Dmitriĭ Yur’evich Grigor’ev - Author Profile

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Grigor’ev, Dmitriĭ Yur’evich

Author ID:	grigorev.dimitri-yu
Published as:	Grigoriev, Dima; Grigor’ev, D. Yu.; Grigoriev, D.; Grigor’ev, D. Ju.; Grigoriev, D. Yu.; Grigoriev, Dima Yu.; Grigoriev, Dmitry; Grigor’ev, Dima Yurevitch; Grigor’ev, Dimitri Yu.; Grigoriev, Dimitri; Grigor’ev, D. more...less
Homepage:	https://logic.pdmi.ras.ru/~grigorev/
External Links:	MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp
Videos:	carmin.tv

Documents Indexed:	229 Publications since 1974, including 1 Book and 11 Additional arXiv Preprints
	9 Contributions as Editor
Co-Authors:	103 Co-Authors with 147 Joint Publications
	2,700 Co-Co-Authors

all top 5

Co-Authors

91	single-authored
19	Karpinski, Marek
19	Vorob’ëv, Nikolaĭ N. jun.
15	Shpilrain, Vladimir
12	Vakulenko, Sergei A.
10	Hirsch, Edward A.
10	Weber, Andreas Günter
9	Radulescu, Ovidiu
7	Schwarz, Fritz
6	Singer, Michael F.
6	Sturm, Thomas
5	Chistov, Alexandre L.
5	Errami, Hassan
5	Milman, Pierre D.
5	Podol’skiĭ, Vladimir Vladimirovich
5	Ponomarenko, Ilya Nikolaevich
5	Slisenko, A. O.
4	Cucker, Felipe
4	Pasechnik, Dmitrii V.
3	England, Matthew
3	Matiyasevich, Yuriĭ Vladimirovich
3	Orevkov, V. P.
3	Samal, Satya Swarup
3	Slissenko, Anatol
3	Smolensky, Roman
2	Alekseev, Yaroslav
2	Artemov, Sergei
2	Bessonov, Mariya
2	Bierstone, Edward
2	Bradford, Russell J.
2	Buss, Samuel R.
2	Chen, Jiale
2	Dantsin, Evgeny
2	Davenport, James Harold
2	Davydov, G. V.
2	Diekert, Volker
2	Eiswirth, Markus
2	Fomin, Sergey Vladimirovich
2	Fröhlich, Holger
2	Gerdt, Vladimir Petrovich
2	Hoyt, Charles Tapley
2	Impagliazzo, Russell
2	Konev, B. Yu.
2	Koshevoy, Gleb A.
2	Košta, Marek
2	Lakshman, Y. N.
2	Lifschitz, Vladimir
2	Meyer auf der Heide, Friedhelm
2	Mints, Grigoriĭ Efroimovich
2	Noel, Vincent
2	Odlyzko, Andrew M.
2	Pitassi, Toniann
2	Seiler, Werner M.
2	Tzameret, Iddo
2	Vsemirnov, Maxim
2	Włodarczyk, Jarosław
2	Yao, Andrew Chi-Chih
1	Beauquier, Danièle
1	Berenstein, Arkady
1	Bertrand, Edouard
1	Burago, Dmitri
1	Canny, John F.
1	Chernov, V. P.
1	Davydow, Alex
1	Douaihy, Maria
1	Elizarov, Nikita Vyacheslavovich
1	Girsh, È. A.
1	Grigorchuk, Rostislav Ivanovich
1	Grigorieva, Alla
1	Heintz, Joos
1	Ilmer, Ilia
1	Iosif, Alexandru
1	Ivanov, Aleksandr Aleksandrovich
1	Ivanov, Nikolai V.
1	Karavaev, Eh. F.
1	Kish, Laszlo B.
1	Kossovsky, N. K.
1	Lagha, Mounia
1	Makshanov, Andrey
1	Margenstern, Maurice
1	Musaev, Alexander
1	Muzychuk, Mikhail E.
1	Nikolenko, S. J.
1	Nikolenko, Sergey I.
1	Nogneng, Dorian
1	Ovchinnikov, Alexey Igorevich
1	Pervyshev, K. V.
1	Pervyshev, Konstantin
1	Pliuškevičius, Regimantas
1	Radchenko, Danylo V.
1	Rahkooy, Hamid
1	Razborov, Aleksandr Aleksandrovich
1	Roy, Marie-Françoise
1	Sashina, Elena
1	Schost, Éric
1	Seiß, Matthias
1	Solernó, Pablo
1	Solov’ëv, Sergeĭ Vladimirovich
1	Spivakovsky, Mark
1	Suchkov, Andrey
1	Sudakov, Ivan
...and 4 more Co-Authors

all top 5

Serials

16	Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova
15	Journal of Soviet Mathematics
11	Computational Complexity
10	Theoretical Computer Science
9	Journal of Symbolic Computation
9	Journal of Mathematical Sciences (New York)
8	Soviet Mathematics. Doklady
7	SIAM Journal on Computing
6	Advances in Applied Mathematics
6	Groups, Complexity, Cryptology
5	Journal of Complexity
5	Applicable Algebra in Engineering, Communication and Computing
5	St. Petersburg Mathematical Journal
5	Foundations of Computational Mathematics
4	Discrete & Computational Geometry
3	Russian Mathematical Surveys
3	Annals of Pure and Applied Logic
2	Communications in Algebra
2	Advances in Mathematics
2	International Journal of Foundations of Computer Science
2	Theory of Computing Systems
2	Moscow Mathematical Journal
2	Mathematical Modelling of Natural Phenomena
1	Journal of Computational Physics
1	Mathematical Methods in the Applied Sciences
1	Mathematical Notes
1	Physics Letters. B
1	Uspekhi Matematicheskikh Nauk [N. S.]
1	Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1	Bulletin of Mathematical Biology
1	Computing
1	Journal of Computer and System Sciences
1	Mathematics of the USSR. Izvestiya
1	Studies in Applied Mathematics
1	Transactions of the American Mathematical Society
1	Annales Societatis Mathematicae Polonae. Series IV
1	Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
1	U.S.S.R. Computational Mathematics and Mathematical Physics
1	Comptes Rendus de l’Académie des Sciences. Série I
1	Zapiski Nauchnykh Seminarov POMI
1	The Asian Journal of Mathematics
1	Communications in Nonlinear Science and Numerical Simulation
1	Comptes Rendus. Mathématique. Académie des Sciences, Paris
1	International Journal of Pure and Applied Mathematics
1	Lecture Notes in Computer Science
1	Mathematics in Computer Science
1	Dependence Modeling
1	Arnold Mathematical Journal

