Justin Chen

My research interests include commutative algebra, (numerical) algebraic geometry and combinatorics, with a focus on computation particularly with Macaulay2.

From 2021 - 2022 I was a Bridge postdoc at ICERM.

From 2018 - 2021 I was a Hale postdoc at Georgia Tech, mentored by Anton Leykin.

I received a Ph.D. in Math in 2018 from the University of California, Berkeley. My advisor was David Eisenbud.

I received a B.S. in Math in 2012 from Purdue University, where I first learned commutative algebra from Bernd Ulrich.

You can reach me at jchen AT math.berkeley.edu. My CV can be found here. My thesis is available here.

Publications (Scholar):

Local dual spaces and primary decomposition (joint with Marc Härkönen and Anton Leykin), J. Symbolic Comput. 128 (2025), 102400 (Journal ref, arXiv:2401.00597).
Units of Hyperelliptic Curves over F2 (joint with Vishal Muthuvel), Rocky Mountain J. Math. 55 (2025), no. 2, pp. 333--346 (Journal ref, arXiv: 2306.04838, code available at GitHub).
On the ideal avoidance property (joint with Abolfazl Tarizadeh), J. Pure Appl. Algebra 228 (2024), no. 3, 107500 (Journal ref, arXiv:2203.04256).
Sums of Squares, Hankel index and Almost Real Rank (joint with Greg Blekherman and Jaewoo Jung), Forum of Math, Sigma 12 (2024) (Journal ref, arXiv:2108.06635).
Primary decomposition of modules: a computational differential approach (joint with Yairon Cid-Ruiz), J. Pure Appl. Algebra 226 (2022), no. 10, 107080 (Journal ref, arXiv:2104.03385).
Computing multiplicity sequences (joint with Youngsu Kim and Jonathan Montaño), J. Softw. Alg. Geom. 14 (2024), no. 1, pp. 13--18 (Journal ref, arXiv:2103.14175).
Noetherian Operators in Macaulay2 (joint with Yairon Cid-Ruiz, Marc Härkönen, Robert Krone and Anton Leykin), J. Softw. Alg. Geom. 12 (2022), no. 1, pp. 33--41 (Journal ref, arXiv:2101.01002).
Noetherian operators and primary decomposition (joint with Marc Härkönen, Robert Krone and Anton Leykin), J. Symbolic Comput. 110 (2022), pp. 1--23 (Journal ref, arXiv:2006.13881).
Avoidance and Absorbance (joint with Abolfazl Tarizadeh), J. Algebra 582 (2021), pp. 88--99 (Journal ref, arXiv:2006.12332).
The 4 x 4 orthostochastic variety (joint with Papri Dey), Exp. Math. 32 (2021), no. 4, pp. 692--700 (Journal ref, arXiv:2001.10691).
Free resolutions of function classes via order complexes (joint with Chris Eur, Greg Yang and Mengyuan Zhang), Adv. Appl. Math. 120 (2020), 102074 (Journal ref, arXiv:1909.02159).
Computing symmetric determinantal representations (joint with Papri Dey), J. Softw. Alg. Geom. 10 (2020), no. 1, pp. 9--15 (Journal ref, arXiv:1905.07035, code available at GitHub).
Computing unit groups of curves (joint with Sameera Vemulapalli and Leon Zhang), J. Symbolic Comput. 104 (2021), pp. 236--255 (Journal ref, arXiv:1808.02742).
Infinite prime avoidance, Beitr. Algebra Geom. 62 (2020), pp. 587--593 (Journal ref, arXiv:1710.05496).
Surjections of unit groups and semi-inverses, J. Commut. Algebra 13 (2020), no. 3, pp. 323--331 (Journal ref, arXiv:1710.05492).
Numerical Implicitization (joint with Joe Kileel), J. Softw. Alg. Geom. 9 (2019), no. 1, pp. 55--63 (Journal ref, arXiv:1610.03034, code available at GitHub).
Matroids: A Macaulay2 package, J. Softw. Alg. Geom. 9 (2019), no. 1, pp. 19--27 (Journal ref, arXiv:1511.04618, code available at GitHub).
Graded-irreducible modules are irreducible (joint with Youngsu Kim), Comm. Algebra 45 (2017), no. 5, pp. 1907--1913 (Journal ref, arXiv:1508.07518).

Preprints (on arXiv):

Representing matroids via pasture morphisms (joint with Tianyi Zhang) (arXiv:2307.14275).
Flat maps to and from Noetherian rings (arXiv:1711.04958).
Mono: an algebraic study of torus closures (arXiv:1710.04614).
Closed points on schemes (arXiv:1708.06494).
Invertible sums of matrices (arXiv:1603.06696).

Miscellaneous

The determinant is the most natural multiplicative function on matrices

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