Commutative Algebra with applications to
Algebraic Geometry: Frobenius complexity, intersection algebras, tight closure theoy, multiplicity theory, Hilbert and Hilbert-Kunz functions, integral closure of
ideals, homological conjectures, filtrations of ideals, local cohomology and singularities of local rings. I am also interested in applications of algebra to digital circuit design. Publication List
Honors and Awards:
National Science Foundation, 1910368 (P.I.) –SHF:Small: Collaborative Research: Rectification of Arithmetic Circuits with Craig Interpolants in Algebraic Geometry, $189,861, 06/15/2019-05/31/2022.
National Science Foundation, 1300835 (P.I.) –SFH: Small: Collaborative Proposal: Efficient Computer Algebra Techniques for Scalable Verification of Galois Field Arithmetic Circuits, $188,241 ($62,787 annually), 08/01/2013-07/31/2016-no cost extension until 01/31/2018.
National Science Foundation (co-P.I.) - Conference Grant for Recent developments in positive characteristic methods in commutative algebra: Frobenius opeartors and Cartier algebras, $24,530 02/15/2015-01/31/2016.
STEM Mini-grant, STEM II Funding University System of Georgia (co-P.I.), Reading, Writing and Comprehending Mathematical Proofs and Transitioning to Secondary School Classroom, 05/01/2014-06/30/2015, $6340.
National Security Agency, Young Investigators Grant (P.I.) - Contributions to problems on Hilbert-Kunz multiplicities and local cohomology
in
positive characteristic, $39,914, 03/01/2013-02/28/2014.
National Security Agency, Young Investigators Grant (P.I.) - Hilbert-Kunz multiplicities and local cohomology questions in
positive characteristic, $14,991, 01/2010-01/2012.
National Security Agency/University of South Carolina Subcontract (P.I.) - GSU-USC Commutative
Algebra Seminar, $15,280 ($7,640 annually) 10/2008-10/2010.
National Security Agency, Young Investigators Grant (P.I.) - Special chapters in the theory of rings of positive
characteristic, $29,130 ($14,565 annually), 01/2007-12/2008.
NSF Grant CCF-0515010 - Collaborative research: a new theoretical and algorithmic frame work for RTL datapath verification using polynomial algebra over finite
rings, 2005-2006.
Research Initiation Grant, Georgia State University, 2005-2006.
Outstanding Instructor Award, University of Utah, April 2004
Rackham Predoctoral Fellowship, University of Michigan, 2000-2001.
National Merit Fellowship, University of Bucharest, Romania, 1991-1996.
Most Recent Talks:
• (September 2018), Generating functions and the twisted construction for graded rings, Special Session on Commutative Algebra, Amer. Math. Soc. Sectional Meeting, Univ of Delaware.
• (June 2018), The generating function of the twisted construction of a local ring, “Nicolae Radu Algebra Seminar”, University of Bucharest, Romania.
• (April 2018), The Frobenius complexity, its generating function and non-standard gradings on the polynomial ring over a field, Meeting on Applied Algebraic Geometry, Georgia Tech.
• (January 2018), The Frobenius complexity in graded setting, Commutative Algebra Seminar, University of Utah.
• (September 2017), The free resolution of fan algebras in the plane, Commutative Algebra Seminar, University of Michigan.
• (June 2017), On certain aspects of the Frobenius homomorphism, Commutative Algebra meets Algebraic Geometry International Conference, Bucharest.
• (March 2017), On finiteness of the Frobenius complexity, AMS Southeastern Meeting, Special Session on Commutative Algebra, Charleston, South Carolina.
• (November 2016), Free Resolution of Fan Algebras of Principal Ideals in the Plane, North Carolina State University, AMS Southeastern Meeting, Special Session in Homological Methods in Commutative Algebra.
• (April 2016), Frobenius Complexity, University of Michigan, Commutative Algebra Seminar
• (March 2016), Fan Algebras, University of Georgia, AMS Southeastern Meeting, Special Session in Commutative Algebra.
• (October 2015),The Frobenius Complexity of Determinantal Rings, University of Memphis, Special Session on Recent Advances in Commutative Algebra.
• (July 2015),The Frobenius Complexity of a Local Ring, University of Kentucky, International Conference in Homological Algebra in Honor of E. Enochs.
• (June 2015),The Frobenius Complexity of a Local Ring, University of Barcelona, Algebra Seminar.
• (June 2015),The Frobenius Complexity of a Local Ring, Iasi, The Congress of Romanian Mathematicians, Commutative Algebra Session.
• (April 2015), The Frobenius Complexity of Local Rings, Commutative Algebra Seminar, Department of Mathematics, University of Utah.
• (February 2015), Intersection algebras, Colloquium, Department of Mathematics, University of Mississippi.
Teaching Experience:
Georgia State University:
Modern Algebra I and II, Abstract Algebra I and II, Discrete Mathematics, Applied Combinatorics, Intro to Math Modeling, Applied Algebra-Polynomials, Complex Analysis, Linear Algebra I
University of Utah:
Business Algebra, Geometry for Teachers, Applied Complex
Variables, Foundations of Analysis II, Commutative Algebra
University of Michigan
Calculus I, Ordinary Differential Equations
Professional service:
Co-organizer (with Yongwei Yao) of the Special Session in Commutative Algebra at Southeastern Meeting of the Amer. Math. Soc. at Vanderbilt University, Nashville, April 14-15 2018.
Co-organizer (with Carlos D’Andrea) of the mini-symposium “Free resolutions governed by geometric and/or combinatorial data”, SIAM on Applied Algebraic Geometry Meeting, August 4 2017, Georgia Tech, Atlanta.
Co-organizer (with Yongwei Yao) of the meeting “Recent developments in positive characteristic methods in commutative algebra: Frobenius operators and Cartier algebras”, 03/13/15-03/15/15, Georgia State University, Atlanta.
Co-organizer (with Cristodor Ionescu) of the Special Session in Commutative Algebra at the Joint International Meeting between the Amer. Math. Soc. and the Romanian Math. Soc. in Romania, June 26-30 2013.
Co-organizer (with Yongwei Yao) of the meeting “Commutative Algebra at Georgia State”, 02/10/12-02/12/12, Georgia State University.
Co-organizer (with Yongwei Yao) of the meetings "Commutative Algebra in the Southeast" at Georgia State University. A
national meetings was held between September 24-26 2010, and a regional meeting between March 20-21 2010.
Co-organizer (together with M. Blickle, M. Brion, S. Kumar, M. Mustata, K. Schwede) of the conference "Frobenius splittings in algebraic geometry, commutative algebra and representation theory" held at the University of Michigan, May 17-May 22 2010
Organizer (with Yongwei Yao) of the regional and national meetings
Commutative algebra meetings in the Southeast Georgia State University, , Oct 20 2006, March 17-18 2007, Sept 16 2007, April 25-27 2008, September 13-14 2009.
Organizer (with Andy Kustin and Adela Vraciu) of the special session Commutative algebra and algebraic geometry AMS South-East Section,
March 2007, Davidson College, NC.
Organizer (with Adela Vraciu) of the special session Local and homological algebra AMS South-East Section, October 2004, Nashville, TN.
Organizer (with Anurag K. Singh and Karen E. Smith) of the special session Commutative algebra AMS Central Section, March 2002, Ann Arbor, MI.
Referee for various mathematical journals and reviewer for Mathematical Reviews and Zentralblatt. Click here to see my
reviews for Mathematical Reviews (if your institution subscribes to this database).
Significant Activities:
Graduate Director for Mathematics, Georgia State University, 2015-2018.