Jose Israel Rodriguez


Email

JoIsRo@UChicago.edu

Affiliation

University of Chicago,
Department of Statistics

CV (12/17) and Headshot

Recent Talk

Google Scholar

Advisors and Mentors

Postdoc Mentor: Lek-Heng Lim

Previous Mentor: Jonathan Hauenstein

PhD Advisor: Bernd Sturmfels

Undergraduate Advisor: Eric Katz

Organizing/Software

SIAM AN16: Alg Stat Session

JMM17: Num Alg Session

AG17: Likelihood Geometry

Bertini.m2

Galois Groups


I am a University of Chicago Provost's Career Enhancement Postdoc working with Lek-Heng Lim after transitioning from a NSF Postdoc. My previous postdoc was at the Simon's Institute and University of Notre Dame with Jonathan Hauenstein. In May 2014, I graduated from UC Berkeley with a PhD in mathematics. My thesis is titled Numerical algebraic geometry for maximum likelihood estimation, and my advisor was Bernd Sturmfels.

My interests are in applied algebraic geometry and algebraic statistics. In particular, I am interested in developing algorithms to solve systems of polynomial equations.

Here is a link to a talk at the Simons Institute about my thesis work: Link.

Weekly Seminars: Mon: 4-5pm Tues: 2-3pm 4:30-6pm Thurs: 4:30pm


New SIAM Journal in Applied Algebra and Geometry (SIAGA). See Seven Pictures and Tomorrow.


Travel and Mentoring/Teaching

Mentoring/Teaching


Research and Writings

Numerical computation of braid groups .
We give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations using homotopy continuation.

Accurate Solutions of Polynomial Eigenvalue Problems.
We use homotopy continuation to solve the polynomial eigenvalue problem. We show that this method produces substantially more accurate resultsfor th and finds all eigenvalues with a certificate of correctness via Smale's alpha-theory.

A numerical algorithm to compute Euler obstruction functions.
Tools from algebraic topology have been used to solve problems in algebraic statistics. In this paper, we go the other way. We use the idea of maximum likelihood degree from algebraic statistics to compute values of the Euler obstruction function in algebraic topology.

The Maximum Likelihood Degree of Toric Varieties.
We study the maximum likelihood degree (ML degree) of toric varieties, known as discrete exponential models in statistics.

Solving parameterized polynomial system with decomposable projections.
We exploit the structure of decomposable projections in problems from statistics, kinematics, and benchmark problems in computational algebra. (Accepted for presentation at MEGA 2017 and Code).

Trace test.
We give a brief derivation of the trace test to verify completeness of a partial witness set of an irreducible variety in affine or projective space.

Numerical computation of Galois groups.
We use numerical homotopy continuation to compute Galois groups. Applications include formation shape control, the Alt-Burmester 4-Bar mechanism, and maximum likelihood estimation. Accepted to Foundations of Computational Mathematics.

Multiprojective witness sets and a trace test.
We generalize regeneration, the trace test, and numerical irreducible decomposition to the multiprojective case. Applications include Alt's problem and tensor decomposition.

The maximum likelihood degree of mixtures of independence models.
We use Euler characteristics to prove an outstanding conjecture by Hauenstein, the first author, and Sturmfels by giving a recursion to determine ML degrees for mixtures of independence models. The recursion has been implemented here.

A Probabilistic Algorithm for Computing Data-Discriminants of Likelihood Equations. Journal of Symbolic Computation (2016)
We develop a probabilistic algorithm with three different strategies for computing Data-Discriminants improving our previous version presented in ISSAC2015.

The maximum likelihood data singular locus, Journal of Symbolic Computation.
We describe the special locus of data for which the likelihood equations have a solution in the model's singular locus.

Critical points via monodromy and local methods, Journal of Symbolic Computation.
We use the numerical algebraic geometry tool of monodromy and local methods to compute critical points of the likelihood function and Euclidean distance function.

Data discriminants of likelihood equations, ISSAC'15.
We develop a probabilistic algorithm for computing data discriminants that is experimentally more efficient than the standard elimination algorithm. Based on the computational results, we propose the real root classification conjecture for the 3 by 3 symmetric matrix model.

Maximum likelihood for dual varieties. SNC '14 Proceedings of the 2014 Symposium on Symbolic-Numeric Computation (2014) Pages 43-49.
MLE for statistical models with discrete data is studied from an algebraic statistics viewpoint. A reformulation of the MLE problem in terms of dual varieties and conormal varieties is given.

