This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting "Homological and Computational Methods in Commutative Algebra" held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns' research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.
received a Ph.D. in mathematics from the University of Essen (Germany) in 1993. Since 2000 he has been a professor of algebra at the University of Genova (Italy). His main research interest lies in commutative algebra and its interactions with algebraic geometry and combinatorics.
Joseph Gubeladze graduated from Tbilisi State University in 1983. He received his Ph.D. in mathematics in 1985 and Doctor of Science in 1990 from St. Petersburg State University. He worked at Razmadze Mathematical Institute in Tbilisi from 1983. After several research positions in Europe and the USA, he joined San Francisco State University in 2003, where he is currently a professor of mathematics. He is interested in K-theory of toric varieties and lattice polytopes.
Tim Römer received his Ph.D. from the University of Essen (Germany) in 2001. Since 2008 he has been a professor of algebra at the University of Osnabrück (Germany). His main research interests are in the area of commutative algebra with applications to algebraic/discrete geometry, algebraic combinatorics and algebraic statistics.
1 Betti sequances over standard graded algebras commutative algebras with two relations.- 2 Betti diagrams with special shapes.- 3 Koszul algebras defined by three relations.- 4 Some algebras with the weak Lefschetz property.- 5 Multigraded gereric initial ideals of determinantal ideals.- 6 A stronger local monomialization theorem.- 7 The Cayley trick for tropical hypersurfaces with a view towards Ricardian economics.- 8 Ideals Associated to poset homomorphisms: a survey.- 9 How to flatten a soccer ball.- 10 The smallest normal edge polytopes with no regular unimodular triangulations.- 11 Homological conjectures and lim Cohen-Macaulay sequences.- 12 Algebras with the Weak Lefschetz Property.- 13 About multiplicities and applications of Bezout numbers.- 14 A polynomial identity via differential operators.- 15 F-threshold, integral closure, convexity.