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The Diverse World of PDEs: Algebraic and Cohomological Aspects
 
Edited by: I. S. Krasil′shchik Independent University of Moscow, Moscow, Russia
A. B. Sossinsky Independent University of Moscow, Moscow, Russia
A. M. Verbovetsky Independent University of Moscow, Moscow, Russia
Softcover ISBN:  978-1-4704-7355-6
Product Code:  CONM/789
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-1-4704-7409-6
Product Code:  CONM/789.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7355-6
eBook: ISBN:  978-1-4704-7409-6
Product Code:  CONM/789.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
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The Diverse World of PDEs: Algebraic and Cohomological Aspects
Edited by: I. S. Krasil′shchik Independent University of Moscow, Moscow, Russia
A. B. Sossinsky Independent University of Moscow, Moscow, Russia
A. M. Verbovetsky Independent University of Moscow, Moscow, Russia
Softcover ISBN:  978-1-4704-7355-6
Product Code:  CONM/789
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-1-4704-7409-6
Product Code:  CONM/789.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7355-6
eBook ISBN:  978-1-4704-7409-6
Product Code:  CONM/789.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 7892023; 223 pp
    MSC: Primary 13; 14; 34; 35; 46; 53; 55; 58; 68; 81;

    This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia.

    The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras.

    The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

    Readership

    Graduate students and research mathematicians interested in the modern theory of partial differential equation in the wide context of commutative and noncommutative algebra and cohomology theories.

  • Table of Contents
     
     
    • Articles
    • Luca Amata and Francesco Oliveri — Automatic determination of optimal systems of Lie subalgebras: The package SymboLie
    • Orest D. Artemovych, Denis L. Blackmore, Radosław A. Kycia and Anatolij K. Prykarpatski — New Dubrovin-type integrability theory applications of differential rings
    • I. A. Bobrova and V. V. Sokolov — Non-abelian Painlevé systems with generalized Okamoto integral
    • Alexei Bocharov — Mathematical etudes on quantum computation
    • Dimitry Gurevich and Pavel Saponov — Quantum vector fields via quantum doubles and their applications
    • Hovhannes M. Khudaverdian — Non-linear homomorphisms of algebras of functions are induced by thick morphisms
    • H. M. Khudaverdian and Th. Th. Voronov — On the Buchstaber–Rees theory of “Frobenius $n$-homomorphisms” and its generalization
    • Jacob Kryczka — Differential calculus over graded commutative algebras and vector bundles with inner structures
    • Fabrizio Pugliese, Giovanni Sparano and Luca Vitagliano — Vinogradov’s cohomological geometry of partial differential equations
    • Jean-Pierre Magnot, Enrique G. Reyes and Vladimir Rubtsov — Frölicher structures, diffieties, and a formal KP hierarchy
    • G. Sharygin — Quasi-derivations on $U\mathfrak {gl}_n$ and the argument shift method
    • Piergiulio Tempesta and Giorgio Tondo — Polarization of generalized Nijenhuis torsions
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 7892023; 223 pp
MSC: Primary 13; 14; 34; 35; 46; 53; 55; 58; 68; 81;

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia.

The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras.

The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

Readership

Graduate students and research mathematicians interested in the modern theory of partial differential equation in the wide context of commutative and noncommutative algebra and cohomology theories.

  • Articles
  • Luca Amata and Francesco Oliveri — Automatic determination of optimal systems of Lie subalgebras: The package SymboLie
  • Orest D. Artemovych, Denis L. Blackmore, Radosław A. Kycia and Anatolij K. Prykarpatski — New Dubrovin-type integrability theory applications of differential rings
  • I. A. Bobrova and V. V. Sokolov — Non-abelian Painlevé systems with generalized Okamoto integral
  • Alexei Bocharov — Mathematical etudes on quantum computation
  • Dimitry Gurevich and Pavel Saponov — Quantum vector fields via quantum doubles and their applications
  • Hovhannes M. Khudaverdian — Non-linear homomorphisms of algebras of functions are induced by thick morphisms
  • H. M. Khudaverdian and Th. Th. Voronov — On the Buchstaber–Rees theory of “Frobenius $n$-homomorphisms” and its generalization
  • Jacob Kryczka — Differential calculus over graded commutative algebras and vector bundles with inner structures
  • Fabrizio Pugliese, Giovanni Sparano and Luca Vitagliano — Vinogradov’s cohomological geometry of partial differential equations
  • Jean-Pierre Magnot, Enrique G. Reyes and Vladimir Rubtsov — Frölicher structures, diffieties, and a formal KP hierarchy
  • G. Sharygin — Quasi-derivations on $U\mathfrak {gl}_n$ and the argument shift method
  • Piergiulio Tempesta and Giorgio Tondo — Polarization of generalized Nijenhuis torsions
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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