all top 5

Fields

146	Computer science (68-XX)
53	Algebraic geometry (14-XX)
34	Field theory and polynomials (12-XX)
30	Mathematical logic and foundations (03-XX)
27	Information and communication theory, circuits (94-XX)
22	Linear and multilinear algebra; matrix theory (15-XX)
22	Numerical analysis (65-XX)
20	Commutative algebra (13-XX)
19	Ordinary differential equations (34-XX)
19	Biology and other natural sciences (92-XX)
14	Combinatorics (05-XX)
12	Associative rings and algebras (16-XX)
10	Number theory (11-XX)
9	General and overarching topics; collections (00-XX)
9	Partial differential equations (35-XX)
7	Real functions (26-XX)
5	Several complex variables and analytic spaces (32-XX)
4	Group theory and generalizations (20-XX)
4	Operator theory (47-XX)
4	Probability theory and stochastic processes (60-XX)
3	History and biography (01-XX)
3	Dynamical systems and ergodic theory (37-XX)
3	Convex and discrete geometry (52-XX)
3	Quantum theory (81-XX)
3	Operations research, mathematical programming (90-XX)
2	Approximations and expansions (41-XX)
2	Global analysis, analysis on manifolds (58-XX)
2	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1	Topological groups, Lie groups (22-XX)
1	Algebraic topology (55-XX)
1	Manifolds and cell complexes (57-XX)
1	Classical thermodynamics, heat transfer (80-XX)
1	Systems theory; control (93-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

