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:

  • Primary decomposition of modules: a computational differential approach (joint with Yairon Cid-Ruiz). J. Pure Appl. Algebra (2021), to appear (arXiv:2104.03385).

  • The 4 x 4 orthostochastic variety (joint with Papri Dey). Exp. Math. (2021), to appear (Journal ref, arXiv:2001.10691).

  • Noetherian operators and primary decomposition (joint with Marc Härkönen, Robert Krone and Anton Leykin). J. Symbolic Comput. 110 (2021), pp. 1--23 (Journal ref, arXiv:2006.13881).

  • Avoidance and Absorbance (joint with Abolfazl Tarizadeh), J. Algebra 582 (2020), pp. 88--99 (Journal ref, arXiv:2006.12332).

  • Infinite prime avoidance, Beitr. Algebra Geom. 62 (2020), pp. 587--593 (Journal ref, arXiv:1710.05496).

  • 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 unit groups of curves (joint with Sameera Vemulapalli and Leon Zhang), J. Symbolic Comput. 104 (2020), pp. 236--255 (Journal ref, arXiv:1808.02742).

  • 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).

  • Surjections of unit groups and semi-inverses, J. Commut. Algebra (2020), to appear (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):

  • Sums of Squares, Hankel index and Almost Real Rank (joint with Greg Blekherman and Jaewoo Jung) (arXiv:2108.06635).

  • Computing multiplicity sequences (joint with Youngsu Kim and Jonathan Montaño) (arXiv:2103.14175).

  • Noetherian Operators in Macaulay2 (joint with Yairon Cid-Ruiz, Marc Härkönen, Robert Krone and Anton Leykin) (arXiv:2101.01002).

  • 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).