Research Interests of Dmitri Zaitsev

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Title: Research Interests of Dmitri Zaitsev
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# Research Interests of Dmitri Zaitsev

**Source**: https://www.maths.tcd.ie/~zaitsev/research.html
**Parent**: https://www.maths.tcd.ie/~zaitsev/

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# Research Interests of Dmitri Zaitsev

**Several Complex Variables:**

*The shortest path between two truths \
in the real domain passes through the \
complex domain.*

*J. Hadamard*

- Normal forms of real submanifolds in complex spaces
- Proper holomorphic mappings and correspondences
- Rigidity of proper and CR maps
- Bounded symmetric domains
- Meromorphic and bimeromorphic mappings
- Automorphism groups of complex spaces
- Semi-analytic and sub-analytic sets
- CR manifolds
- Holomorphic foliations and webs

**Real and Complex Algebraic Geometry:**

- Algebraic and analytic cycle spaces
- Real algebraic and semialgebraic sets
- Nash functions and manifolds

**Symplectic Geometry and Lie Group actions**

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### Check [my arXiv.org list](http://arxiv.org/find/math/1/au:+Zaitsev_D/0/1/0/all/0/1) for the most recent papers and [my publication list from MathSciNet](http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=362388)

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## Selected Papers:

- **Kolar, M.; Meylan, F.; Zaitsev, D.**  --- Chern-Moser operators and polynomial models in CR geometry.
   *[Advances in Mathematics](http://www.sciencedirect.com/science/article/pii/S0001870814002230)*  **263**  (2014), no. 2, 321-356.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kolar-meylan-zaitsev.pdf)

- **O'Farrell, A.G.; Zaitsev, D.**  --- Formally reversible maps of C2.
   *[Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. (Serie V)](http://annaliscienze.sns.it/)*  **13** (2014), no. 2, 371-397.
   [PDF](http://arxiv.org/pdf/1111.6984v1.pdf)

- **O'Farrell, A.G.; Zaitsev, D.**  --- Factoring formal maps into reversible or involutive factors.
   *[Journal of Algebra](http://www.journals.elsevier.com/journal-of-algebra/)* **399** (2014), 657-674.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/ofarrell-zaitsev-jalgebra.pdf)

- **Kim, S.Y.; Zaitsev, D.**  --- Rigidity of CR maps between Shilov boundaries
  of bounded symmetric domains.
   *[Inventiones Mathematicae](http://www.springer.com/mathematics/journal/222)*  **193**  (2013), no. 2, 409-437.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/Kim-Zaitsev-Invent-final.pdf)

- **Bracci, F.; Zaitsev, D.**  --- Dynamics of one-resonant biholomorphisms.
  *[Journal of the European Mathematical Society (JEMS)](http://www.ems-ph.org/journals/journal.php?jrn=jems)* **15** (2013), no. 1, 179-200.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/bracci-zaitsev.pdf)

- **Zaitsev, D.**  --- Normal forms for nonintegrable almost CR structures.
  *[American Journal of Mathematics](http://muse.jhu.edu/journals/ajm/)* **134** (2012), no. 4, 915-947.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/zaitsev-amerj.pdf)

- **Dolbeault, P.; Tomassini, G.; Zaitsev, D.**  --- Boundary problem for Levi flat graphs.
  *[Indiana University Mathematics Journal](http://www.iumj.indiana.edu/)* **60** (2011), no. 1, 161-170.
   [PDF](http://arxiv.org/pdf/0912.1332.pdf)

- **Zaitsev, D.**  --- Formal and finite order equivalences. *[Mathematische Zeitschrift](http://link.springer.com/journal/209)*
  **269** (2011), no. 3-4, 687-696.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/zaitsev-matz.pdf)

- **Dolbeault, P.; Tomassini, G.; Zaitsev, D.**  --- On Levi-flat hypersurfaces with prescribed boundary.
  *[Pure and Applied Mathematics Quarterly](http://intlpress.com/site/pub/pages/journals/items/pamq/_home/_main/index.html)*
  **6** (2010), no. 3, Special Issue: In honor of Joseph J. Kohn. Part 1, 725-753.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/dtz-prescribed.pdf)

- **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](http://www.tandfonline.com/loi/lpde20)* **34** (2009), no. 10-12, 1180-1207.
   [PDF](http://arxiv.org/pdf/0811.1255v1.pdf)

- **Lamel, B.; Mir, N.; Zaitsev, D.** --- Lie group structures on automorphism groups of real-analytic CR manifolds.
   *[American Journal of Mathematics](https://www.press.jhu.edu/journals/american_journal_of_mathematics/)*
  **130** (2008), no. 6, 1709-1726.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/lmz-amerj.pdf)

- **Zaitsev, D.**  --- Obstructions to embeddability into hyperquadrics and explicit examples.
  *[Mathematische Annalen](http://link.springer.com/journal/208)*
  **342** (2008), no. 3, 695-726.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/zaitsev-obstructions.pdf)

- **Zaitsev, D.**  --- On different notions of homogeneity for CR-manifolds.
   *[The Asian Journal of Mathematics](http://www.intlpress.com/AJM/)*  **11**  (2007), no. 2, 331-340.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/homogeneous-asian.pdf)

- **Kim, S.-Y.; Zaitsev, D.**  --- Remarks on the rigidity of CR-manifolds.
   *[Compositio Mathematica](http://journals.cambridge.org/action/displayJournal?jid=COM)*  **142**  (2006), no. 4, 1009-1017.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kim-zaitsev-compositio.pdf)

