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Summer Graduate School

Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame) May 22, 2023 - June 02, 2023
Parent Program:
Location: University of Notre Dame
Organizers Steven Cutkosky (University of Missouri), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame), Steven Sam (University of California, San Diego), Kevin Tucker (University of Illinois at Chicago)

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Commutative Algebra has seen an extraordinary development in the last few years. Long standing conjectures have been proven and new connections to different areas of mathematics have been built.This summer graduate school will consist of three mini-courses (4 lectures each) on fundamental topics in commutative algebra that are not covered in the standard courses. Each course will be accompanied by problem sessions focused on research. Six general colloquium-style lectures will be given by invited scholars who will also attend the school and help with afternoon research activities. 

The topics of the mini-courses are:

  1. Finiteness problems in Commutative Algebra (Daniel Erman)
  2. Liasion Theory (Elisa Gorla)
  3. Differential operators, determinantal varieties, and D-modules (Anurag Singh)

School Structure

The three lecture series and the colloquia will take place in the morning. To address the differing abilities and backgrounds of the graduate students, two levels of problem sessions will be held in the afternoons: one more elementary and one more advanced. In addition, student-led teaching sessions will allow less advanced students to be taught by more experienced ones. Numerous social and informal events are planned including several dinners, a cookout, a Karaoke night, a night at the Greek Festival and a game night.

Suggested Prerequisites

  • First course in commutative algebra, at the level of Atiya-MacDonald (Introduction to Commutative Algebra)
  • Commutative Algebra with a view towards algebraic geometry by David Eisenbud
  • Chapters 1 - 10 of Twenty-Four Hours of Local Cohomology
  • Some experience with: free resolutions, computation in Macaulay2, and/or elementary algebraic geometry would be helpful, but not strictly necessary

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 nominating institution will be eligible to be funded by MSRI.

Keywords and Mathematics Subject Classification (MSC)
  • Liaison

  • Weyl algebra

  • differential operators

  • syzygies

  • free resolutions

  • projective dimension

  • D-modules

  • determinantal varieties

  • Hilbert functions

  • regularity

  • local cohomology

  • tight closure

  • symbolic powers

  • Gorenstein rings

  • Cohen-Macaulay rings

  • canonical modules

  • Frobenius map

  • Hilbert multiplicity

  • Hilbert–Kunz multiplicity

  • strongly F-regular rings

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