MTM 2016-75024-P
Computational Methods in Algebra, D-modules, Representation Theory and Optimization

Research topics

D-módules and singularities.

Hypergeometric D-modules and their formal solutions for special paramaters; connection formulas; monodromy of hypergeometric systems; hypergeometric integrals in the non-regular case; multisummability of formal solutions for A-hypergeometric systems.
Logarithmic D-modules and quasifree divisors: Artin approximations, Bernstein polynomials of holonomic modules, hyperplane arrangements and annihilators of rational functions.

Combinatorial representation theory and invariants.

Symmetries of the structural constants in representation theory (Littlewood-Richardson coefficients, Kronecker coefficients, plethysm coefficients).

Effective Methods for Lie, Leibniz and Malcev Algebras.

Description, classification and effective computations for filiform Lie algebras.
Minimal matrix representations of the Leibniz and Malcev algebras.
Computation of the laws of evolution algebras.

Effective Methods in (Non Linear) Integer Programming.

Algebraic tools for solving exactly the reliability problem with capacity constraints.
Solution of integer programming problems with nonlinear constraints, using combinations of heuristic techniques with test sets of linear subproblems .
Exact integer multiobjective optimization.

Members

Postdoctoral Researchers

Collaborators in Foreign Institutions

Recent Publications by the members of Project MTM2016-75024-P

• [MRS21] Mishna, M.; Rosas, M.; Sundaram, S. Vector partition functions and Kronecker coefficients JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 54(29) art.num. 205204 (2021)

• [CGN20] F.J. Castro-Jiménez; M. Ceballos; J. Núñez-Valdés. Filiform Lie algebras with low derived length. Mediterranean Journal of Mathematics, 2020, 17(6), 198. https://doi.org/10.1007/s00009-020-01642-z WOS(JCR) Mathematics, Q1.

• [BF] Ch. Berkesch, M.-C. Fernández-F. Characteristic cycles and Gevrey series solutions of A-hypergeometric systems. Algebra & Number Theory, Vol. 14 (2020), no. 2, 323-347.

• [BLR2020] E. Briand, S. Lopes and M. Rosas. Normally ordered forms of powers of differential operators and their combinatorics. Journal of Pure and Applied Algebra. vol. 224(8) article num. 106312 (august 2020).

• [CMN] F.J. Castro Jiménez, D. Mond, L. Narváez Macarro. Algebraic Groups, Quivers, Quasi-Free divisors … a theory of almost everything. Preprint, septiembre 2020.

• [B2020] E. Briand. On partitions with k corners not containing the staircase with one more corner. e-print, arXiv:2004.13180 [math.CO] (2020)

• [BR2020] E. Briand, M. Rosas. The 144 symmetries of the Littlewood-Richardson coefficients of SL3. e-print, arXiv:2004.04995 [math.CO] (2020)

• [F20] M. C. Fernández-F. Gevrey and formal Nilsson solutions of A-hypergeometric systems. Journal of Pure and Applied Algebra, Vol. 224 (2020), no. 8, 106350, 14pp.

• [R2019b] Mercedes Rosas. Schur generating functions and the asymptotics of structural constants from combinatorial representation theory. In Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity. Oberwolfach report 2020/9, pp. 32-24 (2020).

• [CC20] F.J. Castro-Jiménez; H. Cobo Pablos. On certain polynomial systems involving Stirling numbers of second kind. Journal of Symbolic Computation. Available online 8 July 2020. https://doi.org/10.1016/j.jsc.2020.07.008 WOS(JCR) Computer Science, Theory & Methods, Q4

• [CFG] F.J. Castro-Jiménez, M.C. Fernández-Fernández, M. Granger. Gevrey Expansions of Hypergeometric Integrals II. International Mathematics Research Notices, rnz303, https://doi.org/10.1093/imrn/rnz303. Published: 01 December 2019. WOS(JCR) Mathematics, Q1

• [CPR] Castro-Jiménez, F.J., Popescu, D. and Rond, G. Linear nested Artin approximation theorem for algebraic power series. Manuscripta Math. 158 (1-2), 55-73 (2019). https://doi.org/10.1007/s00229-018-1025-0 WOS(JCR) Mathematics, Q3.

• [BMOR2019] E. Briand, P. R.W. McNamara, R. Orellana and M. Rosas. Commutation and normal ordering for operators on symmetric functions. Séminaire Lotharingien de combinatoire, vol.80, article B80d (2019)

• [F19] M. C. Fernández-F. On the local monodromy of A-hypergeometric functions and some monodromy invariant subspaces. Revista Matemática Iberoamericana, Vol. 35 (2019), no. 3, pp. 949-961.

• [R2019] M. Rosas, A comment of the combinatorics of the vertex operator G(t|X). Rocky Mountain Journal of Mathematics, Volume 49, Number 7, 2281-2295. (2019).

• [MRS2018] M. Mishna, M. Rosas, Sh. Sundaram. An elementary approach to the quasipolynomiality of the Kronecker coefficients. E-print arxiv:1811.10015 (2018).

• [ACHK] Alonso, M.E., Castro-Jiménez, F.J., Hauser, H., Koutschan, Ch. Echelons of power series and Gabrielov’s counterexample to nested linear Artin approximation. Bull. London Math. Soc. 50 (2018) 649-662. https://doi.org/10.1112/blms.12162 - WOS(JCR) Mathematics, Q2

• [ACH] Alonso, M.E., Castro-Jiménez, F.J., Hauser, H. Encoding algebraic power series. Found. Comput. Math. 18 (2018), no. 3, 789-833. https://doi.org/10.1007/s10208-017-9354-z - WOS(JCR) Mathematics, Q1-D1.

• [CG15] F.J. Castro-Jiménez, M. Granger. Gevrey expansions of hypergeometric integrals I. International Mathematics Research Notices, 2015, no. 5, 1338-1370.

Former projects

• MTM2013-40455-P (1 Jan 2014 - 31 Dec 2016, extended 31 Dec 2017)
• MTM2010-19336 (1 Jan 2011 - 31 Dec 2013, extended 31 Dec 2014)
• MTM2007-64509 (1 Oct 2007 - 31 Jul 2011)
• MTM2004-01165 (13 Dec 2004 - 12 Dec 2007)
• BFM2001-3164 (28 Dec 2011 - 27 Dec 2004)