157 Publications have been cited 1,425 times in 898 Documents	Cited by ▼	Year ▼
Solving systems of polynomial inequalities in subexponential time. Zbl 0662.12001 Grigor’ev, D. Yu.; Vorobjov, N. N. jun.	127	1988
Complexity of deciding Tarski algebra. Zbl 0689.03021 Grigor’ev, D. Yu.	72	1988
Linear lower bound on degrees of Positivstellensatz calculus proofs for the parity. Zbl 0974.68192 Grigoriev, D.	59	2001
Complexity of Positivstellensatz proofs for the knapsack. Zbl 0992.68077 Grigoriev, D.	44	2001
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields. Zbl 0711.68059 Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F.	40	1990
Complexity of Null- and Positivstellensatz proofs. Zbl 0992.03073 Grigoriev, Dima; Vorobjov, Nicolai	36	2002
Linear gaps between degrees for the polynomial calculus modulo distinct primes. Zbl 1007.03052 Buss, Sam; Grigoriev, Dima; Impagliazzo, Russell; Pitassi, Toniann	33	2001
Complexity of quantifier elimination in the theory of algebraically closed fields. Zbl 0562.03015 Chistov, A. L.; Grigor’ev, D. Yu.	31	1984
Complexity of factoring and calculating the GCD of linear ordinary differential operators. Zbl 0728.68067 Grigor’ev, D. Yu.	30	1990
Counting connected components of a semialgebraic set in subexponential time. Zbl 0900.68253 Grigor’ev, D. Yu.; Vorobjov, N. N. jun.	30	1992
An exponential lower bound for depth 3 arithmetic circuits. Zbl 1028.68069 Grigoriev, Dima; Karpinski, Marek	28	1998
Detection of Hopf bifurcations in chemical reaction networks using convex coordinates. Zbl 1349.92168 Errami, Hassan; Eiswirth, Markus; Grigoriev, Dima; Seiler, Werner M.; Sturm, Thomas; Weber, Andreas	24	2015
Solving ordinary differential equations in terms of series with real exponents. Zbl 0758.12004 Grigor’ev, D. Yu.; Singer, M. F.	23	1991
Tropical cryptography. Zbl 1301.94114 Grigoriev, Dima; Shpilrain, Vladimir	21	2014
Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Zbl 1040.68045 Grigoriev, D.; Razborov, A.	21	2000
Complexity of semi-algebraic proofs. Zbl 1054.03035 Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrii V.	20	2002
Factoring and solving linear partial differential equations. Zbl 1052.35008 Grigoriev, D.; Schwarz, F.	20	2004
Polynomial-time factoring of the multivariable polynomials over a global field. Zbl 0509.68029 Chistov, A. L.; Grigor’ev, D. Yu.	20	1982
Complexity of semialgebraic proofs. Zbl 1027.03044 Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrij V.	20	2002
Polynomial-time computing over quadratic maps i: sampling in real algebraic sets. Zbl 1082.14065 Grigoriev, Dima; Pasechnik, Dmitrii V.	18	2005
Complexity of quantifier elimination in the theory of ordinary differential equations. Zbl 1209.68679 Grigor’ev, D. Yu.	17	1989
An application of separability and independence notions for obtaining lower bounds of circuit complexity. Zbl 0341.94020 Grigor’ev, D. Ju.	16	1976
Computational complexity of sparse rational interpolation. Zbl 0802.68060 Grigoriev, Dima; Karpinski, Marek; Singer, Michael F.	16	1994
Complexity of solving tropical linear systems. Zbl 1282.68137 Grigoriev, Dima	14	2013
On the power of real Turing machines over binary inputs. Zbl 0874.68110 Cucker, Felipe; Grigoriev, Dima	13	1997
Factorization of polynomials over a finite field and solution of a system of algebraic equations. Zbl 0561.12011 Grigor’ev, D. Yu.	13	1984
A zero-test and an interpolation algorithm for the shifted sparse polynomials. Zbl 0809.68072 Grigoriev, Dima; Karpinski, Marek	13	1993
Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2. Zbl 1287.14004 Grigoriev, Dima; Milman, Pierre D.	13	2012
A case study on the parametric occurrence of multiple steady states. Zbl 1444.92034 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas	13	2017
Model reduction of biochemical reactions networks by tropical analysis methods. Zbl 1369.92047 Radulescu, O.; Vakulenko, S.; Grigoriev, D.	12	2015
Complexity of tropical and MIN-plus linear prevarieties. Zbl 1326.15039 Grigoriev, Dima; Podolskii, Vladimir V.	12	2015
Fast decomposition of polynomials into irreducible ones and the solution of systems of algebraic equations. Zbl 0596.12021 Grigor’ev, D. Yu.; Chistov, A. L.	12	1984
Factorization of polynomials over a finite field and the solution of systems of algebraic equations. Zbl 0596.12023 Grigor’ev, D. Yu.	12	1986
Tropical cryptography. II: Extensions by homomorphisms. Zbl 1451.14179 Grigoriev, Dima; Shpilrain, Vladimir	12	2019
Generalized Loewy-decomposition of \(D\)-modules. Zbl 1360.13061 Grigoriev, Dima; Schwarz, Fritz	11	2005
Tropicalization and tropical equilibration of chemical reactions. Zbl 1320.92091 Noel, Vincent; Grigoriev, Dima; Vakulenko, Sergei; Radulescu, Ovidiu	11	2014
Tropical geometries and dynamics of biochemical networks application to hybrid cell cycle models. Zbl 1283.92043 Noel, Vincent; Grigoriev, Dima; Vakulenko, Sergei; Radulescu, Ovidiu	11	2012
Algebraic proof systems over formulas. Zbl 1044.68146 Grigoriev, Dima; Hirsch, Edward A.	11	2003
Identifying the parametric occurrence of multiple steady states for some biological networks. Zbl 1442.92056 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas	11	2020
A complete public-key cryptosystem. Zbl 1158.94384 Grigoriev, Dima; Hirsch, Edward A.; Pervyshev, Konstantin	11	2009
Weak Bézout inequality for D-modules. Zbl 1080.32010 Grigoriev, Dima	10	2005
Effective Hironaka resolution and its complexity. Zbl 1315.14022 Bierstone, Edward; Grigoriev, Dima; Milman, Pierre; Włodarczyk, Jarosław	10	2011
Additive complexity in directed computations. Zbl 0486.68028 Grigor’ev, D. Yu.	10	1982
Semi-algebraic proofs, IPS lower bounds, and the \(\tau\)-conjecture: can a natural number be negative? Zbl 07298230 Alekseev, Yaroslav; Grigoriev, Dima; Hirsch, Edward A.; Tzameret, Iddo	10	2020
Testing shift-equivalence of polynomials by deterministic, probabilistic and quantum machines. Zbl 1044.68946 Grigoriev, D.	10	1997
Symbolic versus numerical computation and visualization of parameter regions for multistationarity of biological networks. Zbl 1455.92058 England, Matthew; Errami, Hassan; Grigoriev, Dima; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas	10	2017
Bounds on numers of vectors of multiplicities for polynomials which are easy to compute. Zbl 1326.68354 Grigoriev, Dima; Vorobjov, Nicolai	9	2000
Subtraction-free complexity, cluster transformations, and spanning trees. Zbl 1352.68104 Fomin, Sergey; Grigoriev, Dima; Koshevoy, Gleb	9	2016
The interpolation problem for \(k\)-sparse sums of eigenfunctions of operators. Zbl 0785.12004 Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F.	9	1991
