This is the current homepage of the UW Student Algebraic Geometry Seminar. The seminar will usually* be held at 3:00PM in PDL C-401 on Thursdays during the Spring 2025 quarter. The seminar will also feature some talks by faculty in the department. If you would like to give a talk or have any questions, please contact Daniel Rostamloo (rostam[at]uw[dot]edu).
Talks for the Winter 2025 Quarter
Click on a title to reveal the corresponding abstract. Titles and abstracts may appear first on the math department calendar.
| April 3 | Andrew TawfeekThe quest towards a tropical Brill-Noether TheoremWe will open with a discussion of the Brill-Noether Theorem, a statement concerning the topology of the Brill-Noether locus: the collection line bundles of degree $d$ and rank $r$ over a variety $X$. We then shift to discussing its conjectural tropical formulation and a recent attempt to attack the problem by mimicking the classical proof: developing a tropical Porteous formula and applying it to an analogue of the Poincaré bundle. This talk is largely based on the work of arXiv 2411.10578. |
| April 11* | Jarod AlperThe Picard group of the moduli of vector bundles on a curveWe will revisit Drezet and Narasimhan’s computation from the 80s. |
| April 17 | Soham GhoshOn the Casas-Alvero conjectureAround 2001, motivated by his work on singularities, Casas-Alvero conjectured the following: If a monic univariate polynomial $f(X)$ of degree $n$, over a field of characteristic $0$, has a non-trivial gcd with each of its formal derivatives $f^{(i)}(X)$ for $1\leq i\leq n-1$, then $f(X)$ is a pure power of a monic linear polynomial. In this talk, we will show that over any field of characteristic $p>0$, there are “finitely many” counter-examples to the conjecture, and also sketch a proof of the conjecture over characteristic $0$. As a corollary, we will also obtain a new proof of the fact that rational normal curves are set-theoretic complete intersections (in characteristic $0$). Based on the preprints arxiv: 2402.18717 and arxiv:2501.09272. |
| April 24 | Giovanni InchiostroSmooth blow-downsGiven a closed subscheme $Y$ of a scheme $X$, one can construct $B$ the blow-up of $X$ along $Y$. In this talk I will explain some special cases of the opposite situation: given a smooth variety $B$, when can one construct another smooth variety $X$ such that $B$ is the blow-up of $X$ at a smooth subvariety $Y$? |
| May 1 | Sándor KovácsKollár’s principle: Topological origin leads to vanishing theoremsHodge theory is a powerful tool that connects topological and holomorphic/algebraic information about complex manifolds. In particular, there is a close connection between singular and coherent cohomology of complex manifolds. The natural embedding of constant functions in the structure sheaf induces a natural morphism from singular cohomology of a complex manifold with complex coefficients to the coherent cohomology of its structure sheaf. Hodge theory tells us, among many other things, that this natural map is surjective. This may be interpreted as saying that the coherent cohomology of the structure sheaf has topological origin. Kollár’s principle states that when that happens, it leads to vanishing theorems for certain (coherent) cohomology groups. I will explain how this principle leads to an elegant proof (due to Kollár) of the Kodaira vanishing theorem. Time permitting, I will mention how the same principle can be used to prove more general vanishing theorems. |
| May 15 | Arkamouli DebnathTBATBA |
| May 22 | Jackson MorrisTBATBA |
| May 29 | Haoming NingTBATBA |
| June 5 | Michael ZengTBATBA |
The seminar was founded in Fall 2023 by Arkamouli Debnath, who also organized it through Fall 2024. Since January 2025, it has been organized by Daniel Rostamloo.