Jordy Cheyem Lopez Garcia

Office:	B17 Hayes-Healy
E-mail:	jlopezga@nd.edu

About Me

I am a Postdoctoral Research Associate in the Department of Applied and Computational Mathematics and Statistics at the University of Notre Dame, working with Jon Hauenstein to perform research on nonlinear systems.

I obtained my Ph.D. in Mathematics from Texas A&M University, where I was supervised by Frank Sottile. Here is my CV.

Research interests: Computational algebraic geometry, toric geometry, algebraic geometry in spectral theory, algebro-geometric methods in mathematical biology

News

Connor Parrow and I organize the new ACMS Graduate and Postdoc Seminar at the University of Notre Dame.

Preprints

• Common Real Secants to Pairs of Real Twisted Cubic Curves. Joint work with Saima Aslam, Matthew Faust, Jonathan D. Hauenstein, Bryson Kagy, Margaret H. Regan, Charles W. Wampler, and Albert Zhang.
• Elimination Without Eliminating: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets. Joint work with Paul Breiding, John Cobb, Aviva K. Englander, Nayda Farnsworth, Jonathan D. Hauenstein, Oskar Henriksson, David K. Johnson, Jordy Lopez Garcia, Deepak Mundayur.
• Transfers and Unstable Degrees in the A1-Brouwer Degrees Package in Macaulay2. Joint work with Stephanie Atherton, Somak Dutta, Wern Juin Gabriel Ong, Joel Louwsma, Yuyuan Luo, and Ruzho Sagarayaj.

Publications

• Identifiability of catenary and directed-cycle linear compartmental models. Joint work with Saber Ahmed, Natasha Crepeau, Paul R. Dessauer Jr., Alexis Edozie, Odalys Garcia-Lopez, Tanisha Grimsley, Viridiana Neri, and Anne Shiu. SIAM Journal on Applied Dynamical Systems. 25-1 (2026), 304-350. DOI 10.1137/25M1728636
• Additive Invariants of Open Petri Nets Joint work with Benjamin Bumpus, Sophie Libkind, Layla Sorkatti and Sam Tenka. Compositionality, Volume 7 (2025). DOI 10.46298/compositionality-7-4
• Irreducibility of the Dispersion Polynomial for Periodic Graphs Joint work with Matthew Faust. SIAM Journal on Applied Algebra and Geometry, 9-1 (2025), 83-107. DOI 10.1137/23M1600256
• Deficiency of chemical reaction networks: The effect of operations that preserve multistationarity and periodic orbits. Joint work with Awildo Gutierrez, Elijah Leake, Caelyn Rivas-Sobie, and Anne Shiu. Discrete and Continuous Dynamical Systems - B (2024). DOI 10.3934/dcdsb.2024157
• A1-Brouwer Degrees in Macaulay2. Joint work with Nikita Borisov, Thomas Brazelton, Frenly Espino, Thomas Hagedorn, Zhaobo Han, Joel Louwsma, Wern Juin Gabriel Ong and Andrew Tawfeek. Journal of Software for Algebra and Geometry, 14-1 (2024), 175-187. DOI 10.2140/jsag.2024.14.87
• Real Solutions to Systems of Polynomial Equations in Macaulay2. Joint work with Kelly Maluccio, Frank Sottile, and Thomas Yahl. Journal of Software for Algebra and Geometry, 14-1 (2024), 87-95. DOI 10.2140/jsag.2024.14.175

Software

• A1BrouwerDegrees (joint with Nikita Borisov, Thomas Brazelton, Frenly Espino, Thomas Hagedorn, Zhaobo Han, Joel Louwsma, Wern Juin Gabriel Ong and Andrew Tawfeek). A Macaulay2 package for computing local and global A1-Brouwer degrees.
• RealRoots (joint with Kelly Maluccio, Frank Sottile, and Thomas Yahl). A Macaulay2 package using symbolic computation to study real solutions of systems of polynomial equations.