Complexity lower bounds for computation trees with elementary transcendental function gates. Zbl 0877.68086 Grigoriev, D.; Vorobjov, N.	9	1996
Authentication schemes from actions on graphs, groups, or rings. Zbl 1236.94076 Grigoriev, Dima; Shpilrain, Vladimir	9	2010
Skyrmed monopoles. Zbl 0996.81059 Grigoriev, D. Yu.; Sutcliffe, P. M.; Tchrakian, D. H.	9	2002
Authentication from matrix conjugation. Zbl 1191.94104 Grigoriev, Dima; Shpilrain, Vladimir	9	2009
Tropical differential equations. Zbl 1348.14140 Grigoriev, Dima	9	2017
Tropical effective primary and dual Nullstellensätze. Zbl 1356.14058 Grigoriev, Dima; Podolskii, Vladimir V.	9	2015
Loewy and primary decompositions of \(\mathcal D\)-modules. Zbl 1126.35008 Grigoriev, D.; Schwarz, F.	8	2007
Computational complexity in polynomial algebra. Zbl 0667.68054 Grigor’ev, D. Yu.	8	1987
A geometric method for model reduction of biochemical networks with polynomial rate functions. Zbl 1342.92079 Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Weber, Andreas; Radulescu, Ovidiu	7	2015
Lower bounds in the algebraic computational complexity. Zbl 0504.68024 Grigor’ev, D. Yu.	7	1982
Complexity of solving systems of linear equations over the rings of differential operators. Zbl 0749.16015 Grigor’ev, Dimitri Yu.	7	1991
Multiplicative complexity of a pair of bilinear forms and of the polynomial multiplication. Zbl 0381.68045 Grigor’ev, D. Ju.	7	1978
Tropical effective primary and dual Nullstellensätze. Zbl 1420.14140 Grigoriev, Dima; Podolskii, Vladimir V.	7	2018
Efficient methods to compute Hopf bifurcations in chemical reaction networks using reaction coordinates. Zbl 1412.34132 Errami, Hassan; Eiswirth, Markus; Grigoriev, Dima; Seiler, Werner M.; Sturm, Thomas; Weber, Andreas	6	2013
Complexity of tropical Schur polynomials. Zbl 1329.65060 Grigoriev, Dima; Koshevoy, Gleb	6	2016
Complexity of a standard basis of a \(D\)-module. Zbl 1206.16050 Grigoriev, D. Yu.; Chistov, A. L.	6	2009
An analogue of the Bruhat decomposition for the closure of the cone of a Chevalley group of the classical series. Zbl 0479.22003 Grigor’ev, D. Yu.	6	1981
Complexity of solving systems with few independent monomials and applications to mass-action kinetics. Zbl 1373.68461 Grigoriev, Dima; Weber, Andreas	6	2012
Polytime algorithm for the shortest path in a homotopy class amidst semi-algebraic obstacles in the plane. Zbl 0961.14039 Grigoriev, D.; Slissenko, A.	6	1998
Algorithms for sparse rational interpolation. Zbl 0920.65004 Grigoriev, Dima Yu.; Karpinski, Marek	6	1991
Finding connected components of a semialgebraic set in subexponential time. Zbl 0783.14036 Canny, J.; Grigor’ev, D. Yu.; Vorob’ev, N. N. jun.	6	1992
Lower bounds in algebraic computational complexity. Zbl 0563.68040 Grigor’ev, D. Yu.	6	1985
Linear gaps between degrees for the polynomial calculus modulo distinct primes. Zbl 1345.03105 Buss, Sam; Grigoriev, Dima; Impagliazzo, Russell; Pitassi, Toniann	5	1999
Reduction methods and chaos for quadratic systems of differential equations. Zbl 1359.92036 Vakulenko, S.; Grigoriev, D.; Weber, A.	5	2015
On a tropical dual Nullstellensatz. Zbl 1247.14067 Grigoriev, Dima	5	2012
Analysis of reaction network systems using tropical geometry. Zbl 1400.92201 Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Radulescu, Ovidiu	5	2015
Application of separability and independence notions for proving lower bounds of circuit complexity. Zbl 0449.94030 Grigor’ev, D. Yu.	5	1980
Homomorphic public-key cryptosystems over groups and rings. Zbl 1149.94318 Grigoriev, Dima; Ponomarenko, Ilia	5	2004
Lower bounds on testing membership to a polyhedron by algebraic decision trees. Zbl 1345.68158 Grigoriev, Dima; Karpinski, Marek; Vorobjov, Nicolai	5	1994
Efficiently and effectively recognizing toricity of steady state varieties. Zbl 1495.14095 Grigoriev, Dima; Iosif, Alexandru; Rahkooy, Hamid; Sturm, Thomas; Weber, Andreas	5	2021
Imbedding theorems for Turing machines of different dimensions and Kolmogorov’s algorithms. Zbl 0386.03019 Grigor’ev, D. Ju.	5	1977
Algorithms for computing sparse shifts for multivariate polynomials. Zbl 0924.68105 Grigoriev, Dima Yu.; Lakshman, Y. N.	5	1995
Testing shift-equivalence of polynomials using quantum machines. Zbl 0928.68045 Grigoriev, D.	5	1996
A lower bound for randomized algebraic decision trees. Zbl 0922.68090 Grigoriev, Dima; Karpinski, Marek; Meyer auf der Heide, Friedhelm; Smolensky, Roman	5	1996
Computational complexity of sparse real algebraic function interpolation. Zbl 0801.68087 Grigoriev, D.; Karpinski, M.; Singer, M. F.	5	1993
Public-key cryptography and invariant theory. Zbl 1081.94026 Grigoriev, D.	4	2002
Complexity of gene circuits, Pfaffian functions and the morphogenesis problem. Zbl 1050.92003 Vakulenko, Sergey; Grigoriev, Dmitry	4	2003
On the Eisenbud-Levine formula over a perfect field. Zbl 0514.55005 Grigor’ev, D. Yu.; Ivanov, N. V.	4	1980
Topological complexity of the range searching. Zbl 0951.68024 Grigoriev, Dima	4	2000
Homomorphic public-key cryptosystems and encrypting Boolean circuits. Zbl 1104.94022 Grigoriev, Dima; Ponomarenko, Ilia	4	2006
Algorithms for computing sparse shifts for multivariate polynomials. Zbl 0968.68199 Grigoriev, Dima Yu.; Lakshman, Y. N.	4	2000
The complexity of the decision problem for the first order theory of algebraically closed fields. Zbl 0631.03006 Grigor’ev, D. Yu.	4	1987
Bounds on the number of connected components for tropical prevarieties. Zbl 1401.14235 Davydow, Alex; Grigoriev, Dima	4	2017
Algebraic cryptography: new constructions and their security against provable break. Zbl 1206.94069 Grigoriev, D.; Kojevnikov, A.; Nikolenko, S. J.	3	2009
Approximating shortest path for the skew lines problem in time doubly logarithmic in 1/epsilon. Zbl 1075.68090 Burago, D.; Grigoriev, D.; Slissenko, A.	3	2004
Complexity of ”wild” matrix problems and of isomorphism of algebras and graphs. Zbl 0509.68030 Grigor’ev, D. Yu.	3	1983
Counting connected components of a semi-algebraic set in single exponential time. (Comptage des composantes connexes d’un ensemble semi-algébrique en temps simplement exponentiel.) Zbl 0752.14043 Grigor’ev, Dima Yurevitch; Heintz, Joos; Roy, Marie-Françoise; Solernó, Pablo; Vorobjov, Nicolai Nicolaievitch jun.	3	1990
Exponential lower bound for static semi-algebraic proofs. Zbl 1056.03037 Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrii V.	3	2002
Improved lower bound on testing membership to a polyhedron by algebraic decision trees. Zbl 0938.68868 Grigoriev, Dima; Karpinski, Marek; Vorobjov, Nicolai	3	1995
