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

Professor Luchezar Avramov 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.

Assistant Professor Kyungyong Lee is interested in algebraic geometry, algebraic combinatorics, cluster algebras, commutative algebras, non-commutative algebras, representation theory, and mathematical physics. His research lies in the intersection of commutative algebra, algebraic geometry, and discrete mathematics.

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.

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 commutative algebra, algebraic geometry and algebraic K-theory. Recently, much of his work has focused on the geometric and algebraic properties of complete intersections with isolated singularities.

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.

Current Graduate Students

Solomon Akesseh
Advised by: Brian Harbourne

Eric Canton
Advised by: Mark Walker and Brian Harbourne

Benjamin Drabkin
Advised by: Alexandra Seceleanu

Christopher Evans
Advised by: Tom Marley

Brittney Falahola
Advised by: Tom Marley

Luigi Ferraro
Advised by: Lucho Avramov

Mohsen Gheibi
Advised by: Mark Walker and Roger Wiegand

Seth Lindokken
Advised by: Mark Walker

Matthew Mills
Advised by: Kyungyong Lee

John Myers
Advised by: Lucho Avramov

Nicholas Packauskas
Advised by: Lucho Avramov and Mark Walker

Josh Pollitz
Advised by: Lucho Avramov and Mark Walker

Neil Steinburg
Advised by: Tom Marley and Roger Wiegand

Andrew Windle
Advised by: Mark Walker

Recent Graduates

Michael Brown (PhD 2015)
Advised by: Mark Walker

Ela Celikbas (PhD 2012)
Advised by: Sylvia Wiegand

Amanda Croll (PhD 2013)
Advised by: Srikanth Iyengar

Doug Dailey (PhD 2016)
Advised by: Tom Marley

Annika Denkert (PhD 2013)
Advised by: Brian Harbourne

Becky Egg (PhD 2016)
Advised by: Tom Marley

Courtney Gibbons (PhD 2013)
Advised by: Luchezar Avramov and Roger Wiegand

Jason Hardin (PhD 2014)
Advised by: Mark Walker

Michael Janssen (PhD 2013)
Advised by: Brian Harbourne

Brian Johnson (PhD 2012)
Advised by: Tom Marley

Jason Lutz (PhD 2016)
Advised by: Luchezar Avramov and Srikanth Iyengar

Katharine Shultis (PhD 2015)
Advised by: Brian Harbourne and Roger Wiegand

Peder Thompson (PhD 2016)
Advised by: Mark Walker

Marcus Webb (PhD 2015)
Advised by: Tom Marley

Xuan Yu (PhD 2013)
Advised by: Mark Walker

Zheng Yang (PhD 2015)
Advised by: Lucho Avramov