Publications and Presentations

Publications & Presentations

Alexander B. Levin

List of Publications

Books

1. Levin, A. B. Difference Algebra. Springer, New York, 2008. 522 pp.

ISBN-10: 9781402069468. ISBN-13: 978-1402069468

2. Kondrateva, M. V.; Levin, A. B.; Mikhalev, A. V.; Pankratev E. V. Differential and Difference Dimension Polynomials. Kluwer Academic Publishers, Dordrecht-Boston-London, 1999, 436 pp. ISBN-10: 9048151414. ISBN-13: 978-9048151417

Book chapters

1. Levin, A. B. Computation of the Strength of Systems of Difference Equations via Generalized Groebner Bases. Groebner Bases in Symbolic Analysis, 43-73. Walter de Gruyter, Berlin - New York, 2007. ISBN: 311019323X, 9783110193237

2. Levin, A. B. Difference Algebra. Handbook of Algebra, Vol. 4, 241 - 334. Elsevier, 2006.

ISBN-13: 978-0-444-52213-9

Papers

1. Levin, A. A New Type of Difference Dimension Polynomials. Accepted for publication in Mathematics in Computer Science, Vol. 16 (2022), 15 pp.

Doi: https://doi.org/10.1007/s11786-022-00540-9

2. Levin, A. Reduction with Respect to the Effective Order and a New Type of Dimension Polynomials of Difference Modules. ISSAC’22. Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, 55 – 62.

DOI: https://doi.org/10.1145/3476446.3535497.

3. Levin, A. Bivariate Kolchin-type dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation. Journal of Symbolic Computation, Vol. 102 (2021), 173 - 188. Doi: https://doi.org/10.1016/j.jsc.2019.10.014

4. Levin, A. Generalized Groebner Bases and New Properties of Multivariate Difference Dimension Polynomials. ISSAC '21: Proceedings of the 46th International Symposium on Symbolic and Algebraic Computation, July 2021, 273 – 280.

Doi: https://doi.org/10.1145/3452143.3465544

5. Evgrafov, A.; Levin, A. Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations. Mathematics in Computer Science, Vol. 14 (2020), 347 – 360. Doi: https://doi.org/10.1007/s11786-019-00430-7

6. Levin, A. Some properties of multivariate differential dimension polynomials and their invariants. ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, July 2020, 320 – 327. Doi: https://doi.org/10.1145/3373207.3404013

7. Levin, A. Multivariate Difference–Differential Dimension Polynomials. Mathematics in Computer Science, Vol. 14 (2020), 361 – 374. Doi: https://doi.org/10.1007/s11786-019-00436-1

8. Levin, A. Hilbert-Type Dimension Polynomials of Intermediate Difference-Differential Field Extensions. Lect. Notes in Comput. Sci. (Mathematical Aspects of Computer and Information Science), 11989 (2020), 64 -79. Doi: https://doi.org/10.1007/978-3-030-43120-4_7

9. A. Evgrafov, A; Goyal, S; Levin, A. Some properties and applications of multivariate dimension polynomials and their computation in Python. Proceedings of the 25^th International Conference on Applications of Computer Algebra. Montreal, Canada, 2019, 43 – 44.

10. A. Levin. Hilbert-type Functions of Non-reflexive Prime Difference Polynomial Ideals. Proceedings of the 25^th International Conference on Applications of Computer Algebra. Montreal, Canada, 2019, 87 – 88.

11. Levin, A. Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals. The Case of One Translation. Proceeding of the 43rd International Symposium on Symbolic and Algebraic Computation. New York, NY, 2018, 255 – 262

12. Levin, A. Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals. The Case of One Translation. Proceeding of the 43rd International Symposium on Symbolic and Algebraic Computation. New York, NY, 2018, 255 – 262.

