Last updated: November 2021
Publications and Preprints
The reviews of my published
papers can be found on MathSciNet. Copies of manuscripts are on the arXiv.
- Papers submitted and accepted
- Newton-Okounkov body, Rees algebra, and analytic spread of graded families of monomial ideals (with Thai Thanh Nguyen)
- Depth functions and symbolic depth functions of homogeneous ideals (with Ngo Viet Trung)
- Saturation bounds for smooth varieties (with Lawrence Ein and Robert Lazarsfeld)
To appear in Algebra and Number Theory.
- The Alexander-Hirschowitz theorem and related problems (with Paolo Mantero)
- Density of f-ideals and f-ideals of mixed small degrees (with Graham Keiper, Hasan Mahmood and Jonathan O'Rourke)
To appear in Mathematica Scandinavica.
- Chudnovsky's Conjecture and the stable Harbourne-Huneke containment (with Sankhaneel Bisui, Eloísa Grifo and Thai Thanh Nguyen)
To appear in Transactions of American Mathematical Societ.
- Published in 2021-present
- Demailly's Conjecture and the containment problem (with Sankhaneel Bisui, Eloísa Grifo and Thai Thanh Nguyen)
Journal of Pure and Applied Algebra 226 (2022), no. 4, Paper No. 106863, 21 pp.
- Resurgence numbers of fiber products of projective schemes (with Sankhaneel Bisui, A.V. Jayanthan and Abu C. Thomas)
Collectanea Mathematica 72 (2021), no. 3, 605-614.
- Symbolic powers of cover ideals of graphs and Koszul property (with Yan Gu and Joseph Skelton)
International Journal of Algebra and Computation 31 (2021), no. 5, 865-881.
- Max Min vertex cover and the size of Betti tables (with Takayuki Hibi)
Annals of Combinatorics 25 (2021), no. 1, 115-132.
- Depth functions of powers of homogeneous ideals (with Hop D. Nguyen, Ngo Viet Trung and Tran Nam Trung)
Proceedings of American Mathematical Society 149 (2021), no. 5, 1837-1844.
- Published in 2016-2020
- Ideals of powers and powers of ideals: intersecting algebra, geometry, and combinatorics (with Enrico Carlini, Brian Harbourne and Adam Van Tuyl)
Lecture Notes of the Unione Matematica Italiana, 27. Springer, Cham, 2020. xix+159 pp. ISBN: 978-3-030-45246-9; 978-3-030-45247-6.
- Regularity of powers of edge ideals: from local properties to global bounds (with Arindam Banerjee and Selvi Beyarslan)
Algebraic Combinatorics 3 (2020), no. 4, 839-854.
- Depth of powers of squarefree monomial ideals (research) (with Louiza Fouli and Susan Morey)
Advances in Mathematical Sciences, 161-171.
Association for Women in Mathematics Series, 21, Springer, Cham, 2020.
- Symbolic powers of edge ideals of graphs (with Yan Gu, Jonathan L. O'Rourke and Joseph W. Skelton)
Communications in Algebra 48 (2020), no. 9, 3743-3760.
- Initially regular sequences and depths of ideals (with Louiza Fouli and Susan Morey)
Journal of Algebra 559 (2020), 33-57.
- Fiber invariants of projective morphisms and regularity of powers of ideals (with Sankhaneel Bisui and Abu C. Thomas)
Acta Mathematica Vietnamica 45 (2020), no. 1, 183-198..
- Symbolic powers of sums of ideals (with Dang Hop Nguyen, Ngo Viet Trung and Tran Nam Trung)
- Edge ideals of oriented graphs (with Kuei-Nuan Lin, Susan Morey, Enrique Reyes and Rafael H. Villarreal)
International Journal of Algebra and Computation 29 (2019), no. 3, 535-559.
- Membership criteria and containments of powers of monomial ideals (with Ngo Viet Trung)
Acta Mathematica Vietnamica 44 (2019), no. 1, 117-139.
- Algebraic properties of toric rings of graphs (with Selvi Beyarslan and Augustine O'Keefe)
Communications in Algebra 47 (2019), no. 1, 1-16.
- Regularity of edge ideals and their powers (with Arindam Banerjee and Selvi Beyarslan)
Advances in Algebra, 17-52.
Springer Proceedings in Mathematics and Statistics 277, Springer, Cham, 2019.
