This seminar is aimed at presenting several advanced topics in algebraic geometry. Students interested in participating can send me an email. Below is the program (which will be updated regularly).
2026
Monday March 2nd. HG02.032
The Riemann hypothesis for curves over finite fields and Hasse-Weil. Finn.
Abstract: We explain the proof of the Hasse-Weil inequality using intersection theory on surfaces. We also discuss its application to the Riemann hypothesis for curves over finite fields.
Monday March 9th
Rigidity of pointed maps. Sièna
Abstract: Which varieties X have the property that the space of pointed maps (C,c) ->(X,x) is zero-dimensional for every choice of C, c, and x? If X is projective, this is well-understood: it is precisely the class of varieties with no rational curves. We explain how to prove this, and indicate a partial generalization to quasi-projective varieties.
Monday March 23rd
Can one parametrize the equations of the general curve of given genus? Robin de Jong
Abstract: We will use the question in the title as an excuse to talk about: moduli spaces of curves, unirationality, and Kodaira dimensionl.
Monday March 30th
Scholl's finiteness theorem for Del Pezzo surfaces with good reduction. Piotr
Abstract: We explain why the set of isomorphism classes of smooth proper del Pezzo surfaces over O_{K,S} is finite for any number field K and finite set of finite places S of K.
Monday April 13th
Hilbert properties for fibrations. Midas
Abstract:
Monday April 20th
TBD
Monday May 4th
ADE Singularities. Finn
Monday May 11th
TBD
2024
Tuesday September 17th 2024, HG03.082 13:30-15:15
Etale cohomology (speaker: Ben)
Tuesday October 1st 2024, HG03.082 13:30-15:15
The Mordell-Weil theorem for abelian varieties over number fields (speaker: Ariyan)
Tuesday October 8th, HG03.082 13:30-15:15
Grothendieck-Riemann-Roch (speaker: Ben)
Tuesday October 15th, HG03.082 13:30-15:15
Points of degree d on smooth projective curves, Part 1 (speaker: Ariyan)
Tuesday October 22nd, HG03.082 13:30-15:15
Points of degree d on smooth projective curves, Part 2 (speaker: Finn)
Tuesday October 29th, HG03.082 13:30-15:15
NO MEETING
Tuesday November 5th
NO MEETING
Tuesday November 12th, HG03.082 13:30-15:15
Fourier duality for abelian varieties (speaker: Winand)
Tuesday November 19th, HG03.082 13:30-15:15
Stable reduction theorem for curves (speaker: Finn)
Tuesday November 26th, HG03.082 13:30-15:15
NO MEETING
Tuesday December 3rd, HG03.082 13:30 - 15:15
NO MEETING
Tuesday December 10th, HG01.029 13:30 - 15:15
Mordell implies Siegel (Speaker: Sièna)
Tuesday January 21st, HG01.028 13:30 - 15:15
An introduction to F-zips (Speaker: Ben)
Tuesday January 28th
No meeting
Tuesday February 4th
No meeting
Tuesday February 11th
Automorphisms of projective varieties (Speaker: Ariyan)
Tuesday February 18th
Degeneration of the Hodge-de Rham spectral sequence (Speaker: Finn)
Tuesday April 8th
Criterion for degeneration of a spectral sequence with applications (Speaker: Winand)
Tuesday May 20th
Faltings's proof of the Mordell conjecture (Speaker: Ariyan)
Tuesday May 27th
Higher degree points on curves over function fields (Speaker: Siena)