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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.

To further help fighting coronavirus, Dr Zaitsev joined several global communities including the global CoronaWhy community and Just One Giant Lab" with Campaign for Open & Trustworthy Science.

Publications and Further Research Outputs

Peer-Reviewed Publications

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 Journal Article, 2020 DOI

Zaitsev, D., A geometric approach to Catlin's boundary systems, Annales de l'Institut Fourier, 69, (6), 2020, p2635-2679 Journal Article, 2020

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 Journal Article, 2019

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 Journal Article, 2019 DOI

Kossovskiy, I., Zaitsev, D., Normal Form for Second Order Differential Equations , Journal of Dynamical and Control Systems, 24, (4), 2018, 541-562 Journal Article, 2018 DOI

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 Journal Article, 2018 TARA - Full Text URL

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 Journal Article, 2018

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 Journal Article, 2018 TARA - Full Text

Normal forms in Cauchy-Riemann geometry in, Contemporary Mathematics, 2018, pp153-177 , [ Kolar, M., Kossovskiy, I., Zaitsev, D. ] Book Chapter, 2018 DOI

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 Conference Paper, 2017

Cherkis, S.A., O'Hara, C., Zaitsev, D., A compact expression for periodic instantons, Journal of Geometry and Physics, 110, 2016, p382-392 Journal Article, 2016 DOI

Kossovskiy, Ilya; Zaitsev, Dmitri, Convergent normal form for real hypersurfaces at generic Levi degeneracy, Journal für die reine und angewandte Mathematik, 2016 Journal Article, 2016 URL

Kossovskiy, I., Zaitsev, D., Convergent normal form and canonical connection for hypersurfaces of finite type in C2, Advances in Mathematics, 281, 2015, p670-705 Journal Article, 2015 DOI

Kim, S.-Y. Zaitsev, D., Rigidity of proper holomorphic maps between bounded symmetric domains, Mathematische Annalen, 362, (1-2), 2015, p639-677 Journal Article, 2015 DOI URL

Kolar, M. Meylan, F. Zaitsev, D., Chern-Moser operators and polynomial models in CR geometry, Advances in Mathematics, 263, 2014, p321 - 356 Journal Article, 2014 URL DOI

O'Farrell, A.G. Zaitsev, D., Factoring formal maps into reversible or involutive factors, Journal of Algebra, 399, 2014, p657 - 674 Journal Article, 2014 DOI URL

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 Journal Article, 2014 URL

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 Journal Article, 2013 TARA - Full Text DOI

Kim, SY, Zaitsev, D, Rigidity of CR maps between Shilov boundaries of bounded symmetric domains, INVENTIONES MATHEMATICAE, 193, (2), 2013, p409-437 Journal Article, 2013 DOI TARA - Full Text

Bracci, F., Raissy, J., Zaitsev, D., Dynamics of multi-resonant biholomorphisms, International Mathematics Research Notices, 2013, (10), 2013, p4772 - 4797 Journal Article, 2013

Huang, XJ, Zaitsev, D, Non-embeddable real algebraic hypersurfaces, Mathematische Zeitschrift, 275, (3-4), 2013, p657-671 Journal Article, 2013 TARA - Full Text DOI

Filippo Bracci, Dmitri Zaitsev, Dynamics of one-resonant biholomorphisms, The Journal of the European Mathematical Society (JEMS), 15, (1), 2013, p179-20 Journal Article, 2013 TARA - Full Text DOI URL

Zaitsev, D., Normal forms for nonintegrable almost CR structures, American Journal of Mathematics , 134, (4), 2012, p915-947 Journal Article, 2012 DOI TARA - Full Text

Zaitsev, D., A normal form for all Levi-nondegenerate almost CR structures, Illinois Journal of Mathematics, 56, (1), 2012, p273-280 Journal Article, 2012


Dolbeault, P., Tomassini, G., Zaitsev, D., Boundary problem for levi flat graphs, Indiana University Mathematic Journal, 60, (1), 2011, p161-170 Journal Article, 2011 DOI TARA - Full Text

Zaitsev, D. , Formal and finite order equivalences , Mathematische Zeitschrift, 169, (3-4), 2011, p687-696 Journal Article, 2011 DOI TARA - Full Text