13. Levin, A. Some Properties and Invariants of Multivariate Difference-Differential Dimension Polynomials. Proceedings of the 24^th International Conference on Applications of Computer Algebra. Santa de Compostela, Spain, 2018, 168 – 169.

https://par.nsf.gov/servlets/purl/10066959

14. Levin, A. Difference Dimension Quasi-polynomials. Advances in Appl. Math., 89 (2017), 1 – 17. Doi: https://doi.org/10.1016/j.aam.2017.02.003

15. Fuerst, C.; Levin, A. Relative Reduction and Buchberger’s Algorithm in Filtered Free Modules. Mathematics in Computer Science, Vol. 11 (2017), no. 3 - 4, 329 – 339.

Doi: https://doi.org/10.1007/s11786-017-0317-1

16. Levin, A. Dimension Polynomials of Intermediate Fields of Inversive Difference Field

Extensions. Lect. Notes in Comp. Sci., 9582 (2016), 362–376.

Doi: https://doi.org/10.1007/978-3-319-32859-1_31

17. Levin, A. Dimension polynomials of difference local algebras. Advances in Appl. Math., 72

(2016), 166–174. Doi: https://doi.org/10.1016/j.aam.2015.09.011

18. Levin, A. On the ascending chain condition for mixed difference ideals. International

Mathematics Research Notices, v. 2015, no. 10, 2830–2840.

Doi: https://doi.org/10.1093/imrn/rnu021

19. Levin, A. Multivariate Dimension Polynomials of Inversive Difference Field Extensions. Lecture Notes in Comput. Sci., 8372 (2014), 146–163.

Doi: https://doi.org/10.1007/978-3-642-54479-8_7

20. Levin, A. B. Multivariate Difference-Differential Polynomials and New Invariants of Difference-Differential Field Extensions. ISSAC’22. Proceedings of the 2013 International Symposium on Symbolic and Algebraic Computation, 267–274.

Doi: https://doi.org/10.1145/2465506.2465521

21.. Doench, C.; Levin, A. B. Bivariate Dimension Polynomials and New Invariants of Finitely Generated D-Modules. International Journal of Algebra and Computation, 23, no. 7 (2013) , 1625 - 1651. Doi: https://doi.org/10.1142/S0218196713500409

22. Doench, C.; Levin, A. B. Computation of the Strength of PDEs of Mathematical Physics and their Difference Approximations. Doctoral Program Computational Mathematics. Numerical Analysis and Symbolic Computation. Austrian Acad.of Sci. DK-Report 2012-09, 39 pp.

https://www.dk-compmath.jku.at/publications/dk-reports/2012-07-02/view

23. Doench, C.; Levin, A. B. Computation of Bivariate Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras. arXiv:1212.1833v1.

24. Levin, A. B. Dimension polynomials of intermediate fields and Krull-type dimension of finitely generated differential field extensions. Mathematics in Computer Science, 4 (2010), no. 2-3, 143-150. Doi: https://doi.org/10.1007/s11786-010-0048-z

25. Levin, A. B. Dimension Polynomials of Intermediate Differential Fields and the Strength of a System of Differential Equations with Group Action. Journal of Mathematical Sciences, 163, no. 5 (2009), 554-562. Doi: https://doi.org/10.1007/s10958-009-9693-7

26. Levin, A. B. Computation of the Strength of Systems of Difference Equations via Generalized Groebner Bases. Groebner Bases in Symbolic Analysis. Walter de Gruyter, 2007, 43 - 73. Doi: https://doi.org/10.1515/9783110922752.43

27. Levin, A. B. Groebner bases with respect to several orderings and multivariable dimension polynomials. Journal of Symbolic Computation, 42 (2007), 561-578.

Doi: https://doi.org/10.1016/j.jsc.2006.05.006

28. Levin, A. B. Inversive Difference Modules and Solvability of Systems of Linear Difference Equations. Rocky Mountain Journal of Mathematics, 37, no. 2 (2007), 519-532.

Doi: https://doi.org/10.1216/rmjm/1181068764

29. Levin, A. B. Groebner Bases with respect to Several Term Orderings and Multivariate Dimension Polynomials. ISSAC’07. Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, 251-260.

Doi:

30. Levin, A. B. Multivariable Difference Dimension Polynomials. Journal of Mathematical Sciences, 131, no. 6 (2005), 6060 - 6082. Doi: https://doi.org/10.1007/s10958-005-0461-z

31. Bhutani, K.; Levin, A. B. Graceful Numbers. International Journal of Mathematics and Mathematical Sciences, 29 (2002), no. 8, 495 - 499.

