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# Topic: Homological conjectures in commutative algebra

###### In the News (Tue 23 Apr 19)

 books about: commutative (multiplicities multiplicative computational)   (Site not responding. Last check: 2007-10-22) This is the easiest introduction to algebraic geometry and commutative algebra, the authors had done a great job in writing a book that assume very little from the readers. Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. The subject of the book is not restricted to commutative algebra developed as a pure discipline for its own sake, nor is it aimed only at algebraic geometry where the intrinsic geometry of a general n-dimensional variety plays the central role. www.very-clever.com /books/commutative   (1312 words)

 UC Davis Math: Glossary   (Site not responding. Last check: 2007-10-22) Homology and cohomology are algebraic objects associated to a manifold or other mathematical object which give one measure of the number of holes of the object. An algebraic structure on a vector space which describes multiplication of elements of a Lie group which are very close to the identity (infinitesimal transformations). An algebraic relation arising in statistical mechanics, topological quantum field theory, and quantum groups in which two tensors, one naturally represented by a right-side-up triangle and the other by an upside-down triangle, are equal. math.ucdavis.edu /profiles/glossary.html   (9932 words)

 Suggestions for Honours Theses Algebraic geometry is an old subject with deep connections with commutative algebra, number theory, complex analysis, representation theory, topology... The Nullstellensatz is one of the pillars of (commutative) algebraic geometry. Commutative algebras arise naturally in mathematics in two ways: firstly as functions on some geometric object and secondly, as systems of numbers, or more precisely, rings of integers. web.maths.unsw.edu.au /~danielch/honthesis.html   (1775 words)

 Mirago : Science: Math: Algebra: Conferences: Past Conferences Algebra and Discrete Mathematics - A Euresco conference on the interplay between model theory, infinite combinatorics and various subfields of algebra. Antalya Cebir Gunleri III - Antalya Algebra Days III - The third in a sequence of annual conferences organized in Antalya whose aim is to increase interactions between Turkish mathematicians working in various fields of Algebra, and in particular to create relations between Turkish Mathematicians and mathematicians from other countries. IAC04 - International Algebraic Conference on the occasion of the 250-th anniversary of Moscow State University and the 75-th anniversary of the Department of Algebra. www.mirago.com /scripts/dir.aspx?cat=Top/Science/Math/Algebra/Conferences/Past_Conferences   (1450 words)

 commalg.org - the center for commutative algebra During the past 30 years, the homological conjectures and related questions have had a significant impact on the development of commutative algebra. This area of research remains a rich one and is as influential today in the development of commutative algebra as it was decades ago. Professorship in Algebra at the University of Copenhagen. www.commalg.org /confs/salt_lake_city_04.shtml   (418 words)

 algebra help-algebra software-algebra math tutor The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map. Practising Algebra is aimed at the students in the senior years of secondary education and covers work which spans Years 11and 12, with some more advanced material, depending upon course content and state. www.softmath.com /algebra13.htm   (1238 words)

 [No title] Therefore the spectral sequence is one of commutative (A*-comodule) algebras ov* *er the Dyer-Lashof algebra. It follows that the homological homotopy fixed point spectral sequence for X is a module o* *ver the corresponding spectral sequence for S, which is an algebra spectral sequence by our previous remarks (since S is a commutative S-algebra). The commutative S-algebra structure of R induces Steenrod operations in the E2-term of the Adams spectral sequence, which are the analog in this situation of the Dyer-Lashof operations in H*(R; F2). hopf.math.purdue.edu /Bruner-Rognes/bruner.txt   (7226 words)

 Adela Vraciu's Research Interests My main research area is commutative algebra, and I am particularly interested in charamcteristic p methods, such as tight closure. The understanding of this algebra structure is central to the applications and development of tight closure theory. In commutative algebra, linkage is defined as an equivalence relation on the set of ideals in a given Gorenstein ring. www.math.sc.edu /~vraciu/research.html   (374 words)

 No Title Those years that a course in algebraic geometry will be offered the next year, we propose to continue with the representation theory; those years that a course in representation theory is offered, we propose to continue with the algebraic geometry. Hom and tensor functors, condensed introduction to homological algebra. Hopf algebra duality between the enveloping algebra of a semisimple Lie algebra and the coordinate ring of the corresponding semisimple algebraic group. www.math.ucsb.edu /~mckernan/algebra_courses/algebra_courses.html   (1441 words)

