Western Algebraic Geometry Symposium

WAGS aims to build a regional community among algebraic geometers of all career stages, from advanced undergraduates to full professors. The meetings are centered around research talks delivered by leading mathematicians from around the world highlighting exciting recent results in and around algebraic geometry. In addition to the research talks, the typical WAGS also includes poster sessions and/or other organized opportunities for interaction among participants. 

Schedule:

Saturday, April 26, 2025

• 9:00 - 9:30: Refreshments and registration
• 9:30 - 10:30: Daniel Litt
  • Title: On the converse to Eisenstein's last theorem

  • Abstract: I'll explain a conjectural characterization of algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the arithmetic of the coefficients of their Taylor expansions, strengthening the Grothendieck-Katz p-curvature conjecture. I'll give some evidence for the conjecture coming from algebraic geometry: in joint work with Josh Lam, we verify the conjecture for algebraic differential equations (both linear and non-linear) and initial conditions of algebro-geometric origin. In this case the conjecture turns out to be closely related to basic conjectures on algebraic cycles, motives, and so on.

• 10:30 - 11:00: Break
• 11:00 - 12:00: Emily Clader
  • Title: Nontautological Cycles on Moduli Spaces of Smooth Curves

  • Abstract: The cohomology of the moduli space of stable curves has been widely studied, but in general, understanding the full cohomology ring of this space is too much to ask.  Instead, one generally settles for studying the tautological ring, a subring of the cohomology that is simultaneously tractable to study and yet rich enough to contain most cohomology classes of geometric interest.  The first known example of an algebraic cohomology class that is *not* tautological was discovered by Graber and Pandharipande, in work that was later significantly generalized by van Zelm to produce an infinite family of non-tautological classes on the moduli space of stable curves.  A similar study can be undertaken on the moduli space of smooth curves, but in this case, almost no non-tautological classes were previously known.  I will report on joint work with V. Arena, S. Canning, R. Haburcak, A. Li, S.C. Mok, and C. Tamborini (from the 2023 AGNES Summer School), in which we produce non-tautological algebraic classes on the moduli space of smooth curves in an infinite family of cases, including on M_g for all g>15.

• 12:00-1:30: Lunch Break 
• 1:30 - 2:30: Hannah Larson
  • Title: Moduli spaces of curves with polynomial point count

  • Abstract: How many isomorphism classes of genus g curves are there over a finite field F_q? In joint work with Samir Canning, Sam Payne, and Thomas Willwacher, we prove that the answer is a polynomial in q if and only if g is at most 8. One of the key ingredients is our recent progress on understanding low-degree odd cohomology of moduli spaces of stable curves with marked points.

• 2:30 - 3:00: Break
• 3:00 - 4:00: Felix Thimm
  • Title: CY3 Wall-Crossing using Virtual Classes

  • Abstract: A fundamental problem in enumerative geometry is to count curves on Calabi-Yau 3-folds. There are different approaches to this and wall-crossing is a technique that allows us to vary the counting problem and compare the enumerative invariants with the original ones. It has emerged as a powerful tool for computations and in the study of properties of generating series of such enumerative invariants. I will present joint work with N. Kuhn and H. Liu on how to use localization of virtual classes to wall-cross more general invariants with descendant insertions. In the process I will explain how Juanolou's trick from more classical algebraic geometry comes in as a useful and central ingredient.

• 4:30 - 6:00: Poster session and reception

Sunday, April 27, 2025

• 8:45 - 9:15: Refreshments
• 9:15 - 10:15: Sanath Devalapurkar
  • Title: Arithmetic geometry and (chromatic) homotopy theory

  • Abstract: In recent years, there has been an explosion of ideas in integral p-adic Hodge theory, following the breakthrough work of Bhatt, Drinfeld, Lurie, Morrow, and Scholze which introduced the theory of prismatization. This is a very interesting deformation of algebraic de Rham cohomology on p-adic schemes which unifies all previously known cohomology theories (like crystalline and p-adic etale cohomology). I'll explain some joint work with Jeremy Hahn, Arpon Raksit, and Allen Yuan, where we extend the theory of prismatization to include as input commutative ring *spectra*: these are a homotopy-theoretic generalization of commutative rings  which (as I will explain) are intimately tied to p-adic Hodge theory. I will illustrate an application of this generalization to Hodge theory in characteristic p for varieties of dimension > p, generalizing work of Deligne-Illusie and Drinfeld.

• 10:15-10:45: Break
• 10:45-11:45: Kirsten Wickelgren
• 11:45-12:00: Break 
• 12:00-1:00: Burt Totaro
  • Title: Endomorphisms of varieties

  • Abstract: A natural class of dynamical systems is obtained by iterating polynomial maps, which can be viewed as maps from projective space to itself. One can ask which other projective varieties admit endomorphisms of degree greater than 1. This seems to be an extremely restrictive property, with all known examples coming from toric varieties (such as projective space) or abelian varieties. We describe what is known in this direction, with the new ingredient being the "Bott vanishing" property. Joint work with Tatsuro Kawakami.

Accommodation:

We have made a group booking at the Holiday Inn Vancouver Centre.  There is a selection of rooms, from CAD $249 (before tax) per night. This hotel is a 30 minute bus ride from the UBC campus (directly served by express bus #99).

Booking instructions:

• Click the link 
• Once you click the link, click on Book Now
• Select the date between or during April 25, 2025 as check-in and April 28, 2025 as check-out
• The rate preference should show Group Rate and the Group Code should already be inputted as VRN
• Select the room type you would prefer
• Follow the prompts, enter your IHG Rewards number and pay for the room

There may be limited on campus accommodation available, you may try your luck here or here or here or here.
Of course, there are the usual sites you can try, as well. Vancouver is a popular travel destination, so please book early.