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Tsikh, Avgust Karlovich
Professor
Doctor of physico-mathematical sciences
E-mail:
Keywords: discriminant locus, linearization of algebraic set, logarithmic Gauss mapping.

https://www.mathnet.ru/eng/person8358
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/200018
https://orcid.org/0000-0002-2905-9167

Publications in Math-Net.Ru Citations
2023
1. Matvey E. Durakov, Roman V. Ulvert, August K. Tsikh, “On the non-standard interpolations in $\mathbb{C}^n$ and combinatorial coefficients for Weil polyhedra”, J. Sib. Fed. Univ. Math. Phys., 16:6 (2023),  758–772  mathnet
2. Irina A. Antipova, Timofey A. Efimov, Avgust K. Tsikh, “Mellin transforms for rational functions with quasi-elliptic denominators”, J. Sib. Fed. Univ. Math. Phys., 16:6 (2023),  738–750  mathnet
3. M. E. Durakov, E. K. Leinartas, A. K. Tsikh, “Multidimensional Hermite interpolation”, Sib. Èlektron. Mat. Izv., 20:2 (2023),  700–710  mathnet
2022
4. Evgeny D. Leinartas, August K. Tsikh, “On a multidimensional version of the principal theorem of difference equations with constant coefficients”, J. Sib. Fed. Univ. Math. Phys., 15:1 (2022),  125–132  mathnet  mathscinet  isi 2
2020
5. E. N. Mikhalkin, V. A. Stepanenko, A. K. Tsikh, “Geometry of factorization identities for discriminants”, Dokl. RAN. Math. Inf. Proc. Upr., 493 (2020),  21–25  mathnet  zmath  elib; Dokl. Math., 102:1 (2020), 279–282 2
2019
6. Lisa Nilsson, Mikael Passare, August K. Tsikh, “Domains of convergence for $A$-hypergeometric series and integrals”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019),  509–529  mathnet  isi 8
2018
7. Irina A. Antipova, Evgeny N. Mikhalkin, Avgust K. Tsikh, “Singular points of complex algebraic hypersurfaces”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018),  670–679  mathnet  isi 1
8. I. A. Antipova, E. N. Mikhalkin, A. K. Tsikh, “Rational expressions for multiple roots of algebraic equations”, Mat. Sb., 209:10 (2018),  3–30  mathnet  mathscinet  zmath  elib; Sb. Math., 209:10 (2018), 1419–1444  isi  scopus 5
2015
9. Evgeny N. Mikhalkin, Avgust K. Tsikh, “On the structure of the classical discriminant”, J. Sib. Fed. Univ. Math. Phys., 8:4 (2015),  426–436  mathnet 1
10. E. N. Mikhalkin, A. K. Tsikh, “Singular strata of cuspidal type for the classical discriminant”, Mat. Sb., 206:2 (2015),  119–148  mathnet  mathscinet  zmath  elib; Sb. Math., 206:2 (2015), 282–310  isi  scopus 6
2014
11. Natalia A. Bushueva, Konstantin V. Kuzvesov, Avgust K. Tsikh, “On the asymptotic of homological solutions to linear multidimensional difference equations”, J. Sib. Fed. Univ. Math. Phys., 7:4 (2014),  417–430  mathnet 2
2012
12. I. A. Antipova, A. K. Tsikh, “The discriminant locus of a system of $n$ Laurent polynomials in $n$ variables”, Izv. RAN. Ser. Mat., 76:5 (2012),  29–56  mathnet  mathscinet  zmath  elib; Izv. Math., 76:5 (2012), 881–906  isi  elib  scopus 15
13. N. A. Bushueva, A. K. Tsikh, “On amoebas of algebraic sets of higher codimension”, Trudy Mat. Inst. Steklova, 279 (2012),  59–71  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 279 (2012), 52–63  isi 8
2009
14. Dmitry Yu. Pochekutov, Avgust K. Tsikh, “On the Asymptotics of Laurent Coefficients and its Application in Statistical Mechanics”, J. Sib. Fed. Univ. Math. Phys., 2:4 (2009),  483–493  mathnet 3
