For more information visit my personal website.
I was awarded the 2018 Harold and Esther Edgerton Junior Faculty Award for creative research, extraordinary teaching abilities, and academic promise.
In the news: When life gives you lemons, make mathematicians, an article in the Notices of the AMS about the Polymath program - a large scale online REU I mentored.
Videos from Selected Talks
- Reflection arrangements, syzygies, and the containment problem Fellowship of the Ring national commutative algebra seminar organized by MSRI, Jul 2020
- Connected sums of graded artinian Gorenstein algebras and the Lefschetz properties BIRS workshop New Trends in Syzygies in Banff, June 2018
- Combinatorial methods for symbolic powers CMO Workshop on Symbolic and Ordinary Powers of Ideals in Oaxaca, May 2017
- A hands-on approach to tensor product surfaces of bidegree (2,1) CMO Workshop on Computational Algebra and geometric Modeling in Oaxaca, Aug 2016
My research is in commutative algebra, with an interest in computational algebra, homological methods and connections to algebraic geometry.
Below are some of my publications:
- Real powers of monomial ideals (with Polymath) .
- Consequences of the packing problem (with Polymath) J. Algebraic Combinatorics, forthcoming.
- Convex bodies and asymptotic invariants for powers of monomial ideals (with Polymath).
- Symbolic Rees algebras (with E. Grifo).
- Canonical Resolutions over Koszul Algebras (with E. Faber, M. Juhnke-Kubitzke, H. Lindo, C. Miller, R. R.G.) Proceedings of the WICA Conference, forthcoming.
- Quadratic Gorenstein algebras with many surprising properties (with J. McCullough) Arch. Math. (Basel) 115 (2020), no. 5, 509-521.
- Singular loci of reflection arrangements and the containment problem (with B. Drabkin) Math. Z., forthcoming..
- Implicitization of tensor product surfaces via virtual projective resolutions (with E. Duarte) Mathematics of Computation 89 (2020), no. 326, 3023-3056.
- Betti numbers of symmetric shifted ideals (with J. Biermann, H. de Alba, F. Galetto, S. Murai, U. Nagel, A. O’Keefe, T. Römer) J. Algebra 560 (2020), 312–342.
- Connected sums of graded artinian Gorenstein algebras and Lefschetz properties (with A. Iarrobino and C. McDaniel) J. Pure Applied Algebra, forthcoming.
- General minimum distance functions and algebraic invariants of Geramita ideals (with S. Cooper, Ș. Tohăneanu, M. Vaz Pinto and R. Villarreal), Advances in Applied Mathematics 112 (2020) 101940.
- Frieze varieties: A characterization of the finite-tame-wild trichotomy for acyclic quivers (with K. Li, L. Li, M. Mills and R. Schiffler) Advances in Math. 367 (2020).
- Computations involving symbolic powers and the Macaulay2 package SymbolicPowers (with B. Drabkin, E. Grifo, B. Stone). J. Software for Algebra and Geometry vol. 9, no.1 (2019), 71–80.
- Negative curves on symmetric blowups of the projective plane, resurgences and Waldschmidt constants (with Th. Bauer, S. Di Rocco, B. Harbourne, J. Huizenga, T. Szemberg) International Math. Research Notices IMRN 2019, no. 24, 7459–7514.
- Symbolic powers of codimension two Cohen-Macaulay ideals (with S. Cooper, G. Fatabbi, E. Guardo, A. Lorenzini, J. Migliore, U. Nagel, J. Szpond, A. Van Tuyl) Comm. Algebra 48 (2020), no.11, 4663-4680.
- The Waldschmidt constant for squarefree monomial ideals (with C. Bocci, S. Cooper, E. Guardo, B. Harbourne, M. Janssen, U. Nagel, A. Van Tuyl, T. Vu) J. Algebraic Combinatorics 44 (2016) no. 4, 875-904.
- A homological criterion for the failure of containment of the symbolic cube in the square of some ideals of points in P^2 J. Pure Applied Algebra 219 (2015) no.11, 4857-4871.
- Determinants of incidence and Hessian matrices arising from the vector space lattice (with S. Nasseh and J. Watanabe) J. Commut. Algebra 11 (2019) no. 1, 131-154.
- Resurgences for ideals of special point configurations in P^N coming from hyperplane arrangements (with M. Dumnicki, B. Harbourne, U. Nagel, T. Szemberg and H. Tutaj-Gasińska) J. Algebra 443 (2015), 383-394.
- A tight bound on the projective dimension of four quadrics (with C. Huneke, P. Mantero and J. McCullough) with accompanying Macaulay 2 code. J. Pure Appl. Algebra 222 (2018) no. 9, 2524-2551.
- A multiplicity bound for graded rings and a criterion for the Cohen-Macaulay property (with C. Huneke, P. Mantero and J. McCullough) Proc. Amer. Math. Soc. 143 (2015) no.6, 2365-2377.
- Containment counterexamples for ideals of various configurations of points in P^N (with B. Harbourne) J. Pure Appl. Algebra 219 (2015), 1062-1072.
- The projective dimension of codimension two algebra presented by quadrics (with C. Huneke, P. Mantero and J. McCullough) J. Algebra 393 (2013), 170-186.
- Multiple structures with arbitrarily large projective dimension on linear subspaces. (with C. Huneke, P. Mantero and J. McCullough) J. Algebra 447 (2016), 183-205
- Computations in intersection rings of flag bundles (with D. Grayson and M. Stillman).
- Bounding projective dimension (with J. McCullough) a chapter in the book Commutative Algebra, Springer-Verlag London, 2013.
- Syzygies and singularities of tensor product surfaces of bidegree (2,1) (with H. Schenck and J. Validashti), Math. Comp. 83 (2014), 1337-1372.
- Syzygy theorems via comparison of order ideals on a hypersurface (with P. A. Griffith) J. Pure Appl. Algebra 216 (2012), no. 2, 468-479.
- Inverse systems, fat points and the weak Lefschetz property (with B. Harbourne and H. Schenck) J. Lond. Math. Soc. (2) 84 (2011), no. 3, 712-730.
- The Weak Lefschetz Property and powers of linear forms in K[x, y, z] (with H. Schenck) Proc. Amer. Math. Soc. 138 (2010), no. 7, 2335-2339.