Dr. Dmitri Zaitsev
Associate Professor, Pure & Applied Mathematics
Dmitri Zaitsev is an Associate Professor in the School of Mathematics, which he joined in 2003. He grew up in Kiev, Ukraine, where he won several Mathematics Olympiads, including All-Soviet-Union mathematical competitions. He studied Mathematics at Lomonosov Moscow State University and completed his Diploma in 1993 and his PhD, within 1 year from Diploma, in 1994 at Ruhr-University, Bochum, Germany.
Prior to joining Trinity College Dublin, he held researcher and visiting professor positions in Germany, France, Italy and the USA.
Dr Zaitsev's research comprises contributions to Geometry and Analysis of Several Complex Variables as well as connected areas of Mathematics, such as Lie Groups, Differential Geometry, Real and Complex Algebraic Geometry, Partial Differential Equations and Dynamical Systems.
He has over 20 international collaborators from over 10 countries and has authored over 60 peer-reviewed research articles. One of the conferences he co-founded and co-organised in Italy for many years, "CR Geometry and PDEs", became one of the major international conferences in the field.
In 2014, Dr Zaitsev founded a Trinity Campus Company, Personalotels Ltd, employing mathematical algorithms to help travellers finding hotels matching their personal preferences and avoiding the information overload problem.
Between 2013 and 2019, Dr Zaitsev served as School of Mathematics' Erasmus and Exchange Coordinator, during which period he expanded School's Erasmus agreements from 2 to 8, including 2 new countries, as well as negotiated one University-wide Memorandum of Understanding agreement - the first of this kind initiated by our School.
In 2018, Dr Zaitsev, being concerned with the numbers of academic journals using paywalls, co-founded Global Public Forum for scholarly publishing reform towards Fair Open Access and lead the campaign to collect signatures of support from many distinguished scientists.
In the same year, Dr Zaitsev co-founded Free Journal Network - an ecosystem of community-run high quality academic journals that are free for readers and authors.
Since 2019, Dr Zaitsev has been serving on TCD Open Scholarship Taskforce .
In April 2020 at the beginning of COVID-19 Pandemic, Dr Zaitsev entered as academic mentor multiple hackathons to fight against the virus, including the EUvsVirus hackathon hosted by European Commission, and currently advising over 10 projects among the winners, some of them being listed here.
Publications and Further Research Outputs
Hyland, Jack, Kouker, Alexander, Zaitsev, Dmitri, Open Access eXchange (OAeX): an economic model and platform for fundraising open scholarship services, Insights the UKSG journal, 33, 2020
Zaitsev, D., A geometric approach to Catlin's boundary systems, Annales de l'Institut Fourier, 69, (6), 2020, p2635-2679
Ebenfelt, P., Zaitsev, D., A new invariant equation for umbilical points on real hypersurfaces in C2 and applications, Communications in Analysis and Geometry, 27, (7), 2019, p1549-1582
Kossovskiy, I., Zaitsev, D. , Convergent normal form for real hypersurfaces at a generic Levi-degeneracy , Journal fur die Reine und Angewandte Mathematik , 749, 2019, p201-225
Kossovskiy, I., Zaitsev, D., Normal Form for Second Order Differential Equations , Journal of Dynamical and Control Systems, 24, (4), 2018, 541-562
Ebenfelt, Peter; Lamel, Bernhard; Zaitsev, Dmitri, Normal form for infinite type hypersurfaces in ℂ2 with nonvanishing Levi form derivative, Documenta Mathematica, 22, 2018, p165 - 190
Kim, S.-Y., Zaitsev, D., Jet vanishing orders and effectivity of Kohn's algorithm in dimension 3, Asian Journal of Mathematics, 22, (3), 2018, p545-568
Peter Ebenfelt, Duong Ngoc Son, Dmitri Zaitsev, A family of compact strictly pseudoconvex hypersurfaces in C, 2 without umbilical points, Mathematical Research Letters, 25, (1), 2018, p75-84
Normal forms in Cauchy-Riemann geometry in, Contemporary Mathematics, 2018, pp153-177 , [ Kolar, M., Kossovskiy, I., Zaitsev, D. ]
