Recent Publications:

• M. Gekhtman, M. Shapiro, and A. Vainshtein, A plethora of cluster structures on GL_n, Mem. Amer. Math. Soc., (2024), 297, 1486, 104pp.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Generalized cluster structures related to the Drinfeld double of GL_n, J. London Math. Soc. (2022) 105, 1601--1633.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Periodic staircase matrices and generalized cluster structures, Int. Math. Res. Notes (2022), 4181--4221.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Drinfeld double of GL_n and generalized cluster structures, Proc. London Math. Soc. (2018) 116, 429--484.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Exotic cluster structures on SL_n: the Cremmer-Gervais case, Mem. Amer. Math. Soc. (2017) 246, 1165, 94pp.
• M. Gekhtman, M. Shapiro, S. Tabachnikov, and A. Vainshtein, Integrable cluster dynamics of directed networks and pentagram maps, Adv. Math. (2016) 300, 390--450.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Generalized cluster structure on the Drinfeld double of GL_n, C. R. Math. Acad. Sci. Paris (2016) 354, 345–349.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Cremmer-Gervais cluster structure on SL_n, PNAS, (2014) 111 (27), 9688--9695.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification, Moscow Math. J., (2012) 12, 293--312.
• M. Gekhtman, M. Shapiro, A. Stolin and A. Vainshtein, Poisson structures compatible with the cluster algebra structure in Grassmannians, Lett. Math. Phys., (2012) 100, 139--150.
• M. Gekhtman, M. Shapiro, S. Tabachnikov, and A. Vainshtein, Higher pentagram maps, weighted directed networks, and cluster dynamics, Electron. Res. Announc. Math. Sci., (2012) 19, 1--17.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Poisson geometry of directed networks in an annulus, J. Europ. Math. Soc., (2012) 14, 541--570.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Generalized Backlund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective, Acta Math., (2011) 206, 245--310.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster algebras and Poisson geometry. American Mathematical Society, Providence, RI, 2010. xvi+246 pp. ISBN: 978-0-8218-4972-9
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Poisson geometry of directed networks in a disk, Selecta Math., (2009) 15, 61--103.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, On the properties of the exchange graph of a cluster algebra, Math. Res. Lett., (2008) 15, 321--330.
• S. Shadrin, M. Shapiro, and A. Vainshtein, Chamber behavior of double Hurwitz numbers in genus 0, Adv. Math., (2008) 217, 79-96
• A. Eremenko, A. Gabrielov, M. Shapiro, and A. Vainshtein, Rational functions and real Schubert calculus, Proc. Amer. Math. Soc., (2006) 134, 949-957
• B. Shapiro, M. Shapiro, and A. Vainshtein, Periodic de Bruijn triangles: exact and asymptotic results, Discr. Math., (2005) 298, 321--333.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster algebras and Weil-Petersson forms, Duke Math. J., (2005) 127, 291--311. Correction: Duke Math. J., (2007) 139, 407--409.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster algebras and Poisson geometry, Moscow Math. J., (2003) 3, 899--934.
• B. Shapiro and A. Vainshtein, Counting real rational functions with all real critical values, Moscow Math. J. (2003) 3, 647--659.
• G. Gutin, A. Vainshtein, and A. Yeo, Domination analysis of combinatorial optimization problems, Discr. Appl. Math. (2003) 129, 513--520.
• B. Shapiro and A. Vainshtein, On the number of connected components in the space of M-polynomials in hyperbolic functions, Adv. Appl. Math. (2003) 30, 273--282.
• M. Gekhtman, M. Shapiro, and A. Vainshtein, The number of connected components in the double Bruhat cells for nonsimply-laced groups, Proc. AMS (2003) 131, 731--739.
• S. Natanzon, B. Shapiro and A. Vainshtein, Topological classification of generic real rational functions, J. Knot Theory Ramifications (2002), 11, 1063--1075.
• O. Sharon, A. Vainshtein, and A. Likholat, On the relation between the throughput gain with slot reuse and the number of address bits in the dual bus configuration. Part 1: Maximum throughput, Computer Systems Science & Engineering (2002) 17, 223--236.
• T. Mansour and A. Vainshtein, Counting occurrences of 132 in a permutation, Adv. Appl. Math. (2002) 28, 185--195.
