This is the current homepage of the UW Student Algebraic Geometry Seminar. The seminar will be held on Thursdays at 3:00PM in PDL C-401 during the Winter 2026 quarter. The goal of the seminar is to foster engagement with modern research in algebraic geometry (broadly interpreted) and provide a forum for graduate students to present and discuss aspects of their work and readings. 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 2026 Quarter
Click on a title to reveal the corresponding abstract. Titles and abstracts may appear first on the math department calendar.
| January 8 | Napoleon Wang (University of Arizona)Vector bundles on Fargues-Fontaine curvesThe Fargues–Fontaine curve $X_{FF}$ is a $p$-adic analogy to the projective line $\mathbb P^1$, constructed by Fargues-Fontaine in a way that $p$-adic Hodge theoretic objects can be expressed via vector bundles with additional structure at a distinguished point $x_\infty$. In analogy with the Beauville-Laszlo gluing description of Hecke modifications via the affine Grassmannian, modifications of $G$-bundles at $x_\infty$ are described by the $B^+_{dR}$-affine Grassmannian (Fargues-Scholze). By Fargues-Fontaine and Anschütz, vector bundles on $X_{FF}$ are classified and formulated as an equivalence with isocrystals. More recent work by Birkbeck et al. and Hong refines this by studying extensions, subbundles, and quotient bundles using the Harder-Narasimhan polygons. In the end, we will briefly discuss the relative versions of the Fargues-Fontaine curve over a perfectoid base following Kedlaya-Liu and Fargues-Scholze. |
| January 15 | Sándor KovácsUnexpected relations for dualizing complexesI will explain some surprising relations between dualizing complexes and dualizing sheaves. Time permitting I will explain some applications as well. |
| January 22 | Jay ReiterHomotopy colimitsA common technique when studying a category $\mathcal{C}$ is to study a localization $\mathcal{C}[W^{-1}]$ instead — this is what we’re doing when we study the homotopy category of spaces or the derived category of complexes in an abelian category. These localizations tend to have nice formal properties but can be slippery in other ways. For example, colimits in these settings are often not functorial! In this talk, we’ll see examples of this problem in topology, algebra, and geometry, and then discuss how the theory of homotopy colimits addresses this issue by giving us precise control over many of the localizations we care about. Finally, we’ll see how these homotopy-coherent constructions are best understood in the language of $\infty$-categories. |
| January 29 | Daniel RostamlooPrismatic cohomology II will give a site-theoretic introduction to prismatic cohomology (and its prerequisite structures) with a view toward discussing the Hodge-Tate comparison theorem. |
| February 5 | Riku Kurama (University of Michigan)Flops, derived categories, and liftability of threefoldsUsing mixed characteristic minimal model program for fourfolds (under an assumption on mixed characteristic resolution of singularities), Hacon and Witaszek proved that liftability of Calabi-Yau threefolds in positive characteristic is preserved under birational equivalence. In this talk, I will explain the joint work in progress with Perry where we unconditionally prove this result by extending Bridgeland’s work on threefolds flops. This celebrated work of Bridgeland describes threefold flops over the complex numbers as moduli spaces of certain complexes of sheaves, and our work generalizes this description to a relative setting. |
| February 12 | Daniel RostamlooPrismatic cohomology III will continue the discussion from the previous talk. |
| February 19 | Soham GhoshCharacterization of projective space and hyperquadricsProjective space and hyperquadrics are amongst the simplest smooth projective varieties, and characterizing them has been a long studied problem. In this talk, I will provide an account of the existing results due to Mori, Wahl, Andreatta-Wiśniewski, Kobayashi-Ochiai, Araujo-Druel-Kovács, with particular emphasis on a result due to Druel and Paris. Furthermore, I will derive a new characterization of projective space and hyperquadrics, conjectured by Kovács, unifying the above characterizations. |
| February 26 | Preston CranfordPrismatic Cohomology of Ring SpectraI will introduce prismatic cohomology of commutative ring spectra via the even filtration. If time permits, I’ll discuss how the even filtration recovers constructions from classical algebra. |
| March 5 | Cancelled |
| March 12 | Tyson KlingnerSurface SingularitiesThis talk will cover the foundations of surface singularities. I will introduce the basics and characterise ADE singularities. |
The seminar was founded in Fall 2023 by Arkamouli Debnath, who also organized it through Fall 2024. The old seminar homepage can be found here. Since January 2025, it has been organized by Daniel Rostamloo. The seminar is grateful for funding provided by the Pacific Insitute for the Mathematical Sciences (PIMS).