This is the former homepage of the UW Student Algebraic Geometry Seminar. The seminar will be held on Thursdays at 3:00PM in PDL C-401 during the Fall 2025 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 Fall 2025 Quarter
Click on a title to reveal the corresponding abstract. Titles and abstracts may appear first on the math department calendar.
| September 25 | Daniel RostamlooPerfectoid spaces and diamonds IIn this two-part talk, I will give an introduction to Scholze’s theory of perfectoid spaces and diamonds, starting from basic elements of $p$-adic geometry and providing many examples along the way. Time permitting, I will discuss their role in Scholze’s proof of Deligne’s weight-monodromy conjecture. |
| October 2 | Daniel RostamlooPerfectoid spaces and diamonds IIHaving established the formalism of adic spaces, we will introduce perfectoid spaces and diamonds along with several examples. Time permitting, we will discuss Scholze’s proof of Deligne’s weight-monodromy conjecture. |
| October 9 | Ting GongGrothendieck ring, motivic classes and zeta functionsGrothendieck ring of varieties/stacks has received a lot of attention recently for its applications in rationality. In this talk, we are going to introduce the audience to the study of the Grothendieck ring of varieties and it connection to rationality. Finally, if time allows, we present a few results on rationality of motivic zeta function. |
| October 16* | Andrei Okounkov (Columbia)Quantum groups and enumerative geometryThis will be an introductory talk explaining what a quantum group is and how quantum groups can be used to answer enumerative geometry questions. |
| October 23 | Bryan LuMaking Toric Varieties CountRichard Stanley’s resolution of McMullen’s g-conjecture in the 1970s using the cohomology of toric varieties sparked the use of toric geometry in geometric combinatorics. Since then, combinatorialists have looked to toric varieties and toric ideals as a source of questions and techniques for reasoning about polytopes. We take the former point of view and describe the correspondence between this large class of (normal, complex) varieties and the combinatorial data of polytopes. In particular, we discuss how the combinatorics of polytopes and polytopal fans not only characterizes all toric varieties, but also encodes a wealth of intrinsic geometric information about the variety itself. Time-permitting, we discuss some of the aforementioned combinatorial applications of toric geometry (and adjacent ideas). (Based on Toric Varieties by Cox, Little, and Schenck.) |
| October 30 | Jackson MorrisAlgebraic K-theoryAlgebraic K-theory is a powerful invariant with surprising connections to algebraic geometry and number theory. This talk will develop algebraic K-theory from the perspective of these connections. I will introduce lower K-groups, Milnor K-theory, and higher algebraic K-theory, focusing on conjectures in number theory (both open and solved) which are phrased in the language of algebraic K-theory. Time permitting, I will discuss connections with syntomic cohomology. |
| November 6 | Alexander GalarragaThe Potential Density Degree SetIn order to study the arithmetic of curves over global fields, I’ll introduce the density degree set and its more geometric analogue, the potential density degree set. We will see how the Mordell-Lang conjecture gives a geometric description of the potential density degree set and use the geometry of the Picard group to compute the potential density degree set for some nice curves. |
| November 6** | Yu Shen (Michigan State University)Picard group action on the category of twisted sheavesIn this talk, we study the category of twisted sheaves over a scheme $X$. Let $M$ be a quasi-coherent sheaf on $X$, and $\alpha$ in $\mathrm{Br}(X)$. We show that the functor $- \otimes_{\mathcal{O}_X} M:\mathrm{QCoh}(X,\alpha) \to \mathrm{QCoh}(X,\alpha)$ is naturally isomorphic to the identity functor if and only if $M \cong \mathcal{O}_X$. As a corollary, the action of $\mathrm{Pic}(X)$ on $\mathrm{D}^b(X,\alpha)$ is faithful for any Noetherian scheme $X$. |
| November 13 | Ethan MacBroughResolution of singularitiesMost algebraic geometers regard Hironaka’s resolution of singularities as an esoteric monolith, useful to be aware of and use as a black box but too complicated to justify learning how it actually works. In reality, the modern revised form of Hironaka’s proof is surprisingly simple and conceptually elegant. Furthermore, the techniques used illustrate several fundamental principles of birational geometry in a relatively concrete setting, which makes it a great starting point for learning the modern theory. In this talk I will explain the core ideas of the proof, and hopefully be able to give you a fairly complete sketch of how it works. |
| November 20 | Tyson KilngnerUniformisation of Stacky CurvesThe classical uniformisation in complex geometry states that the universal cover of a given compact Riemann surface is either the Riemann sphere, the complex plane, or the Poincaré disc. In this talk we will introduce the notion of a stacky curve and discuss a uniformisation style result. |
| December 4 | Jay ReiterDeformations of stable infinity categoriesTo a stable infinity category $C$ equipped with a well-behaved homology functor to an abelian category $A$, Patchkoria–Pstrągowski associate a derived category which, in a precise sense, interpolates between cohomology objects in $C$ and descent spectral sequences in $A$ abutting to them. In this talk, we will begin by showing how this derived category arises naturally when trying to infinity-categorify injective resolutions and then take a close look at its construction which axiomatizes the deformation-theoretic ideas behind synthetic spectra. |
* Note from the organizer – this is a special graduate colloquium hosted by the student AG seminar on the occasion of Andrei Okounkov’s visit. It will take place on Thursday, October 16, at 3PM in Miller Hall 301. All graduate students are welcome and encouraged to attend. Participants are invited to a reception in Padelford Hall C-120 starting at 2PM prior to the talk.
** Note from the organizer – this talk will be from 4 to 5PM as part of a double-header seminar.
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.