An exponential lower bound on the size of algebraic decision trees for MAX. Zbl 0918.68032 Grigoriev, Dima; Karpinski, Marek; Yao, Andrew C.	3	1998
Loewy decomposition of third-order linear aPDE’s in the plane. Zbl 1489.12020 Grigoriev, Dima; Schwarz, Fritz	3	2008
Excitable media store and transfer complicated information via topological defect motion. Zbl 1501.35133 Sudakow, Ivan; Vakulenko, Sergey A.; Grigoriev, Dima	1	2023
On a tropical version of the Jacobian conjecture. Zbl 1471.14128 Grigoriev, Dima; Radchenko, Danylo	1	2022
Efficiently and effectively recognizing toricity of steady state varieties. Zbl 1495.14095 Grigoriev, Dima; Iosif, Alexandru; Rahkooy, Hamid; Sturm, Thomas; Weber, Andreas	5	2021
Complexity of deciding whether a tropical linear prevariety is a tropical variety. Zbl 1462.14059 Grigoriev, Dima; Vorobjov, Nicolai	2	2021
Identifying the parametric occurrence of multiple steady states for some biological networks. Zbl 1442.92056 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas	11	2020
Semi-algebraic proofs, IPS lower bounds, and the \(\tau\)-conjecture: can a natural number be negative? Zbl 07298230 Alekseev, Yaroslav; Grigoriev, Dima; Hirsch, Edward A.; Tzameret, Iddo	10	2020
Tropical recurrent sequences. Zbl 1441.14204 Grigoriev, Dima	2	2020
Tropical combinatorial Nullstellensatz and sparse polynomials. Zbl 1455.14126 Grigoriev, Dima; Podolskii, Vladimir V.	1	2020
Tropical cryptography. II: Extensions by homomorphisms. Zbl 1451.14179 Grigoriev, Dima; Shpilrain, Vladimir	12	2019
Tropical effective primary and dual Nullstellensätze. Zbl 1420.14140 Grigoriev, Dima; Podolskii, Vladimir V.	7	2018
Tropical Newton-Puiseux polynomials. Zbl 1453.14148 Grigoriev, Dima	3	2018
On semiring complexity of Schur polynomials. Zbl 1408.68072 Fomin, Sergey; Grigoriev, Dima; Nogneng, Dorian; Schost, Éric	2	2018
Orthogonal tropical linear prevarieties. Zbl 1453.14147 Grigoriev, Dima; Vorobjov, Nicolai	1	2018
Upper bounds on Betti numbers of tropical prevarieties. Zbl 1420.14141 Grigoriev, Dima; Vorobjov, Nicolai	1	2018
A case study on the parametric occurrence of multiple steady states. Zbl 1444.92034 Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas	13	2017
Symbolic versus numerical computation and visualization of parameter regions for multistationarity of biological networks. Zbl 1455.92058 England, Matthew; Errami, Hassan; Grigoriev, Dima; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas	10	2017
Tropical differential equations. Zbl 1348.14140 Grigoriev, Dima	9	2017
Bounds on the number of connected components for tropical prevarieties. Zbl 1401.14235 Davydow, Alex; Grigoriev, Dima	4	2017
Tropical combinatorial Nullstellensatz and fewnomials testing. Zbl 1497.14125 Grigoriev, Dima; Podolskii, Vladimir V.	2	2017
Subtraction-free complexity, cluster transformations, and spanning trees. Zbl 1352.68104 Fomin, Sergey; Grigoriev, Dima; Koshevoy, Gleb	9	2016
Complexity of tropical Schur polynomials. Zbl 1329.65060 Grigoriev, Dima; Koshevoy, Gleb	6	2016
Detection of Hopf bifurcations in chemical reaction networks using convex coordinates. Zbl 1349.92168 Errami, Hassan; Eiswirth, Markus; Grigoriev, Dima; Seiler, Werner M.; Sturm, Thomas; Weber, Andreas	24	2015
Model reduction of biochemical reactions networks by tropical analysis methods. Zbl 1369.92047 Radulescu, O.; Vakulenko, S.; Grigoriev, D.	12	2015
Complexity of tropical and MIN-plus linear prevarieties. Zbl 1326.15039 Grigoriev, Dima; Podolskii, Vladimir V.	12	2015
Tropical effective primary and dual Nullstellensätze. Zbl 1356.14058 Grigoriev, Dima; Podolskii, Vladimir V.	9	2015
A geometric method for model reduction of biochemical networks with polynomial rate functions. Zbl 1342.92079 Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Weber, Andreas; Radulescu, Ovidiu	7	2015
Reduction methods and chaos for quadratic systems of differential equations. Zbl 1359.92036 Vakulenko, S.; Grigoriev, D.; Weber, A.	5	2015
Analysis of reaction network systems using tropical geometry. Zbl 1400.92201 Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Radulescu, Ovidiu	5	2015
Algorithms to study large metabolic network dynamics. Zbl 1331.34087 Grigoriev, D.; Samal, S. S.; Vakulenko, S.; Weber, A.	2	2015
Polynomial complexity recognizing a tropical linear variety. Zbl 1439.14175 Grigoriev, Dima	1	2015
Tropical cryptography. Zbl 1301.94114 Grigoriev, Dima; Shpilrain, Vladimir	21	2014
Tropicalization and tropical equilibration of chemical reactions. Zbl 1320.92091 Noel, Vincent; Grigoriev, Dima; Vakulenko, Sergei; Radulescu, Ovidiu	11	2014
Yao’s millionaires’ problem and decoy-based public key encryption by classical physics. Zbl 1302.94049 Grigoriev, Dima; Shpilrain, Vladimir	2	2014
Complexity of solving tropical linear systems. Zbl 1282.68137 Grigoriev, Dima	14	2013
Efficient methods to compute Hopf bifurcations in chemical reaction networks using reaction coordinates. Zbl 1412.34132 Errami, Hassan; Eiswirth, Markus; Grigoriev, Dima; Seiler, Werner M.; Sturm, Thomas; Weber, Andreas	6	2013
Secrecy without one-way functions. Zbl 1290.94080 Grigoriev, Dima; Shpilrain, Vladimir	1	2013
Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2. Zbl 1287.14004 Grigoriev, Dima; Milman, Pierre D.	13	2012
Tropical geometries and dynamics of biochemical networks application to hybrid cell cycle models. Zbl 1283.92043 Noel, Vincent; Grigoriev, Dima; Vakulenko, Sergei; Radulescu, Ovidiu	11	2012
Complexity of solving systems with few independent monomials and applications to mass-action kinetics. Zbl 1373.68461 Grigoriev, Dima; Weber, Andreas	6	2012
On a tropical dual Nullstellensatz. Zbl 1247.14067 Grigoriev, Dima	5	2012
No-leak authentication by the Sherlock Holmes method. Zbl 1272.94081 Grigoriev, Dima; Shpilrain, Vladimir	2	2012
Effective Hironaka resolution and its complexity. Zbl 1315.14022 Bierstone, Edward; Grigoriev, Dima; Milman, Pierre; Włodarczyk, Jarosław	10	2011
Authentication schemes from actions on graphs, groups, or rings. Zbl 1236.94076 Grigoriev, Dima; Shpilrain, Vladimir	9	2010
A low complexity probabilistic test for integer multiplication. Zbl 1196.68104 Grigoriev, Dima; Tenenbaum, Gérald	1	2010
A complete public-key cryptosystem. Zbl 1158.94384 Grigoriev, Dima; Hirsch, Edward A.; Pervyshev, Konstantin	11	2009
Authentication from matrix conjugation. Zbl 1191.94104 Grigoriev, Dima; Shpilrain, Vladimir	9	2009
Complexity of a standard basis of a \(D\)-module. Zbl 1206.16050 Grigoriev, D. Yu.; Chistov, A. L.	6	2009
Algebraic cryptography: new constructions and their security against provable break. Zbl 1206.94069 Grigoriev, D.; Kojevnikov, A.; Nikolenko, S. J.	3	2009
