¡Bienvenides!
Who am I?
Since 2023, I have been working as a researcher (
My research focuses on polynomial systems, where I study algorithms for solving them and their applications in various domains. My PhD thesis specifically dealt with effective algorithms for solving sparse polynomial systems using Gröbner bases and Resultants. Take a look!
Publications

Solving sparse polynomial systems using Groebner bases and resultants
Proceedings of the 47th International Symposium on Symbolic and Algebraic Computation, 2022. In press.
Invited paper complementing tutorial.
ArXiv version. 
Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
Matías R. Bender and Simon Telen
Mathematics of Computation  AMS, 2022. In press.
ArXiv version. 
Koszultype determinantal formulas for families of mixed multilinear systems
Matías R. Bender, JeanCharles Faugère, Angelos Mantzaflaris, and Elias Tsigaridas
SIAM Journal on Applied Algebra and Geometry, 2021.
ArXiv version, MATLAB code 
Classifier Construction in Boolean Networks Using Algebraic Methods
Robert Schwieger, Matías R. Bender, Heike Siebert, and Christian Haase
Computational Methods in Systems Biology, Lecture Notes in Computer Science, 2020.
ArXiv version, Python code 
A nearly optimal algorithm to decompose binary forms
Matías R. Bender, JeanCharles Faugère, Ludovic Perret, and Elias Tsigaridas
Journal of Symbolic Computation, 2021.
HAL version 
Groebner Basis over Semigroup Algebras: Algorithms and Applications for Sparse Polynomial Systems
Matías R. Bender, JeanCharles Faugère, and Elias Tsigaridas
Proceedings of the 44th International Symposium on Symbolic and Algebraic Computation, 2019
HAL version  Towards Mixed Groebner Basis algorithms: the Multihomogeneous and Sparse case
Matías R. Bender, JeanCharles Faugère, and Elias Tsigaridas
Proceedings of the 43th International Symposium on Symbolic and Algebraic Computation, 2018
HAL version  Bilinear systems with two supports: Koszul resultant matrices, eigenvalues, and eigenvectors
Matías R. Bender, JeanCharles Faugère, Angelos Mantzaflaris, and Elias Tsigaridas
Proceedings of the 43th International Symposium on Symbolic and Algebraic Computation, 2018
HAL version, Examples and data, Video.  A Superfast Algorithm to Decompose Binary Forms
Matías R. Bender, JeanCharles Faugère, Ludovic Perret, and Elias Tsigaridas
Proceedings of the 41th International Symposium on Symbolic and Algebraic Computation, 2016
SIGSAM's ISSAC Distinguished Student Author Award 2016
HAL version
Preprints

Dimension results for extremalgeneric polynomial systems over complete toric varieties
Matías R. Bender and PierreJean Spaenlehauer
Submitted, May 2023. (24 pages) 
Efficient computation of multiparameter persistence
Matías R. Bender, Oliver Gäfvert, and Michael Lesnick
In preparation. (48 pages) 
Yet another eigenvalue algorithm for solving polynomial systems
Matías R. Bender and Simon Telen
Accepted, May 2021. (28 pages)
Julia package EigenvalueSolver.jl
Software