15. Anastasiya Yu. Semusheva, August K. Tsikh, “Domains of Convergence of Hypergeometric Series of Several Complex Variables”, J. Sib. Fed. Univ. Math. Phys., 2:2 (2009),  221–229  mathnet  elib 2
2008
16. Alexandr G. Aleksandrov, Avgust K. Tsikh, “Multi-Logarithmic Differential Forms on Complete Intersections”, J. Sib. Fed. Univ. Math. Phys., 1:2 (2008),  105–124  mathnet  elib 5
17. E. K. Leinartas, M. Passare, A. K. Tsikh, “Multidimensional versions of Poincaré's theorem for difference equations”, Mat. Sb., 199:10 (2008),  87–104  mathnet  mathscinet  zmath  elib; Sb. Math., 199:10 (2008), 1505–1521  isi  elib  scopus 14
2006
18. A. Yger, A. K. Tsikh, “Residue currents”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 108 (2006),  181–264  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 120:6 (2004), 1916–1971 13
19. A. V. Shchuplev, A. K. Tsikh, A. Yger, “Residual Kernels with Singularities on Coordinate Planes”, Trudy Mat. Inst. Steklova, 253 (2006),  277–295  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 253 (2006), 256–274  scopus 13
2005
20. E. K. Leinartas, M. Passare, A. K. Tsikh, “Asymptotics of multidimensional difference equations”, Uspekhi Mat. Nauk, 60:5(365) (2005),  171–172  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 60:5 (2005), 977–978  isi  elib  scopus 2
21. V. P. Krivokolesko, A. K. Tsikh, “Integral representations in linearly convex polyhedra”, Sibirsk. Mat. Zh., 46:3 (2005),  579–593  mathnet  mathscinet; Siberian Math. J., 46:3 (2005), 453–466  isi 7
1998
22. O. N. Zhdanov, A. K. Tsikh, “Investigation of multiple Mellin–Barnes integrals by means of multidimensional residues”, Sibirsk. Mat. Zh., 39:2 (1998),  281–298  mathnet  mathscinet  zmath; Siberian Math. J., 39:2 (1998), 245–260  isi 49
1996
23. T. O. Ermolaeva, A. K. Tsikh, “Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues”, Mat. Sb., 187:9 (1996),  45–64  mathnet  mathscinet  zmath; Sb. Math., 187:9 (1996), 1301–1318  isi  scopus 10
24. M. Passare, A. K. Tsikh, A. A. Cheshel, “Iterated Mellin–Barnes integrals as periods on the Calabi–Yau manifolds with several modules”, TMF, 109:3 (1996),  381–394  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 109:3 (1996), 1544–1555  isi 32
1995
25. V. M. Trutnev, A. K. Tsikh, “On the structure of residue currents and functionals orthogonal to ideals in the space of holomorphic functions”, Izv. RAN. Ser. Mat., 59:5 (1995),  203–224  mathnet  mathscinet  zmath; Izv. Math., 59:5 (1995), 1083–1102  isi 5
26. N. A. Buruchenko, A. K. Tsikh, “Homology reduction of cycles in the complement of an algebraic hypersurface”, Mat. Sb., 186:10 (1995),  31–40  mathnet  mathscinet  zmath; Sb. Math., 186:10 (1995), 1417–1427  isi 2
1992
27. M. Passare, A. Tsikh, “On the relations between the local structure of holomorphic mappings, multidimensional residues and generalized Mellin transforms”, Dokl. Akad. Nauk, 325:4 (1992),  664–667  mathnet  mathscinet  zmath; Dokl. Math., 46:1 (1993), 88–91
1991
28. A. K. Tsikh, “Conditions for absolute convergence of the Taylor coefficient series of a meromorphic function of two variables”, Mat. Sb., 182:11 (1991),  1588–1612  mathnet  mathscinet  zmath; Math. USSR-Sb., 74:2 (1993), 337–360  isi 16
1989
29. A. K. Tsikh, “Integrals of rational functions over the space $\mathbf{R}^n$”, Dokl. Akad. Nauk SSSR, 307:6 (1989),  1325–1329  mathnet  mathscinet  zmath; Dokl. Math., 40:1 (1990), 258–262 3
1988
