Talk till you are stuck, Spring 2025

    Description of the seminar

The seminar will focus on Algebraic Geometry, and PhD students will present their research or recent thoughts until they reach questions they are currently grappling with. While the seminar is primarily AG-centered, it is very much open to number theorists and algebraic topologists due to the many connections between these fields. But essentially anyone with "AG-questions" and an "AG-audience" in mind is welcome to present.

The format is of 1 hour and 30/15 minutes: the first hour for a proper introduction and presentation of known or new results, and the remaining time for discussion. During the discussion, the speaker and audience can ask questions, share suggestions, and brainstorm ideas. Speakers should aim to distill the "I am stuck with" part of their talk into something the audience can engage with during the seminar.

Hopefully, this will be a fun way to foster collaboration in the Department or just learn more about each other's research.

    Logistics Info

The seminar will be held on Thursdays from 4:10pm to 5:30pm in Room 622 in the Math Department at Columbia.

Please email me at mp3947 at columbia dot edu if you are interested in giving a talk and/or you want to be added to the mailing list.

    Schedule

1. January 30th
           Organizational meeting


2. February 6th
           Speaker: Sofia Wood
           Title: Invariants of compactifications of the universal Jacobian over the moduli space of curves
           Abstract: We discuss some invariants of compactified Jacobians over the moduli space of curves, and some related questions.


3. February 13th
           Speaker: Morena Porzio
           Title: Stable birationality of Symmetric powers Sym^n_X of cubic hypersurfaces X for small n
           Abstract: Today we will discuss the stable birational type of Sym^n_X where X is a hypersurface. For cubic surfaces this is well understood for big n: however the arguments involved break down in higher dimensions and for small n. Ad hoc arguments have been developed to tackle this issue but they still leave some "leftovers" even in the surface case. Today we will go over the known results, see what the leftovers n's are and discuss what can and cannot work in these cases.


4. February 20th : No seminar


5. February 27th
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6. March 6th
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7. March 13th
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8. March 27th
           Speaker: Nicolás Vilches
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9. April 3rd (I will be away this time)
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10. April 10th
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11. April 17th
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12. April 24th
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13. May 1st
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