HR job title
- Professor
- Contact Info
- 1 979 862 4089
- Websites
- ORCiD
- 0000-0002-1657-2674
Rojas, Joseph Professor
Positions
- Affiliated Professor, Computer Science and Engineering, College of Engineering
- Associate head of graduate programs, Mathematics, College of Arts and Sciences
- Professor, Mathematics, College of Arts and Sciences
My research focuses on Algorithmic Algebraic Geometry (including real and arithmetic methods), Polyhedral Combinatorics, Complexity Theory, and Scientific Computation.
Research Areas
- Overview
- Publications
- Research
- Teaching
- Works By Students
- Background
- Contact
- Other
- View All
Overview
Publications
selected publications
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academic article
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Cheng, Q. i., Rojas, J. M., & Wan, D.
(2022).
Computing zeta functions of large polynomial systems over finite fields. Journal of Complexity.
73, 101681-101681.
-
Rojas, J. M., & Zhu, Y.
(2022).
Root repulsion and faster solving for very sparse polynomials over p-adic fields. Journal of Number Theory.
241, 655-699.
-
Rojas, J. M.
(2022).
Counting Real Roots in Polynomial-Time via Diophantine Approximation. Foundations of Computational Mathematics.
1-43.
-
Ergur, A., Paouris, G., & Rojas, J. M.
(2021).
SMOOTHED ANALYSIS FOR THE CONDITION NUMBER OF STRUCTURED REAL POLYNOMIAL SYSTEMS. Mathematics of Computation.
90(331), 2161-2184.
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Ergur, A. A., Paouris, G., & Rojas, J. M.
(2021).
Tropical varieties for exponential sums (vol 377, pg 863, 2020). Mathematische Annalen.
380(3-4), 2073-2077.
-
Rojas, J. M., & Zhu, Y.
(2020).
A Complexity Chasm for Solving Sparse Polynomial Equations Over p-adic Fields (Extended Abstract). 54(3), 86-90.
-
Erguer, A. A., Paouris, G., & Rojas, J. M.
(2020).
Tropical varieties for exponential sums. Mathematische Annalen.
377(3-4), 863-882.
-
Rojas, J. M.
(2020).
Kolmogorov complexity and algorithmic randomness. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
57(2), 339-346.
-
Kopp, L., Randall, N., Rojas, J. M., & Zhu, Y.
(2020).
RANDOMIZED POLYNOMIAL-TIME ROOT COUNTING IN PRIME POWER RINGS. Mathematics of Computation.
89(321), 373-385.
-
Erguer, A. A., Paouris, G., & Rojas, J. M.
(2019).
Probabilistic Condition Number Estimates for Real Polynomial Systems I: A Broader Family of Distributions. Foundations of Computational Mathematics.
19(1), 131-157.
-
Paouris, G., Phillipson, K., & Rojas, J. M.
(2019).
A Faster Solution to Smale's 17th Problem I: Real Binomial Systems. abs/1901.09739, 323-330.
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Ergr, A. A., Paouris, G., & Rojas, J. M.
(2018).
Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems. abs/1809.03626.
-
Avendano, M., Kogan, R., Nisse, M., & Rojas, J. M.
(2018).
Metric estimates and membership complexity for Archimedean amoebae and tropical hypersurfaces. Journal of Complexity.
46, 45-65.
-
Bi, J., Cheng, Q. i., & Rojas, J. M.
(2016).
SUBLINEAR ROOT DETECTION AND NEW HARDNESS RESULTS FOR SPARSE POLYNOMIALS OVER FINITE FIELDS. SIAM Journal on Computing.
45(4), 1433-1447.
-
Rojas, J. M.
(2013).
Book Review: Inevitable randomness in discrete mathematics. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
50(3), 481-487.
-
Avendano, M., Ibrahim, A., Rojas, J. M., & Rusek, K.
(2012).
Faster p-adic feasibility for certain multivariate sparse polynomials. 47(4), 454-479.
-
Passare, M., Rojas, J. M., & Shapiro, B.
(2011).
NEW MULTIPLIER SEQUENCES VIA DISCRIMINANT AMOEBAE. MOSCOW MATHEMATICAL JOURNAL.
11(3), 547-560.
-
Pebay, P., Rojas, J. M., & Thompson, D. C.
(2011).
Optimizing n-variate (n plus k)-nomials for small k. 412(16), 1457-1469.
-
Rojas, J. M.
(2008).