Doi: https://doi.org/10.1155/S0161171202007615

32. Bhutani, K.; Levin, A. B. The Problem of Sawing a Chain. Journal of Recreational Mathematics, 31, no.1 (2002-2003), 32 - 35.

33. Levin, A. B. On the Set of Hilbert Polynomials. Bulletin of the Australian Mathematical Society, 64 (2001), 291 - 305. Doi: https://doi.org/10.1017/S0004972700039952

34. Levin, A. B. Multivariable Dimension Polynomials and New Invariants of Differential Field Extensions. International Journal of Mathematics and Mathematical Sciences, 27 (2001), no. 4, 201 - 214. https://www.emis.de/journals/HOA/IJMMS/Volume27_4/214.pdf

35. Levin, A. B. Reduced Groebner bases, free difference-differential modules and difference-differential dimension polynomials. Journal of Symbolic Computation, 30 (2000), 357-382.

Doi: https://doi.org/10.1006/jsco.1999.0412

36. Levin, A. B. Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras. Bulletin of the Australian Mathematical Society, 61 (2000), no. 3, 387 - 403.

Doi: https://doi.org/10.1017/S0004972700022425

37. Levin, A. B. Generalized Characteristic Sets and Multivariable Differential Dimension Polynomials. Collection of Papers of VI International IMACS Conference on Applications of Computer Algebra, St. Petersburg, Russia, 2000, 69-72.

38. Levin, A. B. Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras. Collection of Papers of VI International IMACS Conference on Applications of Computer Algebra, St. Petersburg, Russia, 2000, 23 - 28.

39. Levin, A. B. Computation of Hilbert polynomials in two variables. Journal of Symbolic Computation, 28 (1999), 681 - 709. Doi: https://doi.org/10.1006/jsco.1999.0320

40. Levin, A. B.; Mikhalev, A. V. Type and Dimension of Finitely Generated G-algebras. Contemporary Mathematics, 184 (1995), 275 - 280.

40. Kondrateva, M. V.; Mikhalev, A. V.; Pankratev, E. V.; Levin, A. B. Computation of Dimension Polynomials. International Journal of Algebra and Computation, 3, no. 2 (1992), 117 - 137. Doi: https://doi.org/10.1142/S0218196792000098

42. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Filtered Differential G-modules and Extensions of Differential G-fields. Contemporary Mathematics, 131 (1992), Part 2, 469 – 489.

43. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Difference-Differential Modules and of Difference-Differential Field Extensions. Abelian Groups and Modules, no. 10 (1991), 56-82 (Russsian).

44. Levin, A. B.; Mikhalev, A. V. Type and Dimension of Finitely Generated G-algebras. Collection of Papers of the International Conference on Algebra in the Memory of A. Shirshov. Barnaul, Russia, 1991, p. 70 (Russian).

45. Levin, A. B. Type and Dimension of a Finitely Generated Module over a Twisted Group Algebra. Collection of Papers of the International Conference on Algebra in the Memory of A. Shirshov. Barnaul, Russia, 1991, p. 69 (Russian).

46. Levin, A. B.; Mikhalev, A. V. Type and Dimension of Finitely Generated Vector G-spaces. Vestnik of Moscow University, Ser. I, 1991, no. 4, 72 - 74 (Russian). English translation: Moscow University Mathematics Bulletin, 46, no. 4, 51 - 52.

47. Levin, A. B.; Mikhalev, A. V. Characteristic Polynomials of Filtered Modules over Twisted Group Rings. Collection of Papers of VI National Symposium on the Theory of Rings, Algebras, and Modules. Lvov, Ukraine, 1990, p. 80 (Russian).

48. Levin, A. B. Dimension Polynomial of a Finitely Generated Difference Field Extension. Collection of Papers of VI National Symposium on the Theory of Rings, Algebras, and Modules. Lvov, Ukraine, 1990, p. 79 (Russian).