- Depth and regularity modulo a principal ideal (with Giulio Caviglia, Jürgen Herzog, Manoj Kummini, Naoki Terai and Ngo Viet Trung)
Journal of Algebraic Combinatorics 49 (2019), no. 1, 1-20.
- Symbolic powers of monomial ideals (with Susan M. Cooper, Robert J.D. Embree and Andrew H. Hoefel)
Proceedings of Edinburg Mathematical Society (2) 60 (2017), no. 1, 39-55.
- Depth and regularity of powers of sums of ideals (with Ngo Viet Trung and Tran Nam Trung)
Mathematische Zeitschrift 282 (2016), no. 3-4, 819-838.
- Growth of graded families of ideals (with Pham An Vinh)
Journal of Algebra, 452 (2016), 311-323.
- Published in 2011-2015
- Regularity of powers of forests and cycles (with Selvi Beyarslan and Tran Nam Trung)
Journal of Algebraic Combinatorics 42 (2015) no. 4, 1077-1095.
- Betti numbers of subgraphs (with Duc Ho)
Australasian Journal of Combinatorics 63 (2015), 182-195.
- Normal 0-1 polytopes (with Kuei-Nuan Lin)
SIAM Journal of Discrete Mathematics 29 (2015), no. 1, 210-223.
- Partial colorings, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes (with Jennifer Biermann, Chris Francisco and Adam Van Tuyl)
Journal of Commutative Algebra 7 (2015) no. 3, 337-352.
- Squarefree monomial ideals that fail the persistence property and non-increasing depth (with Mengyao Sun)
Acta Mathematica Vietnamica, 40 (2015), no. 1, 125-137.
- Results on the regularity of squarefree monomial ideals (with Russ Woodroofe)
Advances in Applied Mathematics, 58 (2014), 21-36.
- Regularity of squarefree monomial ideals
In S. Cooper and S. Sather-Wagstaff (Ed.) Connections between Algebra, Geometry and Combinatorics, 251-276. Springer Proceedings in Mathematics and Statistics, Vol. 56, 2014.
- Eventual shape of Betti tables of powers of ideals (with Amir Bagheri and Marc Chardin)
Mathematical Research Letters 20 (2013), no. 6, 1033-1046.
- Pure O-sequences and matroid h-vectors (with Fabrizio Zanello and Erik Stokes)
Annals of Combinatorics 17 (2013), no. 3, 495-508.
- Powers of squarefree monomial ideals and combinatorics (with Chris A. Francisco and Jeff Mermin)
In I. Peeva (Ed.) Commutative Algebra, 373-392, Springer, 2013.
- Hilbert functions of double point schemes in P^2 (with A. V. Geramita)
Vietnam Journal of Mathematics 39 (2011), 327-342.
- Path ideals of rooted trees and their graded Betti numbers (with Rachelle R. Bouchat and Augustine O'Keefe)
Journal of Combinatorial Theory, Series A 118 (2011), 2411-2425.
- Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals (with Francisco and Van Tuyl)
Journal of Algebra 331 (2011), 224-242.
- Asymptotic linearity of regularity and a*-invariant of powers of ideals
Mathematical Research Letters 18 (2011), no. 1, 1-9.
- Published in 2006-2010
- A conjecture on critical graphs and connections to the persistence of associated primes (with C. A. Francisco and A. Van Tuyl)
Discrete Math. 310 (2010), 2176-2182.
- Associated primes of monomial ideals and odd holes in graphs (with Chris A. Francisco and Adam Van Tuyl)
Journal of Algebraic Combinatorics 32 (2010), no. 2, 287-301.
- Embedded associated primes of powers of square-free monomial ideals (with Susan Morey)
Journal of Pure Applied Algebra 214 (2010), no. 4, 301-308.
- Splittings of monomial ideals (with Chris A. Francisco and Adam Van Tuyl)
Proc. Amer. Math. Soc. 137 (2009), 3271-3282.
- Cohen-Macaulay admissible clutters (with Susan Morey and Rafael H. Villarreal)
Journal of Commutative Algebra 1 (2009), 463-480.
- Cohen-Macaulay multigraded modules (with C-Y. Jean Chan and Christine Cumming)
Illinois Journal of Mathematics 52 (2008), no. 4, 1147-1163.