Talks

• Computing Real Secant Lines of Twisted Cubic Curves. AMS Special Session Numerical Algebraic Geometry and Its Applications (a Mathematics Research Communities Session), Joint Mathematics Meetings, Washington D.C., 4-7 January 2026.
• Toric Compactifications of Periodic Graph Operators. AMS Special Session Applied and Computational Algebra, Fall Central Sectional Meeting, St. Louis, MO, 17-19 October 2025.
• Toric Compactifications of Periodic Graph Operators. Minisymposium Spectral Theory and Applications of Schrödinger Operators, 8th Annual Meeting of the SIAM Texas-Louisiana Section, The University of Texas at Austin, 26-28 September 2025.
• Toric Compactifications of Periodic Graph Operators. Geometry Seminar, Department of Mathematics, Texas A&M University, TX, 25 September 2025.
• Algebraic Geometry in Spectral Theory. Graduate and Postdoc Seminar, Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, IN, 3 September 2025.
• Toric compactifications of periodic graph operators. Minisymposium Algebraic Geometry in Spectral Theory, SIAM Conference on Applied Algebraic Geometry (AG25), University of Wisconsin-Madison, WI, 7-11 July 2025.
• Toric compactifications of periodic graph operators. AMS Special Session Applications of Algebraic Geometry, Joint Mathematics Meetings, Seattle, WA, 8-11 January 2025.
• Toric compactifications of periodic graph operators. Minisymposium Periodic Operators, 7th Annual Meeting of the SIAM Texas-Louisiana Section, Baylor University, 11-13 October 2024.
• Toric compactifications of discrete periodic operators. AMS Special Session Applications of Algebraic Geometry, Fall Central Sectional Meeting, San Antonio, TX, 14-15 September 2024.
• Algebraic geometry in spectral theory. Mathematical Pathways to an Excellent Future workshop, The University of California, Riverside, 24 May 2024.
• Algebraic Fermi curves. AMS student chapter GIG'EM conference, Texas A&M University, 20 April 2024.
• Algebraic geometry in spectral theory. Algebra and Combinatorics seminar, The University of Texas at Dallas, 17 April 2024.
• Algebraic geometry in spectral theory. Eleventh Discrete Geometry and Algebraic Combinatorics Conference, The University of Texas Rio Grande Valley, 24-25 February 2024.
• Operators, polytopes and toric geometry. AMS Special Session Combinatorial Insights into Algebraic Geometry, Joint Mathematics Meetings, San Francisco, CA, 3-6 January 2024.
• Operators, polytopes and toric Geometry. Minisymposium Discrete and Continuous Schrödinger Operators, 6th Annual Meeting of the SIAM Texas-Louisiana Section, The University of Louisiana at Lafayette, 3-5 November 2023.
• A1-Brouwer degrees in Macaulay2. Minisymposium Applications of Combinatorial and Computational Algebraic Geometry, 6th Annual Meeting of the SIAM Texas-Louisiana Section, The University of Louisiana at Lafayette, 3-5 November 2023.
• Discrete periodic operators and algebraic geometry. AMS Special Session Disordered and Periodic Quantum Systems, AMS Southeastern Regional Meeting, Georgia Institute of Technology, 18-19 March 2023.
• Functors on open Petri nets. AMS Special Session Applied Category Theory (A Mathematics Research Communities session), Joint Mathematics Meetings, Boston, MA, 4-7 January 2023.
• Discrete periodic operators and algebraic geometry.. MSRI Special Session The MSRI Undergraduate Program (MSRI-UP), Joint Mathematics Meetings, Boston, MA, 4-7 January 2023.
• Extending irreducibility of Bloch varieties. Minisymposium Applications and computation in algebraic geometry, 5th Annual Meeting of the SIAM Texas-Louisiana Section, University of Houston, 4-6 November 2022.
• Functors on open Petri nets. Mathematics Research Communities on Applied Category Theory, Java Center, NY, 29 May-4 June 2022.
• Using Macaulay2 to count real roots of univariate polynomials. Fall 2021Graduate Algebra Symposium, The University of North Texas, 12 November 2021.
• Using Macaulay2 to count real roots of univariate polynomials. Minisymposium Algorithmic Algebra and Geometry, 4th Annual Meeting of the SIAM Texas-Louisiana Section, The University of Texas Rio Grande Valley, 5-6 November 2021.
• What is a scheme? AMS student chapter GIG'EM conference, Texas A&M University, 27 April 2021.
• Hypergroups and buildings 2. Pure mathematics seminar, The University of Texas at Brownsville, April 2015
• Hypergroups and buildings 1. Pure mathematics seminar, The University of Texas at Brownsville, April 2015
• On Galois theory. Algebra Day, The University of Texas at Brownsville, April 2015