Book Review S. Basu, R. Pollack, and M.-F. Roy: Algorithms in Real Algebraic Geometry. Foundations of Computational Mathematics.
8(6), 765-771.
-
Dickenstein, A., Rojas, J. M., Rusek, K., & Shih, J.
(2007).
EXTREMAL REAL ALGEBRAIC GEOMETRY AND A-DISCRIMINANTS. MOSCOW MATHEMATICAL JOURNAL.
7(3), 425-452.
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Parsons, J., Holmes, J. B., Rojas, J. M., Tsai, J., & Strauss, C.
(2005).
Practical conversion from torsion space to Cartesian space for in silico protein synthesis. Journal of Computational Chemistry.
26(10), 1063-1068.
-
Rojas, J. M., & Ye, Y. Y.
(2005).
On solving univariate sparse polynomials in logarithmic time. Journal of Complexity.
21(1), 87-110.
-
Rojas, J. M.
(2004).
Arithmetic multivariate Descartes' Rule. American Journal of Mathematics.
126(1), 1-30.
-
Malajovich, G., & Rojas, J. M.
(2004).
High probability analysis of the condition number of sparse polynomial systems. Theoretical Computer Science.
315(2-3), 525-555.
-
Li, T. Y., Rojas, J. M., & Wang, X. S.
(2003).
Counting real connected components of trinomial curve intersections and m-nomial hypersurfaces. 30(3), 379-414.
-
Rojas, J. M.
(2000).
Some Speed-Ups and Speed Limits for Real Algebraic Geometry. Journal of Complexity.
16(3), 552-571.
-
Rojas, J. M.
(2000).
Uncomputably large integral points on algebraic plane curves?. Theoretical Computer Science.
235(1), 145-162.
-
Rojas, J. M.
(1999).
Solving Degenerate Sparse Polynomial Systems Faster. Journal of Symbolic Computation.
28(1-2), 155-186.
-
Rojas, J. M.
(1999).
Toric intersection theory for affine root counting. Journal of Pure and Applied Algebra.
136(1), 67-100.
-
Rojas, J. M.
(1999).
On the complexity of Diophantine geometry in low dimensions. Conference Proceedings of the Annual ACM Symposium on Theory of Computing.
527-536.
-
Rojas, J. M., & Wang, X. S.
(1996).
Counting affine roots of polynomial systems via pointed Newton polytopes. 12(2), 116-133.
-
Rojas, J. M.
(1994).
A convex geometric approach to counting the roots of a polynomial system. Theoretical Computer Science.
133(1), 105-140.
-
Cheng, Q. i., Rojas, J. M., & Wan, D.
(2022).
Computing zeta functions of large polynomial systems over finite fields. Journal of Complexity.
73, 101681-101681.
-
chapter
-
Rojas, J. M.
(2007).
On interpolating between quantum and classical complexity classes. Mathematics of Quantum Computation and Quantum Technology.
67.
-
Rojas, J. M.
(2007).
On interpolating between quantum and classical complexity classes. Mathematics of Quantum Computation and Quantum Technology.
67.
-
conference paper
-
Anthony, E., Grant, S., Gritzmann, P., & Rojas, J. M.
(2015).
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving. Mathematics and visualization.
255-277.
-
Phillipson, K., & Rojas, J. M.
(2013).
Fewnomial systems with many roots, and an Adelic Tau Conjecture. Contemporary Mathematics.
45-71.
-
Avendao, M., Ibrahim, A., Rojas, J. M., & Rusek, K.
(2010).
Randomized NP-completeness for p-adic rational roots of sparse polynomials in one variable. 331-338.
-
Pebay, P., Rojas, J. M., & Thompson, D. C.
(2009).
Optimization and NPR-Completeness of Certain Fewnomials. 133-141.
-
Bihan, F., Rojas, J. M., & Stella, C. E.
(2009).
Faster Real Feasibility via Circuit Discriminants. 39-46.
-
Bihan, F., Rojas, J. M., & Sottile, F.
(2008).
On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces. Ima Volumes in Mathematics and Its Applications.
15-+.
-
Rojas, J. M.
(2007).
Efficiently detecting torsion points and subtori. Contemporary Mathematics.
215-235.
-
Mortari, D., Rojas, J. M., & Junkins, J. L.
(2005).
Attitude and position estimation from vector observations. Spaceflight Mechanics 2005, Vol 120, Pts 1 and 2.
575-592.
-
Keyser, J., Ouchi, K., & Rojas, J. M.
(2005).
The exact rational univariate representation for detecting degeneracies. 299-328.