 Midwest Algebraic Geometry Conference Originally, the impetus for defining tight closure came from three sources: work on the homological conjectures in commutative algebra, work on the Cohen-Macaulay property of rings of invariants and understanding the concept of F-purity, and finally work on the integral closure of ideals, especially the so-called Briançon-Skoda Theorem. Mukai's conjecture (and stronger variants of it) regarding projective normality and normal presentation for surfaces of Kodaira dimension zero. A recent conjecture of Boris Shapiro and Michael Shapiro concerning the Schubert calculus of enumerative geometry on a general flag manifold gives a precise method to select real Schubert varieties all of whose (finitely many) points of intersection are real. www.nd.edu /~rosen/MAGC97/magc97/magc97.html   (7511 words)

 [No title] Commutative Rings and Their Modules - Main emphases of the workshop included integer valued polynomials, and Krull and Mori domains. Algebra and Discrete Mathematics - Highlighted the interplay among model theory, infinite combinatorics, and various subfields of algebra. Homological Conjectures for Finite Dimensional Algebras - Held August 12-19, 2001, in Nordfjordeid, Norway. botw.org /new/Science/07232005.cfm   (1127 words)

 [No title]   (Site not responding. Last check: 2007-10-22) Title : Mathematical Sciences: Homological Questions in Commutative Algebra Abstract : This award is concerned with the study of certain invariants, known as local Chern characters, defined for modules over local rings. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. Nowadays, the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in theoretical computer science and robotics. www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/MPS/DMS.MPS.a9204297.txt   (164 words)

 Mel Hochster's Publications   (Site not responding. Last check: 2007-10-22) The Zariski-Lipman conjecture in the graded case, J. of Algebra 47 (1977), 411-424. Associated graded rings derived from integrally closed ideals and the local homological conjectures, in Proceedings of the Conference on Commutative Algebra (at Rennes, France, May, 1981), 1-27. The local homological conjectures, in Proceedings of the Durham Symposium on Commutative Algebra, London Math. www.math.lsa.umich.edu /~hochster/bib.html   (1149 words)

 Group Theory - Books - Magic Bean Dip   (Site not responding. Last check: 2007-10-22) Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. v1.magicbeandip.com /store/browse_books_13940   (2068 words)

 Réunion d'hiver 2000 de la SMC This result can be viewed as a step towards proving a conjecture of Dolgachev and Weisfeiler which asserts that any such family is a fiber bundle. The problem of defining intersection multiplicities in Algebraic Geometry has given rise to a number of fundamental questions in Commutative Algebra. Serre gave a definition using homological methods which satisfies many of the desired properties, and he stated several other properties as conjectures. camel.math.ca /Events/winter00/abs/ag-f.html   (2248 words)

 On the Charney-Davis and Neggers-Stanley Conjectures (ResearchIndex)   (Site not responding. Last check: 2007-10-22) 82 Combinatorics and Commutative Algebra (context) - Stanley - 1996 9 the Neggers-Stanley conjecture and Eulerian polynomials (context) - Gasharov - 1998 2 Vanishing theorems and conjectures for the # homology of rig.. sherry.ifi.unizh.ch /621291.html   (766 words)

 VVh0am1's Xanga Site The study of algebraic number fields, and these days also of infinite algebraic extensions of the rational number field, is the central topic of algebraic number theory. His work in algebraic number theory was important both from the point of view of proving fundamental results in class field theory, and in introducing contemporary mathematics in Japan. In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H www.xanga.com /VVh0am1   (1358 words)

 Boca Raton Algebra Seminar Corresponding to a (commutative and associative) 2-dimensional algebra A over a field k, there is an invariant way of defining harmonic functions u (x_1, x_2) and their conjugates v (x_1, x_2). Starting with an algebra A over a field k, there are lots of ways of defining a multiplication on A x A. Homological Conjectures for Finite Dimensional Algebras (Summerschool, August 12-19, Nordfjordeid, Norway) www.math.fau.edu /Schmidme/AS-spring2001.html   (1006 words)

 Univ at Albany Mathematics Information Service Algebras, extensions of rings acted upon by finite groups or Hopf algebras, connections with algebraic number theory. Algebraic and geometric topology, the Novikov and Borel conjectures, geometric group theory. Commutative algebra: Noetherian rings of geometric, algebraic, or arithmetic type; polynomial and power series algebras over such rings. math.albany.edu:8000 /math/dept/faculty.html   (403 words)

 NCGOA Seminar, Fall 2005 The aim is to explain the phenomenon of Mirror Symmetry in terms of homological algebra and non-commutative geometry. Let $\mathcal B$ be the algebra on the disk generated by the harmonic extensions of the functions in $B$. These algebras have important applications to geometry, topology and analysis, due to the fact that their $K$-theory groups are receptacles of higher indices of elliptic differential operators on noncompact spaces. www.math.vanderbilt.edu /~bisch/NCGOA_seminar_fall05.html   (1331 words)

