Jose Israel Rodriguez
JoIsRo at UChicago dot edu
University of Chicago, Department of Statistics
Advisors and Mentors
Postdoc Mentor: Lek-Heng Lim
Previous Mentor: Jonathan Hauenstein
PhD Advisor: Bernd Sturmfels
Undergraduate Advisor: Eric Katz
I am a NSF Postdoc at the University of Chicago working with Lek-Heng Lim, and next fall I will start the University of Chicago Provost's Career Enhancement 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 numerical algorithms to solve systems of polynomial equations.Here is a link to a talk at the Simons Institute about my thesis work: Link.
Research and Writings
Numerical computation of Galois groups. We use numerical homotopy continuation to compute Galois groups.
A Probabilistic Algorithm for Computing Data-Discriminants of Likelihood Equations. Preprint. 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. Preprint. We describe the special locus of data for which the likelihood equations have a solution in the model's singular locus.
Numerical irreducible decomposition of multiprojective varieties. Preprint. We define multiprojective witness sets which encode the multidegree information of a variety. Furthermore, we generalize the regeneration solving procedure, the trace test, and numerical irreducible decomposition to the multiprojective case.
The maximum likelihood degree of rank 2 matrices via Euler characteristics. Preprint. We use Euler characteristics to prove an outstanding conjecture by Hauenstein, the first author, and Sturmfels; we prove a closed form expression for the ML degree of 3 by n rank 2 matrices. More broadly, we show how these techniques give a recursive expression for the ML degree of m by n rank 2 matrices.
Critical points via monodromy and local methods. Submitted. 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. To appear in the ISSAC'15. We develop an algebraic probability 1 algorithm for computing data discriminants which experimental results show that this method is 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 degreesBertini for Macaulay2. Submitted. 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 (2014) 2014(20): 5648-5666.
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 5 (2014) 18-38. 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 68 (2015) 297-307.
A novel method for the solution of the forward displacement problem of spherical parallel manipulators.
ZAMM Z. Angew. Math. Mech. 93 (2013), no. 1, 73-82.
Bounding The Degree of Belyi Polynomials. J. Number Theory vol. 133 (2013), no. 9, 2892-2900.
Seminars Near Chicago
My Future Whereabouts and VisitorsApplied 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.
Visiting NIMs: June 25-July 6, 2016 Daejeon, South Korea.
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.
Fall Western Sectional Meeting: October 8-9, 2016 University of Denver, Denver, CO.
Algebra, Geometry and Combinatorics Day : October 22-23, 2016 Purdue University (Tentative).
Date saved: October 29, 2016.
AMS special on Applied Algebraic Geometry : November 12-13, 2016 North Carolina State University in Raleigh, North Carolina.
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.
MEGA 2017 : June 12-16, 2017 Sophia Antipolis University, Nice, France (Tentative).
JSM 2017 : July 29 - August 3, 2017 Baltimore, Maryland (Call for submissions in mid-July 2016) (Tentative).
SIAM Conference on Applied Algebraic Geometry (AG17) : July 31-August 4, 2017 Georgia Institute of Technology, Atlanta, Georgia (Call for submissions in October 2016).
Oberwolfach: Algebraic Statistics : April 16 - April 22, 2017 Oberwolfach, Germany.
Mentoring and Past TeachingMRC: Algebraic Statistics: Teaching Assistant: June 12-18, 2016 Snowbird Resort, Utah. 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). Go to top
Invited Talks and Seminars- (July 2016) SIAM Annual Meeting: Special Session on Algebraic Staitistcs, NIMS at Daejeon, South Korea.
- (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.
Go to top
Quick LinksNumerically Solving Polynomial Systems with Bertini
Past WhereaboutsMathematics 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.
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.
IMA Annual Program Year Workshop Optimization and Parsimonious Modeling: January 25-29, 2016 Institute of Mathematics and its Applications (IMA), Minneapolis, MN (Did not attend).
Timo de Wolff: Feb 11-12, 2016 (Visiting University of Chicago).
John Lesieutre: Feb 17, 2016 (Visiting University of Chicago).
Martin Helmer: Feb 23-27ish, 2016 (Visiting University of Chicago).
Luke Oeding: Mar 9-12, 2016 (Visiting University of Chicago).
Applied Algebra Seminar: Apr 7, 2016 University of Wisconsin-Madison, Madison, Wisconsin.
Botong Wang: April 27, 2016 (Visiting University of Chicago).