The seminar will meet Fridays 1112:30 pm (with a 15 minute break in the middle) when there is one talk, and 10:4511:45am and 121pm when there is a double header. Click on the title to see the abstract (when available).
Register in advance for the seminar:
https://stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr_UhGvnr1EGv
Date and Time (Pacific)  Speaker  Title 

April 3, 4 pm  Will Sawin (Columbia)  The Shafarevich conjecture for hypersurfaces in abelian varieties (abstract below) 
April 17, 1112:30  Gavril Farkas (Humboldt)  Green’s Conjecture via Koszul modules 
April 24, 1112:30  Kirsten Wickelgren (Duke)  There are 160,839 + 160,650 3planes in a 7dimensional cubic hypersurface

May 1, 10:4511:45  Borys Kadets (MIT)  38406501359372282063949 & all that: Monodromy of Fano Problems 
May 1, 121  Burt Totaro (UCLA)  
May 8, 10:4511:45  Julie Desjardins (Toronto)  Density of rational points on a family of del Pezzo surface of degree 1 
May 8, 121  Bjorn Poonen (MIT)  
May 15 10:4511:45  Rohini Ramadas (Brown)  The locus of postcritically finite maps in the moduli space of selfmaps of P^n 
May 15, 121  Rob Silversmith (Northeastern)  
May 22, 1112:30  Chenyang Xu (MIT)  Kmoduli of Fano varieties* 
May 29, 10:4511:45  Yuchen Liu (Yale)  Moduli spaces of quartic hyperelliptic K3 surfaces via Kstability 
May 29, 121  Maksym Fedorchuk (Boston College)  Stability of fibrations over onedimensional bases, and standard models of del Pezzo fibrations ** 
June 5, 10:4511:45  TBA  TBA 
June 5, 121  Bhargav Bhatt (Michigan)  TBA 
June 12, 10:4511:45  Margaret Bilu (NYU)  TBA 
June 12, 121  Wei Ho (Michigan)  TBA 
*The discussion for Chenyang Xu’s talk is taking place not in zoomchat, but at https://tinyurl.com/20200522cx (and will be deleted after 37 days).
**The discussion for Maksym Fedorchuk’s talk is taking place not in zoomchat, but at https://tinyurl.com/20200529mf (and will be deleted after 37 days).
Abstracts
Will Sawin (Columbia)
April 3, 2020, 4pm pacific
The Shafarevich conjecture for hypersurfaces in abelian varieties.
Faltings proved the statement, previously conjectured by Shafarevich, that there are finitely many abelian varieties of dimension n, defined over the rational numbers (or another fixed number field), with good reduction outside a fixed finite set of primes, up to isomorphism. In joint work with Brian Lawrence, we prove an analogous finiteness statement for hypersurfaces in a fixed abelian variety with good reduction outside a finite set of primes. I will give a broad, intuitive introduction to some of the ideas in the proof, which combines tools from different areas in algebraic geometry, arithmetic geometry, and number theory, and builds heavily on recent work of Lawrence and Venkatesh.