Andrei Gabrielov

Departments of Mathematics
and Earth and Atmospheric Sciences
Purdue University
West Lafayette, IN 47907, USA

OFFICE: Mathematics 648
PHONE: (765) 494-7911
FAX: (765) 494-0548
E-MAIL: agabriel@math.purdue.edu

Home Vita Publications Preprints Teaching Research

SELECTED PUBLICATIONS

A. Eremenko, A. Gabrielov. PT-symmetric eigenvalues for homogeneous potentials. J. Math. Phys., v.59, i2018. https://doi.org/10.1063/1.5016390. PDF

L. Birbrair, A. Gabrielov. Ambient Lipschitz equivalence of real surface singularities. IMRN, https://doi.org/10.1093/imrn/rnx328, 2018. PDF

Birbrair, L., Fernandes, A., Gabrielov, A., Grandjean, V. Lipschitz contact equivalence of function germs in R^2. Annali SNS Pisa, v.17 (2017) 91-92, DOI 10.2422/2036-2145.201503_014. PDF

A. Eremenko, A. Gabrielov. Circular pentagons and real solutions of Painleve VI equations. Comm. Math. Physics (2017), DOI 10.1007/s00220-017-2921-y. PDF

A. Eremenko, A. Gabrielov, A. Hinkkanen. Exceptional solutions to the Painleve VI equation. J. Math. Physics, 58, 012701 (2017), doi: 10.1063/1.4973440. PDF

A. Gabrielov, N. Vorobjov On Topological Lower Bounds for Algebraic Computation Trees. Foundations of Computational Mathematics, v.17 (2017) 61-72, DOI: 10.1007/s10208-015-9283-7. PDF

A. Gabrielov, N. Vorobjov Topological lower bounds for arithmetic networks. Computational complexity. (2016) DOI: 10.1007/s00037-016-0145-8. PDF

A. Eremenko, A. Gabrielov. Spherical rectangles. Arnold Mathematical Journal, v.2 (2016) p.463-486. PDF

A. Eremenko, A. Gabrielov, V. Tarasov. Metrics with conic singularities and spherical quadrilaterals. Conformal Geometry and Dynamics, v.20 (2016) 28-175. PDF

A. Eremenko, A. Gabrielov, V. Tarasov. Spherical quadrilaterals with three non-integer angles. Journal of Mathematical Physics, Analysis and Geometry, v.12 (2016) 134-167. PDF

A. Eremenko, A. Gabrielov. On metrics of curvature 1 with four conic singularities on tori and on the sphere. Illinois J. Math, v,59 (2015) 925-947. PDF

S. Basu, A. Gabrielov, N. Vorobjov. Triangulations of monotone families I: Two-dimensional families. Proc. LMS v.111 (2015) 1013-1051. PDF

A. Eremenko, A. Gabrielov, V. Tarasov. Metrics with conic singularities and spherical polygons. Illinois J. Math., v.58 (2014) 739-755. PDF

A. Eremenko, A. Gabrielov. Spectral loci of Sturm-Liouville operators with polynomial potentials. In book: Spectral Theory and Differential Equations. V. A. Marchenko 90th Anniversary Collection (editors: E.Khruslov and L.Pastur, AMS Providence, RI, 2014) PDF

A. Gabrielov, V. Keilis-Borok, S. Olsen and I. Zaliapin. Predictability of extreme events in a branching diffusion model. In book: Extreme natural hazards, disaster risks and societal implications. Cambridge University Press (2014) p.126-142. PDF

S. Basu, A. Gabrielov, N. Vorobjov. A Helly-type theorem for semi-monotone sets and monotone maps. Discrete and Comput Geometry, DOI 10.1007/s00454-013-9540-y (2013) PDF

S. Basu, A. Gabrielov, N. Vorobjov. Monotone functions and maps. Revista Real Acad. Cienc. Exactas, Fisicas y Naturales. Ser. A. Matematicas (RACSAM) v.107 (2013) 5-33. PDF

S. Basu, A. Gabrielov, N. Vorobjov. Semi-monotone sets. J. European Math. Soc., v.15 (2013) 635-657. PDF

A. Eremenko, A. Gabrielov. Two-parametric PT-symmetric quartic family. J. Phys. A: Math. Theor. v.45 (2012) 175206. PDF

A. Eremenko, A. Gabrielov. Quasi-exactly solvable quartic: real algebraic spectral locus. J. Phys. A: Math. Theor. v.45 (2012) 175205. PDF

