The seminar will meet Fridays 11-12:30 pm (with a 15 minute break in the middle) when there is one talk, and 10:45-11:45am and 12-1pm when there is a double header. Click on the title to see the abstract (when available).
Register in advance for the seminar:
|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, 11-12:30||Gavril Farkas (Humboldt)||Green’s Conjecture via Koszul modules|
|April 24, 11-12:30||Kirsten Wickelgren (Duke)|
|May 1, 10:45-11:45||Borys Kadets (MIT)|
|May 1, 12-1||Burt Totaro (UCLA)|
|May 8, 10:45-11:45||Julie Desjardins (Toronto)|
|May 8, 12-1||Bjorn Poonen (MIT)|
|May 15 10:45-11:45|
Rohini Ramadas (Brown)
|May 15, 12-1||Rob Silversmith (Northeastern)|
|May 22, 11-12:30||Chenyang Xu (MIT)||K-moduli of Fano varieties*|
|May 29, 10:45-11:45||Yuchen Liu (Yale)||Moduli spaces of quartic hyperelliptic K3 surfaces via K-stability|
|May 29, 12-1||Maksym Fedorchuk (Boston College)||Stability of fibrations over one-dimensional bases, and standard models of del Pezzo fibrations **|
|June 5, 10:45-11:45||TBA||TBA|
|June 5, 12-1||Bhargav Bhatt (Michigan)||TBA|
|June 12, 10:45-11:45||Margaret Bilu (NYU)||TBA|
|June 12, 12-1||Wei Ho (Michigan)||TBA|
*The discussion for Chenyang Xu’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2020-05-22-cx (and will be deleted after 3-7 days).
**The discussion for Maksym Fedorchuk’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2020-05-29-mf (and will be deleted after 3-7 days).
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.