Analogue of Newton-Puiseux series for non-holonomic \(D\)-modules and factoring. Zbl 1187.35020 Grigoriev, Dima	1	2009
Loewy decomposition of third-order linear aPDE’s in the plane. Zbl 1489.12020 Grigoriev, Dima; Schwarz, Fritz	3	2008
Loewy and primary decompositions of \(\mathcal D\)-modules. Zbl 1126.35008 Grigoriev, D.; Schwarz, F.	8	2007
Homomorphic public-key cryptosystems and encrypting Boolean circuits. Zbl 1104.94022 Grigoriev, Dima; Ponomarenko, Ilia	4	2006
Constructions in public-key cryptography over matrix groups. Zbl 1207.94053 Grigoriev, Dima; Ponomarenko, Ilia	3	2006
Algorithms and complexity in biological pattern formation problems. Zbl 1094.92008 Grigoriev, D.; Vakulenko, S.	1	2006
Polynomial-time computing over quadratic maps i: sampling in real algebraic sets. Zbl 1082.14065 Grigoriev, Dima; Pasechnik, Dmitrii V.	18	2005
Generalized Loewy-decomposition of \(D\)-modules. Zbl 1360.13061 Grigoriev, Dima; Schwarz, Fritz	11	2005
Weak Bézout inequality for D-modules. Zbl 1080.32010 Grigoriev, Dima	10	2005
Factoring and solving linear partial differential equations. Zbl 1052.35008 Grigoriev, D.; Schwarz, F.	20	2004
Homomorphic public-key cryptosystems over groups and rings. Zbl 1149.94318 Grigoriev, Dima; Ponomarenko, Ilia	5	2004
Approximating shortest path for the skew lines problem in time doubly logarithmic in 1/epsilon. Zbl 1075.68090 Burago, D.; Grigoriev, D.; Slissenko, A.	3	2004
Algebraic proof systems over formulas. Zbl 1044.68146 Grigoriev, Dima; Hirsch, Edward A.	11	2003
Complexity of gene circuits, Pfaffian functions and the morphogenesis problem. Zbl 1050.92003 Vakulenko, Sergey; Grigoriev, Dmitry	4	2003
Complexity of Null- and Positivstellensatz proofs. Zbl 0992.03073 Grigoriev, Dima; Vorobjov, Nicolai	36	2002
Complexity of semi-algebraic proofs. Zbl 1054.03035 Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrii V.	20	2002
Complexity of semialgebraic proofs. Zbl 1027.03044 Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrij V.	20	2002
Skyrmed monopoles. Zbl 0996.81059 Grigoriev, D. Yu.; Sutcliffe, P. M.; Tchrakian, D. H.	9	2002
Public-key cryptography and invariant theory. Zbl 1081.94026 Grigoriev, D.	4	2002
Exponential lower bound for static semi-algebraic proofs. Zbl 1056.03037 Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrii V.	3	2002
On non-Abelian homomorphic public-key cryptosystems. Zbl 1081.94027 Grigoriev, D.; Ponomarenko, I.	2	2002
Approximation and complexity. II: Iterated integration. Zbl 1020.68041 Grigoriev, Dima	2	2002
Linear lower bound on degrees of Positivstellensatz calculus proofs for the parity. Zbl 0974.68192 Grigoriev, D.	59	2001
Complexity of Positivstellensatz proofs for the knapsack. Zbl 0992.68077 Grigoriev, D.	44	2001
Linear gaps between degrees for the polynomial calculus modulo distinct primes. Zbl 1007.03052 Buss, Sam; Grigoriev, Dima; Impagliazzo, Russell; Pitassi, Toniann	33	2001
Approximation and complexity: Liouvillean-type theorems for linear differential equations on an interval. Zbl 1001.12007 Grigoriev, Dima	3	2001
There are no sparse NP\(_{w}\)-hard sets. Zbl 0992.68061 Cucker, Felipe; Grigoriev, Dima	2	2001
Constructing double-exponential number of vectors of multiplicities of solutions of polynomial systems. Zbl 1050.68048 Grigoriev, Dima	2	2001
Nikolai Aleksandrovich Shanin (on his 80th birthday). Zbl 1017.01517 Vsemirnov, M. A.; Girsh, È. A.; Grigor’ev, D. Yu.; Davydov, G. V.; Dantsin, E. Ya.; Ivanov, A. A.; Konev, B. Yu.; Lifshits, V. A.; Matiyasevich, Yu. V.; Mints, G. E.; Orevkov, V. P.; Slisenko, A. O.	2	2001
Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Zbl 1040.68045 Grigoriev, D.; Razborov, A.	21	2000
Bounds on numers of vectors of multiplicities for polynomials which are easy to compute. Zbl 1326.68354 Grigoriev, Dima; Vorobjov, Nicolai	9	2000
Topological complexity of the range searching. Zbl 0951.68024 Grigoriev, Dima	4	2000
Algorithms for computing sparse shifts for multivariate polynomials. Zbl 0968.68199 Grigoriev, Dima Yu.; Lakshman, Y. N.	4	2000
Linear gaps between degrees for the polynomial calculus modulo distinct primes. Zbl 1345.03105 Buss, Sam; Grigoriev, Dima; Impagliazzo, Russell; Pitassi, Toniann	5	1999
Complexity lower bounds for approximation algebraic computation trees. Zbl 0959.68143 Cucker, Felipe; Grigoriev, Dima	1	1999
Randomized complexity lower bound for arrangements and polyhedra. Zbl 0936.68047 Grigoriev, D.	1	1999
An exponential lower bound for depth 3 arithmetic circuits. Zbl 1028.68069 Grigoriev, Dima; Karpinski, Marek	28	1998
Polytime algorithm for the shortest path in a homotopy class amidst semi-algebraic obstacles in the plane. Zbl 0961.14039 Grigoriev, D.; Slissenko, A.	6	1998
An exponential lower bound on the size of algebraic decision trees for MAX. Zbl 0918.68032 Grigoriev, Dima; Karpinski, Marek; Yao, Andrew C.	3	1998
Randomized complexity lower bounds. Zbl 1027.68608 Grigoriev, D.	3	1998
On the power of real Turing machines over binary inputs. Zbl 0874.68110 Cucker, Felipe; Grigoriev, Dima	13	1997
Testing shift-equivalence of polynomials by deterministic, probabilistic and quantum machines. Zbl 1044.68946 Grigoriev, D.	10	1997
Lower bound on testing membership to a polyhedron by algebraic decision and computation trees. Zbl 0871.68176 Grigoriev, D.; Karpinski, M.; Vorobjov, N.	2	1997
Nearly sharp complexity bounds for multiprocessor algebraic computations. Zbl 0872.68053 Grigoriev, Dima	1	1997
A lower bound for randomized algebraic decision trees. Zbl 0895.68049 Grigoriev, Dima; Karpinski, Marek; Meyer auf der Heide, Friedhelm; Smolensky, Roman	1	1997
Randomization and the computational power of analytic and algebraic decision trees. Zbl 0895.68050 Grigoriev, Dima; Karpinski, Marek; Smolensky, Roman	1	1997
Complexity lower bounds for computation trees with elementary transcendental function gates. Zbl 0877.68086 Grigoriev, D.; Vorobjov, N.	9	1996
Testing shift-equivalence of polynomials using quantum machines. Zbl 0928.68045 Grigoriev, D.	5	1996
A lower bound for randomized algebraic decision trees. Zbl 0922.68090 Grigoriev, Dima; Karpinski, Marek; Meyer auf der Heide, Friedhelm; Smolensky, Roman	5	1996
NC solving of a system of linear ordinary differential equations in several unknowns. Zbl 0871.68096 Grigoriev, D.	1	1996
Computability of the additive complexity of algebraic circuits with root extracting. Zbl 0871.68085 Grigoriev, Dima; Karpinski, Marek	1	1996
Testing the shift-equivalence of polynomials using quantum machines. Zbl 0999.12017 Grigoriev, D.	1	1996
...and 57 more Documents

