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Fellowship of the Ring: A National Commutative Algebra Seminar

April 9 @ 4:30 pm - 6:00 pm EDT

This will be a weekly Commutative Algebra webinar, hosted by MSRI, that will take place at 1:30pm Pacific time every Thursday. The organizing committee is listed below. Each talk will have two parts: the first part should be accessible to graduate students after a first course in commutative algebra, and should survey the basic facts and the goals of some area of commutative algebra; the second part will typically cover recent research.

The first Seminar in the series:

Date/Time: Thursday, April 9, 1:30-3pm Pacific time

Speaker: Linquan Ma, Purdue University

Title: Multiplicities over local rings, Lech’s conjecture, and lim Ulrich sequence

Abstract: We discuss the theory of Hilbert–Samuel multiplicities: their connections with integral closure, Koszul homology, and singularities. We then focus on a long standing conjecture of Lech which states that the multiplicities do not drop under faithfully flat extensions of local rings R–>S. We survey the literature of this conjecture and various attempts to attack it. Finally, we discuss some very recent work that proves Lech’s conjecture when R is standard graded, using lim Ulrich sequence and weakly lim Ulrich sequence that we introduce. Roughly speaking, these are sequences of finitely generated modules that are not necessarily Cohen–Macaulay, but asymptotically behave like Ulrich modules. We show their existence imply Lech’s conjecture, and we construct weakly lim Ulrich sequence for standard graded rings of positive characteristic.

How to join: The goal of the seminar is to reach as wide as possible a group of students and faculty interested in commutative algebra, but some protection is necessary to avoid annoying interference on Zoom. Therefore, to be on the mailing list of the seminar and receive login information for each webinar, one must be a member, vetted by one of the organizers. Students and faculty are invited to send an email requesting membership *from a university account* to any one of the organizers.

Organizing Committee:

  • David Eisenbud <de@msri.org>, chair
  • Mel Hochster <hochster@umich.edu>
  • Craig Huneke <huneke@virginia.edu>
  • Srikanth Iyengar <iyengar@math.utah.edu>
  • Claudia Miller <clamille@syr.edu>
  • Irena Peeva <ivp1@cornell.edu>
  • Steven Sam <ssam@ucsd.edu>
  • Karl E Schwede <schwede@math.utah.edu>
  • Bernd Ulrich <bulrich@purdue.edu>


April 9
4:30 pm - 6:00 pm EDT

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