49. Levin, A. B. The Use of Multilevel Problems in Precalculus and Calculus. Collection of Papers of the International Conference on Mathematics Education. Tula, 1989, 11 - 12 (Russian).

50. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Differential Modules. Abelian Groups and Modules, no. 9 (1989), 51 - 67 (Russian).

51. Levin, A. B. Dimension Polynomials of Filtered G-modules. Moscow State University, VINITI. No. 6849-B88 (1988), 1 - 27 (Russian).

52. Levin, A. B. Difference-Differential Dimension Polynomials. (Jointly with A. Mikhalev) Moscow State University, VINITI, no. 6848-B88 (1988), 1 - 64 (Russian).

53. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Filtered G-modules and of Finitely Generated G-field Extensions. Collection of Papers on Algebra. Moscow State University, 1989, 74 - 94 (Russian).

54. Levin, A. B. Dimension Polynomials of Difference Modules with m-adic Topology. Collection of Papers "Topological Algebra". Kishinev, Moldavia, 1988, p. 40 (Russian).

55. Levin, A. B. Difference-Differential Dimension Polynomials and the Strength of a System of Difference-Differential Equations. Collection of Papers of XIX National Conference on Algebra. Lvov, Ukraine, 1987. Part I, p. 157 (Russian).

56. Levin, A. B.; Mikhalev, A. V. Differential Dimension Polynomial and the Strength of a System of Differential Equations. Collection of Papers "Computable Invariants in the Theory of Algebraic Systems". Novosibirsk, Russia, 1987, 58 - 66 (Russian).

57. Levin, A. B. Some Methods of Teaching Mathematics in a Freshman Class. Collection of Papers of the National Russian Conference on Mathematics Education, Stavropol, Russia, 1985, p. 16 (Russian).

58. Levin, A. B. Characteristic Polynomials of Difference-Differential Modules. Collection of Papers of XVIII National Conference on Algebra, Kishinev, Moldavia, 1985. Part I, p. 307 (Russian).

59. Levin, A. B. Inversive Difference Modules and the Problems of Solvability of Systems of Linear Difference Equations. Moscow State University, VINITI, no. 335-85 (1985), 1 - 20 (Russian).

60. Levin, A. B. Characteristic Polynomials of D-Modules and of Finitely Generated D-Field Extensions. Moscow State University, VINITI, no. 334-85 (1985), 1 - 23 (Russian).

61. Levin, A. B. Characteristic Polynomials of Difference Modules and Difference Field Extensions. Summary of the Dissertation for Ph. D. Degree. Kishinev, Moldavia, 1984, 1 - 21 (Russian).

62. Levin, A. B. Type and Dimension of Finitely Generated Difference Algebras. Collection of Papers of XVII National Conference on Algebra, Minsk, Byelorussia, 1983. Part II, 126 - 127 (Russian).

63. Levin, A. B. Applications of the Theory of Difference Modules to the Study of Systems of Difference Equations. Collection of Papers "Some Problems of Mathematics and Mechanics", Moscow State University, 1983, 15 - 16 (Russian).

64. Levin, A. B. Type and Dimension of Inversive Difference Vector Spaces and Difference Algebras. Moscow State University, VINITI, no. 1606-82 (1982), 1 - 36 (Russian).

65. Levin, A. B. Type and Dimension of Inversive Difference Vector Spaces. Collection of Papers of V National Symposium on the Theory of Rings, Algebras, and Modules, Novosibirsk, Russia, 1987, p. 87 (Russian).

66. Levin, A. B. Characteristic Polynomials of Difference Modules and of Difference Field Extensions. Vestnik of Moscow University, Ser. 1, 1982, no. 4. p. 78 (Russian).

67. Levin, A. B. Difference Local Algebras. Collection of Papers of XVI National Conference on Algebra, Leningrad, Russia, 1981, Part 1, 92 - 93 (Russian).

68. Levin, A. B. Method of Automatic Control of Welding with the Heating. USSR Patient no.743814 (1980).

69. Levin, A. B. Functor EXT in the Category of Inversive Difference Modules. Collection of Papers of IV National Symposium on the Theory of Rings, Algebras, and Modules, Kishinev, Moldavia, 1980, p. 67 (Russian).

