Curriculum vitae

Research:

My interests are in computational algebraic geometry and commutative algebra.

Papers:

• Dimensions of level-1 group-based phylogenetic networks,
     with Elizabeth Gross and Samuel Martin
     Bulletin of Mathematical Biology Vol. 86.8, 2024.
• Noetherian operators in Macaulay2,
     with Justin Chen, Yairon Cid-Ruiz, Marc Härkönen and Anton Leykin
     Journal of Software for Algebra and Geometry Vol. 12.1, 2022.
• Multiple typical ranks in matrix completion,
     with Mareike Dressler
     Linear Algebra and Its Applications Vol. 710, 2025.
• Noetherian operators and primary decomposition,
     with Justin Chen, Marc Härkönen and Anton Leykin
     Journal of Symbolic Computation Vol. 110, 2021.
• Uniqueness of nonnegative matrix factorizations by rigidity theory,
     with Kaie Kubjas
     SIAM Journal on Matrix Analysis and Applications Vol. 42.1, 2021.
• The tropical Cayley-Menger variety,
     with Daniel Irving Bernstein
     SIAM Journal on Discrete Math Vol. 33.3, 2019.
• Average Behavior of Minimal Free Resolutions of Monomial Ideals,
     with Jesús A. De Loera, Serkan Hoşten and Lily Silverstein
     Proceedings of the AMS Vol. 147.8, 2019.
• Dimensions of Group-based Phylogenetic Mixtures,
     with Hector Baños, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Pamela E. Harris, Colby Long, Allen Stewart and Robert Walker
     Bulletin of Mathematical Biology Vol. 81, 2018.
• The degree of SO(n),
     with Madeline Brandt, DJ Bruce, Taylor Brysiewicz and Elina Robeva
     Combinatorial Algebraic Geometry (book), 2016.
• Phylogenetic trees,
     with Hector Baños, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Pamela E. Harris, Colby Long, Allen Stewart and Robert Walker
     Journal of Software for Algebra and Geometry Vol. 11.1, 2021.
• Equivariant Gröbner bases,
     with Chris Hillar and Anton Leykin
     The 50th Anniversary of Gröbner Bases (book), 2018.
• Hilbert series of symmetric ideals in infinite polynomial rings via formal languages,
     with Anton Leykin and Andrew Snowden
     Journal of Algebra Vol. 485, 2017.
• Equivariant Gröbner bases of symmetric toric ideals,
     Proceedings of ISSAC 2016.
• Numerical algorithms for detecting embedded components,
     with Anton Leykin
     Journal of Symbolic Computation Vol. 82, 2017.
• Eliminating dual spaces,
     with Anton Leykin
     Journal of Symbolic Computation Vol. 79, 2017.
• Equivariant lattice generators and Markov bases,
     with Thomas Kahle and Anton Leykin
     Proceedings of ISSAC 2014.
• Noetherianity for infinite-dimensional toric varieties,
     with Jan Draisma, Rob Eggermont and Anton Leykin
     Algebra & Number Theory Vol. 9.8, 2015.
• Numerical algorithms for dual bases of positive-dimensional ideals,
     Journal of Algebra and Its Applications, Vol. 12.6, 2013.

Software:

• kijijijini
     A web app that uses machine learning to suggest prices for items to be listed on the Kijiji classified ad site.
• PhylogeneticTrees
     A Macaulay2 package for group-based models on phylogenetic trees.
• EquivariantGB
     A Macaulay2 package for computing equivariant Gröbner bases.
• NumericalHilbert
     A Macaulay2 package for numerically computing local dual spaces and Hilbert functions of polynomial ideals.
• RegularLanguages/OIModules
     A Macaulay2 package for regular languages and finite state automata, used for equivariant Hilbert series computation.

Thesis:

• Symmetric ideals and numerical primary decomposition. PhD advisor: Anton Leykin.

Teaching:

UC Davis:

• Winter 2020: MAT 150A - Modern Algebra
• Winter 2020: MAT 22A - Linear Algebra
• Fall 2019: MAT 108 - Intro to Abstract Math
• Spring 2019: MAT 16A - Short Calculus
• Winter 2019: MAT 108 - Intro to Abstract Math
• Winter 2018: MAT 16B - Short Calculus
• Fall 2017: MAT 67 - Modern Linear Algebra
• Fall 2017: MAT 16B - Short Calculus

Queen's University:

• Win 2017: MATH/MTHE 228 - Complex Analysis
• Fall 2016: MATH 221 - Multivariable Calculus
• Win 2016: APSC 172 - Calculus II
• Win 2016: APSC 171 - Calculus I

Georgia Tech:

• Fall 2013: MATH 1522 - Linear Algebra
• Fall 2012: TA for MATH 1512 - Honors Calculus II
• Spr 2012: TA for MATH 2602 - Linear and Discrete Math
• Fall 2011: TA for MATH 2605 - Calculus III for Computer Science
• Spr 2011: TA for MATH 2602 - Linear and Discrete Math
• Fall 2010: TA for MATH 2602 - Linear and Discrete Math