(||K_X||)$ which, interestingly, seems to have way better properties when considered in the analytic category. On the other hand, the canonical bundle formula is an important tool in higher dimensional algebraic geometry, as it allows one to relate global pluricanonical sections of a variety $X$ with log pluricanonical sections on its canonical model $Y$.
In this talk I'll show how one can prove deformation invariance of (infinitely many) plurigenera of surfaces via reduction to the log-general type case and modifying suitably the canonical bundle formula. If time permits, I will also outline a possible generalization to higher dimensional families.

Zonglin Jiang
Title: An invitation to Langlands program and its geometrization

Abstract: The Langlands program predicts a connection between the arithmetic of a number field and representations of algebraic groups. The geometric Langlands program is the function field analog of the Langlands program, studied from the point of view of algebraic geometry. Recently, L. Fargues formulated a conjecture to geometrize the local Langlands program which has the local Langlands correspondence as corollary. In this talk, we will give a gentle introduction to the subject(s).

Roman Kitsela
Title: A Tannakian result for Profinite Groups

Abstract: As a generalization of Pontryagin duality, the classical Tannaka-Krein duality states that a compact topological group (not necessarily commutative) is dual to its category of finite dimensional linear representations. We will discuss how a result Schneider and Teitelbaum allows us recover a profinite group from its category of p-adic Banach space representations.

François Thilmany
Title: Buildings

Abstract: Buildings are an important geometric object associated to certain (linear) groups. We will describe their construction and properties, both from the geometric and the group theoretic perspective. We will illustrate their construction and properties on a couple of typical examples.

Hope to see you there,
Peter and François