Maximum likelihood geometry in the presence of data zeros. ISSAC '14 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (2014) Pages 232-239.
We consider discrete algebraic statistical models and study the solutions to the likelihood equations when the data contain zeros. We give new lower bounds for Maximum Likelihood degrees

Bertini for Macaulay2.
Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes implementations of a variety of algorithms based on polynomial homotopy continuation. The Macaulay2 package Bertini.m2 provides an interface to Bertini.

Maximum Likelihood Duality for Determinantal Varieties. Int Math Res Notices.
We prove that the maximum-likelihood degree of the variety of rank-r matrices equals that of the variety of co-rank (r-1)-matrices; and also establish variants for symmetric and skew-symmetric matrices.

Maximum Likelihood for Matrices with Rank Constraints. Journal of Algebraic Statistics.
We use numerical algebraic geometry to find maximum likelihood degrees of determinantal varieties and show these techniques can be useful for statisticians.

Combinatorial Excess Intersection. Journal of Symbolic Computation.
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical algebraic geometry.

A novel method for the solution of the forward displacement problem of spherical parallel manipulators. ZAMM Z. Angew. Math. Mech.
This work uses algebraic geometry to find an analytical (solvable in radicals) solution to a well studied problem in kinematics.

Bounding The Degree of Belyi Polynomials. J. Number Theory vol. 133 (2013), no. 9, 2892-2900.
This work began as an undergraduate research project advised by Eric Katz. A new combinatorial argument is given to bound the degree of a Belyi polynomial using the valuation of its roots.


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Travels, visitors, and advertisements

JMM17: Num AG Special Session: Thursday January 5 (Conference January 4-7), 2017 Hyatt Regency Atlanta and Marriott Atlanta Marquis, Atlanta, GA.

JMM17: MRC Alg Stat Special Session: Thursday January 5 (Conference January 4-7), 2017 Hyatt Regency Atlanta and Marriott Atlanta Marquis, Atlanta, GA.

Scientific and statistical computing seminar: February 2, 2017 Univeristy of Chicago, Chicago IL.

Colloquium: March 10, 2017 University of Chicago, Chicago, Illinois.

Algebraic Geometry Seminar: April 4, 2017 (Return April 5) The Ohio State University, University in Columbus, Ohio.

Oberwolfach: Algebraic Statistics : (Depart Apr 15, Return Apr 24) April 16 - April 22, 2017 Oberwolfach, Germany.

Polynomials, Kinematics, and Robotics : June 5-7, 2017 University of Notre Dame, Indiana.

String Phenomenology Conference (StringPheno 2017) : July 3-7, 2017 Virginia Tech, Blacksburg, Virginia.

Foundations of Computational Mathematics Conference 2017 : (Depart July 8) July 10 -July 19, 2017 Barcelona, Spain.

Applied Macaulay2 tutorials : July 27-29, 2017 Georgia Institute of Technology, Atlanta, Georgia.

SIAM Conference on Applied Algebraic Geometry (AG17) : July 31-August 4, 2017 Georgia Institute of Technology, Atlanta, Georgia.

AMS Special Session on Applicable and Computational Algebraic Geometry : September 9-10, 2017 University of North Texas, Denton TX.

SILO Seminar Series: October 3-5, 2017 University of Wisconsin-Madison.

Geometry Seminar: October 16-October 18, 2017 Massachusetts Institute of Technology, Cambridge, MA.

Algebra meets numerics: condition and complexity : November 5-8, 2017 TU Berlin, Berlin, Germany.

Non-Linear Algebra : November 8-12, 2017 Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.

Seminar: November 12-15, 2017 Sapientia University, Targu Mures, Romania.

Seminar: November 15-18, 2017 KU Leuven, Belgium.

Random Structures Seminar: November 29, 2017 University of Texas, Austin, Texas.

Geometry Seminar: November 30-December 1, 2017 Texas A&M, College Station, Texas.

Seminar: December 6-8, United States Naval Academy, College in Annapolis, Maryland.

2017 Korea-China International Conference on Matrix Theory with Applications: (Arrive in Seoul Dec 11 and depart Dec 22) December 14-December 17, 2017 AORC-IRCTMT Joint Meeting Sungkyunkwan University, Suwon, South Korea.

Applied analysis and algebra seminar: December 18, Yonsei University, Seoul, South Korea.

