# Seminars & Colloquia Calendar

## The Eisenbud-Goto Regularity Conjecture

#### Irena Peeva, Cornell University

Location: ** HILL 705**

Date & time: Friday, 20 October 2017 at 4:00PM - 5:00PM

*Abstract: *Regularity is a numerical invariant that measures the complexity of the structure of homogeneous ideals in a polynomial ring. Papers of Bayer-Mumford and others give examples of families of ideals attaining doubly exponential regularity. In contrast, Bertram-Ein-Lazarsfeld, Chardin-Ulrich, and Mumford have proven that there are nice bounds on the regularity of the ideals of smooth (or nearly smooth) projective varieties. As discussed in an influential paper by Bayer and Mumford (1993), the biggest missing link between the general case and the smooth case is to obtain a decent bound on the regularity of all prime ideals (the ideals that define irreducible projective varieties). The long standing Eisenbud-Goto Regularity Conjecture (1984) predicts an elegant linear bound, in terms of the degree of the variety (also called multiplicity). The conjecture was proven for curves by Gruson-Lazarsfeld-Peskine, for smooth surfaces by Lazarsfeld and Pinkham, for most smooth 3-folds by Ran, and in many other special cases.

Recently, McCullough and I introduced two new techniques related to homogenization and blow-up algebras, and used them to provide many counterexamples to the Eisenbud-Goto conjecture. In fact we show that the regularity of prime ideals is not bounded by any polynomial function of the degree. I will explain the ideas behind these new techniques.

R. Shapiro Organizer's Page

Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Yonah Biers-Ariel, Mingjia Yang, and Doron Zeilberger --> homepage

Paul Feehan, Manousos Maridakis, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Corrine Yap Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Ebru Toprak, Organizer

Fioralba Cakoni Seminar webpage

Organizer: Vladimir Retakh Organizer's webpage

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