Dr Zinaida A Lykova

Reader in Pure Mathematics

Phone: +44 (0)191 208 6479

Department FAX: +44 (0)191 208 8020

Email: Zinaida.Lykova@ncl.ac.uk

Room: 3.13

Address:

School of Mathematics, Statistics and Physics
Newcastle University
Newcastle upon Tyne
NE1 7RU

Roles and Responsibilities:

• Member of the Editorial Advisory Board of the International Open Access Electronic Journal ``Topological Algebras and its Applications" 2012 - present; http://www.degruyter.com/view/j/taa/
• Member of the Editorial Board of the International Open Access Electronic Journal ``Annals of Functional Analysis" 2010 - present; https://www.springer.com/birkhauser/mathematics/journal/43034/
• Member of the Steering Committee of the International Conference on Banach Algebras and their Applications, 2005 - present.
• EPSRC Full College member.

Qualifications:

• BSc, MSc, D.Phil., Moscow State University
• Dotsent, the State Committee of the Russian Federation for Higher Education

Languages:

• Russian, English

Research interests:

• Functional analysis, particularly topological algebras
• Complex Variable, particularly boundary interpolation problems
• Homological theory of topological algebras
• Cyclic type (co)homology of topological algebras
• Higher-dimensional amenability of Banach algebras
• Extensions of topological algebras
• C*-algebras

Undergraduate Teaching 2022/23:

• MAS2702 Complex Analysis http://www.ncl.ac.uk/module-catalogue/module.php?code=MAS2702/
• MAS8714 Functional Analysis http://www.ncl.ac.uk/module-catalogue/module.php?code=MAS8714/

PhD Projects

http://www.mas.ncl.ac.uk/~nzal/PhD_Projects.pdf

Full Publication List:

http://www.mas.ncl.ac.uk/~nzal/ZALpublist22.pdf

Research Monographs:

• Agler, J., Lykova, Z.A. and Young, N.J., Geodesics, retracts, and the norm-preserving extension property in the symmetrized bidisc, Memoirs of the American Mathematical Society, 2019, v. 258, no. 1242, 106pp; https://bookstore.ams.org/memo-258-1242/, arxiv: 1603.04030 [math.CV]
• Bade, W.G., Dales, H.G., Lykova, Z.A. Algebraic and strong splittings of extensions of Banach algebras. Memoirs of the American Mathematical Society 1999, 137, 1-113.https://bookstore.ams.org/memo-137-656/

Recent Publication:

Some of my recent papers can be found on arXiv https://arxiv.org/search/?searchtype=author&query=Lykova%2C+Z

