[Turkmath:5875] Gebze Teknik Üniversitesi Matematik Bölümü Genel Seminerleri

[GTU Mathematics]

Sayın Liste Üyeleri,

9 Aralık Cuma günü saat 16:00'da *Doç. Dr. Olgür Çelikbaş *(West Virginia
University) *"*  *Torsion in tensor products of modules over local rings*
*"* başlıklı bir seminer verecektir. Seminerin detayları aşağıda olup tüm
ilgilenenler davetlidir.

Seminer için Microsoft Teams platformu kullanılacaktır. Seminere katılmak
için aşağıdaki linki kullanabilirsiniz:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1670068534385?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d


Seminere bağlanırken aşağıdaki pencereyi görürseniz,
[image: image.png]

lütfen* Allow (İzin ver) *seçeneğine tıklayınız. Bu sizin toplantıya kamera
ve mikrofonunuzla bağlanabilmenizi sağlar.


Seminere giriş yaparken lütfen gerçek ve tam adınızı kullanınız.


Konuşmadığınız sürece lütfen mikrofonunuzu kapalı tutunuz.

Saygılarımızla.


Dear all,

*Assoc. Prof. Olgür Çelikbaş* from West Virginia University will give a
talk titled *"*  *Torsion in tensor products of modules over local rings*
*”* on December 9th at 16:00. All interested are invited.


Abstract:

The tensor product of two nonzero finitely generated modules over a local
ring (commutative and Noetherian), even when the modules in question are
nice (e.g., torsion-free), is not typically well-behaved (e.g., has nonzero
torsion). Hence the assumption that there is a nonzero torsion-free tensor
product of modules influences the structure of the modules in the tensor
product, as well as that of the ring in question. This connection over
regular local rings made its first appearance in the seminal paper of
Maurice Auslander, Modules over unramified regular local rings (Illinois J.
Math. 5, 1961). Subsequently Craig Huneke and Roger Wiegand extended and
studied Auslander’s results over hypersurface rings in their prominent
paper, Tensor products of modules and the rigidity of Tor (Math. Ann. 299,
no. 3, 1994), and did pioneering work on the study of torsion in tensor
products of modules.

Studies in this direction by Auslander, Huneke and Wiegand, and other
researchers, yielded several questions, which still remain open, on how
nonzero torsion arises in tensor products of modules over certain local
rings. One such example is a long-standing conjecture of Huneke and
Wiegand, which is concerned with the torsion submodule of tensor products
of modules with their algebraic duals. Over Gorenstein rings, an
affirmative answer to this conjecture would imply an affirmative answer to
a celebrated conjecture of Maurice Auslander and Idun Reiten on the
vanishing of Ext for maximal Cohen-Macaulay modules, a conjecture which was
initially proposed over finite dimensional algebras in the 1970s.

In this talk I plan to partly survey results on the existence of torsion in
tensor products. In particular I plan to discuss some of the recent work
done that corroborate the aforementioned conjecture of Huneke and Wiegand.


Microsoft Teams platform will be used for the seminar. To join the seminar,
please use the following link:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1670068534385?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d


If you see the following window when connecting to the seminar,
[image: image.png]

please select *Allow**.* Then you will be able to use your microphone and
camera during the seminar.


Please use your real and complete name when you enter the system.


Please switch your microphone off unless you are speaking.


Sincerely
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20221205/122aec1f/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 7073 bytes
Desc: not available
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20221205/122aec1f/attachment-0002.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 7073 bytes
Desc: not available
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20221205/122aec1f/attachment-0003.png>