70. Levin, A. B. Characteristic Polynomials of Difference Modules and Some Properties of Difference Dimension. Moscow State University, VINITI, no. 2175-80 (1980), 1 - 42 (Russian).

71. Levin, A. B. Characteristic Polynomials of Inversive Difference Modules and Some Properties of Inversive Difference Dimension. Uspekhi Math. Nauk, 35 (1980), no. 1, 201 - 202 (Russian). English translation: Russian Mathematical Surveys, 35, no. 1, 217 - 218.

Doi: https://doi.org/10.1070/RM1980v035n01ABEH001588

72. Levin, A. B.; Lipkin, A. S.; Vigdorchik, S. I. Comprehensive Flow Inspection of Solid Phase Joints and Automatization of Holographic Testing. Collection of papers "Scientific Foundations of Automatization of Industrial Processes", MVTU (Moscow, Russia), 1979, 55 - 57 (Russian).

73. Karakozov, E. S.; Levin, A. B.; Lipkin, A. S. Some Problems of Holographic Flow Inspection. Aviation Materials, VIAM (Moscow, Russia), no. 6 (1979), 200 - 204 (Russian).

74. Levin, A. B.; Lipkin, A. S. Theoretically-experimental Study of Roughness of Surface by the Holographic Methods. Collection of papers "Holographic Methods of Processing of Information", MIREA (Moscow, Russia), 1978, 137 - 143 (Russian).

75. Levin, A. B. Characteristic Polynomials of Filtered Difference Modules and Difference Field Extensions. Uspekhi Math. Nauk, Vol. 33 (1978), no. 3, 177 - 178 (Russian). English translation: Russian Mathematical Surveys, 33, no. 3, 165 - 166.

Doi: https://doi.org/10.1070/RM1978v033n03ABEH002480

Textbooks

1. Levin, A. B. Mathematical Foundation of Automatic Control. Higher School Press, Moscow, 1992 (Russian).

2. Levin, A. B.; Safray, V. M. Differential Calculus. Functions of One Variable. Moscow Metallurgical Institute (MMI) Press, Moscow, Russia, 1991 (Russian).

3. Levin, A. B.; Safray, V. M. Net Functions and Difference Equations. MMI Press, Moscow, Russia, 1990 (Russian).

4. Levin, A. B.; Nikiforovsky, V. A.; Zibul'nikov, A. V. Extremal Problems. MMI Press, Moscow, 1989 (Russian).

5. Levin, A. B.; Safray, V. M. Fourier Series and Fourier Transform. MMI Press, Moscow, 1989 (Russian).

6. Levin, A. B.; Pokrovsky, L. N. Solving of the Fundamental Problem of Linear Programming with the Computer ISKRA. MMI Press, Moscow, 1988 (Russian).

7. Levin, A. B.; Nikiforovsky, V. A. Theory of Functions of One Complex Variable and Laplace Transform. MMI Press, Moscow, Russia, 1987 (Russian).

8. Levin, A. B.; Zulkov, A. I. Elementary Functions and their Graphs. MMI Press, Moscow, 1985 (Russian).

9. Dudin, V. I.; Levin, A. B.; Pokrovsky, L. N. Simplex Method in Linear Programming. MMI Press, Moscow, 1985 (Russian).

10. Dudin, V. I.; Levin, A. B. Mathematical Programming. Geometric Method. MMI Press, Moscow, 1984 (Russian).

11. Levin, A. B.; Safray, V. M. Limits of Sequences and Functions. MMI Press, Moscow, Russia, 1984 (Russian).

12. Levin, A. B. Fourier Series. MMI Press, Moscow, Russia, 1980 (Russian).

Presentations in 2012 – 2022

International Conferences and Seminars

1. Levin, A. Generalized Characteristic Sets and a New Type of Multivariate Difference Dimension Polynomials. The 23d International Conference on Applications of Computer Algebra (ACA 2022). Istanbul, Turkey, August 17, 2022.