• Alshehri, N.M. and Lykova, Z.A., A Schwarz lemma for the pentablock, 15 May 2022, 35 pages. https://arxiv.org/abs/2205.07306
• Agler, J., Lykova, Z.A. and Young, N.J., A Hilbert space approach to singularities of functions, 10th May 2022, 50 pages. https://arxiv.org/abs/2205.05012
• Agler, J., Lykova, Z.A. and Young, N.J., Nonuniqueness of Carath\'eodory extremal functions on the symmetrized bidisc, Analysis Mathematica , 48 (2) (2022), DOI: 10.1007/s10476-022-0138-6, 20 April 2022, 20 pages. https://arxiv.org/abs/2201.09078
• Alsalhi, O.M., Lykova, Z.A., Rational tetra-inner functions and the special variety of the tetrablock, Journal of Mathematical Analysis and Applications, 506 (2022), the article number 125534, https://doi.org/10.1016/j.jmaa.2021.125534 , 52 pages. https://arxiv.org/abs/2101.02739
• Alshammari, H.O., and Lykova, Z.A., Interpolation by holomorphic maps from the disc to the tetrablock, the Jornal of Mathematical Analysis and Applications , 498 (2021) 124951, https://doi.org/10.1016/j.jmaa.2021.124951, 35 pages.
• Agler, J., Lykova, Z.A. and Young, N.J., Intrinsic Directions, Orthogonality and Distinguished Geodesics in the Symmetrized Bidisc, Journal of Geometric Analysis , 2021, https://doi.org/10.1007/s12220-020-00582-0, 36 pages, https://arxiv.org/pdf/2012.03304.pdf
• Chiotis, D., Lykova, Z.A., Young, N. J., Exterior powers and pointwise creation operators, Complex Analysis and Operator Theory, 2021, 15, Article number: 29. https://link.springer.com/article/10.1007/s11785-020-01074-3 . https://arxiv.org/pdf/2004.11993.pdf.
• Chiotis, D., Lykova, Z.A. and Young, N.J., Exterior products of operators and superoptimal analytic approximation, The Transactions of the London Mathematical Society , 8(1) (2021) 299--412, doi:10.1112/tlm3.12035. https://arxiv.org/pdf/2004.06415.pdf .
• Young, N.J., Chiotis, D. and Lykova, Z.A., Superoptimal analytic approximation and exterior products of Hankel operators, Proceedings of the 24th International Symposium on Mathematical Theory of Networks and Systems, 23-27 August, 2021, Cambridge, UK. 4 pages (accepted on the 16th of May 2020).
• Agler, J., Lykova, Z.A. and Young, N.J., A Geometric Characterization of the Symmetrized Bidisc, Journal of Mathematical Analysis and Applications 2019, 473 (2), 1377-1413; https://doi.org/10.1016/j.jmaa.2019.01.027, arXiv:1901.03100 [math.CV].
• Agler, J., Lykova, Z.A. and Young, N.J., Characterizations of some domains via Carathéodory extremals, Journal of Geometric Analysis (2019) 29, Issue 4, 3039--3054, https://doi.org/10.1007/s12220-018-0059-6; arXiv:1802.09056 [math.CV].
• Lykova, Z.A., Young, N.J., and Ajibo, A., Analytic interpolation into the tetrablock and $\mu$-synthesis problem, In: Bolotnikov V., ter Horst S., Ran A., Vinnikov V. (eds) Interpolation and Realization Theory with Applications to Control Theory, Operator Theory: Advances and Applications, v. 272 (2019) pp. 269-281, Birkhäuser, Cham; https://www.springer.com/gp/book/9783030116132/; arXiv:1802.09067 [math.CV].
• Agler, J., Lykova, Z.A. and Young, N.J., Carathéodory extremal functions on the symmetrized bidisc, In: Bart H., ter Horst S., Ran A., Woerdeman H. (eds) Operator Theory, Analysis and the State Space Approach . Operator Theory: Advances and Applications, v. 271 (2018) pp.1-21, Birkhäuser, Cham; https://doi.org/10.1007/978-3-030-04269-1_1 , arXiv:1712.00749 [math.CV].
• Agler, J., Lykova, Z.A. and Young, N.J., Algebraic and geometric aspects of rational G-inner functions, Advances in Mathematics, 2018, 328, 133-159; https://doi.org/10.1016/j.aim.2017.12.018
• Brown, D.C., Lykova, Z.A. and Young, N.J., A rich structure related to the construction of holomorphic matrix functions, Journal of Functional Analysis, 2017, 272(4), 1704--1754. http://dx.doi.org/10.1016/j.jfa.2016.11.013
• Agler, J., Lykova, Z.A. and Young, N.J., Finite Blaschke products and the construction of rational G-inner functions, Journal of Mathematical Analysis and Applications, 2017, 447, 1163--1196. https://dx.doi.org/10.1016/j.jmaa.2016.10.035
• Agler, J., Lykova, Z.A. and Young, The complex geometry of a domain related to mu-synthesis, Journal of Mathematical Analysis and Applications, 2015, 422, 508--543; https://dx.doi.org/10.1016/j.jmaa.2014.08.051
• Agler, J., Lykova, Z.A. and Young, N.J., 3-extremal holomorphic maps and the symmetrised bidisc, Journal of Geometric Analysis, 2015, 25 (3), 2060-2102; https://dx.doi.org/10.1007/s12220-014-9504-3 (arXiv: 1307.7081v1 [math.CV])
• Agler, J., Lykova, Z.A. and Young, N.J. A case of mu-synthesis as a quadratic semidefinite program, SIAM Journal on Control and Optimization, 2013, 51(3), 2472-2508; https://dx.doi.org/10.1137/120873248
• Agler, J., Lykova, Z.A. and Young, N.J. Extremal holomorphic maps and the symmetrised bidisc, Proceedings of the London Math. Soc., 2013, 106 (4), 781-818; available online doi: 10.1112/plms/pds049.
• Cushing, D. and Lykova, Z.A. Projectivity of Banach and C^*-algebras of continuous fields, The Quarterly Journal of Mathematics, 2013, 64(2), 341-371; available online doi:10.1093/qmath/has005.
• Lykova, Z.A. The higher-dimensional amenability of tensor products of Banach algebras, Journal of Operator Theory 2012, 67(1), 73-100.
• Agler, J., Lykova, Z.A. and Young, N.J. Pseudo-Taylor expansions and the Carathéodory-Fejér problem, Journal of Mathematical Analysis and Applications, 2012, 386, 308-318; available online doi:10.1016/j.jmaa.2011.08.001.
• Agler, J., Lykova, Z.A. and Young, N.J. The boundary Carathéodory-Fejér interpolation problem, Journal of Mathematical Analysis and Applications, 2011, 382(2), 645-662; available online doi:10.1016/j.jmaa.2011.04.071.
• Lykova, Z.A. Hochschild cohomology of tensor products of topological algebras, Proceedings of the Edinburgh Math. Soc. 2010, 53(2), 447-470.
• Lykova, Z.A. Cyclic cohomology of certain nuclear Fréchet and DF-algebras, Central European Journal of Math. 2008, 6(3), 405-421.
• Lykova, Z.A. Cyclic-type cohomology of strict inductive limits of Fréchet algebras, Journal of Pure and Applied Algebra 2006, 205, 471-497.
• Lykova, Z.A. Cyclic cohomology of projective limits of topological algebras, Proceedings of the Edinburgh Mathematical Society 2006, 49, 173-199.
• Gourdeau, F., Lykova, Z.A. and White, M.C. A Kunneth formula in topological homology and its applications to the simplicial cohomology of l¹(Z^k+), Studia Mathematica 2005, 166, 29-54.
• Gourdeau, F., Lykova, Z.A. and White, M.C. The simplicial cohomology of L¹(R^k +). Contemporary Mathematics of the American Mathematical Society 2004, 363, 95-109.
• Lykova, Z.A. Relations between the homologies of C^*-algebras and their commutative C^*-subalgebras. Mathematical Proceedings of the Cambridge Philosophical Society 2002, 132, 155-168.
• Brodzki, J. and Lykova, Z.A. Excision in cyclic type homology of Fréchet algebras. Bulletin of the London Mathematical Society 2001, 33, 283-291.
• Lykova, Z.A. Relative cohomology of Banach algebras. J. Operator Theory 1999, 41, 23-53.

