Commutative Algebra and Algebraic Geometry
The commutative algebra group has research interests which include algebraic geometry, algebraic and quantum coding theory, homological algebra, representation theory, and K-theory.
Faculty
Luchezar Avramov , who joined our faculty in January 2002, works on the homological algebra of commutative rings. Recent topics include the structure of ring homomorphisms, finiteness of Andre'-Quillen homology and of Hochschild homology, behavior of infinite resolutions, and the vanishing of Tor and Ext, particularly over complete intersections and Gorenstein rings.
Brian Harbourne works in commutative algebra and algebraic geometry. He has studied the geometry of rational surfaces, and his recent focus is on Hilbert functions and resolutions of homogeneous ideals defining fat point subschemes of the projective plane.
Srikanth Iyengar is interested in homotopical and homological algebra, mainly of commutative rings, but he also likes to talk to like-minded algebraic topologists and representation theorists. His recent research include square-zero matrices, levels in triangulated categories and its applications to the study of finite free complexes, and the homotopy category of commutative rings.
Tom Marley is interested in homological algebra over commutative Noetherian local or graded rings. Specifically, he studies finiteness properties of local cohomology, such as Hartshorne's concept of cofiniteness and the Huneke-Hochster conjecture that the set of associated prime ideals of a local cohomology module is finite. In addition, he works on applications of local cohomology to the theory of Hilbert functions and the depths of Rees algebras.
Judy Walker works in algebraic coding theory. Much of her work uses techniques from number theory, algebraic geometry and graph theory. She has worked with algebraic geometric codes over rings and the relationship between weight measures on these codes and exponential sums. Currently, she studies low density parity check codes, focusing especially on their pseudocodeword structure.
Mark Walker works in algebraic K-theory and motivic cohomology. His recent work concerns "semi-topological" K-theory, a blend of the algebraic and topological theories; this approach is shedding new light on some fundamental questions in algebraic K-theory.
Roger Wiegand works on the homology and representation theory of local rings: On the homological side, he studies depth properties of tensor products of modules and related questions on the vanishing of Tor. In representation theory he is interested in the classification of rings of finite representation type and questions regarding uniqueness of direct-sum decompositions of modules.
Sylvia Wiegand is involved in an on-going investigation of the rings between a local ring and its completion. She also works in representation theory and on the partially ordered set of prime ideals in Noetherian rings of low dimension.
Graduate Students
Suanne Au Mark Walker
Nate Axvig Judy Walker
Jesse Burke Srikanth Iyengar
Ela Celikbas Sylvia Wiegand
Olgur Celikbas Roger Wiegand
Andrew Crabbe Roger Wiegand
Justin DeVries Srikanth Iyengar
Christina Eubanks-Turner Sylvia Wiegand
Mu-wan Huang Mark Walker
Inês Henriques Luchezar Avramov
Micah Leamer Srikanth Iyengar and Roger Wiegand
Laura Lynch Tom Marley
Lori McDonnell Tom Marley
Livia Miller Tom Marley
Frank Moore Luchezar Avramov
Terri Moore Roger Wiegand
Hamid Rahmati Srikanth Iyengar and Luchezar Avramov
Silvia Saccon Roger Wiegand
Deanna Turk Judy Walker