30. A. A. Alyakrinskii, A. K. Tsikh, “Cohomology of rational differential forms of degree $n$ in the space $\mathbb C^n$”, Mat. Zametki, 43:4 (1988),  522–532  mathnet  mathscinet  zmath; Math. Notes, 43:4 (1988), 301–307  isi 1
1987
31. A. K. Tsikh, “Weakly holomorphic functions on complete intersections, and their holomorphic extension”, Mat. Sb. (N.S.), 133(175):4(8) (1987),  429–445  mathnet  mathscinet  zmath; Math. USSR-Sb., 61:2 (1988), 421–436 7
1985
32. A. K. Tsikh, “Higher-dimensional residues and their applications. Chapter 3”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 8 (1985),  45–64  mathnet 2
33. A. K. Tsikh, “A generalization of Bertini's theorem on the index of a prime ideal in the ring $O_a$”, Uspekhi Mat. Nauk, 40:2(242) (1985),  205–206  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:2 (1985), 241–242  isi
1984
34. A. K. Tsikh, “Criteria for representability of integrals over cycles by Grothendieck residues”, Dokl. Akad. Nauk SSSR, 277:5 (1984),  1083–1087  mathnet  mathscinet  zmath 1
35. K. V. Safonov, A. K. Tsikh, “Singularities of the Grothendieck parametric residue and diagonals of a double power series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1984, no. 4,  51–58  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 28:4 (1984), 65–74 2
36. A. K. Tsikh, “Local residues in $\mathbf C^n$. Algebraic applications”, Mat. Sb. (N.S.), 123(165):2 (1984),  230–242  mathnet  mathscinet  zmath; Math. USSR-Sb., 51:1 (1985), 225–237 1
37. A. K. Tsikh, A. P. Yuzhakov, “Properties of the complete sum of residues with respect to a polynomial mapping, and their applications”, Sibirsk. Mat. Zh., 25:4 (1984),  207–213  mathnet  mathscinet  zmath; Siberian Math. J., 25:4 (1984), 677–682  isi
1980
38. L. A. Aizenberg, V. A. Bolotov, A. K. Tsikh, “On the solution of systems of nonlinear algebraic equations using the multidimensional logarithmic residue. On the solvability in radicals”, Dokl. Akad. Nauk SSSR, 252:1 (1980),  11–14  mathnet  mathscinet  zmath 2
1979
39. A. K. Tsikh, “A theorem on a complete sum of residues in $\mathbb CP^n$”, Uspekhi Mat. Nauk, 34:6(210) (1979),  207–210  mathnet  mathscinet  zmath; Russian Math. Surveys, 34:6 (1979), 246–249
40. L. A. Aizenberg, A. K. Tsikh, “Application of a multidimensional logarithmic residue to systems of nonlinear algebraic equations”, Sibirsk. Mat. Zh., 20:4 (1979),  699–707  mathnet  mathscinet  zmath; Siberian Math. J., 20:4 (1979), 485–491  isi 2
1978
41. A. P. Yuzhakov, A. K. Tsikh, “The multiplicity of the zero of a system of holomorphic functions”, Sibirsk. Mat. Zh., 19:3 (1978),  693–697  mathnet  mathscinet  zmath; Siberian Math. J., 19:3 (1978), 489–492  isi 6
1977
42. A. K. Tsikh, “The two-dimensional homology group of the complement of an algebraic curve in $CP^2$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1977, no. 5,  122–124  mathnet  mathscinet  zmath
1975
43. A. K. Tsikh, “Cycles that separate the zeros of analytic functions in $C^n$”, Sibirsk. Mat. Zh., 16:5 (1975),  1118–1121  mathnet  mathscinet  zmath; Siberian Math. J., 16:5 (1975), 859–862  isi 3
2022
44. F. A. Bogomolov, S. O. Gorchinskiy, A. B. Zheglov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, A. N. Parshin, V. L. Popov, V. V. Przyjalkowski, Yu. G. Prokhorov, M. Reid, A. G. Sergeev, D. V. Treschev, A. K. Tsikh, I. A. Cheltsov, E. M. Chirka, “Viktor Stepanovich Kulikov (on his 70th birthday)”, Uspekhi Mat. Nauk, 77:3(465) (2022),  179–181  mathnet  mathscinet; Russian Math. Surveys, 77:3 (2022), 555–557  isi