Dolbeault, P. , Tomassini, G. , Zaitsev, D, On Levi-flat hypersurfaces with prescribed boundary, Pure and Applied Mathematics Quarterly , 6, (3), 2010, p725-753 Journal Article, 2010 URL TARA - Full Text

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 Journal Article, 2009 DOI TARA - Full Text

P. Ebenfelt, B. Lamel, D. Zaitsev, Degenerate real hypersurfaces in C2 with few automorphisms, Trans. Amer. Math. Soc, 361, (6), 2009, p3241-3267 Journal Article, 2009 TARA - Full Text

Dmitri Zaitsev, Obstructions to embeddability into hyperquadrics and explicit examples, Mathematische Annalen, 342, (3), 2008, p695-726 Journal Article, 2008 DOI TARA - Full Text

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 Journal Article, 2008 DOI TARA - Full Text

D. Zaitsev & F. Bracci, Boundary jets of holomorphic maps between strongly pseudoconvex domains, Journal of Functional Analysis, 254, (6), 2008, p1449-1466 Journal Article, 2008 DOI TARA - Full Text

Dmitri Zaitsev, On diff erent notions of homogeneity for CR-manifolds, Asian Journal of Mathematics, 11, (2), 2007, p331-340 Journal Article, 2007 URL

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. Journal Article, 2007 DOI

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 Journal Article, 2007 TARA - Full Text DOI

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 Journal Article, 2006 TARA - Full Text URL

Kim, Sung-Yeon; Zaitsev, Dmitri, Remarks on the rigidity of CR-manifolds, Compositio Mathematica, 142, (4), 2006, p1009 - 1017 Journal Article, 2006 TARA - Full Text URL DOI

Baracco, Luca; Zaitsev, Dmitri; Zampieri, Giuseppe, A Burns-Krantz type theorem for domains with corners, Mathematische Annalen , 336, (3), 2006, p1432 - 1807 Journal Article, 2006 TARA - Full Text URL DOI

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 Journal Article, 2005

Ebenfelt, Peter; Huang, Xiaojun; Zaitsev, Dmitri, The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics, Amer. J. Math., 127, (1), 2005, p169 - 191 Journal Article, 2005 TARA - Full Text URL

Kim, Sung-Yeon; Zaitsev, Dmitri, Equivalence and embedding problems for CR-structures of any codimension, Topology, 44, (3), 2005, p557 - 584 Journal Article, 2005 TARA - Full Text

Ebenfelt, Peter; Huang, Xiaojun; Zaitsev, Dmitri, Rigidity of CR-immersions into spheres, Comm. Anal. Geom., 12, (3), 2004, p631 - 670 Journal Article, 2004 TARA - Full Text URL

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 Journal Article, 2004 URL

Kaup, Wilhelm; Zaitsev, Dmitri, Non-embeddable CR-manifolds of higher codimension, Journal für die Reine und Angewandte Mathematik, 569, 2004, p1 - 12 Journal Article, 2004 URL

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 Journal Article, 2004 URL

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 Journal Article, 2003 TARA - Full Text

Kaup, Wilhelm; Zaitsev, Dmitri, On the CR-structure of compact group orbits associated with bounded symmetric domains. , Invent. Math., 153, (1), 2003, p45 - 104 Journal Article, 2003

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 Journal Article, 2003 URL

Zaitsev, Dmitri; Zampieri, Giuseppe, Extension of CR-functions on wedges., Math. Ann., 326, (4), 2003, p691 - 703 Journal Article, 2003 TARA - Full Text

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 Journal Article, 2003 URL TARA - Full Text

Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri, Approximation and convergence of formal CR-mappings, Int. Math. Res. Not., 2003, (4), 2003, p211 - 242 Journal Article, 2003

Zaitsev, Dmitri, Unique determination of local CR-maps by their jets: A survey"., Rend. Mat. Acc. Lincei,, 9, (13), 2002, p135-145. Journal Article, 2002 TARA - Full Text

Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri, Analytic regularity of CR-mappings, Math. Res. Lett., 9, (1), 2002, p73 - 93 Journal Article, 2002 URL