Current

University of Notre Dame

• Instructor, ACMS 40790. Topics in Applied Mathematics: Computational Algebraic Geometry (Spring 2026).

Previous

University of Notre Dame

• Instructor, ACMS 40630/60630. Nonlinear Dynamical Systems (Fall 2025).

Texas A&M University

• Grader, Math 308. Differential Equations. (Summer 2025).
• No teaching duties. (Spring 2025).
• Teaching Assistant, Math 150. Functions, Trigonometry and Linear Systems (Fall 2024).
• Help Session tutor, Engineering Mathematics III (Summer II 2024).
• No teaching duties (Summer I 2024).
• No teaching duties.
• Grader, Math 696. Mathematical Communication and Technology (Fall 2023).
• No teaching duties.
• Grader, Math 304. Linear Algebra (Summer I 2023).
• Teaching Assistant, Math 152. Engineering Mathematics II (Spring 2023).
• Teaching Assistant, Math 150. Functions, Trigonometry and Linear Systems (Fall 2022).
• No teaching duties. Supported by a Texas A&M Fellowship (Summer 2022).
• Teaching Assistant, Math 147. Calculus I for Biological Sciences (Spring 2022).
• Teaching Assistant, Math 150. Functions, Trigonometry and Linear Systems (Fall 2021).
• Help Session tutor, Math 409. Advanced Calculus (Summer II 2021).
• Instructor of Record, Math 140. Math for Business and Social Sciences (Summer 2021).
• Teaching Assistant, Math 152. Engineering Mathematics II (Spring 2021).
• Teaching Assistant, Math 150. Functions, Trigonometry and Linear Systems (Fall 2020).
• Grader, Math 430. Applied Algebra (Summer 2020).
• Grader, Math 300. Foundations of Mathematics (Spring 2020).
• Grader, Math 431. Structures and Methods in Combinatorics (Fall 2019).

The University of Texas Rio Grande Valley

• Instructor of Record, Math 1342 Elementary Statistical Methods, Math 1351 Fundamentals of Mathematics II, Math 2412 Pre Calculus (Spring 2019).
• Instructor of Record, Math 1314 College Algebra, Math 1350 Fundamentals of Mathematics I, Math 1351 Fundamentals of Mathematics II, Math 1342 Elementary Statistical Methods, Math 4390 Math Project (Fall 2018).
• Instructor of Record, Math 0330 Pre Statistics Jumpstart (Summer II 2018).
• Instructor of Record, Math 2412 Pre Calculus, Math 1342 Elementary Statistical Methods, Math 1332 Contemporary Mathematics (Spring 2018).
• Instructor of Record, Math 1314 College Algebra, Math 1351 Fundamentals of Mathematics II, Math 2412 Pre Calculus (Fall 2017).
• Instructor of Record, Math 1314 College Algebra, Math 2414 Calculus II (Summer II 2017).
• Instructor of Record, Math 2412 Precalculus, MATH 2413 Calculus I, Math 1342 Elementary Statistical Methods, (Spring 2017).
• Instructor of Record, Math 1314 College Algebra, Math 1332 Contemporary Mathematics, Math 1351 Fundamentals of Mathematics II, Math 2412 Pre Calculus (Fall 2016).