P. Alexandersson, A. Gabrielov. On eigenvalues of the Schrodinger operator with a complex-valued polynomial potential. Comput. Methods and Function Theory v.12 (2012) 119-144. PDF

A. Eremenko, A. Gabrielov. Singular perturbations of polynomial potentials in the complex domain with applications to PT-symmetric families. Moscow Math. J., 11 (2011) 473-503. PDF

A. Eremenko, A. Gabrielov. Quasi-exactly solvable quartic: elementary integrals and asymptotics. J. Phys. A: Math. Theor. v.44 (2011) 312001. PDF

M. Azar, A. Gabrielov. Some lower bounds in the B. and M. Shapiro conjecture for flag varieties. Discr. Comput. Geom. 46 (2011) 636-659, DOI: 10.1007/s00454-010-9314-8. PDF

A. Eremenko, A. Gabrielov. Elementary proof of the B. and M. Shapiro conjecture for rational functions. In: Notions of positivity and the geometry of polynomials, Springer (2011), p.167-178. PDF

A. Eremenko, A. Gabrielov Tangencies between holomorphic maps and holomorphic laminations. Proc. Amer. Math. Soc. v.138 (2010) 2489-2492. PDF

V. Keilis-Borok, A. Gabrielov, A. Soloviev Geo-complexity and earthquake prediction. In: Encyclopedia of Complexity and Systems Science, Part 7, p.4178-4194, DOI: 10.1007/978-0-387-30440-3_246, Springer, 2009. PDF

A. Gabrielov, N. Vorobjov Approximation of definable sets by compact families, and upper bounds on homotopy and homology. J. London Math. Soc. v.80 (2009) 45-54, doi: 10.1112/jlms/jdp006 PDF

A. Eremenko, A. Gabrielov Analytic continuation of eigenvalues of a quartic oscillator. Comm. Math. Physics v.287 (2009) 431-457, DOI 10.1007/s00220-008-0663-6 PDF

A. Gabrielov, V. Keilis-Borok, Ya. Sinai, I. Zaliapin Statistical Properties of the Cluster Dynamics of the Systems of Statistical Mechanics. In: Boltzmann's Legacy, ESI Lectures in Mathematics and Physics, EMS Publishing House, 2008, p.203-216. PDF

I. Zaliapin, A. Gabrielov, V. Keilis-Borok, H. Wong Clustering analysis of seismicity and aftershock identification. Phys. Rev. Letters, v.101 (2008) 018501 PDF

A. Eremenko, A. Gabrielov, B. Shapiro Zeros of eigenfunctions of some anharmonic oscillators. Ann. Inst. Fourier, v.58 (2008) 603-624 PDF

A. Eremenko, A. Gabrielov, B. Shapiro High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials. Comput. Methods and Function Theory, v.8 (2008) p.513-529 PDF

A. Gabrielov. Counter-examples to quantifier elimination for fewnomial and exponential expressions. Moscow Math. J., v.7 (2007) p.453-460 PDF

A. Gabrielov, D. Novikov, B. Shapiro Mystery of point charges. Proc. LMS, v.95 (2007) p.443-472; doi:10.1112/plms/pdm012 PDF

A. Gabrielov, V.I. Keilis-Borok, V. Pinsky, O.M. Podvigina, A. Shapira, V.A. Zheligovsky Fluid migration and dynamics of a blocks-and-faults system. Tectonophysics, v.429, p.229-251, 2007. PDF

A. Eremenko, A. Gabrielov, M. Shapiro. A. Vainshtein Rational functions and real Schubert calculus. Proceedings of the AMS, v.134, p.949-957, 2006. PDF

P. Shebalin, V. Keilis-Borok, A. Gabrielov, I. Zaliapin and D. Turcotte Short-term earthquake prediction by reverse analysis of lithosphere dynamics, Tectonophysics, v.413, p.63-75, 2006. PDF

Ilya Zaliapin, Henry Wong and Andrei Gabrielov Hierarchical aggregation in percolation model, Tectonophysics, v.413, p.93-107, 2006. PDF

G. Yakovlev, W.I. Newman, D.L. Turcotte, A. Gabrielov An inverse cascade model for self-organized complexity and natural hazards. Geophys. J. Int., v.163, p.433-442, 2005. PDF

I. Zaliapin, H. Wong, A. Gabrielov Inverse cascade in percolation model: hierarchical description of time-dependent scaling. Phys. Rev. E, v.71, 066118, 2005. PDF

A. Gabrielov, N. Vorobjov Betti numbers of semialgebraic sets defined by quantifier-free formulae. Discrete and Computational Geometry, v.33, p.395-401, 2005. PDF