Baouendi, M. S.; Rothschild, Linda Preiss; Zaitsev, Dmitri, Equivalences of real submanifolds in complex space., J. Differential Geom., 59, (2), 2001, p301 - 351 Journal Article, 2001 TARA - Full Text URL

Huckleberry, A.; Zaitsev, D.; Kus, M.; Haake, F., A symplectic context for level dynamics., J. Geom. Phys., 37, (1-2), 2001, p156 - 168 Journal Article, 2001

Kaup, Wilhelm; Zaitsev, Dmitri, On symmetric Cauchy-Riemann manifolds, Adv. Math. , 149, (2), 2000, p145 - 181 Journal Article, 2000 TARA - Full Text

Zaitsev, Dmitri, Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces., Acta Math., 183, (2), 1999, p273 - 305 Journal Article, 1999 URL TARA - Full Text

Zaitsev, Dmitri, Configurations of linear subspaces and rational invariants, Michigan Math. Journal , 46, 1999, p187-202 Journal Article, 1999

Zaitsev, Dmitri, Domains of polyhedral type and boundary extensions of biholomorphisms, Indiana University of Mathematics Journal , 47, (4), 1998, p1511-1526. Journal Article, 1998 TARA - Full Text

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 Journal Article, 1997 TARA - Full Text URL

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 Journal Article, 1997 DOI

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] Book Chapter, 1996 TARA - Full Text

Zaitsev, Dmitri, On the automorphism groups of algebraic bounded domains, Mathematische Annalen, 302, (1), 1995, p105-129 Journal Article, 1995 DOI TARA - Full Text

Zaitsev, Dmitri, Regularizations of birational group operations in the sense of Weil, Journal of Lie Theory, 5, 1995, p207-224 Journal Article, 1995 URL TARA - Full Text

Non-Peer-Reviewed Publications

Zaitsev, Dmitri, The 5th William Rowan Hamilton Geometry and Topology Workshop, 17-19 Sept, 2009, Trinity College Dublin, Ireland Meetings /Conferences Organised, 2009

Zaitsev, Dmitri, CR Geometry and PDE's, 22-27 Sept, 2008, Trento, Italy Meetings /Conferences Organised, 2008

Zaitsev, Dmitri, The 4th William Rowan Hamilton Geometry and Topology Workshop, 28-30 Aug, 2008, Trinity College Dublin, Ireland Meetings /Conferences Organised, 2008

Zaitsev, Dmitri, The 3rd William Rowan Hamilton Geometry and Topology Workshop, 6-8 Sept, In:Trinity College Dublin, Ireland, 2007 Meetings /Conferences Organised, 2007

Zaitsev, Dmitri , 4th Irish Geometry Conference, 19-20 May, 2006, Trinity College Dublin, Ireland Meetings /Conferences Organised, 2006

Zaitsev, Dmitri , CR Geometry and PDE's, 2-8 Sept, 2006, Trento, Italy Meetings /Conferences Organised, 2006

Zaitsev, Dmitri , The 2nd William Rowan Hamilton Geometry and Topology Workshop, 28 -30 Sept, 2006, Trinity College Dublin, Ireland Meetings /Conferences Organised, 2006

Zaitsev, Dmitri , CR Geometry and Partial Di erential Equations, 12-17 Sept, 2004, Trento, Italy Meetings /Conferences Organised, 2004

Zaitsev, Dmitri , Real Methods in Complex and CR Geometry, 30 June - 6 July , 2002, (Taranto), Italy Meetings /Conferences Organised, 2002

Research Expertise


Complex 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.


  • Title
    • Geometry of Real Submanifolds in Complex Spaces
  • Summary
    • 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
  • Date From
    • 1.9.2006
  • Date To
    • 1.9.2010
  • Title
    • Geometry of Real Submanifolds in Complex Spaces
  • Summary
    • This project is the continuation of the previous same named project
  • Funding Agency
    • Science Foundation Ireland
  • Date From
    • 01.09.2010
  • Date To
    • 01.09.2015


Complex Analysis and Geometry; CR Geometry; Differential geometry; Several Complex Variables


Awards and Honours

Elected Fellow of Trinity College Dublin 2014


Irish Mathematical Society 2003 – present

American Mathematical Society 22/12/2017 – present