-
Rojas, J. M.
(2002).
Additive complexity and roots of polynomials over number fields and p-adic fields. Lecture Notes in Computer Science.
506-515.
-
Rojas, J. M.
(2001).
Computational arithmetic geometry I. Sentences nearly in the polynomial hierarchy. Journal of Computer and System Sciences.
216-235.
-
Rojas, J. M.
(1999).
On the complexity of Diophantine geometry in low dimensions. Proceedings of the Annual IEEE Conference on Computational Complexity.
3.
-
Rojas, J. M.
(1998).
Intrinsic near quadratic complexity bounds for real multivariate root counting. Lecture Notes in Computer Science.
127-138.
-
Rojas, J. M.
(1997).
New approach to counting Nash equilibria. 130-136.
-
Anthony, E., Grant, S., Gritzmann, P., & Rojas, J. M.
(2015).
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving. Mathematics and visualization.
255-277.
-
institutional repository document
-
Pbay, P., Rojas, J. M., & Thompson, D. C.
(2022).
Sturm's Theorem with Endpoints
-
Boniface, E., Deng, W., & Rojas, J. M.
(2022).
Trinomials and Deterministic Complexity Limits for Real Solving
-
Rojas, J. M., & Zhu, Y.
(2021).
Root Repulsion and Faster Solving for Very Sparse Polynomials Over $p$-adic Fields
-
Robelle, C., Rojas, J. M., & Zhu, Y.
(2021).
Sub-Linear Point Counting for Variable Separated Curves over Prime Power Rings
-
Rojas, J. M.
(2020).
Counting Real Roots in Polynomial-Time for Systems Supported on Circuits
-
Rojas, J. M., & Zhu, Y.
(2020).
A complexity chasm for solving univariate sparse polynomial equations over $p$-adic fields
-
Kopp, L., Randall, N., Rojas, J. M., & Zhu, Y.
(2018).
Randomized Polynomial-Time Root Counting in Prime Power Rings
-
Rojas, J. M., & Zhu, Y.
(2018).
Dedekind Zeta Zeroes and Faster Complex Dimension Computation
-
Cheng, Q. i., Gao, S., Rojas, J. M., & Wan, D.
(2017).
Counting Roots of Polynomials Over Prime Power Rings
-
Forsgrd, J., Nisse, M., & Rojas, J. M.
(2017).
New Subexponential Fewnomial Hypersurface Bounds
-
Rojas, J. M., & Rusek, K.
(2016).
A-Discriminants for Complex Exponents, and Counting Real Isotopy Types
-
Cheng, Q. i., Gao, S., Rojas, J. M., & Wan, D.
(2014).
Sparse Univariate Polynomials with Many Roots Over Finite Fields
-
Anthony, E., Grant, S., Gritzmann, P., & Rojas, J. M.
(2013).
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving
-
Koiran, P., Portier, N., & Rojas, J. M.
(2013).
Counting Tropically Degenerate Valuations and p-adic Approaches to the Hardness of the Permanent
-
Avendano, M., Kogan, R., Nisse, M., & Rojas, J. M.
(2013).
Metric Estimates and Membership Complexity for Archimedean Amoebae and Tropical Hypersurfaces
-
Bastani, O., Hillar, C. J., Popov, D., & Rojas, J. M.
(2011).
Randomization, Sums of Squares, and Faster Real Root Counting for Tetranomials and Beyond
-
Avendao, M., Ibrahim, A., Rojas, J. M., & Rusek, K.
(2010).
Faster p-adic Feasibility for Certain Multivariate Sparse Polynomials
-
Avendano, M., Ibrahim, A., Rojas, J. M., & Rusek, K.
(2010).
Near NP-Completeness for Detecting p-adic Rational Roots in One Variable
-
Passare, M., Shapiro, B., & Rojas, J. M.
(2010).
New Multiplier Sequences via Discriminant Amoebae
-
Pebay, P., Rojas, J. M., & Thompson, D. C.
(2009).
Optimization and NP_R-Completeness of Certain Fewnomials
-
Bihan, F., Rojas, J. M., & Stella, C.
(2009).
Faster Real Feasibility via Circuit Discriminants
-
Rojas, J. M., & Sethuraman, S.
(2009).
Refined Asymptotics for Multigraded Sums of Squares
-
Ibrahim, A., Rojas, J. M., & Rusek, K.
(2007).
Algorithmic Arithmetic Fewnomial Theory I: One Variable
-
Gomez, J., Niles, A., & Rojas, J. M.
