byu algebraic geometry seminar
The BYU Algebraic Geometry Seminar is held every Wednesday from 4pm to 5pm in TMCB 301. Each semester, we pick a new topic for all local talks. External speakers give traditional research seminar talks.
fall 2025 ∨∧
For Fall 2025, we will be learning about real quintic threefolds. Here are some of the resources we will use:
Cubic surfaces:
- 27 lines on a smooth cubic surface, by Andreas Gathmann
- More on cubic surfaces (see Chapter 1), by Miles Reid
Topology of real varieties:
- Topology of real varieties, by Degtyarev and Kharlamov
- Classification of cubic threefolds, by Krasnov
- Classification of cubic fourfolds, by Finashin and Kharlamov
| Date | Speaker | Topic | Abstract |
|---|---|---|---|
| Sep 10 | Stephen McKean | Overview | I will give a high-level overview of Schläfli, Klein, and Zeuthen's classification of real cubic surfaces up to rigid isotopy. I will point out which aspects would be nice to study when asking for a similar classification of real quintic threefolds. |
| Sep 17 | Isaac Fisher | 27 lines on the Fermat cubic surface | Define the Fermat cubic surface and prove that it has exactly 27 lines over the complex numbers. |
| Sep 24 | CJ Bott | Intro to computational algebra software | Generate random cubic surfaces and computationally solve for their 27 lines. |
| Oct 1 | Ben DeVries | The moduli space of cubic surfaces | Introduce the moduli space of cubic surfaces and calculate the discriminant locus corresponding to singular cubic surfaces. |
| Oct 8 | Topology of real cubic surfaces | We will discuss methods for computing the topological type of a real cubic surface. |
|
| Oct 15 | No speaker | Working day | We will work together on computing some examples using Macaulay2 or Sage. |
| Oct 22 | Renzo Cavalieri (Colorado State) | ||
| Oct 29 | No seminar | Savage Teaching Award (TMCB 1170) | |
| Nov 5 | |||
| Nov 12 | |||
| Nov 18 | Felipe Espreafico (Sorbonne) | Tuesday at 10:00am | |
| Nov 19 | No seminar | Department devotional (TMCB 1170) | |
| Nov 26 | Thanksgiving Eve (no seminar) | ||
| Dec 3 |
winter 2025 ∨∧
For Winter 2025, we will be learning about K3 surfaces. Here are some of the resources we will use:
- Notes on projective varieties, by Ruxandra Moraru
- Lecture notes for algebraic geometry, by Leonardo Constantin Mihalcea
- Algebraic Geometry, by Andreas Gathmann
| Date | Speaker | Topic | Abstract |
|---|---|---|---|
| Jan 8 | Stephen McKean | Organizational meeting | |
| Jan 15 | Stephen McKean | Counting curves on K3 surfaces | I'll give a very broad overview of Beauville's proof of the Yau—Zaslow formula for counting rational curves of genus g on a K3 surface. The goal is to get you excited about K3 surfaces and some of the topics we might cover along the way. |
| Jan 22 | Caleb Crowther | Projective space and algebraic sets | Section 1.1 of these notes on projective varieties. |
| Jan 29 | Abram Magleby | The Nullstellensatz | Section 1.1 of these notes on projective varieties. |
| Feb 5 | Isaac Fisher | Sheaves | Section 5 of these notes on sheaves. |
| Feb 12 | Cameron Woffinden | Sheaves | Sections 3 and 13 of these notes on algebraic geometry. |
| Feb 19 | Ben DeVries | Structure sheaves and twisting sheaves | Section 15 of these notes on algebraic geometry. |
| Feb 26 | Mark Shoemaker (Colorado State) | ||
| Mar 5 | Archer Clayton | Cotangent sheaves and canonical sheaves | Section 16 of these notes on algebraic geometry. |
| Mar 12 | Candace Bethea (Brown) | Counting rational curves equivariantly | This talk will be a friendly introduction to using topological invariants in enumerative geometry and how one might use equivariant homotopy theory to answer enumerative questions under the presence of a finite group action. Recent work with Kirsten Wickelgren (Duke) defines a global and local degree in stable equivariant homotopy theory that can be used to compute the equivariant Euler characteristic and Euler number. I will discuss an application to counting orbits of rational plane cubics through an invariant set of 8 points in general position under a finite group action on $\mathbb{C}\mathbb{P}^2$, valued in the representation ring and Burnside ring. This recovers a signed count of real rational cubics when $\mathbb{Z}/2$ acts on $\mathbb{C}\mathbb{P}^2$ by complex conjugation. |
| Mar 19 | Anubhav Nanavaty (UC Irvine) | ||
| Mar 26 | Sheaf cohomology | ||
| Apr 2 | Hodge theory | ||
| Apr 9 | Cameron Krulewski (MIT) | ||
| Apr 16 | K3 surfaces: definition and examples | ||
| Apr 23 | 3 surfaces: Hodge decomposition and the Torelli theorem |