**Research**

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)

Submitted.*Depth functions and symbolic depth functions of homogeneous ideals*(with Ngo Viet Trung)

Submitted.*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)

Submitted.*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)

Mathematische Zeitschrift.*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.

**Publications in
non-refereed journals**

*The graph and the image of a rational map from*P^{n}*to*P^{m}. 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.**Honours****Dissertation.***Cycles in graphs*.

Curtin University of Technology, Perth, Australia.