I. Zaliapin, A. Gabrielov, V. Keilis-Borok Multiscale trend analysis for time series. Fractals, v.12, p.275-292, 2004. PDF

V. Keilis-Borok, P. Shebalin, A. Gabrielov, D. Turcotte Reverse tracing of short-term earthquake precursors. Physics of the Earth and Planetary Interiors, v.145, p.75-85, 2004. PDF

A. Gabrielov, N. Vorobjov Complexity of computations with Pfaffian and Noetherian functions. In Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Kluwer 2004. PDF

A. Gabrielov, N. Vorobjov, T. Zell Betti numbers of semialgebraic and sub-Pfaffian sets. J. London Math. Soc., v.69, p.27-43, 2003. PDF

A. Gabrielov, T. Zell On the number of connected components of the relative closure of a semi-Pfaffian family. In Algorithmic and Quantitative Real Algebraic Geometry, AMS 2003, p.65-75. PDF

A. Gabrielov Relative closure and the complexity of Pfaffian elimination. In Discrete and Computational Geometry: The Goodman-Pollack Festschrift, Springer, 2003. PDF

A. Eremenko, A. Gabrielov Pole placement by static output feedback for generic linear systems. SIAM J. on Control and Optimization, v.41 p.303-312, 2002. PDF

A. Eremenko, A. Gabrielov Degrees of real Wronski maps. Discrete and Computational Geometry, v.28, p.331-347, 2002. PDF

A. Eremenko, A. Gabrielov Counterexamples to pole placement by static output feedback. Linear Algebra and its Applications, v.351-352, p.211-218, 2002. PDF

A. Eremenko, A. Gabrielov Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry. Annals of Mathematics, v.155, p.105-129, 2002. PDF

A. Eremenko, A. Gabrielov The Wronski map and Grassmannians of real codimension 2 subspaces. Computational Methods and Function Theory, v.1, p.1-25, 2001. PDF

A. Gabrielov, N. Vorobjov Complexity of cylindrical decompositions of sub-Pfaffian sets. J. Pure and Applied Algebra, v.164, p.179-197, 2001. PDF

D.L. Turcotte, W.I. Newman, A. Gabrielov. A statistical physics approach to earthquakes. In: Geocomplexity and the Physics of Earthquakes, AGU, 2000, p.83-96.

A. Gabrielov, I. Zaliapin, W.I. Newman, V.I. Keilis-Borok. Colliding cascades model for earthquake prediction. Geophys. J. Int., v.143, p.427-437, 2000. PDF

A. Gabrielov, V. Keilis-Borok, I. Zaliapin, W.I. Newman. Critical transitions in colliding cascades. Phys. Rev. E, v.62, p.237-249, 2000. PDF

A. Gabrielov. Coxeter-Dynkin diagrams and singularities. In: Selected Papers of E.B. Dynkin, AMS, 2000, p.367-369. PDF

A. Gabrielov, W.I. Newman, D.L. Turcotte. An exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling. Phys. Rev. E, 1999, v.60, p.5293-5300. PDF

A. Gabrielov. Multiplicity of an analytic function on a trajectory of a vector field. In: The Arnoldfest, Fields Inst. Communications , AMS, 1999, p.191-200. PDF

A. Gabrielov and A.G. Khovanskii. Multiplicity of a Noetherian intersection. In: Geometry of Differential Equations, AMS, 1998, p.119-131. PDF

A. Gabrielov. Frontier and closure of a semi-Pfaffian set. J. Discrete and Computational Geometry, 1998, v.19, p.605-617. PDF

G. Morein, D.L. Turcotte, A. Gabrielov. On the statistical mechanics of distributed seismicity Geophys. J. Int., 1997, v.131, p.552-558. PDF

W.I. Newman, D.L. Turcotte, A. Gabrielov. Fractal trees with side branching. Fractals, 1997, v.5, p.603-614 PDF

A. Gabrielov, V. Keilis-Borok, and D.D. Jackson. Geometric incompatibility in a fault system. Proc. Natl. Acad. Sci. USA, 1996, v.93, p.3838-3842. PDF

A. Gabrielov. Complements of subanalytic sets and existential formulas for analytic functions. Inventiones Mathematicae, 1996, v.125, p.1-12. PDF

W.I. Newman, D.L. Turcotte, and A. Gabrielov. Log-periodic behavior of a hierarchical failure model with applications to precursory seismic activation. Phys. Rev. E, 1995, v.52, p.4827-4835. PDF