Muphasa
(Joint work with Oliver Gäfvert, and Michael Lesnick)
Opensource C++ software (~6k lines) to compute presentations of multiparameter persistent homologies. 
EigenvalueSolver.jl
(Joint work with Simon Telen)
Opensource Julia package (~1k lines) to compute solve numerically polynomial systems.
More information. 
sylvesterMEP
(Joint work with JeanCharles Faugère, Angelos Mantzaflaris, and Elias Tsigaridas)
Opensource Matlab script to solve the multiparameter eigenvalue problem.
More information. 
Classifierconstruction
(Joint work with Robert Schwieger, Heike Siebert, and Christian Haase)
Opensource python code to compute classifiers on Boolean networks using Groebner basis.
More information.
Talks
 Polynomial systems, sparsity, and applications
Caramba team's seminar
(Online) Inria Nancy  Grand Est, Nancy, France, February 2022.  Polynomial systems, sparsity, and applications
Ouragan team's seminar
(Online) INRIA Paris, Paris, France, February 2022.  Polynomial systems, sparsity, and applications
AROMATH team's seminar
(Online) INRIA  Université Côte d'Azur, Sophia Antipolis, France, February 2022.  Polynomial systems, sparsity, and applications
Brainstorming days on measure and polynomial optimization
(Online) Laboratoire d'analyse et d'architecture des systèmes, Toulouse, France, November 2021.  Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
Minisymposium New Trends in Polynomial System Solving
SIAM Conference on Applied Algebraic Geometry
Online, August 2021.  Koszultype determinantal formulas for families of mixed multilinear systems
Seminar on NonLinear Algebra
MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany, August 2021.  Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
Applied Algebra and Analysis Online Seminar
(Online) TU Braunschweig and University of Osnabrueck, Germany, April 2021.  Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
Journées Nationales de Calcul Formel 2021
(Online) CIRM, Luminy, France, March 2021
Video, Slides.  Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
AROMATH team's seminar
(Online) INRIA, Sophia Antipolis, France, December 2020  Gröbner bases and sparse polynomial systems
Session: Gröbner Bases in Theory and Practice
(Online) International Congress on Mathematical Software 2020, July 2020.  Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
Kolloquium on Algorithmic Algebra at TU Berlin
(Online) Technische Universität Berlin, Berlin, Germany, July 2020.  Solving sparse polynomial systems by computing Gröbner bases faster
Seminar on NonLinear Algebra
MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany, March 2020  Solving sparse polynomial systems by computing Gröbner bases faster
Seminar of the Institut für Algebra
OttovonGuerickeUniversität Magdeburg, Magdeburg, Germany, January 2020  Algorithms for sparse polynomial systems: Gröbner bases and resultants
Kolloquium on Algorithmic Algebra at TU Berlin
Technische Universität Berlin, Berlin, Germany, October 2019  Fórmulas determinantales para el resultante de algunos sistemas multilineales mixtos
Departamento de Matemática, FCEN, UBA.
Buenos Aires, Argentina, September 2019  Groebner Basis over Semigroup Algebras: Algorithms and Applications for Sparse Polynomial Systems
44th International Symposium on Symbolic and Algebraic Computation
Beijing, China, July 2019  Algorithms for sparse Groebner basis
Minisymposium Symbolicnumeric methods for nonlinear equations: Algorithms and applications at SIAM Conf. on Applied Algebraic Geometry
Bern, Switzerland, July 2019  Solving sparse polynomial systems using Groebner bases
Summer School on Geometric and Algebraic Combinatorics
Sorbonne Université, Paris, France, June 2019  Determinantal formulas for the resultant of some mixed multilinear systems
Structured Matrix Days 2019
XLIMDMI, Université de Limoges, Limoges, France, May 2019.
Slides  Solving sparse polynomial systems using Groebner bases
GRAPE kickoff meeting
IMBM Bogazici University, Istanbul, Turkey, May 2019  Solving sparse polynomial systems using Groebner bases
CARAMBA team's seminar
INRIA, Nancy, France, April 2019  Solving Polynomial Systems
Inria's Junior Seminar
INRIA, Paris, France, February 2019  Solving sparse polynomial systems using Groebner bases
Facets of Complexity Seminar
Freie Universität Berlin, Berlin, Germany, February 2019  Towards Mixed Groebner Basis algorithms: the Multihomogeneous and Sparse case
43th International Symposium on Symbolic and Algebraic Computation
The City University of New York, New York, NY, United States of America, 1719 July 2018  Bilinear systems with two supports: Koszul resultant matrices, eigenvalues, and eigenvectors
43th International Symposium on Symbolic and Algebraic Computation
The City University of New York, New York, NY, United States of America, 1719 July 2018  A Superfast Algorithm to Decompose Binary Forms
41th International Symposium on Symbolic and Algebraic Computation
Wilfrid Laurier University, Waterloo, Ontario, Canada, 2022 July 2016  Decomposition of Binary Forms
GOAL Workshop in Paris 2016
LIP6, UPMC, Paris, France 2021 May 2016  A Superfast Algorithm to Decompose Binary Forms
Structured Matrix Days 2016
XLIMDMI, Université de Limoges, Limoges, France, 910 May 2016
Education

PhD Student, Sorbonne Université, Paris, France. 2016  2019.
Advisors: JeanCharles Faugère and Elias Tsigaridas (PolSys  LIP6  SU/INRIA/CNRS)
Title: Algorithms for sparse polynomial systems: Gröbner basis and resultants
Manuscript  Licenciatura en Ciencias de la Computación, Universidad de Buenos Aires, Buenos Aires, Argentina. 2010  2015
(Equivalent to Master's degree in Computer Science, 6years studies with a final thesis)
Average: 9.54/10.
Awards, Grants, and Recognitions
 Invited tutorial at the 47th International Symposium on Symbolic and Algebraic Computation . Lille, France. 2022.
 SIAM Early Career Travel Award to attend SIAM Conference on Applied Algebraic Geometry . 2019.

Distinguished Student Author Award.
ACM's SIGSAM. 2016.
For the paper "A Superfast Algorithm to Decompose Binary Forms", published at ISSAC 2016  PhD Fellowship. INRIA. 2015.
Three years funding (CORDIS)  Academic Merit Award. Santander Río Bank. 2015.
 Research Scholarship. INRIA  Campus France. 2015.
Research intership at PolSys.  Exchange Scholarship to Universidad Autónoma de Madrid (UAM), Spain.
Santander Río Bank. 2014.
Fully paid semestral exchange.  Research Fellowship “Beca Estímulo a las Vocaciones Científicas 2013”.
Consejo Interuniversitario Nacional (CIN), Argentina. 2013.
Under the supervision of Esteban Feuerstein.
Teaching and Popular Science
Teaching
 Qualified in sections 25, 26, and 27 for maître de conférences (France).

Teaching Assistant, Computer Science Department, University of Buenos Aires.
March 2012  February 2014
TA at Algorithms & Data Structures II, two semesters in 2012 and one in 2013. Topics include formal specification using ADTs, Software Design, Data Structures, Sorting Algorithms, Divide and Conquer techniques, Complexity Order calculations. Implementations with C++.
TA at Algorithms & Data Structures III, one semester in 2013. Topics include Graph Theory, Complexity Theory (P and NP), Dynamic Programming and Backtracking techniques. 
Informatics Teacher, Escuela Integral Hebrea Natan Gesang, (primary school).
April 2010  January 2012
Computer teacher for kids from six to eight years. Topics include different OSs, basic ofimatics, web design (DreamWeaver) and elementary programming (Scratch).
Popular Science (Click to see)
Reach me
CMAPÉcole Polytechnique
91128 Palaiseau Cedex
FRANCE
Mail:
Office: 03025 (upper floor), Bâtiment 6, CMAP, École Polytechnique