Latinos in the Mathematical Sciences Conference 2018: Discrete Mathematics: March 8 - 10, 2018 IPAM, UCLA.

Western Algebraic Geometry Symposium (WAGS): March 17 - 18, 2018 San Francisco State University, California.

AMS Eastern Sectional: April 21-22, 2018, Northeastern University, Boston, Massachusetts.

SIAM AN18: July 9 - 13, 2018, Oregon Convention Center, Portland, Oregon (Call for presentations will be in September 2017).

Macaulay2 Workshop: June 04 - 08, 2018, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany (Advertisement).

JSM 2018: July 28 - August 2, 2018 Vancouver Convention Centery, Vancouver, British Columbia, Canada (Advertisement).

ICERM Semester Program on Nonlinear Algebra : Sept 5 - Dec 7, 2018 ICERM, Brown University, Providence, RI (Advertisement).

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Mentoring and Past Teaching

MRC: Algebraic Statistics: Teaching Assistant: June 12-18, 2016 Snowbird Resort, Utah.

California Alliance

Berkeley Science Network

The UC Berkeley McNair Scholars Program

Sections of Math 1B with Professor Serganova (Fall 2013).

Sections of Math 1B with Professor Christ (Spring 2013).

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Invited Talks and Seminars

- (Feb 2017) Scientific and Statistical Computing Seminar, University of Chicago, Chicago,IL.

- (Jan 2017) Numerical Algebraic Geometry Day, Georgia Tech, Atlanta, GA.

- (Jan 2017) JMM17: Num AG Special Session, Hyatt Regency Atlanta and Marriott Atlanta Marquis, Atlanta, GA.

- (Nov 2016) AMS special on Applied Algebraic Geometry, North Carolina State University in Raleigh, North Carolina.

- (Oct 2016) AMS special on Foundations of Numerical Algebraic Geometry, University of Denver, Denver, CO.

- (Sep 2016) Algebra, Geometry, and Combinatorics Seminar, San Francisco State University, San Francisco, CA.

- (Jul 2016) XXI Coloquio Latinoamericano de Álgebra , Buenos Aires, Argentina.

- (July 2016) SIAM Annual Meeting: Special Session on Algebraic Statistics, Boston, MA.

- (July 2016) Lectures on Numerical Algebraic Geometry, NIMS at Daejeon, South Korea.

- (June 2016) Introducing the GMM degree, Research Institute of Mathematical Science of Kyoto University, Kyoto, Japan.

- (May 2016) Varieties, Equations, and Monodromy, NIMS at Daejeon, South Korea.

- (April 2016) Applied Algebraic Geometry Seminar, University of Wisconsin-Madison.

- (December 2015) Algorithms and Complexity in Algebraic Geometry Reunion Workshop, Simons Institute, Berkeley, CA.

- (December 2015) Workshop on Algebra, Geometry and Proofs in Symbolic Computation, The Fields Institute, Toronto, Canada.

- (November 2015) Algebraic Geometry Seminar , Stanford University, Stanford, California.

- (November 2015) Colloquium , Santa Clara University, Santa Clara, California.

- (November 2015) Geometry Seminar , Texas A&M, College Station, Texas.

- (October 2015) AMS Sectional Meeting: Algebraic statistics and its interactions with combinatorics, computation, and network science session , Loyola University, Chicago, Illinois.

- (October 2015) Dickson Day , University of Chicago, Chicago, Illinois.

- (August 2015) Algebraic Computational Biology Seminar, Pennsylvania State University, State College, Pennsylvania.

- (August 2015) SIAM Conference on Applied Algebraic Geometry Mini-symposium: Maximum Likelihood Degrees and Critical Points Mini-Symposium, National Institute for Mathematical Sciences-Daejeon, South Korea.

- (August 2015) SIAM Conference on Applied Algebraic Geometry Mini-symposium:Group actions in algebraic geometry and commutative algebra , National Institute for Mathematical Sciences-Daejeon, South Korea.

- (July 2015) Seminar Week on Applied Algebraic Geometry , National Institute for Mathematical Sciences-Daejeon, South Korea.

- (June 2015) Discrete Math Seminar , Technische Universiteit Eindhoven, Eindhoven, Netherlands.

- (June 2015) Algebraic Statistics, Genoa, Italy.

- (June 2015) Algebra and Geometry Seminar, University in Leuven, Belgium.

- (May 2015) GOAL Workshop, University of California, Berkeley.