A. Gabrielov. Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy. Math. Research Letters, 1995, v.2, p.437-451. PDF

A. Gabrielov. Multiplicities of Pfaffian Intersections and the Lojasiewicz Inequality. Selecta Mathematica, New Series, 1995, v.1, p.113-127. PDF

A. Gabrielov and N. Vorobjov. Complexity of stratifications of semi-Pfaffian sets. J. Discrete and Computational Geometry, 1995, v.14, p.71-91. PDF

A. Gabrielov, W.I. Newman, and L. Knopoff. Lattice models of failure: sensitivity to the local dynamics. Phys. Rev. E, 1994, v.50, n.1, p.188-197.

W.I. Newman, A. Gabrielov, and D.L. Turcotte, editors. Nonlinear Dynamics and Predictability of Geophysical Phenomena, AGU, 1994.

A. Gabrielov. Avalanches, Sandpiles and Tutte Decomposition. In: The Gelfand Mathematical Seminars, 1990-1992, Birkhauser, 1993, p.19-26. PDF

A. Gabrielov. Abelian avalanches and Tutte polynomials. Physica A, 1993, v.195, p.253-274. PDF

W.I. Newman and A. Gabrielov. Failure of hierarchical distributions of fiber bundles. I. Internat. J. of Fracture, 1991, v.50, p.1-14.

A. Gabrielov, T. Levshina, and I. Rotwain. Block model of earthquake sequence. Phys. Earth Planetary Interior, 1990, v.61, n.1-2, p.18-28.

A. Gabrielov and V. Keilis-Borok. Patterns of stress corrosion: geometry of the principal stresses. Pure and Applied Geophysics, 1983, v.121, n.3, p.477-494. PDF

M. Caputo, R. Console, A. Gabrielov, V.I. Keilis-Borok, and T. Sidorenko. Long-Term Premonitory Seismicity Patterns in Italy. Geophys. J. R. astr. Soc., 1983, v.75, p.71-75.

A. Gabrielov. Polar curves and intersection matrices of singularities. Inventiones Mathematicae, 1979, v.54, p.15-23.

A. Gabrielov. Combinatorial formulas for Pontryagin classes and GL-invariant cocycles. Funct. Anal. Appl., 1978, v.12, n.2, p.1-7, in Russian. English translation: p.75-80. PDF

M. Alekseevskaya, A. Gabrielov, A. Gvishiani, I. Gel'fand, and E. Rantsman. Formal Morphostructural Zoning of mountain territories. J. of Geoph., 1977, v.43, n.1/2, p.227-235.

D. Fuchs, A. Gabrielov, and I. Gel'fand. The Gauss-Bonnet theorem and the Atiyah-Patodi-Singer functionals for the characteristic classes of foliations. Topology, 1976, v.15, p.165-188.

A. Gabrielov, I. Gel'fand, and M. Losik. Combinatorial calculation of characteristic classes.
Funct. Anal. Appl., 1975, v.9, n.1, p.54-55, in Russian. English translation: p.48-49.
Funct. Anal. Appl., 1975, v.9, n.2, p.12-28, in Russian. English translation: p.103-115.
Funct. Anal. Appl., 1975, v.9, n.3, p.5-26, in Russian. English translation: p.186-202.

A. Gabrielov, and A. Kushnirenko. Description of deformations with constant Milnor number for homogeneous functions. Funct. Anal. Appl., 1975, v.9, n.4, p.67-68, in Russian. English translation: p.329-331. PDF

A. Gabrielov. Bifurcations, Dynkin diagrams, and modality of isolated singularities. Funct. Anal. Appl., 1974, v.8, n.2, p.7-12, in Russian. English translation: p.94-98. PDF

A. Gabrielov. Formal relations between analytic functions. USSR Izv., Ser. Math., 1973, v.37, n.5, p.1056-1090, in Russian. English translation: p.1056-1088.

A. Gabrielov. Formal relations between analytic functions. Funct. Anal. Appl., 1971, v.5, n.2, p.64-65, in Russian. English translation: p.318-319. PDF

A. Gabrielov. On a theorem of Hormander. Funkt. Anal. Appl., 1970, v.4, n.2, p.18-22, in Russian. English translation: p.106-109. PDF

A. Gabrielov. Projections of semi-analytic sets. Funct. Anal. Appl., 1968, v.2, n.4, p.18-30, in Russian. English translation: p.282-291. PDF



Last update: May 11, 2018
URL: http://www.math.purdue.edu/~agabriel/publ.html