ד"ר עדי ניב
I am a researcher and lecturer at the Mathematics unit of SCE since October 2016
My postdoctoral research, hosted by Prof. Gaubert and Prof. Akian, was carried between 2014 and 2016 at École Polytechnique-Paris, and sponsored by INRIA and the French embassy
My Ph.D., earned in 2014, was carried out at the Mathematics Department of Bar-Ilan University, with one year as Erasmus at KUL-Belgium, and supervised by Prof. Rowen
My research concerns the interfaces between matrix theory and graph theory, as well as tropical algebras with focus on combinatorics
Besides teaching at SCE, I have been teaching at Bar-Ilan University between 2008 and 2014, and delivered a summer course at Tel-Aviv college. Throughout the years I privately tutored individuals and groups at the high-school level and at the university level
2014-2016 Postdoctoral fellow, Maxplus team.
INRIA Saclay Ile-de-France and CMAP, École Polytechnique.
Hosts: Prof. Stephane Gaubert and Prof. Marianne Akian.
2010-2014 Ph.D. in Mathematics, Bar-Ilan University.
Dissertation Title: Supertropical Matrix Algebra.
Advisor: Prof. Louis Rowen.
2012 Ph.D. Erasmus-Mundus student.
Mathematics department, Katholieke Universiteit Leuven.
Host: Dr. Filip Cools.
2008-2010 M.Sc. in Mathematics (Cum Laude), Bar-Ilan University.
Thesis Title: Supertropical Linear Algebra.
Advisor: Prof. Louis Rowen.
Jul-Oct 2008 Research summer student, The Oscar and Emma Getz program.
Mathematics department, Weizmann Institute of Science.
Host: Dr. Dimitry Novikov.
2005-2008 B.Sc. in Mathematics (Magna Cum Laude), Bar-Ilan University.
Max-Plus Algebra: Tropical algebraic structures and their extensions, determinantal identities, normal forms, matrix factorization, eigenspaces and eigenvalues.
Matrix Theory: Total positivity and total non-negativity, elementary matrices, weight matrices, boolean matrices, sign-singularity.
Graph Theory: Combinatorics of permutations, weighted quivers, optimal assignment problems, perfect matchings.
Abstract Algebra: Semirings with symmetry, ordered semirings, group actions, path algebra.
Since October 2016 SCE. Departments of Civil Engineering, Mechanical Engineering, Software Engineering and Electrical&Electronics Engineering.
Courses: Calculus I, calculus II, linear algebra.
Peer reviewed papers
Factorization of tropical matrices
J. Algebra Appl., vol 13, 1350066 (2014).
*Selected by the publisher as one of "the best papers published in 2014".
Characteristic Polynomials of Supertropical Matrices
Comm. in Algebra, vol 42, Issue 2, pp. 528-539 (2014).
On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra
Linear Algebra Appl., vol 471, pp. 264-290 (2015).
Dependence of tropical eigenspaces (with L. Rowen).
Comm. in Algebra, vol 45, Issue 3, pp. 924-942 (2017).
Tropical SLn (with Z. Izhakian and L. Rowen)
To appear in Linear and Multilinear Algebra, 2017.
Tropical compound matrix identities (with M. Akian andS. Gaubert)
arXiv:1702.00980, 2017. Submitted.
Tropical totally positive matrices (with S. Gaubert)
arXiv: 1606.00238, 2016. Submitted.
Assignment problems via tropical matrices (with M. MacCaig and S. Sergeev)
Max-Plus determinantal identities
Tropical elementary matrices (with L. Rowen and S. Sergeev)
Tropical planar networks (with S. Gaubert)
2014-2016 INRIA postdoctoral fellowship, Inria Saclay.
Sep-Nov 2014 Chateaubriand postdoctoral fellowship, French embassy.
Oct 2010-Oct 2014 “Hanasi" excellence scholarship for Ph.D., Bar-Ilan University.
Jan-Feb 2014 Research grant in Algebra, Israeli Science foundation.
Aug 2013 Travel grant for academic affairs, Israeli Science foundation.
May 2013 Soffer excellence scholarship for Ph.D., Bar-Ilan University.
Dec 2011-Sep 2012 Erasmus-Mundus scholarship for Ph.D., European Union.
Oct 2008-Oct 2010 Excellence scholarship for M.Sc., Bar-Ilan University.
Oct 2009 Prize for outstanding teaching, Math. dept., Bar-Ilan University.
Jul-Oct 2008 The Oscar & Emma Getz grant, Weizmann Institute of Science.
Feb 2007-Feb 2008 B.Sc. excellence grant & CCNA course, Israeli Science Ministry.
My postdoctoral research at INRIA's `Tropical-team' is led by Stephane Gaubert, which is funded for his tropical research by the phone company ORANGE, the French electricity company EDF and by the French fire department. This is an ongoing collaboration.