The commutative algebra group has research interests which include algebraic geometry, algebraic and quantum coding theory, homological algebra, representation theory, and K-theory.
Professor 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.
Professor 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.
Professor 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.
Research assistant professor Alexandra Seceleanu is interested in homological problems in local commutative algebra, but also likes to think about graded structures. Her thesis focused on extending lower bounds on ranks of syzygies to the case of certain hypersurface rings in mixed characteristic and separately on studying the Weak Lefschetz property in instances that can be related to the geometry of fat point schemes. She is also interested in computational algebra problems.
Professor 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.
Professor 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.
Emeritus professor 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.
Emeritus professor Sylvia Wiegand 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.
Solomon Akesseh Brian Harbourne
Michael Brown Mark Walker
Ela Celikbas (PhD 2012) Sylvia Wiegand
Amanda Croll (PhD in 2013)
Advised by: Srikanth Iyengar
Annika Denkert (PhD in 2013) Brian Harbourne
Becky Egg Tom Marley
Luigi Ferraro Lucho Avramov and Srikanth Iyengar
Courtney Gibbons (PhD in 2013) Luchezar Avramov and Roger Wiegand
Jason Hardin Mark Walker
Michael Janssen (PhD in 2013) Brian Harbourne
Brian Johnson (PhD in 2012) Tom Marley
Haydee Lindo Srikanth Iyengar
Jason Lutz Luchezar Avramov and Srikanth Iyengar
Katharine Shultis Srikanth Iyengar
Advised by: Mark Walker
Brittney Turner Tom Marley
Marcus Webb Tom Marley
Xuan Yu (PhD in 2013) Mark Walker
Zheng Yang Lucho Avramov