Kolar, Martin; Kossovskiy, Ilya; Zaitsev, Dmitri, Normal forms in Cauchy-Riemann geometry, Contemp. Math., Analysis and geometry in several complex variables, Doha, Qatar, January 4-8, 2015, edited by Shiferaw Berhanu, Nordine Mir, and Emil Straube. , 681, Amer. Math. Soc., 2017, pp153 - 177
Cherkis, S.A., O'Hara, C., Zaitsev, D., A compact expression for periodic instantons, Journal of Geometry and Physics, 110, 2016, p382-392
Kossovskiy, Ilya; Zaitsev, Dmitri, Convergent normal form for real hypersurfaces at generic Levi degeneracy, Journal für die reine und angewandte Mathematik, 2016
Kossovskiy, I., Zaitsev, D., Convergent normal form and canonical connection for hypersurfaces of finite type in C2, Advances in Mathematics, 281, 2015, p670-705
Kim, S.-Y. Zaitsev, D., Rigidity of proper holomorphic maps between bounded symmetric domains, Mathematische Annalen, 362, (1-2), 2015, p639-677
Kolar, M. Meylan, F. Zaitsev, D., Chern-Moser operators and polynomial models in CR geometry, Advances in Mathematics, 263, 2014, p321 - 356
O'Farrell, A.G. Zaitsev, D., Factoring formal maps into reversible or involutive factors, Journal of Algebra, 399, 2014, p657 - 674
O'Farrell, A.G. Zaitsev, D., Formally reversible maps of -2, Annali della Scuola normale superiore di Pisa - Classe di scienze, 13, (2), 2014, p371 - 397
Isaev, A, Zaitsev, D, Reduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms, JOURNAL OF GEOMETRIC ANALYSIS, 23, (3), 2013, p1571-1605
Kim, SY, Zaitsev, D, Rigidity of CR maps between Shilov boundaries of bounded symmetric domains, INVENTIONES MATHEMATICAE, 193, (2), 2013, p409-437
Bracci, F., Raissy, J., Zaitsev, D., Dynamics of multi-resonant biholomorphisms, International Mathematics Research Notices, 2013, (10), 2013, p4772 - 4797
Huang, XJ, Zaitsev, D, Non-embeddable real algebraic hypersurfaces, Mathematische Zeitschrift, 275, (3-4), 2013, p657-671
Filippo Bracci, Dmitri Zaitsev, Dynamics of one-resonant biholomorphisms, The Journal of the European Mathematical Society (JEMS), 15, (1), 2013, p179-20
Zaitsev, D., Normal forms for nonintegrable almost CR structures, American Journal of Mathematics , 134, (4), 2012, p915-947
Zaitsev, D., A normal form for all Levi-nondegenerate almost CR structures, Illinois Journal of Mathematics, 56, (1), 2012, p273-280
Zaitsev, D, A NORMAL FORM FOR ALL LEVI-NONDEGENERATE ALMOST CR STRUCTURES, ILLINOIS JOURNAL OF MATHEMATICS, 56, (1), 2012, p273-280
Dolbeault, P., Tomassini, G., Zaitsev, D., Boundary problem for levi flat graphs, Indiana University Mathematic Journal, 60, (1), 2011, p161-170
Zaitsev, D. , Formal and finite order equivalences , Mathematische Zeitschrift, 169, (3-4), 2011, p687-696
Dolbeault, P. , Tomassini, G. , Zaitsev, D, On Levi-flat hypersurfaces with prescribed boundary, Pure and Applied Mathematics Quarterly , 6, (3), 2010, p725-753
Baouendi, M. S.; Ebenfelt, P.; Zaitsev, D., A Cauchy-Kowalevsky theorem for overdetermined systems of nonlinear partial differential equations and geometric applications., Communications in Partial Differential Equations, 34, (10), 2009, p1180--1207
P. Ebenfelt, B. Lamel, D. Zaitsev, Degenerate real hypersurfaces in C2 with few automorphisms, Trans. Amer. Math. Soc, 361, (6), 2009, p3241-3267
Dmitri Zaitsev, Obstructions to embeddability into hyperquadrics and explicit examples, Mathematische Annalen, 342, (3), 2008, p695-726
D. Zaitsev, B. Lamel and N. Mir, Lie group structures on automorphism groups of real-analytic CR manifolds, American Journal of Mathematics, 130, (6), 2008, p1709-1726
D. Zaitsev & F. Bracci, Boundary jets of holomorphic maps between strongly pseudoconvex domains, Journal of Functional Analysis, 254, (6), 2008, p1449-1466
Dmitri Zaitsev, On diff erent notions of homogeneity for CR-manifolds, Asian Journal of Mathematics, 11, (2), 2007, p331-340
Luca Baracco, Dmitri Zaitsev and Giuseppe Zampieri, Rays condition and extension of CR functions from manifolds of higher type, Journal d'Analyse Mathématique, 101, (1), 2007, p95-121.