2. Levin, A. Reduction with respect to the Effective Order and a New Type of Dimension Polynomials of Difference Modules. ISSAC’2022. International Symposium on Symbolic and Algebraic Computation (). Lille, France. July 5, 2022.

3. Levin, A. Multivariate Bernstein-type Polynomials of Finitely Generated D-Modules. The 26th International Online Conference on Applications of Computer Algebra. July 27, 2021.

4. Levin, A. A New Type of Difference Dimension Polynomials. The 26th International Online Conference on Applications of Computer Algebra. July 23, 2021.

5. Levin, A. Generalized Groebner bases and new properties of multivariate difference dimension polynomials. ISSAC’2021. International Symposium on Symbolic and Algebraic Computation, Saint Petersburg, July 23, 2021.

6. Levin, A. Bivariate dimension polynomials of finitely generated modules over Weyl algebras. International Colloquium at the Ramakrishna Mission Vivekananda Educational & Research Institute, Belur, India. March 25, 2021.

7. Levin, A. Some properties of multivariate differential dimension polynomials and their invariants. ISSAC '20: International Symposium on Symbolic and Algebraic Computation Kalamata Greece. July 20, 2020.

8. Levin, A. Hilbert-Type Dimension Polynomials of Intermediate Difference-Differential Field Extensions. Mathematical Aspects of Computer and Information Sciences. 8th International Conference, MACIS 2019. November 14, 2019.

9. Evgrafov, A.; Goyal, S.; Levin, A. Some properties and applications of multivariate dimension polynomials and their computation in Python. 25^th International Conference on Applications of Computer Algebra (ACA 2019). Montreal, Canada, July 19, 2019.

10. Levin, A. Hilbert-type Functions of Non-reflexive Prime Difference Polynomial Ideals. 25^th International Conference on Applications of Computer Algebra (ACA 2019). Montreal, Canada, July 17, 2019.

11. Levin, A. Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals. The Case of One Translation. The 43rd International Symposium on Symbolic and Algebraic Computation. New York, NY, July 18, 2018.

12. Levin, A. Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations. 24^th International conference on applications of computer algebra. Santa de Compostela, Spain, June 21, 2018.

13. Evgrafov, A.; Levin, A. Some Properties and Invariants of Multivariate Difference-Differential Dimension Polynomials. 24^th International Conference on Applications of Computer Algebra. Santa de Compostela, Spain, June 20, 2018.

14. Levin, A. Chain Conditions and Hilbert-type functions for difference polynomial ideals. International Colloquium at the Research Institute for Symbolic Computation. Johann Kepler University, Linz, Austria. November 20, 2017.

15. Levin, A. Dimension Quasi-polynomials of Inversive Difference Field Extensions. MACIS 2017: 7th International Conference on Mathematical Aspects of Computer and Information Sciences. Vienna, Austria. November 15, 2017.

16. Levin, A. Bivariate Dimension Quasi-polynomials of Difference-Differential Field Extensions with Weighted Basic Operators. 23nd International Conference on Applications of Computer Algebra. Jerusalem, Israel. July 18, 2017.

17. Levin, A. Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations. American Mathematical Society meeting. New York, NY. July 7, 2017.

18. Levin, A. B. Difference Dimension Quasi-polynomials. The 22nd International Conference on Applications of Computer Algebra. Kassel, Germany. August 1, 2016.

19. Levin, A. B. Difference-Differential Dimension Polynomials and their Invariants. The 22^nd International Conference on Applications of Computer Algebra. Kassel, Germany. August 1, 2016.

20. Levin, A. B. Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions. Sixth International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2015). Berlin, Germany. November 13, 2015.

21. Levin, A. B. Method of generalized characteristic sets and multivariate dimension polynomials of differential field extensions with a group action. The 20th International Conference on Applications of Computer Algebra. New York, July 10, 2014.

22. Levin, A. B. Generalized Gröbner bases and dimension polynomials of modules over some finitely generated non-commutative algebras. The 20th International Conference on Applications of Computer Algebra. New York, July 12, 2014.

23. Levin, A. B. Generalized Characteristic Sets and Multivariate Dimension Polynomials of Inversive Difference-Differential Field Extensions. Invited presentation at Beihang University, Beijing, China. June 17, 2014.