 Amazon.com: Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra : Ams-Ims-Siam Summer Research ...   (Site not responding. Last check: 2007-10-22) The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra. www.amazon.com /exec/obidos/tg/detail/-/0821851888?v=glance   (479 words)

 [No title]   (Site not responding. Last check: 2007-10-22) So there are areas which are in the traditions of algebraic topology and which are inherently not tractable by stable methods. Also for me a major interest is that the basic problems of homotopy types reveal the need for and construction of new algebraic structures, and that these new structures have already been of proven interest in other areas. To go further back, the Hopf formula for H_2(G) was one of the origins of homological algebra, which itself plays a not inconsiderable role in the work of of A.Grothendieck which led to a solution of the Weil conjectures. www.lehigh.edu /~dmd1/rb35   (609 words)

 [No title] Abstract: A graded Artinian algebra of socle degree vector s and codimension c is said to be compressed if its Hilbert function is the maximal possible, given s and c. In this talk I will discuss the connection between this type of almost vanishing property and the homological conjectures, present some related questions that are interesting also for rings of characteristic zero, and describe some recent joint results with V. Srinivas where these questions can be answered. Several estimations are obtained which are used to bound the length of chains of algebras occurring in any construction of the integral closure of a graded domain. www.math.purdue.edu /~lipman/Fest/talks.html   (2706 words)

 Citations: Controlled algebra and the Novikov conjectures for K- and L-theory - Carlsson, Pedersen (ResearchIndex)   (Site not responding. Last check: 2007-10-22) Carlsson and E. Pedersen, Controlled algebra and the Novikov conjecture for K and L theory, Topology 34 (1995), 731-758. Carlsson and E. Pedersen, Controlled algebra and the Novikov conjectures for K and L theory, Topology 34 (1995), 731--758. Carlsson and E.K. Pedersen, Controlled algebra and the Novikov conjectures for K and L theory, Topology 34 (1994), 731-758. citeseer.ist.psu.edu /context/72403/0   (1534 words)

 Institutt for matematiske fag In the sequel, R denotes a commutative noetherian ring with unique maximal ideal m and residue field k=R/m, while M, N stand for finite R-modules. The category of commutative rings is naturally contained in the category of commutative DG (= differential graded) algebras. Two constructions of this algebra will be sketched, and its name will be explained by describing its analogy with the rational homotopy Lie algebra of a topological space. www.math.ntnu.no /~oyvinso/Nordfjordeid/Program/avramov.html   (321 words)

 Amazon.ca: Idempotent Matrices over Complex Group Algebras: Books   (Site not responding. Last check: 2007-10-22) The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with deep geometric problems and conjectures. A variety of techniques is employed from commutative algebra, homological algebra and functional analysis. Ioannis Emmanouil was initiated to mathematics in Athens, Greece and then moved to Berkeley, where he studied homological algebra, algebraic geometry and K-theory with Mariusz Wodzicki. www.amazon.ca /exec/obidos/ASIN/3540279903   (366 words)

 Florian Enescu - Curriculum Vitæ Commutative Algebra with applications to Algebraic Geometry: Tight closure theoy, multiplicity theory, Hilbert and Hilbert-Kunz functions, integral closure of ideals, homological conjectures, filtrations of ideals, local cohomology and singularities of local rings. Organizer (with Paul Roberts) of the national mini-course Fundamental problems in commutative algebra University of Utah, June 2004. Commutative algebra AMS Central Section, March 2002, Ann Arbor, MI. www.mathstat.gsu.edu /~matfxe/vita/vita_html   (356 words)

 Bernt Tore Jensen's homepage Strong no-loop conjecture for algebras with two simples and radical cube zero. On the geometry of syzygies for self-injective algebras. I have given reading courses on commutative algebra and homological algebra for master students. www.amsta.leeds.ac.uk /~bjensen   (430 words)

 Institutt for matematiske fag Anick, E. Green, On the homology of quotients of path algebras, Comm. Auslander, I. Reiten, Homological finite subcategories, Representations of algebras and related topics (Tsukuba, 1990), 1--42, London Math. Xi, On the representation dimension of finite dimensional algebras, J. www.math.ntnu.no /~oyvinso/Nordfjordeid/Program/references.html   (417 words)

 [No title] Lattices, Universal Algebra and Applications - Held on May 28-30, 2003, at the Centro de Algebra da Universidade de Lisboa, Lisbon, Portugal. Representations of Algebraic Groups, Quantum Groups, and Lie Algebras - Held on July 11-15, 2004, in Snowbird, Utah, USA. SIAM Conference on Applied Linear Algebra - Held on July 15-19, 2003, at the College of William and Mary, Williamsburg, Virginia, USA. botw.org /top/Science/Math/Algebra/Conferences/Past_Conferences   (1741 words)

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