M.S. Baouendi, L.P. Rothschild and D. Zaitsev, Deformation of generic submanifolds in a complex manifold, Advances in Mathematics, 212, (1), 2007, p157-180
Kaup, Wilhelm; Zaitsev, Dmitri , On local CR-transformation of Levi-degenerate group orbits in compact Hermitian symmetric spaces, Journal of the European Mathematical Society (JEMS), 8, (3), 2006, p465 - 490
Kim, Sung-Yeon; Zaitsev, Dmitri, Remarks on the rigidity of CR-manifolds, Compositio Mathematica, 142, (4), 2006, p1009 - 1017
Baracco, Luca; Zaitsev, Dmitri; Zampieri, Giuseppe, A Burns-Krantz type theorem for domains with corners, Mathematische Annalen , 336, (3), 2006, p1432 - 1807
Dolbeault, Pierre; Tomassini, Giuseppe; Zaitsev, Dmitri, On boundaries of Levi-flat hypersurfaces in Cn, C. R. Math. Acad. Sci. Paris, 341, (6), 2005, p343 - 348
Ebenfelt, Peter; Huang, Xiaojun; Zaitsev, Dmitri, The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics, Amer. J. Math., 127, (1), 2005, p169 - 191
Kim, Sung-Yeon; Zaitsev, Dmitri, Equivalence and embedding problems for CR-structures of any codimension, Topology, 44, (3), 2005, p557 - 584
Ebenfelt, Peter; Huang, Xiaojun; Zaitsev, Dmitri, Rigidity of CR-immersions into spheres, Comm. Anal. Geom., 12, (3), 2004, p631 - 670
Baouendi, M. Salah; Rothschild, Linda Preiss; Winkelmann, Jörg; Zaitsev, Dmitri, Lie group structures on groups of diffeomorphisms and applications to CR manifolds., Ann. Inst. Fourier (Grenoble), 54, (5), 2004, p1279 - 1303
Kaup, Wilhelm; Zaitsev, Dmitri, Non-embeddable CR-manifolds of higher codimension, Journal für die Reine und Angewandte Mathematik, 569, 2004, p1 - 12
Zaitsev, Dmitri; Zampieri, Giuseppe, Extension of CR-functions into weighted wedges through families of nonsmooth analytic discs, Trans. Amer. Math. Soc., 356, (4), 2004, p1443 - 1462
Ebenfelt, P.; Lamel, B.; Zaitsev, D, Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case., Geom. Funct. Anal., 13, (3), 2003, p546 - 573
Kaup, Wilhelm; Zaitsev, Dmitri, On the CR-structure of compact group orbits associated with bounded symmetric domains. , Invent. Math., 153, (1), 2003, p45 - 104
Hayashimoto, Atsushi; Kin, Sung-Yeon; Zaitsev, Dmitri, Decomposition of CR-manifolds and splitting of CR-maps, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2, (3), 2003, p433 - 448
Zaitsev, Dmitri; Zampieri, Giuseppe, Extension of CR-functions on wedges., Math. Ann., 326, (4), 2003, p691 - 703
Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri, Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds, Asian Journal of Mathematics, 7, (4), 2003, p493 - 509
Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri, Approximation and convergence of formal CR-mappings, Int. Math. Res. Not., 2003, (4), 2003, p211 - 242
Zaitsev, Dmitri, Unique determination of local CR-maps by their jets: A survey"., Rend. Mat. Acc. Lincei,, 9, (13), 2002, p135-145.
Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri, Analytic regularity of CR-mappings, Math. Res. Lett., 9, (1), 2002, p73 - 93
Baouendi, M. S.; Rothschild, Linda Preiss; Zaitsev, Dmitri, Equivalences of real submanifolds in complex space., J. Differential Geom., 59, (2), 2001, p301 - 351
Huckleberry, A.; Zaitsev, D.; Kus, M.; Haake, F., A symplectic context for level dynamics., J. Geom. Phys., 37, (1-2), 2001, p156 - 168
Kaup, Wilhelm; Zaitsev, Dmitri, On symmetric Cauchy-Riemann manifolds, Adv. Math. , 149, (2), 2000, p145 - 181
Zaitsev, Dmitri, Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces., Acta Math., 183, (2), 1999, p273 - 305
Zaitsev, Dmitri, Configurations of linear subspaces and rational invariants, Michigan Math. Journal , 46, 1999, p187-202
Zaitsev, Dmitri, Domains of polyhedral type and boundary extensions of biholomorphisms, Indiana University of Mathematics Journal , 47, (4), 1998, p1511-1526.