24. Levin, A. B. New results on difference polynomial ideals. Invited presentation at Beihang University, Beijing, China. June 19, 2014.

25. Levin, A. B. Multivariate Difference-Differential Dimension Polynomials and New Invariants of Difference-Differential Field Extensions. ISSAC’2013, International Symposium on Symbolic and Algebraic Computation. Boston, MA. June 28, 2013.Quasi-polynomials

26. Levin, A. B. On the Maximality Condition for Certain Types of Difference Ideals. Kolchin Seminar in Differential Algebra. Graduate Center Series. New York, November 30, 2012.

27. Levin, A. B. New Developments in the Theory of Difference Ideals. Computer Algebra Seminar at the Research Institute for Symbolic Computation. Linz, Austria, August 1, 2012.

28. Levin, A. B. Introduction to Difference Algebra. Mathematics and System Science Seminar at Beihang University. Beijing, China, June 11, 2012.

29. Levin, A. B. Dimension Polynomials and Strength of Systems of Differential and Difference Equations and PDEs with Group Action. Mathematics and System Science Seminar at Beihang University. Beijing, China, June 15, 2012.

30. Doench, C.; Levin, A. B. Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Difference and Differential Dimension Polynomials. Part I. Kolchin Seminar in Differential Algebra. Graduate Center Series. New York, February 3, 2012.

31. Doench, C.; Levin, A. B. Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Difference and Differential Dimension Polynomials. Part II. Kolchin Seminar in Differential Algebra. Graduate Center Series. New York, February 3, 2012.

Seminar in Functional Analysis and Related Areas at The Catholic University of America

1. Levin, A. An algebraic approach to the study of ordinary differential equations and integration in terms of elementary functions. September 21, 2022.

2. Levin, A. The set of Hilbert Polynomials. March 2, 2022.

3. Levin, A. Generalized Gröbner bases and bivariate Bernstein-type polynomials of D-modules. September 22, 2021.

4. Levin, A. Generalized Gröbner bases and multivariate differential dimension polynomials. February 17, 2021.

5. Levin, A. Properties of certain classes of difference ideals. October 28, 2020.

6. Levin, A. Compatibility of Differential and Difference Field Extensions. February 12, 2020.

7. Levin, A. Dimension Polynomials of Intermediate Difference Fields and the Krull-type Dimension of Difference Field Extensions. October 9, 2019.

8. Levin, A. Hilbert-type dimension functions of non-reflexive prime difference ideals. March 6, 2019.

9. Levin, A. Dimension Polynomials and the Einstein’s Strength of Some Systems of Linear and Quasi-linear Difference Equations. October 17, 2018.

10. Levin, A. Characteristic sets and dimension polynomials of prime difference polynomial ideals. February 14, 2018.

11. Levin, A. Groebner bases and some their applications. April 5, 2017.

12. Levin, A. Difference polynomial ideals. March 29, 2017.

13. Levin, A. Difference Dimension Quasi-polynomials. October 12, 2016.

14. Levin, A. Dimension quasi-polynomials. April 13, 2016.

15. Levin, A. Krull-type Dimension of Difference Field Extensions. October 28, 2015.

16. Levin, A. Elements of the differential Galois Theory. February 11, 2015.

17. Levin, A. Algebraic approach to differential equations. November 19, 2014.

18. Levin, A. Conservative systems of ideals. October 19, 2014.

19. Levin, A. Autoreduced sets of difference polynomials and their applications. March 5, 2014.

20. Levin, A. Characteristic Sets of Difference Polynomials and their Applications. November 20, 2013.

21. Levin, A. Characteristic sets of differential polynomials and their applications. March 20, 2013.

22. Levin, A. On chain conditions in difference-differential algebraic structures. February 13, 2013.

23. Levin, A. Ascending Chain Condition in Certain Classes of Difference Ideals. October 10, 2012.

24. Levin, A. Differential Dimension Quasi-polynomials. May 2, 2012.

25. Doench, C.; Levin, A. B. Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Differential and Difference Dimension Polynomials. January 25, 2012.