This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil. The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.
Combinatorics of symbolic Rees algebras of edge ideals of clutters by J. Martinez-Bernal, C. Renteria-Marquez, and R. H. Villarreal Hilbert depth of powers of the maximal ideal by W. Bruns, C. Krattenthaler, and J. Uliczka A note on reductions of monomial ideals in $k[x,y]_{(x,y)}$ by C-Y.J. Chan and J.-C. Liu Plucker-Clebsch formula in higher dimension by C. Ciliberto and V. di Gennaro Invariants of ideals generated by pfaffians by E. De Negri and E. Gorla Hilbert polynomial and the intersection of ideals by J. Elias and J. Martinez-Borruel Polynomial vector fields with algebraic trajectories by V. Ferrer and I. Vainsencher Minimal free resolutions for certain affine monomial curves by P. Gimenez, I. Sengupta, and H. Srinivasan Uniform bounds for Hilbert coefficients of parameters by S. Goto and K. Ozeki Absolute integral closure by C. Huneke A property of the Frobenius map of a polynomial ring by G. Lyubeznik, W. Zhang, and Y. Zhang A note on the variety of pairs of matrices whose product is symmetric by M. Majidi-Zolbanin and B. Snapp Reconciling Riemann-Roch results by P. Roberts and A. K. Singh Hilbert functions of Cohen-Macaulay local rings by M. E. Rossi Some homological properties of almost Gorenstein rings by J. Striuli and A. Vraciu