- **Kaup, W.; Zaitsev, D.** --- On local CR-transformations of Levi-degenerate group orbits
  in compact Hermitian symmetric spaces.
  *[Journal of the European Mathematical Society (JEMS)](http://www.ems-ph.org/journals/journal.php?jrn=jems)*
   **8**  (2006), no. 3, 465-490.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kaup-zaitsev-jems.pdf)

- **Kim, S.-Y.; Zaitsev, D.**  --- Equivalence and embedding problems for CR-structures of any codimension.
   *[Topology](http://www.elsevier.com/wps/find/journaldescription.cws_home/261/description#description)*  **44**  (2005), no. 3, 557-584.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kim-zaitsev-topology.pdf)

- **Ebenfelt, P.; Huang, X.; Zaitsev, D.** --- The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics.
   *[American Journal of Mathematics](https://www.press.jhu.edu/journals/american_journal_of_mathematics/)*
   **127**  (2005), no. 1, 169-191.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/ehz-amj.pdf)

- **Ebenfelt, P.; Huang, X.; Zaitsev, D.** --- Rigidity of CR-immersions into spheres.
   *[Communications in Analysis and Geometry](http://intlpress.com/CAG/)*
   **12**  (2004), no. 3, 631-670.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/ehz-cag.pdf)

- **Baouendi, M.S.; Rothschild, L.P.; Winkelmann, J.; Zaitsev, D.** --- Lie group structures on groups of diffeomorphisms and applications to CR manifolds.
  *[Annales de l'Institut Fourier (Grenoble)](http://aif.cedram.org/?lang=en)*
   **54** (2004), no. 5, 1279-1303.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/brwz.pdf)

- **Kaup, W.; Zaitsev, D.** --- Non-embeddable CR-manifolds of higher codimension.
  *[Journal für die Reine und Angewandte Mathematik (Crelle's Journal)](http://www.degruyter.com/view/j/crll)*
   **569**  (2004), 1-12.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kaup-zaitsev-crelle.pdf)

- **Zaitsev, D.; Zampieri, G.**  --- Extension of CR-functions into weighted wedges through families of nonsmooth analytic discs.
   *[Transactions of the American Mathematical Society](http://www.ams.org/tran/)*
   **356**  (2004), no. 4, 1443-1462.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/zz-trans.pdf)

- **Kaup, W.; Zaitsev, D.** --- On the CR-structure of compact group orbits associated with bounded symmetric domains.
  *[Inventiones Mathematicae](http://www.springer.com/mathematics/journal/222)*
   **153**  (2003), no. 1, 45-104.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kaup-zaitsev-inv.pdf)

- **Zaitsev, D.; Zampieri, G.**  --- Extension of CR-functions on wedges.
  *[Mathematische Annalen](http://link.springer.com/journal/208)*
   **326**  (2003), no. 4, 691-703.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/zz-ma.pdf)

- **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.
  *[Geometric and Functional Analysis](http://www.springer.com/birkhauser/mathematics/journal/39)*
  **13**  (2003), no. 3, 546-573.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/elz-gafa.pdf)

- **Meylan, F.; Mir, N.; Zaitsev, D.**  --- Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds.
  *[The Asian Journal of Mathematics](http://www.ims.cuhk.edu.hk/~ajm/)*
   **7**, (2003), no. 4, 493-509.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/mmz-asian.pdf)

- **Meylan, F.; Mir, N.; Zaitsev, D.**  --- Approximation and convergence of formal CR-mappings.
  *[International Mathematics Research Notices](http://imrn.oxfordjournals.org/)*
  **2003**, no. 4, 211-242.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/mmz-imrn.pdf)

- **Hayashimoto, A.; Kim, S.-Y.; Zaitsev, D.**  --- Decomposition of CR-manifolds and splitting of CR-maps.
   *[Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. (Serie V)](http://annaliscienze.sns.it/)* 
   **2**  (2003), no. 3, 433-448.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/hkz-annali.pdf)

- **Zaitsev, D.**  --- Unique determination of local CR-maps by their jets: A survey.
   *Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni*  **13** (2002), 295-305.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/lincei.pdf)

- **Meylan, F.; Mir, N.; Zaitsev, D.**  --- Analytic regularity of CR-mappings.
  *[Mathematical Research Letters](http://www.mrlonline.org/mrl/)* **9** (2002), no. 1, 73-93.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/mmz-mrl.pdf)

- **Baouendi, M.S.; Rothschild, L.P.; Zaitsev, D.** --- Equivalences of real submanifolds in complex space.
  *[Journal of Differential Geometry](http://intlpress.com/jdg)*
  **59** (2001), no. 2, 301-351.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/brz-jdg.pdf)

- **Kaup, W.; Zaitsev, D.** --- On symmetric Cauchy-Riemann manifolds.
   *[Advances in Mathematics](http://www.elsevier.com/wps/find/journaldescription.cws_home/622779/description#description)*  **149**  (2000), no. 2, 145-181.  [PDF](https://www.maths.tcd.ie/~zaitsev/papers/kaup-zaitsev-adv.pdf)

- **Zaitsev, D.**
  --- Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces.
  *[Acta Mathematica](http://www.actamathematica.org/)*
  **183** (1999), 273-305.
   [PDF](https://www.maths.tcd.ie/~zaitsev/papers/acta.pdf)

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