all cited Publications top 5 cited Publications

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Cited by 1,110 Authors

75	Grigor’ev, Dmitriĭ Yur’evich
21	Safey El Din, Mohab
19	Basu, Saugata
19	Vorob’ëv, Nikolaĭ N. jun.
14	Heintz, Joos
14	Roy, Marie-Françoise
13	Kurpisz, Adam
12	Sturm, Thomas
11	Cucker, Felipe
11	Karpinski, Marek
11	Shparlinski, Igor E.
10	Giusti, Marc
10	Hirsch, Edward A.
10	Kayal, Neeraj
10	Pardo, Luis Miguel
10	Vakulenko, Sergei A.
9	Davenport, James Harold
9	England, Matthew
9	Giesbrecht, Mark W.
9	Koiran, Pascal
9	Mastrolilli, Monaldo
9	Radulescu, Ovidiu
9	Saha, Chandan
9	Schost, Éric
9	Tzameret, Iddo
9	von zur Gathen, Joachim
8	Bank, Bernd
8	Kaltofen, Erich L.
8	Kumar, Mrinal
8	Leppänen, Samuli
8	Nordström, Jakob
8	Shpilrain, Vladimir
8	Singer, Michael F.
7	Atserias, Albert
7	Bürgisser, Peter
7	Duarte, Daniel
7	Gao, Xiaoshan
7	Kothari, Pravesh K.
7	Levandovskyy, Viktor
7	O’Donnell, Ryan
6	Bradford, Russell J.
6	Falkensteiner, Sebastian
6	Kahrobaei, Delaram
6	Kondrat’eva, Marina Vladimirovna
6	Lee, Wen-shin
6	Montaña, José Luis
6	Nikolenko, Sergey I.
6	Pitassi, Toniann
6	Raghavendra, Prasad
6	Schwarz, Fritz
5	Barak, Boaz
5	Boulier, François
5	de Wolff, Timo
5	Göös, Mika
5	Hong, Hoon
5	Itsykson, Dmitry M.
5	Jeronimo, Gabriela
5	Lauria, Massimo
5	Magron, Victor
5	Razborov, Aleksandr Aleksandrovich
5	Robere, Robert
5	Sabia, Juan
5	Saptharishi, Ramprasad
5	Schramm, Tselil
5	Shemyakova, Ekaterina
5	Solernó, Pablo
5	Walcher, Sebastian
5	Weber, Andreas Günter
5	Weiß, Armin
4	Banaji, Murad
4	Basu, Amitabh
4	Buss, Samuel R.
4	Feliu, Elisenda
4	Fomin, Sergey Vladimirovich
4	Galesi, Nicola
4	Goryuchkina, Irina V.
4	Heinle, Albert
4	Kamath, Pritish
4	Labahn, George
4	León Sánchez, Omar
4	Limaye, Nutan
4	Myasnikov, Alexei G.
4	Pasechnik, Dmitrii V.
4	Piazza, Carla
4	Pollack, Richard M.
4	Potechin, Aaron Henry
4	Rahkooy, Hamid
4	Romanovskiĭ, Valeriĭ Georgievich
4	Rosenkranz, Markus
4	Rouillier, Fabrice
4	Saraf, Shubhangi
4	Shpilka, Amir
4	Srinivasan, Srikanth
4	Sturmfels, Bernd
4	Tompa, Martin
4	Yukna, Stasys P.
3	Alekseev, Yaroslav
3	Anjos, Miguel F.
3	Barvinok, Alexander I.
3	Beaumont, James C.
...and 1,010 more Authors