(2007).
New Complexity Bounds for Certain Real Fewnomial Zero Sets
-
Dickenstein, A., Rojas, J. M., Rusek, K., & Shih, J.
(2006).
Extremal Real Algebraic Geometry and A-Discriminants
-
Rojas, J. M.
(2006).
A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes
-
Rojas, J. M.
(2005).
Efficiently Detecting Torsion Points and Subtori
-
Bihan, F., Rojas, J. M., & Stella, C. E.
(2004).
First Steps in Algorithmic Fewnomial Theory
-
Rojas, J. M.
(2002).
Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields
-
Rojas, J. M., & Vidyasagar, M.
(2001).
An Improved Bound on the VC-Dimension of Neural Networks with Polynomial Activation Functions
-
Rojas, J. M.
(2001).
Arithmetic Multivariate Descartes' Rule
-
Rojas, J. M., & Ye, Y.
(2001).
On Solving Fewnomials Over Intervals in Fewnomial Time
-
Pbay, P., Rojas, J. M., & Thompson, D. C.
(2022).
Sturm's Theorem with Endpoints
editor of
-
book
-
Gurvits, L.
(2011).
Randomization, Relaxation, and Complexity in Polynomial Equation Solving Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario, Canada
Rojas, J. M. (Eds.),
American Mathematical Soc..
-
Gurvits, L.
(2011).
Randomization, Relaxation, and Complexity in Polynomial Equation Solving Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario, Canada
Rojas, J. M. (Eds.),
American Mathematical Soc..
Research
principal investigator on
- AF: Medium: Collaborative Research: Arithmetic Geometry Methods in Complexity and Communication- awarded by National Science Foundation - (Arlington, Virginia, United States) 2019 - 2022
- REU Site: Undergraduate Research in the Mathematical Sciences and their Applications awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2021
- NSF IPA awarded by National Science Foundation - (Arlington, Virginia, United States) 2019 - 2020
- REU Site: Undergraduate Research in the Mathematical Sciences and Their Applications -- awarded by National Science Foundation - (Arlington, Virginia, United States) 2015 - 2019
- Sparse Polynomials, Complexity, and Algorithms awarded by National Science Foundation - (Arlington, Virginia, United States) 2014 - 2018
- MCS: Randomization in Algorithmic Fewnomial Theory Over Complete Fields awarded by National Science Foundation - (Arlington, Virginia, United States) 2009 - 2013
Teaching
teaching activities
- CSCE491 Hnr-research Instructor
- MATH304 Linear Algebra Instructor
- MATH323 Hnr-linear Algebra Instructor
- MATH411 Math Probability Instructor
- MATH415 Hnr-modern Algebra I Instructor
- MATH416 Modern Algebra Ii Instructor
- MATH470 Comm And Cryptography Instructor
- MATH478 Topological Data Analysis Instructor
- MATH485 Directed Studies Instructor
- MATH491 Hnr-research Instructor
- MATH491 Hnr-research Instructor
- MATH620 Algebraic Geometry I Instructor
- MATH648 Computational Alg Geom Instructor
- MATH662 Seminar In Algebra Instructor
- MATH663 Seminar In Analysis Instructor
- MATH673 Info Sec Auth I Instructor
- MATH678 Intro Topologial Data Analysis Instructor
- MATH684 Prof Internship Instructor
- MATH685 Directed Studies Instructor
- MATH689 Sptp: Security, Information, A Instructor
- MATH689 Sptp: Semi-def & Alg. Optimiza Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Rusek, Korben Allen (2013-05). A-Discriminant Varieties and Amoebae.
Background
education and training
- Ph.D. in Applied Mathematics, University of California, Berkeley - (Berkeley, California, United States) 1995
- M.A. in Mathematics, University of California, Berkeley - (Berkeley, California, United States) 1991
- M.S. in Computer Science, University of California, Berkeley - (Berkeley, California, United States) 1991
- B.S. in Mathematics/ Applied Sciences, University of California Los Angeles - (Los Angeles, California, United States) 1988
awards and honors
- Outstanding Teaching Award, conferred by Texas A&M University - (College Station, Texas, United States), 2007
- Faculty Early Career Development (CAREER) Program, conferred by National Science Foundation - (Arlington, Virginia, United States), 2004
- Postdoctoral Fellowship, conferred by National Science Foundation - (Arlington, Virginia, United States), 1995
Contact
first name
- Joseph
has last name
- Rojas
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- rojas@math.tamu.edu