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Re: Countdown to the 2010 Fields medal(s)
Posted:
Aug 8, 2010 1:30 AM
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Here is some additional information about the 26-th International Congress of Mathematicians (ICM2010) that will be held in Hyderabad, in India, from Thursday, August 19, to Friday, August 27, 2010.
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As announced in my previous posting and on the following two Web pages
http://www.icm2010.org.in/scientific-program/invited-speakers
http://www.icm2010.org.in/wp-content/icmfiles/docs/schedule/plenary_jul2_3.pdf
in addition to the 20 plenary lectures, and about 150 invited talks, the program of the 26-th International Congress of Mathematicians also includes the following two special lectures:
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1. The Abel lecture,
delivered by Srinivasa Varadhan, USA.
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2. The Emmy Noether lecture,
delivered by Idun Reiten, Norway.
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In my previous posting, I gave some additional information about the first of these two special talks. Below, I give some additional information about the second one.
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The following Web page
http://www.icm2010.org.in/wp-content/icmfiles/docs/schedule/plenary_jul2_3.pdf
says that the second talk will be given on the last day of the congress. It is announced as follows:
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Friday, August 27, 2010, 13:45-14:45
Emmy Noether Lecture
Idun Reiten, NTNU, Norway
Cluster categories
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Below is some information about Idun Reiden extracted from the following Web page of the online Wikipedia Encyclopedia:
http://en.wikipedia.org/wiki/Idun_Reiten
Idun Reiten is a Norwegian professor of mathematics at the Norwegian University of Science and Technology. She is considered to be one of Norway's greatest mathematicians today.
In 2007, Idun Reiten was awarded the Möbius prize.
In 2009 she was awarded the Fridtjof Nansens reward for successful researchers.
In 2009, she was awarded the Nansen medal for astonishing research.
Her research area is representation theory for artinian algebras, commutative algebra, and homological algebra. Her work with Maurice Auslander now forms the part of the study of artinian algebras known as Auslander-Reiten theory.
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We can see on the following Web page
http://muse.jhu.edu/login?uri=/journals/american_journal_of_mathematics/v130/130.4.iyama.pdf
that Idun Reiten has published the following joint paper in the highly rated American Journal of Mathematics:
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Osamu Iyama and Idun Reiten
Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
American Journal of Mathematics
Volume 130, Number 4, August 2008, pp. 1087-1149
DOI: 10.1353/ajm.0.0011
E-ISSN: 1080-6377
Print ISSN: 0002-9327
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Abstract:
We say that an algebra $\Lambda$ over a commutative noetherian ring $R$ is Calabi-Yau of dimension $d$ ($d$-CY) if the shift functor $[d]$ gives a Serre functor on the bounded derived category of the finite length $\Lambda$-modules. We show that when $R$ is $d$-dimensional local Gorenstein the $d$-CY algebras are exactly the symmetric $R$-orders of global dimension $d$. We give a complete description of all tilting modules of projective dimension at most one for 2-CY algebras, and show that they are in bijection with elements of affine Weyl groups, preserving various natural partial orders. We show that there is a close connection between tilting theory for 3-CY algebras and the Fomin-Zelevinsky mutation of quivers (or matrices). We prove a conjecture of Van den Bergh on derived equivalence of noncommutative crepant resolutions.
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We can see on the following Web page of the online Wikipedia Encyclopedia about Krull-Schmidt categories
http://en.wikipedia.org/wiki/Krull%E2%80%93Schmidt_category
that her name is associated with the concept of Auslander-Reiten quiver.
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On the following Web page
http://sciencewatch.com/dr/fbp/2008/08augfbp/08augfbpKellerET/
there is an interview of Bernhard Keller and Idun Reiten by ScienceWatch.com about their following highly cited paper
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Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
Bernhard Keller and Idun Reiten
Advances in Mathematics, Volume: 211, Issue: 1,
Pages 123-151, MAY, 2007
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In that interview, they say notably:
"Our paper contributes to the study of certain systems, called 2- and 3-Calabi-Yau categories, which are of two and three dimensions, respectively. These categories have turned out to be important in a branch of theoretical physics called string theory, where the elementary particles are modeled by small strings. In this theory, in addition to the four dimensions of classical physics, time plus three spatial dimensions, one has to deal with six real or equivalently three complex dimensions, whose behavior is expected to be controlled by certain 3-Calabi-Yau categories."
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Idun Reiten is co-author of co-editor of each of the following books, ordered in chronological order of publication:
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Two Dimensional Tame and Maximal Orders of Finite Representation Type
Idun Reiten and Michel Van Den Bergh
American Mathematical Society, 1989
Paperback, 72 pages
ISBN-10: 0821824694
ISBN-13: 978-0821824696
$20.00
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Tilting in Abelian Categories and Quasitilted Algebras
Dieter Happel, Idun Reiten, and Sverre O. Smalo
American Mathematical Society, 1996
Paperback, 88 pages
ISBN-10: 0821804448
ISBN-13: 978-0821804445
Price: $39.00
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Representation Theory of Artin Algebras
Maurice Auslander, Idun Reiten, and Sverre O. Smalo
Cambridge University Press, 1997
Paperback, 440 pages
ISBN-10: 0521599237
ISBN-13: 978-0521599238
$80.00
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Algebras and Modules I:
Workshop on Representations of Algebras and Related Topics,
July 29-August 3, 1996, Trondheim, Norway
Idun Reiten, Sverre O. Smalo, and Yvind Solberg, Editors
American Mathematical Society, 1998
Paperback, 198 pages
ISBN-10: 0821808508
ISBN-13: 978-0821808504
$45.00
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Algebras and Modules II:
Eighth International Conference on Representations of Algebras (IRCA VIII),
August 4-10, 1996, Geiranger, Norway
Idun Reiten, Sverre O. Smalø, Øyvind Solberg, Editors
American Mathematical Society and Canadian Mathematical Society, 1998
Paperback, 569 pages
ISBN-10: 0821810766
ISBN-13: 978-0821810767
$114.00
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Selected Works of Maurice Auslander
Idun Reiten, Sverre O. Smalo, and Oyvind Solberg, Editors
American Mathematical Society, 1999
Hardcover, 1638 pages, in two volumes
ISBN-10: 0-8218-0679-3
ISBN-13: 978-0-8218-0679-1
$318.00
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Dualities on Generalized Koszul Algebras
Edward L. Green, Idun Reiten, and Oyvind Solberg
American Mathematical Society, 2002
Paperback, 67 pages
ISBN-10: 0821829343
ISBN-13: 978-0821829349
$50.00
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Homological and Homotopical Aspects of Torsion Theories
Apostolos Beligiannis and Idun Reiten
American Mathematical Society, 2007
Paperback, 207 pages
ISBN-10: 0821839969
ISBN-13: 978-0821839966
$72.00
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Countdown: The Fields medals 2010 will be awarded in 11 days, on Thursday, August 19, 2010.
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