The commutative algebra group has research interests which include algebraic geometry, algebraic and quantum coding theory, homological algebra, representation theory, and K-theory.

## Faculty

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.

Assistant Professor**Wenliang Zhang** Wenliang Zhang works in commutative algebra and algebraic geometry. More specifically, he is interested in local cohomology and applications to topology of algebraic varieties, singularities and their invariants in positive characteristic and their arithmetic behaviors, algebraic D-modules, and questions related to homological conjectures.

## Graduate Students

Solomon Akesseh Brian Harbourne

Michael Brown Mark Walker

Ela Celikbas (PhD 2012) Sylvia Wiegand

Amanda Croll (PhD in 2013)

Advised by: Srikanth Iyengar

Doug Dailey

Tom Marley

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 (PhD in 2014) 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

Peder Thompson

Advised by: Mark Walker

Brittney Turner Tom Marley

Marcus Webb Tom Marley

Xuan Yu (PhD in 2013) Mark Walker

Zheng Yang Lucho Avramov