Event date:
Feb 12 2024 4:00 pm

John Conway Spirited Seminar Series: Rings of Teter Type and the Trace of the Canonical Module

Jürgen Herzog (Essen, Germany)
In this talk, we introduce the concept of rings of Teter type. This definition refers to the canonical trace. Our definition of Teter type is inspired by the paper of William Teter "Rings which Are a Factor of a Gorenstein Ring by Its Socle", Inventiones math. in 1974. We presented various classes 0-dimensional graded and monomial K-algebras which are of Teter type. The concluding segment of the talk focuses on the canonical trace of generic determinantal rings and provides a sufficient condition for the trace to specialize.

Professor Jürgen Herzog, a distinguished mathematician at Universität Duisburg-Essen, Germany, has made substantial contributions to commutative algebra. With over 250 papers and several influential books to his credit, Herzog has left an indelible mark on the field. Collaborating with Winfried Bruns, he authored "Cohen-Macaulay Rings" (1993), exploring the fundamental importance of these rings and their connections to determinantal rings and rings of invariants. Alongside Takayuki Hibi, Herzog co-authored "Monomial Ideals" (2011), providing a comprehensive overview of the intersection between commutative algebra and finite multi-sets, simplicial complexes, and graphs. His interest in computational methods is evident in "Gröbner Bases in Commutative Algebra" (2012), co-authored with Viviana Ene. In "Binomial Ideals" (2018), Herzog, Hibi, and Hidefumi Ohsugi jointly contributed to the exploration of binomial ideals. Jürgen Herzog's extensive body of work, comprising numerous papers and influential books, stands as an invaluable resource, enriching the realms of algebra, algebraic geometry, and combinatorics.

About the John Conway Spirited Seminar Series: The John Conway Spirited Seminar series was started in 2021 by the Department of Mathematics at Syed Babar Ali School of Science and Engineering-LUMS, Pakistan. These seminars allow mathematicians from all over the World to indulge in productive discussions on recently evolved theories, expositions, and research. These seminars are purposefully kept online (through Zoom) to avoid the logistics limitations of inviting a speaker from the mathematically developed World and provide a latitude for researchers and students to benefit from these seminars. Almost all the talks are recorded with the speaker's prior consent, and these recorded talks are available on the website. Stay connected with recent developments through seminars is highly important for cultivating effective ideas. Though John Conway never visited Pakistan, it is an endeavor to live his spirited enthusiasm for promoting mathematics. It is a humble tribute to his grand legacy and spirited attitude to promoting mathematical discussions. We invite all mathematicians, young researchers, and students to these seminars.