# Seminars & Events for Algebraic Geometry Seminar

##### TBA - McLean

**Please note special day.**

##### TBA - Griffiths

##### TBA - Doran

**Please note special day and time.**

##### TBA - Sam Grushevsky

##### Transfinite limits in topos theory

##### TBA - Luca Migliorini

##### Projectivity of the moduli space of KSBA stable pairs and applications

KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work in progress with Sándor Kovács on proving the projectivity of this moduli space, by showing that certain Hodge-type bundles are ample on it. I will also mention applications to the subadditivity of logarithmic Kodaira dimension, and to the ampleness of the CM line bundle.

##### Automorphisms of smooth canonically polarised surfaces in characteristic 2

Let X be a smooth canonically polarised surface defined over an algebraically closed field of characteristic 2. In this talk I will present some results about the geometry of X in the case when the automorphism scheme Aut(X) of X is not smooth, or equivalently X has nontrivial global vector fields. This is a situation that appears only in positive characteristic and is intimately related to the structure of the moduli stack of canonically polarised surfaces in positive characteristic because the smoothness of the automorphism scheme is the obstruction for the moduli stack to be Deligne-Mumford, something that is always true in characteristic zero but not in general in positive characteristic.

##### TBA - Mircea Mustata

##### TBA - Patrick Graf

##### TBA - Qile Chen

##### Constructing buildings and harmonic maps

##### Framed motives of algebraic varieties (after V. Voevodsky)

This is joint work with G .Garkusha. Using the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives is introduced and studied. To any smooth algebraic variety X, the framed motive Mfr(X) is associated in that category. Theorem. The bispectrum (MfrX,Mfr(X)(1),Mfr(X)(2),...), each term of which is a twisted framed motive of X, has motivic homotopy type of the suspension bispectrum of X. (this result is an A1-homotopy analog of a theorem due to G.Segal). We also construct a compactly generated triangulated category of framed bispectra and show that it reconstructs the Morel--Voevodsky category SH(k). This machinery allows to recover in characteristic zero the celebrated theorem due to F. Morel stating that the stable π0,0(k)= the Grothendiek-Witt ring of the field k .