2018
45. A. I. Aptekarev, V. K. Beloshapka, V. I. Buslaev, V. V. Goryainov, V. N. Dubinin, V. A. Zorich, N. G. Kruzhilin, S. Yu. Nemirovski, S. Yu. Orevkov, P. V. Paramonov, S. I. Pinchuk, A. S. Sadullaev, A. G. Sergeev, S. P. Suetin, A. B. Sukhov, K. Yu. Fedorovskiy, A. K. Tsikh, “Evgenii Mikhailovich Chirka (on his 75th birthday)”, Uspekhi Mat. Nauk, 73:6(444) (2018),  204–210  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 73:6 (2018), 1137–1144  isi

Presentations in Math-Net.Ru
1. Нестандартные интерполяции в $\mathbb C^n$
A. K. Tsikh

November 7, 2022 15:00
2. Logarithmic Gauss mapping as branched covering
A. K. Tsikh
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
November 2, 2022 16:45
3. Counting function in complex and tropical algebraic geometry
A. K. Tsikh
Algebra and geometry: conference on the occasion of V.S. Kulikov 70th birthday
May 24, 2022 11:00   
4. Multivariate Hermite interpolation
A. K. Tsikh
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
February 16, 2022 17:00
5. Multidimensional residues and interpolations
A. K. Tsikh
Virtual Workshop “Complex Analysis and Geometry”
November 19, 2021 15:00   
6. Amoebas, residues and algebraic interpolations
A. K. Tsikh
International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin
October 15, 2021 15:00   
7. Региональный научно-образовательный математический центр «Красноярский математический центр»
A. K. Tsikh
General Meeting of the Branch of Mathematical Sciences, RAS, 2021
April 19, 2021 13:40   
8. Counting function in complex and tropical geometries
A. K. Tsikh
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
March 24, 2021 16:45
9. Convexity properties for complements of analytic sets and their amoebas
August Tsikh
Conference on Complex Analysis and Mathematical Physics, dedicated to the 70th birthday of A. G. Sergeev
March 21, 2019 13:10   
10. Multiple roots of polynomial systems
A. K. Tsikh
International Conference on Complex Analysis, dedicated of 75th anniversary E. M. Chirki
December 4, 2017 14:00   
11. Logarithmic Gauss mapping for complex surfaces and solutions to algebraic equations
A. K. Tsikh
International Conference "Geometric Analysis and Control Theory"
December 10, 2016 10:40   
12. Rational expressions for multiple roots of algebraic equations
A. K. Tsikh
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
November 16, 2016 16:45
13. О структуре универсальной алгебраической функции
A. K. Tsikh
International conference on algebraic geometry, complex analysis and computer algebra
August 5, 2016 10:50
14. New versions of the Cauchy-Kovalevskaya theorem and the Weierstrass preparation theorem
A. K. Tsikh
The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
May 12, 2016 11:20   
15. О структуре общей алгебраической функции и ее дискриминанта
A. K. Tsikh
One-day conference "Complex Analysis and Geometry" dedicated to the memory of A. G. Vituskin
October 7, 2014 11:40   
16. Amoebas of complex analytic sets
Avgust Tsikh
Russian–German conference on Several Complex Variables
February 27, 2012 15:30   
17. Amoebas in higher codimensions and difference equations
A. K. Tsikh
Second Russian-Armenian Workshop on Mathematical Physics, Complex Analysis and Related Topics
October 10, 2008 10:00   

Organisations
 
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