- Monomial ideals, edge ideals of hypergraphs, and their minimal graded Betti numbers (with Adam Van Tuyl)
Journal of Algebraic Combinatorics 27 (2008), no. 2, 215-245.
- Whiskers and sequentially Cohen-Macaulay graphs (with Chris A. Francisco)
Journal of Combinatorial Theory, Series A 115 (2008), no. 2, 304-316.
- Resolution of square-free monomial ideals via facet ideals: a survey (with Adam Van Tuyl)
Contemporary Mathematics 448 (2007), 91-117.
- Adjoint line bundles and syzygies of projective varieties
Vietnam Journal of Mathematics 35 (2007), no. 2, 135-151.
- Minimal free resolutions and asymptotic behaviour of multigraded regularity (with Brent Strunk)
Journal of Algebra 311 (2007), no. 2, 492-510.
- Multigraded regularity, a*-invariants and the minimal free resolution
Journal of Algebra 310 (2007), no. 1, 156-179.
- Splittable ideals and the resolutions of monomial ideals (with Adam Van Tuyl)
Journal of Algebra 309 (2007), no. 1, 405-425.
- Homology multipliers and the relation type of parameter ideals (with Ian M. Aberbach and Laura Ghezzi)
Pacific Journal of Mathematics 226 (2006), no. 1, 1-40.
- Toroidalization of generating sequences in dimension two function fields (with Olga Kashcheyeva and Laura Ghezzi)
Journal of Algebra 301 (2006), no. 2, 838-866.
- Published in 2001-2005
- Asymptotic behaviour of the length of local cohomology (with S.Dale Cutkosky, Hema Srinivasan and Emanoil Theodorescu)
Canadian Journal of Mathematics 57 (2005), no. 6, 1178-1192.
- Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups (with N.V. Trung)
Transactions of American Mathematical Society 357 (2005), no. 9, 3655-3672.
- Arithmetic Macaulayfication of projective schemes (with S.Dale Cutkosky)
Journal of Pure and Applied Algebra. 201 (2005), no. 1-3, 49-61. (in the special volume for Vasconcelos).
- The depth of the associated graded ring of ideals with any reduction number (with Ian M. Aberbach and Laura Ghezzi)
Journal of Algebra 276 (2004), 168-179.
- Projective embeddings of projective schemes blown up at subschemes
Mathematische Zeitschrift 246 (2004), no 1-2, 111-124.
- The regularity of points in multiprojective spaces (with A. VanTuyl)
Journal of Pure and Applied Algebra 187 (2004), no 1-3, 153-167.
- On the Rees algebra of certain codimension two perfect ideals
Manuscripta Mathematica 107 (2002), 479-501.
- Box-shaped matrices and the defining ideal of certain blown up surfaces
Journal of Pure and Applied Algebra 167 (2002), no 2-3, 203-224.
- Computing the Spreading and Covering numbers (with E. Carlini and A. Van Tuyl)
Communications in Algebra 29 (2001), no 12, 5687-5699.
- The graph and the image of a rational
map from Pn to Pm. The Curves Seminar at Queen's. Vol. XII. 141-162, Queen's
Papers in Pure and Appl. Math. 114, Queen's Univ., Kingston, ON, 1998.
(with A. Van Tuyl).
- Tutorial 2: A Chess Puzzle. Proceedings of COCOA VI International
School, Queen's Papers in Pure and Appl. Math. 120 (2001), 215-221.
(with E. Carlini and A. Van Tuyl).
- Tutorial 3: Hilbert Function of Points. Proceedings
of COCOA VI International School, Queen's Papers in Pure and
Appl. Math. 120 (2001), 227-237. (with E.
Carlini and A. Van Tuyl).
- Tutorial 5: The Ideal Generation Conjecture. Proceedings
of COCOA VI International School, Queen's Papers in Pure and Appl Math. 120 (2001), 245-262. (with E. Carlini and A. Van Tuyl).
- Tutorial 6: The Minimal Resolution Conjecture. Proceedings
of COCOA VI International School, Queen's Papers in Pure and
Appl. Math. 120 (2001), 263-273. (with E. Carlini and A. Van Tuyl).
Thesis and Dissertation
- PhD Thesis. Rational surfaces from an algebraic
perspective. (PDF, PS).
Queen's University, Kingston, Canada.
Dissertation. Cycles in graphs.
Curtin University of Technology, Perth, Australia.