all top 5

Cited in 196 Serials

73	Journal of Symbolic Computation
36	Theoretical Computer Science
23	Journal of Complexity
20	SIAM Journal on Computing
20	Computational Complexity
19	Applicable Algebra in Engineering, Communication and Computing
17	Discrete & Computational Geometry
17	Journal of Mathematical Sciences (New York)
16	Foundations of Computational Mathematics
14	Information Processing Letters
14	Journal of Computer and System Sciences
14	Advances in Applied Mathematics
14	Mathematical Programming. Series A. Series B
13	Journal of Pure and Applied Algebra
12	Annals of Pure and Applied Logic
11	Mathematics in Computer Science
10	SIAM Journal on Optimization
9	Information and Computation
9	Linear Algebra and its Applications
9	Groups, Complexity, Cryptology
8	Journal of Algebra
7	Discrete Applied Mathematics
7	Advances in Mathematics
7	Theory of Computing Systems
6	Communications in Algebra
6	Mathematics of Computation
6	Bulletin of Mathematical Biology
6	Algorithmica
5	Mathematical Notes
5	Annales de l’Institut Fourier
5	Programming and Computer Software
5	Computational Geometry
5	Annals of Mathematics and Artificial Intelligence
5	SIAM Journal on Applied Dynamical Systems
5	Journal of Mathematical Cryptology
4	Linear and Multilinear Algebra
4	Journal of Soviet Mathematics
4	SIAM Journal on Discrete Mathematics
4	Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
4	Journal of Systems Science and Complexity
4	ACM Transactions on Computational Logic
4	Theory of Computing
3	Artificial Intelligence
3	Journal of Mathematical Physics
3	Mathematical Methods in the Applied Sciences
3	Physics Letters. B
3	Journal of Computational and Applied Mathematics
3	St. Petersburg Mathematical Journal
3	Qualitative Theory of Dynamical Systems
3	Comptes Rendus. Mathématique. Académie des Sciences, Paris
3	Journal of Algebra and its Applications
3	Oberwolfach Reports
3	Prikladnaya Diskretnaya Matematika
2	Computer Physics Communications
2	Annali di Matematica Pura ed Applicata. Serie Quarta
2	Applied Mathematics and Computation
2	Automatica
2	Bulletin of the London Mathematical Society
2	Computing
2	Geometriae Dedicata
2	Manuscripta Mathematica
2	Mathematische Zeitschrift
2	Results in Mathematics
2	Transactions of the American Mathematical Society
2	Combinatorica
2	Revista Matemática Iberoamericana
2	Computational Mathematics and Mathematical Physics
2	SIAM Journal on Applied Mathematics
2	Journal of Dynamics and Differential Equations
2	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2	Cybernetics and Systems Analysis
2	Experimental Mathematics
2	Journal of Algebraic Combinatorics
2	Formal Methods in System Design
2	Russian Journal of Mathematical Physics
2	Finite Fields and their Applications
2	Journal of Combinatorial Optimization
2	Journal of the ACM
2	Journal of Discrete Mathematical Sciences & Cryptography
2	Annals of Mathematics. Second Series
2	Lobachevskii Journal of Mathematics
2	Quantum Information Processing
2	Mathematical Biosciences and Engineering
2	Discrete and Continuous Dynamical Systems. Series S
2	Forum of Mathematics, Sigma
2	Journal of Logical and Algebraic Methods in Programming
1	Acta Informatica
1	American Mathematical Monthly
1	Archive for History of Exact Sciences
1	Biological Cybernetics
1	Computers & Mathematics with Applications
1	Communications in Mathematical Physics
1	Israel Journal of Mathematics
1	Journal of Computational Physics
1	Journal of Mathematical Analysis and Applications
1	Moscow University Mathematics Bulletin
1	Nonlinearity
1	Nuclear Physics. B
1	Physica A
1	Problems of Information Transmission
...and 96 more Serials

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Cited in 57 Fields

520	Computer science (68-XX)
182	Algebraic geometry (14-XX)
105	Field theory and polynomials (12-XX)
102	Mathematical logic and foundations (03-XX)
96	Operations research, mathematical programming (90-XX)
81	Commutative algebra (13-XX)
78	Numerical analysis (65-XX)
75	Information and communication theory, circuits (94-XX)
68	Ordinary differential equations (34-XX)
59	Linear and multilinear algebra; matrix theory (15-XX)
52	Number theory (11-XX)
52	Biology and other natural sciences (92-XX)
50	Combinatorics (05-XX)
32	Associative rings and algebras (16-XX)
30	Partial differential equations (35-XX)
29	Group theory and generalizations (20-XX)
27	Quantum theory (81-XX)
24	Dynamical systems and ergodic theory (37-XX)
20	Several complex variables and analytic spaces (32-XX)
17	Convex and discrete geometry (52-XX)
14	Approximations and expansions (41-XX)
13	Real functions (26-XX)
13	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
12	Algebraic topology (55-XX)
11	Systems theory; control (93-XX)
10	Special functions (33-XX)
9	Statistics (62-XX)
7	Differential geometry (53-XX)
6	General and overarching topics; collections (00-XX)
6	Functions of a complex variable (30-XX)
6	Operator theory (47-XX)
6	Probability theory and stochastic processes (60-XX)
4	Nonassociative rings and algebras (17-XX)
4	Classical thermodynamics, heat transfer (80-XX)
3	History and biography (01-XX)
3	Order, lattices, ordered algebraic structures (06-XX)
3	General algebraic systems (08-XX)
3	Category theory; homological algebra (18-XX)
3	Difference and functional equations (39-XX)
3	Calculus of variations and optimal control; optimization (49-XX)
3	Geometry (51-XX)
3	Global analysis, analysis on manifolds (58-XX)
2	Abstract harmonic analysis (43-XX)
2	Functional analysis (46-XX)
2	Manifolds and cell complexes (57-XX)
2	Mechanics of particles and systems (70-XX)
2	Statistical mechanics, structure of matter (82-XX)
2	Relativity and gravitational theory (83-XX)
1	Topological groups, Lie groups (22-XX)
1	Potential theory (31-XX)
1	Integral transforms, operational calculus (44-XX)
1	General topology (54-XX)
1	Mechanics of deformable solids (74-XX)
1	Fluid mechanics (76-XX)
1	Optics, electromagnetic theory (78-XX)
1	Geophysics (86-XX)
1	Mathematics education (97-XX)

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