The commutative algebra group has research interests which include algebraic geometry, algebraic and quantum coding theory, homological algebra, representation theory, and K-theory.
Faculty
Assistant Professor Eloísa Grifo works in commutative algebra. She is interested in applications of homological algebra and prime characteristic tools to commutative algebra. Her recent research relates to topics such as symbolic powers, local cohomology, and the homological algebra of local rings. She is also interested in computational algebra problems.
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.
Postdoctoral associate Levi Heath works in Gromov-Witten theory and algebraic geometry more broadly. He studies moduli spaces of curves and of maps to varieties/orbifolds.
Assistant Professor Jack Jeffries works in commutative algebra. Some of his recent interests include differential operators, local cohomology, positive/mixed characteristic techniques, and applications to neuroscience.
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 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.
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
Jordan Barret
Advised by: Jack Jeffries
Allison Ganger
Advised by: Brian Harbourne
Juliann Geraci
Advised by: Alexandra Seceleanu
Nawaj KC
Advised by: Mark Walker and Jack Jeffries
Katie Lee
Advised by: Brian Harbourne
David Lieberman
Advised by: Jack Jeffries
Taylor Murray
Advised by: Jack Jeffries
Shah Roshan Zamir
Advised by: Alexandra Seceleanu
Andrew Soto Levins
Advised by: Mark Walker
Advised by: Brian Harbourne
Recent Graduates
Matthew Bachmann (PhD 2023)
Advised by: Mark Walker
Laila Awadalla (PhD 2022)
Advised by: Tom Marley
Michael DeBellevue (PhD 2022)
Advised by: Alexandra Seceleanu and Mark Walker
Taran Funk (PhD 2021)
Advised by: Tom Marley
Su Ji Hong (PhD 2021)
Advised by: Tri Lai
Eric Hopkins (PhD 2021)
Advised by: Mark Walker
Erica Hopkins (PhD 2021)
Advised by: Mark Walker and Alexandra Seceleanu
Jake Kettinger (PhD 2023)
Advised by: Brian Harbourne
Amadeus Martin (PhD 2021)
Advised by: Mark Walker
Benjamin Drabkin (PhD 2020)
Advised by: Alexandra Seceleanu
Nicholas Packauskas (PhD 2019)
Advised by: Lucho Avramov and Mark Walker
Josh Pollitz (PhD 2019)
Advised by: Lucho Avramov and Mark Walker
Eric Canton (PhD 2018)
Advised by: Mark Walker and Brian Harbourne
Mohsen Gheibi (PhD 2018)
Advised by: Mark Walker and Roger Wiegand
Seth Lindokken (PhD 2018)
Advised by: Mark Walker
Matthew Mills (PhD 2018)
Advised by: Kyungyong Lee
Neil Steinburg (PhD 2018)
Advised by: Tom Marley and Roger Wiegand
Solomon Akesseh (PhD 2017)
Advised by: Brian Harbourne
Brittney Falahola (PhD 2017)
Advised by: Tom Marley
Luigi Ferraro (PhD 2017)
Advised by: Lucho Avramov
John Myers (PhD 2017)
Advised by: Lucho Avramov
Andrew Windle (PhD 2017)
Advised by: Mark Walker
Doug Dailey (PhD 2016)
Advised by: Tom Marley
Becky Egg (PhD 2016)
Advised by: Tom Marley
Jason Lutz (PhD 2016)
Advised by: Luchezar Avramov and Srikanth Iyengar
Peder Thompson (PhD 2016)
Advised by: Mark Walker
Michael Brown (PhD 2015)
Advised by: Mark Walker
Katharine Shultis (PhD 2015)
Advised by: Brian Harbourne and Roger Wiegand
Marcus Webb (PhD 2015)
Advised by: Tom Marley
Zheng Yang (PhD 2015)
Advised by: Lucho Avramov
Jason Hardin (PhD 2014)
Advised by: Mark Walker
Amanda Croll (PhD 2013)
Advised by: Srikanth Iyengar
Annika Denkert (PhD 2013)
Advised by: Brian Harbourne
Courtney Gibbons (PhD 2013)
Advised by: Luchezar Avramov and Roger Wiegand
Michael Janssen (PhD 2013)
Advised by: Brian Harbourne
Xuan Yu (PhD 2013)
Advised by: Mark Walker
Ela Celikbas (PhD 2012)
Advised by: Sylvia Wiegand
Brian Johnson (PhD 2012)
Advised by: Tom Marley