Zaitsev, Dmitri, Germs of local automorphisms of real analytic CR structures and analytic dependence on the k-jets, Mathematical Research Letters, 4, 1997, p1-20
Marek Kus, Fritz Haake, Dmitri Zaitsev and Alan Huckleberry, Level dynamics for conservative and dissipative quantum systems, Journal of Physics A: Mathematical and General, 30, (24), 1997, p8635-8651
Actions of groups of birationally extendible automorphisms in, editor(s)Noguchi et al., Hayama , Geom. Complex Analysis, River Edge, NJ, World Sci. Publishing, 1996, pp261-285. , [D. Zaitsev & A. Huckleberry]
Zaitsev, Dmitri, On the automorphism groups of algebraic bounded domains, Mathematische Annalen, 302, (1), 1995, p105-129
Zaitsev, Dmitri, Regularizations of birational group operations in the sense of Weil, Journal of Lie Theory, 5, 1995, p207-224
Zaitsev, Dmitri, The 5th William Rowan Hamilton Geometry and Topology Workshop, 17-19 Sept, 2009, Trinity College Dublin, Ireland
Zaitsev, Dmitri, CR Geometry and PDE's, 22-27 Sept, 2008, Trento, Italy
Zaitsev, Dmitri, The 4th William Rowan Hamilton Geometry and Topology Workshop, 28-30 Aug, 2008, Trinity College Dublin, Ireland
Zaitsev, Dmitri, The 3rd William Rowan Hamilton Geometry and Topology Workshop, 6-8 Sept, In:Trinity College Dublin, Ireland, 2007
Zaitsev, Dmitri , 4th Irish Geometry Conference, 19-20 May, 2006, Trinity College Dublin, Ireland
Zaitsev, Dmitri , CR Geometry and PDE's, 2-8 Sept, 2006, Trento, Italy
Zaitsev, Dmitri , The 2nd William Rowan Hamilton Geometry and Topology Workshop, 28 -30 Sept, 2006, Trinity College Dublin, Ireland
Zaitsev, Dmitri , CR Geometry and Partial Di erential Equations, 12-17 Sept, 2004, Trento, Italy
Zaitsev, Dmitri , Real Methods in Complex and CR Geometry, 30 June - 6 July , 2002, (Taranto), Italy
DescriptionComplex Analysis and Geometry, Several Complex Variables, Dynamical Systems, CR Geometry, Normal forms, Rigidity, Bounded Symmetric Domains, Instantons.
Building bridges between Analysis and Geometry with Partial Differential Equations via multiplier ideal sheaves, inspired and building on the work by J.J. Kohn, J.P. D'Angelo, Y.-T.Siu and others.
Algebraic and Analytic theory of Singularities (where objects cease to be regular) arising in Geometry and Partial Differential Equations. Developing connections between singularities and Graph via associating new invariant graph-like structures to singularities. Applying Complexity Theory to measure and control the numbers of steps in algorithms for resolution of singularities.
Geometric Analysis by means of Cartan's method of moving frames and umbiliticy (vanishing of curvature). Replacing complicated curvature formalism by a new direct determinant formula. Answered long-standing question from the work of S.-S. Chern and J. K. Moser in 1974 about the existence of umibilical points.
Deriving a simple formula for instantons with one periodic direction for ADHM-Nahm transform in Theoretical Physics.
Discovering rigidity phenomena for proper holomorphic and CR maps in for bounded symmetric domains and their boundary components.
Dynamics or local holomorphic maps in several variables, building hierarchy of (multi-)resonant maps and dynamics reduction to lower dimension, with applications to normal forms and existence and description of bassins of attraction.
- Geometry of Real Submanifolds in Complex Spaces
- It is well-known that any surface in the euclidean space can be locally transformed into a plane by a suitably chosen differentiable coordinate change. However, this is no more true if the coordinates are complex and the coordinate change is holomorphic, i.e. "differentiable" in the complex sense. In fact, it is an old and still unsolved problem to decide, which surfaces can be transformed into each other by such a coordinate change. A deeper understanding of this problem is the subject of my project. Accomplishments include construction of normal forms, i.e. finding natural distinguished coordinates, in which the surfaces can be compared explicitly; comparison of various natural equivalence relations for surfaces - under coordinate changes given by formal power series and equivalences at the level of lower order terms of any order.
- Funding Agency
- Science Foundation Ireland
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- Geometry of Real Submanifolds in Complex Spaces
- This project is the continuation of the previous same named project
- Funding Agency
- Science Foundation Ireland
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