Mathematical Sciences Research Institute

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Summer Graduate School

Commutative Algebra and its Interaction with Algebraic Geometry June 03, 2019 - June 14, 2019
Parent Program: --
Location: Center for Mathematics of University of Notre Dame
Organizers Craig Huneke (University of Virginia), Sonja Mapes (University of Notre Dame), Juan Migliore (University of Notre Dame), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame)

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The school will consist of the following four courses with exercise sessions plus a Macaulay2 workshop

  • Linkage and residual intersections
  • Characteristic p methods and applications
  • Blowup algebras
  • Multiplicity theory

Suggested prerequisites:

An introduction to Commutative Algebra by Atiyah and MacDonald and the first few chapters of Commutative Algebra with a view towards algebraic geometry by David Eisenbud.

For eligibility and how to apply, see the Summer Graduate Schools homepage

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.

Keywords and Mathematics Subject Classification (MSC)
  • Linkage

  • residual intersections

  • multiplicities

  • Hilbert functions

  • Rees algebras

  • associated graded rings

  • tight closure

  • integral closure

  • symbolic powers

  • reductions

  • resolutions

  • Gorenstein rings

  • Cohen-Macaulay rings

  • canonical modules

  • local cohomology

  • Frobenious map

  • 7 F-signature

  • Hilbert multiplicity

  • Hilbert-Kunz multiplicity

  • strongly F-regular rings

  • etale fundamental group

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC