Jose Israel Rodriguez 

jo dot ro at ND dot edu Affiliation University of Notre Dame, Department of Applied and Computational Mathematics and Statistics, Advisors and Mentors 

Research and Writings
The maximum likelihood degree of rank 2 matrices via Euler characteristics. Preprint.
Critical points via monodromy and local methods. Submitted.
Data discriminants of likelihood equations. To appear in the ISSAC'15.
Maximum likelihood for dual varieties. SNC '14 Proceedings of the 2014 Symposium on SymbolicNumeric Computation (2014)
Pages 4349.
Maximum likelihood geometry in the presence of data zeros. ISSAC '14 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation
(2014) Pages 232239.
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): 56485666. We prove that the maximumlikelihood degree of the variety of rankr matrices equals that of the variety of corank (r1)matrices; and also establish variants for symmetric and skewsymmetric matrices. Maximum Likelihood for Matrices with Rank Constraints. Journal of Algebraic Statistics 5 (2014) 1838. 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) 297307.
A novel method for the solution of the forward displacement problem of spherical parallel manipulators.
ZAMM Z. Angew. Math. Mech. 93 (2013), no. 1, 7382.
Bounding The Degree of Belyi Polynomials. J. Number Theory vol. 133 (2013), no. 9, 28922900.
Interests 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. Last summer I was in Korea, participating in the 2014 NIMS thematic program on applied algebraic geometry. Now, I am an NSF postdoc working with Jonathan Hauenstein at Notre Dame. My interests are in applied algebraic geometry and algebraic statistics. In particular, I am interested in solving systems of polynomial equations numerically. Here is a link to a talk at the Simons Institute about my thesis work: Link.My Future and Recent 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 WisconsinMadison. Algebra, Geometry, and Combinatorics Seminar: May 1, 2015 UIUC. GOAL workshop: May 1819, 2015 University of California, Berkeley. UC Berkeley Commencement: May 2223, 2015 University of California, Berkeley. Tropical Doener Workshop: May 2728, 2015 Freie Universität Berlin, Germany. Workshop on NonLinear Algebra: May 2930, 2015 in Berlin, Germany. GAeL XXIII: June 15, 2015 KU Leuven, Belgium. Algebraic Statistics 2015: June 811, 2015 in Genoa, Italy. MEGA 2015: Effective Methods in Algebraic Geometry: June 1519, 2015 at The University of Trento, Povo (Trento), Italy. Theory and applications of syzygies: July 13, 2015 Universität des Saarlandes, Saarbrücken, Germany. (Tentative) ISSAC 2015: July 79, 2015 The University of Bath, Bath, UK. SWAAG: July 1317, 2015 NIMS, Daejeon, Korea. SIAM AG15: August 0307, 2015. I am coorganizing a minisymposium Maximum Likelihood Degrees and Critical Points. AMS Sectional Meeting: Algebraic statistics and its interactions with combinatorics, computation, and network science session: October 34, 2015 Loyola University Chicago, Chicago, IL. Workshop on Algebra, Geometry and Proofs in Symbolic: December 613, 2015 The Fields InstituteToronto, Canada. Books I like Numerically Solving Polynomial Systems with Bertini The Numerical Solution of Systems of Polynomials Arising In Engineering and Science Teaching and Mentoring Sections of Math 1B with Professor Serganova (Fall 2013): Techniques of integration; applications of integration. Infinite sequences and series. Firstorder ordinary differential equations. Secondorder ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. Sections of Math 1B with Professor Christ (Spring 2013): Techniques of integration; applications of integration. Infinite sequences and series. Firstorder ordinary differential equations. Secondorder ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. Berkeley Science Network The UC Berkeley McNair Scholars Program University of Notre Dame ACMS Department Events Invited Talks and Seminars  (December 2015) Workshop on Algebra, Geometry and Proofs in Symbolic Computation, The Fields InstituteToronto, Canada.  (August 2015) SIAM Conference on Applied Algebraic Geometry Minisymposium: Maximum Likelihood Degrees and Critical Points MiniSymposium, National Institute for Mathematical SciencesDaejeon, South Korea.  (August 2015) SIAM Conference on Applied Algebraic Geometry Minisymposium:Group actions in algebraic geometry and commutative algebra , National Institute for Mathematical SciencesDaejeon, South Korea.  (July 2015) Seminar Week on Applied Algebraic Geometry , National Institute for Mathematical SciencesDaejeon, South Korea.  (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 WisconsinMadison.  (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, GoetheUniversitat.  (July 2013) Algebra Seminar, Universitat Konstanz.  (June 2013) Effective Methods in Algebraic Geometry, GoetheUniversitat.  (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. Quick Links Fields Institute for Research in Mathematical Sciences Applied Algebraic Geometry at NIMS Algebraic Statistics Conference at NIMS Optimization Conference at NIMS Combinatorial Algebraic Geometry at the Fields Institute Algebraic Statistics Conference at IIT ISSAC: International Symposium on Symbolic and Algebraic Computation SNC: Symbolic Numeric Computation International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Bertini Documentation Latin@s in the Mathematical Sciences Conference
