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Morgantown Algebra Days

Speakers 

Speakers

View the Schedule for presentation times and locations.





Herzog

Jürgen Herzog

University of Duisburg-Essen, Germany
Haydee Lindo Profile Photo

Haydee Lindo

Harvey Mudd College, U.S. 
Personal Website
Linquan Ma Profile Photo

Linquan Ma

Purdue University, U.S. 
Personal Website
Profile photo for Sarasij Maitra

Sarasij Maitra

University of Utah, U.S.
Sarasij Maitra Personal Website
Takumi-Murayama

Takumi Murayama

Purdue University, U.S. 
Personal Website
Rebecca R.G. photo

Rebecca R.G.

George Mason University, U.S.
Personal Website
Liana Sega photo

Liana Şega

University of Missouri-Kansas City, U.S.
Personal Website

TALK TITLES AND ABSTRACTS

Talks will be at G15 Life Sciences Building (First Floor). View the Full Schedule.


JÜrgen herzog


Rings of Teter type and the trace of the canonical module and the Teter number of determinantal rings

A 0-dimensional local ring $(R, \mathfrak{m})$ is called a Teter ring, if there exists a local Gorenstein ring $G$ such that $R\simeq G/(0:\mathfrak{m}_G)$. This class of rings was introduced in 1974 by William Teter. It has been shown by Huneke, Vraciu and others that $R$ is a Teter ring if and only if there exists an epimorphism $\varphi: \omega_R\to \mathfrak{m}$. We call $R$ of Teter type, if there exists an epimorphism $\omega_R\to \mbox{tr}(\omega_R)$, and we define the {\em Teter number} of $R$ to be the smallest number $s$ for which there exist $R$-module homomorphisms $\varphi_i: \omega_R\to R$ such that $\mbox{tr}(\omega_R)=\sum_{i=1}^s\varphi_i(\omega_R)$.

Various characterizations of rings of Teter type are given and families of rings of Teter type are presented. We determine the canonical trace of generic determinantal rings and compute its Teter numbers. As an application we determine the canonical trace of a Cohen-Macaulay ring $R$ of codimension two, which is generically Gorenstein. It is shown that if the defining ideal $I$ of $R$ is generated by $n$ elements, then $\mbox{tr}(\omega_R)$ is generated by the (n-2)-minors of the Hilbert-Burch matrix of $I$.

This is joint work with Gasanova, Hibi and Moradi, and with Ficarra, Stamate and Trivedi.


Talk Title / Abstract

Haydee Lindo 

Coming soon...


Linquan Ma


Vanishing and non-negativity of the first normal Hilbert coefficient

Let $(R,m)$ be a Noetherian local ring such that $\widehat{R}$ is reduced. We prove that, when $\widehat{R}$ is $S_2$, if there exists a parameter ideal $Q\subseteq R$ such that the first normal Hilbert-coefficient $\overline{e_1}(Q)$ vanishes, then $R$ is regular and $\nu(m/Q)\leq 1$. This leads to an affirmative answer to a problem raised by Goto-Hong-Mandal. We also give a new proof of the non-negativity of the first normal Hilbert-coefficient (which also shows the non-negativity of the first tight Hilbert-coefficient in positive characteristic).

This is joint work with Pham Hung Quy. 


Talk Title / Abstract

Sarasij Maitra

Coming soon...


Talk Title / Abstract

Takumi Murayama

Coming soon...


Talk Title / Abstract

Rebecca R.G. 

Coming soon...


Talk Title / Abstract

Liana Şega

Coming soon...