- (May 2015) Algebra, Geometry, and Combinatorics Seminar, University of Illinois at Urbana–Champaign.

- (March 2015) Algebraic Geometry Seminar, University of Wisconsin-Madison.

- (February 2015) Algebraic Geometry/Commutative Algebra Seminar, University of Notre Dame.

- (February 2015) Algebraic Geometry and Number Theory Seminar, Rice University.

- (January 2015) Topology and Combinatorics Seminar, Freie Universität Berlin.

- (December 2014) Colloquium, University of Texas at Dallas.

- (October 2014) Algebraic Statistics Special Section, AMS Fall Western Sectional Meeting.

- (October 2014) Computational Algebraic Geometry and Applications in Science and Engineering Special Section, AMS Fall Western Sectional Meeting, SS17A.

- (October 2014) Solving Polynomial Equations Conference, Simons Institute, Berkeley, California.

- (August 2014) ICMS 2014 Session: Software for Numerical Algebraic Geometry, Hanyang University, Seoul, Korea.

- (July 2014) Symbolic Numeric Computation 2014, East China Normal University, Shanghai, China.

- (July 2014) International Symposium on Symbolic and Algebraic Computation 2014, Kobe, Japan.

- (June 2014) Algebraic Geometry Seminar, Korea Institute for Advanced Study, Seoul, Korea.

- (June 2014) Optimization and Algebraic Geometry, NIMS at Daejeon, South Korea.

- (May 2014) Applied Algebra Days 2, University of Madison at Wisconsin.

- (April 2014) Tropical April, University of California at Berkeley.

- (April 2014) Algebraic Statistics Seminar, Illinois Institute of Technology.

- (March 2014) Algebraic Statistics Seminar, University of California at Berkeley.

- (August 2013) Symbolic Computation Seminar, North Carolina State University.

- (August 2013) Algebra Seminar, Georgia Institute of Technology, Atlanta.

- (August 2013) SIAM Conference of Applied Algebraic Geometry , Colorado State University.

- (July 2013) Computational Algebra Seminar, Max Planck Institute for Mathematics, Bonn.

- (July 2013) Algebra Seminar, Universitat des Saarlandes.

- (July 2013) Discrete Mathematics Seminar, Goethe-Universitat.

- (July 2013) Algebra Seminar, Universitat Konstanz.

- (June 2013) Effective Methods in Algebraic Geometry, Goethe-Universitat.

- (April 2013) Graduate Student Combinatorics Conference, University of Minnesota, Twin Cities.

- (March 2013) Math/ICES Center of Numerical Analysis Seminar, University of Texas at Austin.

- (March 2013) Colloquium, Sam Houston State University.

- (March 2013) AVID Program Seminar, Grand Prairie High School.

- (March 2013) SIAM Student Chapter Seminar, Texas Tech University.

- (March 2013) Colloquium, Southern Methodist University.

- (March 2013) Algebraic Statistics Workshop, University of California at Berkeley.

- (March 2013) AGC Seminar, San Francisco State University.

- (March 2013) Algebra and Discrete Mathematics, University of California at Davis.

- (February 2013) SIAM Student Chapter Seminar, University of California at Berkeley.

- (February 2013) FRAGMENT Seminar, Colorado State University.

- (February 2013) Colloquium, University of Colorado at Boulder.

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Quick Links

Setup: Configure Xmail Lyx shortcut file UofC Website Macaulay2 Bertini Cyberduck

Institutes: Fields Simons NIMS MSRI

Other: Kaggle Data Science Lego Grad Student

Advice: Heilmeier's Catechism Serre on writing

YouTube: Solving Polynomials Tensor Decoomposition Condition Proof by contradiction

Conferences: ISSAC SNC SYNASC AG Conferences

Fellow McNair Scholars: Oscar D. Ayala Kyle Hale Martinque 'Marti' Jones Esmeralda Rodriguez

Coathors: Carlos Amendola Dan Bates Nathan Bliss Isaac Burke Jan Draisma Courtney Gibbons Elizabeth Gross Jonathan Hauenstein Martin Helmer Emil Horobet Serkan Hosten Anton Leykin Abraham Martin del Campo Evan D. Nash Maurizio Ruggiu Daniel Smolkin Frank Sottile Bernd Sturmfels Xiaoxian Tang Botong Wang

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Past Whereabouts

Mathematics Colloquium: December 1, 2014 UT Dallas.

Top Com Seminar: January 7, 2015 Freie Universität Berlin.

