Uploaded March 2026 | Updated September 2026, 3 weeks ago
Workshop on Recent Developments in Hodge Theory and O-minimality
12:00pm|Simonyi Hall 101
Topic: On the Completions of General Period Mappings
Speaker: Haohua Deng
Affiliation: Dartmouth College
Date: March 12, 2026
Constructing completions of period mappings with significant geometric and Hodge-theoretical meaning is an important topic in Hodge theory and its applications. There are rich theories for the classical case in which the period domain is Hermitian symmetric. In this talk I will talk about recent breakthroughs in the non-classical settings, particularly the generalized toroidal completion in the sense of Ash--Mumford--Raport--Tai and Kato--Nakayama--Usui. Joint works with Colleen Robles and Jacob Tsimerman.
Workshop on Recent Developments in Hodge Theory and O-minimality
12:00pm|Simonyi Hall 101
Topic: On the Completions of General Period Mappings
Speaker: Haohua Deng
Affiliation: Dartmouth College
Date: March 12, 2026
Constructing completions of period mappings with significant geometric and Hodge-theoretical meaning is an important topic in Hodge theory and its applications. There are rich theories for the classical case in which the period domain is Hermitian symmetric. In this talk I will talk about recent breakthroughs in the non-classical settings, particularly the generalized toroidal completion in the sense of Ash--Mumford--Raport--Tai and Kato--Nakayama--Usui. Joint works with Colleen Robles and Jacob Tsimerman.










![Singularities in Mixed Characteristic - Linquan Ma
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. Singularities in Mixed Characteristic - Linquan Ma](https://i.ytimg.com/vi/gTOsV2vXFz8/mqdefault.jpg)