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DTSTART;TZID=America/New_York:20260407T150000
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DTSTAMP:20260407T033033
CREATED:20260325T135109Z
LAST-MODIFIED:20260325T135109Z
UID:10003105-1775574000-1775577600@www.math.harvard.edu
SUMMARY:Perturbation of mixed characteristics test ideals
DESCRIPTION:Given a normal integral scheme of finite type over a mixed characteristic complete DVR or a perfect field of characteristic p\, one can define the notion of a test ideal. This sheaf is used to characterize a class of mild singularities known as splinter singularities\, which are analogous to rational singularities in characteristic 0. In equal characteristics\, it is a well-known result that test and multiplier ideals are stable under small perturbations. In this talk\, I will explain how to extend this stability result to the mixed characteristic setting and discuss some of its applications. Time permitting\, I will also outline the key ideas and tools from p-adic geometry that underlie the proof.This is based on joint work in progress with Bhargav Bhatt and Linquan Ma.
URL:https://www.math.harvard.edu/event/perturbation-of-mixed-characteristics-test-ideals/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:HARVARD-MIT ALGEBRAIC GEOMETRY
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CREATED:20260402T150218Z
LAST-MODIFIED:20260402T150218Z
UID:10003122-1775578500-1775586600@www.math.harvard.edu
SUMMARY:A Mumford form on infinite Grassmannians
DESCRIPTION:The Polyakov measure in bosonic string theory can be expressed in terms of the Mumford form\, which is a trivializing section of a product of determinant line bundles over the moduli space of genus g curves. We will discuss the work in https://arxiv.org/abs/2412.18570\, which reviews how the moduli space can be embedded in an infinite dimensional Grassmannian as a Virasoro orbit and generalizes the Mumford form to other such orbits. In particular\, this “universal Mumford form” can be described in terms of coordinates in the Grassmannian\, which are amenable to computation and thus could have implications to the evaluation of amplitudes. \n\n 
URL:https://www.math.harvard.edu/event/a-mumford-form-on-infinite-grassmannians/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:GEOMETRY AND QUANTUM THEORY
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