Algebraic Geometry and Number Theory Seminar: February 3, 2015 Rice University, Houston.

Algebraic Geometry/Commutative Algebra Seminar: February 25, 2015 University of Notre Dame.

Algebraic Geometry Seminar: March 13, 2015 University of Wisconsin-Madison.

Algebra, Geometry, and Combinatorics Seminar: May 1, 2015 UIUC.

GOAL workshop: May 18-19, 2015 University of California, Berkeley.

UC Berkeley Commencement: May 22-23, 2015 University of California, Berkeley.

Tropical Doener Workshop: May 27-28, 2015 Freie Universität Berlin, Germany.

Workshop on Non-Linear Algebra: May 29-30, 2015 in Berlin, Germany.

GAeL XXIII: June 1-5, 2015 KU Leuven, Belgium.

Algebraic Statistics 2015: June 8-11, 2015 in Genoa, Italy.

MEGA 2015: Effective Methods in Algebraic Geometry: June 15-19, 2015 at The University of Trento, Povo (Trento), Italy.

Eindhoven Discrete Math Seminar : June 24, 2015 Technische Universiteit Eindhoven, Eindhoven, Netherlands.

ISSAC 2015: July 7-9, 2015 The University of Bath, Bath, UK.

SWAAG: July 13-17, 2015 NIMS, Daejeon, South Korea.

Applied Algebraic Geometry Workshop: July 30, 2015 Daegu Gyeongbuk Institute of Science and Technology, Daegu, South Korea.

SIAM AG15: August 03-07, 2015. I co-organized a mini-symposium Maximum Likelihood Degrees and Critical Points.

Dickson Day: October 2, 2015 University of Chicago, Chicago, IL.

AMS Sectional Meeting: Algebraic statistics and its interactions with combinatorics, computation, and network science session: October 3-4, 2015 Loyola University, Chicago, IL.

Geometry Seminar : November 1-3, 2015 Texas A&M, College Station, Texas.

Colloquium : November 16-18, 2015 Santa Clara University, Santa Clara, California.

California Alliance visit to Stanford : November 18-24, 2015 Stanford University, Stanford, California.

Algebraic Geometry Seminar : November 20, 2015 Stanford University, Stanford, California.

Workshop on Algebra, Geometry and Proofs in Symbolic: December 6-13, 2015 The Fields Institute-Toronto, Canada.

Algorithms and Complexity in Algebraic Geometry Reunion Workshop: December 14-17, 2015 Simons Institute, Berkeley, CA.

Joint Mathematics Meetings: January 6-9, 2016 Washington State Convention Center, Seattle, WA.

Applied Algebra Seminar: Apr 7, 2016 University of Wisconsin-Madison, Madison, Wisconsin.

Applied Algebra Days 3: Apr 29-May 1, 2016 University of Wisconsin-Madison, Madison, Wisconsin.

Special session for applied algebraic geometry: (Depart May 13) May 14-May 22, 2016 KSIAM Daejeon, Korea.

Bertini Workshop: May 23-25, 2016 Notre Dame University, Notre Dame, Indiana.

Spring Research Conference 2016: May 25-27, 2016 Illinois institute of Technology, Chicago, Illinois.

MRC: Algebraic Statistics: June 12-18, 2016 Snowbird Resort, Utah.

Applications of Algebraic Methods to Statistics: (Depart June 18) June 19-25, 2016 Research Institute of Mathematical Science of Kyoto University, Kyoto, Japan.

SIAM Annual Meeting: July 11-14, 2016 Westin Boston Waterfront, Boston, Massachusetts.

Algebraic Statistics Session: July 11, 2016 Westin Boston Waterfront, Boston, Massachusetts.

XXI Coloquio Latinoamericano de Álgebra : (Depart July 26) July 27-29, 2016 Buenos Aires, Argentina.

Computational Algebra, Algebraic Geometry and Applications : August 1-3, 2016 Buenos Aires, Argentina.

Research Seminar: (Bay area Sept 16-21) September 19, 2016 San Jose State University, San Jose, CA.

Algebra, Geometry, and Combinatorics Seminar: September 21, 2016 San Francisco State University, San Francisco, CA.

Fall Western Sectional Meeting: (Depart Oct 7) October 8-12, 2016 University of Denver, Denver, CO.

AMS special on Applied Algebraic Geometry: November 12-13, 2016 North Carolina State University in Raleigh, North Carolina.

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