讲座提要：

Equations of canonical birational models of thin Schubert cells

8:30--9:30

Abstract: By Mnev's universality, thin Schubert cells exhibit all possible singularities in algebraic geometry. In this first lecture, we introduce certain standard birational models of thin Schubert cells and describe their defining equations in certain smooth ambient schemes. These equations may be considered as the normalized equations of singularities. Based upon these normalized equations, we will then describe three sequential blowups of the smooth ambient schemes, collectively, called h-blowups.

Birational transforms of thin Schubert cells after h-blowups

9:50--10:50

Abstract: We will continue to study the h-blowups, and more importantly, describe certain birational transforms of thin Schubert cells under the h-blowups, in terms of defining equations.

Smoothness and applications to resolution of singularities

11:20--12:20

Abstract: Based upon the descriptions of their defining equations, we will prove that the birational transforms of thin Schubert cells after the final h-blowup are smooth. This immediately implies that every singularity type over a perfect field admits a resolution. By reviewing Lafforgue's version of Mnev's universality, we will apply the above to prove that every affine or projective singular variety over a perfect field admits a resolution.