SMRI Seminar: Taji -- Projective families of varieties through birational geometry and Hodge theory

***REMINDER TO REGISTER - SEMINAR TODAY***

SMRI Seminar
'Projective families of varieties through birational geometry and Hodge theory'
Behrouz Taji (The University of Sydney)

When: Thursday 10 June 3.30pm-4.30pm (AEST)
Where: via Zoom -register here  
https://uni-sydney.zoom.us/meeting/register/tZ0vduygrT4qHNMyplsBtr1bSuEIWj5ih-10
and Quad S227 (University of Sydney staff, students & affiliates only)

Abstract:
In the 1920s, building on Fermat's Last Theorem, Mordell conjectured that the set of 
rational points of any smooth projective curve of genus at least two, over any number 
field, is finite. In the 1960s, Shafarevich turned this into a purely algebro geometric 
conjecture involving families of smooth projective curves. Parshin , Arakelov and 
Faltings settled this conjecture by showing that the base spaces of such families are 
in some sense hyperbolic, as long as there is some variation in the algebraic structure 
of the fibers. Inspired by recent advances in Birational Geometry, Kebekus and Kovács 
conjectured that these hyperbolicity type properties should hold for a vast class of 
projective families, with fibers of arbitrary dimension. In this talk I will discuss 
this conjecture and my solution to it. I will also talk about more recent progress in 
this area, based on a joint work with Kovács (University of Washington).

Notes
University of Sydney staff, students & affiliates are also invited to join us for 
afternoon tea on the SMRI terrace at 3pm please note in your registration or email 
smri.admin@sydney.edu.au to RSVP.


This seminar will be recorded (participants only when asking questions) and uploaded 
to the SMRI YouTube Channel
https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI