Lectures on Universal Equations for Singularities and Birational Geometry

Speaker：

Yi Hu (University of Arizona)

Time：

Tues. & Thur., 10:00-12:00, June 23, June 25, July 2, July 7, July 9, 2026

Venue：

B725, Tsinghua University Shuangqing Complex Building A; ;

Online：

Zoom Meeting ID: 687 513 9542 Passcode: YMSC

Abstract:

As a general viewpoint, describing singularities by equations appears to require collections of polynomials of arbitrary degree and form with no intrinsic relations among them. In his work on the surgery of Grassmannians, Laurent Lafforgue provided a remarkable framework in which only linear and quadratic equations are needed, and more importantly these simple polynomials are structurally well organized through the Plücker relations. Building on Lafforgue’s works, themselves rooted in Mnev’s universality theorem, we further transform these equations into even simpler forms: linearized Plücker relations and binomials, which we call universal equations for singularities. We will discuss why these simple and highly organized universal relations naturally arise, and how they can be applied in algebraic geometry.

These five introductory lectures will be accessible to non-specialists, including graduate students.

June 23 Varieties as configuration spaces.

June 25 Varieties as Grassmannian strata.

July 2 Constructing a new universe for all singularities.

July 7 Universal equations for singularities.

July 9 Applications to birational geometry.