Uploaded March 2026 | Updated September 2026, 3 weeks ago
Members' Colloquium
Topic: Singularities in Mixed Characteristic
Speaker: Linquan Ma
Affiliation: Institute for Advanced Study
Date: March 23, 2026 1:30pm
Simonyi 101 and Remote Access
Singularities are local properties of algebraic varieties. For example, the solution set of a polynomial in several variables such as y2=x3
has a singularity at the origin (0,0)
. In algebra, one often studies singularities through the quotient ring, such as C[x,y]/y2−x3
for this example. In this talk, we will give an introduction to recent progress in the study of singularities in mixed characteristic, roughly speaking, these correspond to quotients of Z[x1,...,xn]
by polynomials with integer coefficients. A central theme in this study is the use of so-called big Cohen-Macaulay algebras, these are often "large" (non-Noetherian) rings that nevertheless enjoys remarkably nice homological properties (and whose existence is related to recent developments in p-adic Hodge theory). We also discuss some applications of the mixed characteristic singularity theory to questions in birational geometry.
Members' Colloquium
Topic: Singularities in Mixed Characteristic
Speaker: Linquan Ma
Affiliation: Institute for Advanced Study
Date: March 23, 2026 1:30pm
Simonyi 101 and Remote Access
Singularities are local properties of algebraic varieties. For example, the solution set of a polynomial in several variables such as y2=x3
has a singularity at the origin (0,0)
. In algebra, one often studies singularities through the quotient ring, such as C[x,y]/y2−x3
for this example. In this talk, we will give an introduction to recent progress in the study of singularities in mixed characteristic, roughly speaking, these correspond to quotients of Z[x1,...,xn]
by polynomials with integer coefficients. A central theme in this study is the use of so-called big Cohen-Macaulay algebras, these are often "large" (non-Noetherian) rings that nevertheless enjoys remarkably nice homological properties (and whose existence is related to recent developments in p-adic Hodge theory). We also discuss some applications of the mixed characteristic singularity theory to questions in birational geometry.
