Home /  Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame)

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)
Lecturer(s)

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Speaker(s)

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Description
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This summer school is held at the University of Notre Dame. Here is where one can find additonal information about the summer school: https://sites.nd.edu/msri-cmnd-2023workshop/workshop-details/.

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. The geometry of (nonstandard) syzygies (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

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.

Schedule, Notes/Handouts & Videos
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May 22, 2023
Monday
All Day
  Arrivals
May 23, 2023
Tuesday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Daniel Erman (University of Hawaii at Manoa)
11:30 AM - 12:30 PM
  Lecture
Anurag Singh (University of Utah)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 04:00 PM
  Meet and Greet
04:00 PM - 06:30 PM
  Homework Session
May 24, 2023
Wednesday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Daniel Erman (University of Hawaii at Manoa)
11:30 AM - 12:30 PM
  Lecture
Anurag Singh (University of Utah)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Bounds on the Number of Generators of Prime Ideals
Giulio Caviglia
03:30 PM - 06:30 PM
  Homework Session
May 25, 2023
Thursday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Daniel Erman (University of Hawaii at Manoa)
11:30 AM - 12:30 PM
  Liaison and Residual Intersection I
Bernd Ulrich (Purdue University)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 05:00 PM
  Homework Session
05:00 PM - 06:30 PM
  Panel
May 26, 2023
Friday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Daniel Erman (University of Hawaii at Manoa)
11:30 AM - 12:30 PM
  Lecture
Anurag Singh (University of Utah)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Multiplicities in Commutative Algebra: Past, Present, and Future
Jonathan Montaño (Arizona State University)
04:00 PM - 06:30 PM
  Homework Session
May 29, 2023
Monday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Liaison and Residual Intersection II
Bernd Ulrich (Purdue University)
11:30 AM - 12:30 PM
  Infinite Free Resolutions
David Eisenbud (University of California, Berkeley)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 04:00 PM
  Open Problem Session
04:00 PM - 06:30 PM
  Homework Session
May 30, 2023
Tuesday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Anurag Singh (University of Utah)
11:30 AM - 12:30 PM
  Liaison and Residual Intersection III
Bernd Ulrich (Purdue University)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Differential Graded Algebra Resolutions
Claudia Miller (Syracuse University)
03:30 PM - 06:30 PM
  Homework Session
May 31, 2023
Wednesday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Anurag Singh (University of Utah)
11:30 AM - 12:30 PM
  Symbolic Powers I
Alexandra Seceleanu (University of Nebraska)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Symbolic Powers II
Eloísa Grifo (University of Nebraska)
03:30 PM - 05:00 PM
  Homework Session
05:00 PM - 06:30 PM
  Poster Session
Jun 01, 2023
Thursday
09:00 AM - 10:00 AM
  Breakfast
10:00 AM - 11:30 AM
  Lecture
Juan Migliore (University of Notre Dame)
11:30 AM - 12:30 PM
  Differential Operators and Singularities
Jack Jeffries (University of Nebraska)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Computing Local Cohomology of Polynomial Rings of Characteristic Zero
Uli Walther (Purdue University)
04:00 PM - 06:30 PM
  Homework Session
Jun 02, 2023
Friday
All Day
  Departures