Texas Southmost College

• Instructor of Record, College Algebra (Spring 2017).

Valley Christian High School

• Instructor of Record, Advanced Mathematics (Fall 2018).
• Instructor of Record, Advanced Mathematics (Fall 2017).
• Instructor of Record, Advanced Mathematics (Fall 2016).

Description of duties: An Instructor of Record is completely in charge of a course. A Teaching Assistant is in charge of delivering quizzes and (for Math 150 - Math 152) teaching introductory Python to 3 course sections, each of approximately 30 students. Teaching assistants meet twice a week with each course section, outside of lectures. They are also in charge of partially grading homework assignments, quizzes, or exams. A Help Session tutor offers tutoring services for specific courses outside of the classroom. A Grader is in charge of grading homework assignments for an upper-level undergraduate or graduate mathematics course.

Conference organization

• Co-organizer (with Matthew Faust and Kisun Lee) of the special session Applied and Computational Algebraic Geometry at the 2026 AMS Spring Southeastern Sectional Meeting, 28-29 March 2026, at Georgia Southern University--Armstrong Campus in Savannah, GA.
• Co-organizer (with Matthew Faust and Frank Sottile) of the mini symposium Algebraic Geometry in Spectral Theory at the SIAM Conference on Applied Algebraic Geometry (AG25), 7-11 July 2025, at the University of Wisconsin-Madison in Madison, WI.
• Co-organizer (with C.J. Bott and Frank Sottile) of the mini symposium Nonlinear Algebra in Applications at the 7th Annual Meeting of the SIAM Texas-Louisiana Section, 11-13 October 2024, at Baylor University in Waco, TX.
• Co-organizer (with Taylor Brysiewicz, Luis David Garcia Puente, Nickolas Hein, and Kevin Purbhoo) of the Workshop on Applied and Computational Enumerative Geometry, 3-7 June 2024, at the Fields Institute in Toronto, Canada. Supported by the Fields Institute and the U.S. National Science Foundation.
• Co-organizer (with Julia Lindberg) of the mini symposium Nonlinear Algebra in Applications at the 6th Annual Meeting of the SIAM Texas-Louisiana Section, 3-5 November 2023, at the University of Louisiana at Lafayette.
• Local co-organizer (with Gregory Berkolaiko and Matthew Faust) of the conference Spectral Theory and Applications, 10-13 October 2023, at Texas A&M University in College Station, TX.
• Co-organizer (with Josué Tonelli-Cueto and Thomas Yahl) of the mini symposium Applications and Computation in Algebraic Geometry, at the 5th Annual Meeting of the SIAM Texas-Louisiana Section, 4-6 November 2022, at the University of Houston.
• Local co-organizer (with Arpan Pal) of the Spring 2023 Graduate Algebra Symposium, 29 April 2023, at Texas A&M University in College Station, TX.
• Co-organizer (with Mansi Bezbaruah, Agniva Dasgupta, and Valeria Fragiadaki) of the Spring 2022 Gathering in Graduate Expository Mathematics (GIG'EM), 23 April 2022, at Texas A&M University in College Station, TX.

Directed reading programs

• Co-organizer (with Angelique Morvant, Crystal Farris, Anne Shiu, and Matthias Maier), Texas A&M Mathematics Directed Reading Program (Fall 2021 - present). Presentation "How (not?) to give a talk."
• Mentor, Texas A&M Mathematics Directed Reading Program, Spring 2021 and Spring 2024.
• Mentor, Twoples Directed Reading Program, Fall 2022.

Texas A&M Hullabaloo U

• Instructor of Record, Texas A&M Hullabaloo U, Fall 2023.

MSRI Undergraduate Program

• Graduate Research Assistant, Algebraic methods in mathematical biology, Summer 2022.

The University of Texas Rio Grande Valley poster projects

• Co-advisor (with Oleg Musin) of 9 undergraduate students, Fall 2018 and Spring 2019.