• I. Basov and A. Vainshtein, Approximation algorithms for multi-parameter graph optimization problems, Discr. Appl. Math. (2002) 119, 129--138.
• T. Mansour and A. Vainshtein, Layered restrictions and Chebyshev polynomials, Annals of Combinatorics (2001) 5, 451--458.
• T. Mansour and A. Vainshtein, Restricted permutations and Chebyshev polynomials, Sem. Lothar. Combin. (2001) 47, B47c.
• T. Ekedahl, S. Lando, M. Shapiro, and A. Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves, Inventiones Math. (2001) 146, 297--327.
• T. Mansour and A. Vainshtein, Restricted 132-avoiding permutations, Adv. Appl. Math. (2001) 26, 258--269.
• T. Mansour and A. Vainshtein, Avoiding maximal parabolic subgroups of S_k, Discr. Math. Theor. Comp. Sci. (2000) 4, 67--77.
• B. Shapiro, M. Shapiro, A. Vainshtein, and A. Zelevinsky, Simply-laced Coxeter groups and groups generated by symplectic transvections, Michigan Mathematical Journal (2000) 48, 531--552.
• Ye. Dinitz and A. Vainshtein, The general structure of edge-connectivity of a vertex subset in a graph and its incremental maintenance. Odd case, SIAM J. Computing (2000) 30, 753--808.
• T. Mansour and A. Vainshtein, Restricted permutations, continued fractions, and Chebyshev polynomials, Electronic Journal of Combinatorics (2000) 7, R17.
• I. Goulden, D. Jackson, and A. Vainshtein, The number of ramified coverings of the sphere by the torus and surfaces of higher genera, Annals of Combinatorics (2000) 4, 27--46.
• T. Ekedahl, S. Lando, M. Shapiro, and A. Vainshtein, On Hurwitz numbers and Hodge integrals, Comptes Rendus Acad. Sci. Paris (1999) 328, 1175--1180.
• B. Shapiro, M. Shapiro, and A. Vainshtein, Skew-symmetric vanishing lattices and intersections of Schubert cells, Int. Math. Res. Notes (1998) no.11, 563--588.
• B. Shapiro, M. Shapiro, and A. Vainshtein, Kazhdan--Luzstig polynomials for certain varieties of incomplete flags, Discr. Math. (1998) 180, 345--355.
• B. Shapiro, M. Shapiro, and A. Vainshtein, Connected components in the intersection of two open opposite Schubert cells in SL_n(R)/B, Int. Math. Res. Notes (1997) no.10, 469--493.
• A. Berenstein and A. Vainshtein, Concavity of weighted arithmetic means with applications, Arch. Math. (1997) 69, 120--126.
• B. Shapiro, M. Shapiro, and A. Vainshtein, Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs, Adv. in Math. Sci. 34 (1997) 219--228.
• B. Shapiro, M. Shapiro, and A. Vainshtein, On combinatorics and topology of pairwise intersections of Schubert cells in SL_n/B, In: Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory, Birkhauser, 1997, 397--437.
• A. Kreinin and A. Vainshtein, Asymptotics for generalized Morgan numbers of fractional orders, Discr. Math. (1996) 161, 301--308.
• B. Shapiro, M. Shapiro, and A. Vainshtein, Topology of intersections of Schubert cells and Hecke algebra, Discr. Math. (1996) 153, 305--318.
• C. Schwartz, J. Teich, A. Vainshtein, E. Welzl, and B. Evans, Minimal enclosing parallelogram with application, Proc. 11th ACM Symp. Comput. Geometry (1995) c34--c35.
• Ye. Dinitz and A. Vainshtein, Locally orientable graphs, cell structures, and a new incremental algorithm for maintaining the connectivity carcass in a graph, Proc. 6th ACM--SIAM Symp. Discrete Algorithms (1995) 302--311.
• M. Shapiro and A. Vainshtein, Stratification of Hermitean matrices and the Alexander mapping, Comptes Rendus Acad. Sci. Paris (1995) 321, 1599--1604.
• Ye. Dinitz and A. Vainshtein, The connectivity carcass of a vertex subset in a graph and its incremental maintenance, Proc. 26th ACM Symp. Theor. Comp. (1994) 716--725.
• L. Boguslavsky, K. Harzallah, A. Kreinin, K. Sevcik, and A. Vainshtein, Optimal strategies for spinning and blocking, J. of Parallel and Distributed Computing (1994) 21, 246--254.