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SUMMARY:Graduate Course on Tight Closure of Ideals and its Applications |
(smr 3707)
DTSTART;VALUE=DATE-TIME:20220516T120000Z
DTEND;VALUE=DATE-TIME:20220725T200000Z
DTSTAMP;VALUE=DATE-TIME:20220519T124814Z
UID:indico-event-9791@ictp.it
DESCRIPTION:\n An ICTP Virtual Meeting\n The aim of the course is to provi
de training in the foundations of commutative algebra and algebraic geomet
ry in prime characteristic and to present some of the exciting recent deve
lopments. The local theory of prime characteristic singularities is a beau
tiful and historically important subject. Singularities which are defined
in terms of the behaviour of the Frobenius endomorphism have been labeled
“F-singularities”. The course gives an introduction on the most promin
ent F-singularity classes that emerged from Hochster–Huneke’s tight cl
osure theory. Since its introduction in the late 1980s\, it has had a dram
atic effect on the field of commutative algebra. Tight closure gives unifi
ed proofs and strong generalisations of many major theorems in commutative
algebra\, as well stimulated recent proofs of longstanding conjectures.\n
\n Topics:\n\n An overview of tight closure of ideals\n \n Test ideals\n
\n Direct summands\n \n F-rational rings and rational singularities\n \
n Hilbert-Kunz multiplicities\n \n Briançon-Skoda Theorems\n \n Big Co
hen-Macaulay algebras\n \n The absolute integral closure\n \n Symbolic p
owers of ideals\n \n The localisation problem\n \n Uniform Artin-Rees re
sults \n\n Speakers:\n I. ABERBACH\, University of Missouri\, USA\n \n F
. ENESCU\, Georgia State University\, USA\n \n N. EPSTEIN\, George Mason
University\, USA\n \n E. GRIFO\, University of Nebraska\, USA\n \n G. LY
UBEZNIK\, University of Minnesota\, USA\n \n L. MA\, Purdue University\,
USA\n \n T. POLSTRA\, University of Virginia\, USA\n \n I. SWANSON\, Pur
due University\, USA\n \n V. TRIVEDI\, Tata Institute of Fundamental Rese
arch\, India\n \n K. TUCKER\, University of Illinois\, USA\n \n W. ZHANG
\, University of Illinois\, USASchedule: Mondays and Wednesdays\n \n 1.00
-3.00 pm GMT (link)\n \n \n \n Lectures. There will be 3 lectures
and a tutorial on each topic each week. The speakers will provid
e detailed typed notes of their lectures on the day they finish their
lectures. These notes will contain exercises which the participants sho
uld try to solve and submit to the tutorial instructor before 12 pm GMT
on Fridays.\n \n \n \n Tutorials. The tutorial on each topic will be h
eld a week after the lectures are delivered. The tutorial instructor will
present solutions to problems assigned by the Lecturer that are received f
rom the participants and discuss some material covered during the lectur
es. Grades will be assigned to the solutions.\n Registration: There is no
registration fee.\n\n\n//indico.ictp.it/event/9791/
LOCATION:Online - Online
URL://indico.ictp.it/event/9791/
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