Research Council Boards, Editorial Boards, Conferences and Meetings - Scientific and Organising Committees:

• Member of the reviewers panel of the Natural Sciences and Engineering Research Council of Canada since 2007.
• Coorganiser of the Young Functional Analysts Workshop (YFAW), Newcastle, 21st -23rd March 2018, https://sites.google.com/site/yfawuk/past-years/yfaw-2018
• Main organiser of the LMS Invited Lectures Meeting, 18-22 April 2017; http://www.mas.ncl.ac.uk/~nek29/lmslectures2017/function_theory.html
• Coorganiser (jointly with Prof. Jim Agler (UCSD, U.S.A.) and Prof. N. J. Young (Leeds/Newcastle University, UK)) of the ICMS international workshop Function theory in several complex variables in relation to modelling uncertainty, 21-25 July 2014, Edinburgh, UK. It is funded by Heriot-Watt University, the University of Edinburgh, Newcastle University and EPSRC. http://www.icms.org.uk/workshop.php?id=292
• Coorganiser of the Theme Operator Spaces, Locally Compact Quantum Groups and Amenability of Six Month Thematic Program Abstract Harmonic Analysis, Banach and Operator Algebras at the Fields Institute, Canada, May 2014. Principal Organisers: Prof. Neufang Matthias (Lille, France), Prof. Anthony Lau (Edmonton, Alberta, Canada), Prof. Volker Runde (Edmonton, Alberta, Canada). http://www.fields.utoronto.ca/programs/scientific/13-14/harmonicanalysis/
• Member of the Scientific Committee of the 21st International Conference on Banach Algebras, Goteborg, Sweden, August, 2013.
• Member of the Editorial Board of ``Banach Journal of Mathematical Analysis" 2007-2010 http://www.emis.de/journals/BJMA/
• Member of the Scientific Committee of the 20th International Conference on Banach Algebras 2011, Waterloo, Canada, 3-10 August, 2011; http://www.math.uwaterloo.ca/~banalg20/index.shtml
• Member of the Scientific Committee of the 19th Internatinal Conference on Banach Algebras, Bedlewo, Poland, 14-24 July 2009. http://www.siue.edu/MATH/BA2009/
• Member of the Organising Committee of the British Mathematical Colloquium, Newcastle upon Tyne, UK, 10-13 April 2006. http://www.ncl.ac.uk/bmc06/
• Member of the British Mathematical Colloquium Scientific Committee, 2003 - 2006
• Member of the Scientific Committee of the Internatinal Conference on Banach Algebras, Bordeaux, France, 4-15 July 2005. http://www.math.u-bordeaux.fr/ba2005/
• Member of the Scientific and Organising committees of the International Conference on Banach Algebras and Cohomology, Newcastle, England, 23-28 June 2001. http://www.ncl.ac.uk/icbacn/

Recent Conference Presentations:

• 18 - 23 July 2022. A Hilbert space approach to singularities of functions -- the 25th International Conference on Banach Algebras and Applications, Granada, Spain. (https://www.ugr.es/~banachalgebras/page/)
• 16-20 August, 2021, The $\mu$-synthesis interpolation problem and some associated domains (semiplenary talk); and A geometric characterization of the symmetrized bidisc - Special session: Complex Geometry and Operator Theory. The 31st International Workshop on Operator Theory and its Applications (IWOTA 2021), Lancaster, U.K. https://www.lancaster.ac.uk/maths/iwotauk2021/
• 10-14 May, 2021, A geometric characterization of the symmetrized bidisc - Great Plains Operator Theory Symposium (GPOTS), Washington University in St. Louis (Zoom). ~ (https://www.math.wustl.edu/~ylsong/GPOTS.php)
• 18-22 November, 2019, Interpolation problems for analytic functions from the unit disc to the tetrablock - The International Conference "Interpolation in Spaces of Analytic Functions", Centre International de Rencontres Math\'ematiques (CIRM), Luminy, Marseille, France. https://conferences.cirm-math.fr/2055.html/
• 22-26 July 2019. Algebraic aspects of rational inner functions from the unit disc to the tetrablock - Special session: Linear operators and function spaces, and The construction of rational tetra-inner functions - Special session: Multivariable operator theory. The 30th International Workshop on Operator Theory and its Applications (IWOTA 2019), Lisbon, Portugal. https://iwota2019.math.tecnico.ulisboa.pt/
• 11-18 July 2019. Hilbert space methods for the construction of analytic matrix functions and Herbert Kamowitz and Cohomology of Banach algebras . The 24th International Conference on Banach Algebras and Applications, Winnipeg, Canada. https://server.math.umanitoba.ca/~banach2019/index.html/
• *1-5 October 2018. Algebraic and geometric aspects of rational $\Gamma$-inner functions. The International Conference "Complex Approximation and Bounded Holomorphic Functions", The Centro Internazionale per la Ricerca Matematica of Trento (CIRM), Levico Terme, Italy. https://www.uv.es/falbe/Conferences/2018/CABHF/index.html
• 23-27 July 2018. The norm-preserving extension property in the symmetrized bidisc \Gamma and von Neumann-type inequalities for \Gamma-contractions. The 29th International Workshop on Operator Theory and its Applications (IWOTA 2018), Shanghai, China. http://iwota2018.fudan.edu.cn/
• 3-9 July 2017. The norm-preserving extension property in the symmetrized bidisc G and von Neumann-type inequalities for G-contractions. The 23rd International Conference on Banach Algebras and Applications, Oulu, Finland. http://www.oulu.fi/ba2017/
• 29 May - 2 June 2017. The norm-preserving extension property in the symmetrized bidisc G and von Neumann-type inequalities for G-contractions. The International Conference ``Hilbert Function Spaces" -- Gargnano, Italy. https://events.unibo.it/hfs2017/
• 16-23 July 2016. Algebraic and geometric aspects of rational G-inner functions . The 27th International Workshop on Operator Theory and its Applications (IWOTA 2016) -- St. Louis, MO, U.S.A. http://openscholarship.wustl.edu/iwota2016/special/Functionspaces/
• *25-30 June 2016. The norm-preserving extension property in the symmetrized bidisc G and von Neumann-type inequalities for G-contractions. XXV St. Petersburg Summer Meeting in Mathematical Analysis Tribute to Victor Havin -- Euler International Mathematical Institute, Saint-Petersburg, Russia. http://en.chebyshev.spbu.ru/Conferences/
• * 7 September 2015. Complex geometry of the symmetrised bidisc . One Day Function Theory Meeting -- London, UK. https://sites.google.com/site/functiontheorymeeting/home
• 1-4 June 2015. Algebraic and geometric aspects of rational G-inner functions . The International Conference on Harmonic and Functional Analysis, Operator Theory and Applications -- Bordeaux, France. http://esterle.sciencesconf.org/
• 14-17 July 2014. A rich structure related to the construction of analytic matrix functions. The 25th International Workshop on Operator Theory and its Applications (IWOTA 2014) -- Amsterdam, the Netherlands. http://www.math.vu.nl/~ran/iwota2014/
• *17-31 May 2014. Mini-course Higher-dimensional amenability of Banach algebras. The Theme Operator Spaces, Locally Compact Quantum Groups and Amenability of Six Month Thematic Program ``Abstract Harmonic Analysis, Banach and Operator Algebras" at the Fields Institute, Canada. http://www.fields.utoronto.ca/programs/scientific/13-14/harmonicanalysis/

Some Research Visits:

• January 2022, April 2019, Visiting Scholar, Department of Mathematics, University of California, San Diego, U.S.A.
• 18-24 June 2016, Chebyshev Laboratory at St.Petersburg State University, Saint-Petersburg, Russia.
• July-August 2017 and April-May 2016, Visiting Scholar, Department of Mathematics, University of California, San Diego, U.S.A.
• 17--31 May 2014, Fields Institute, Toronto, Canada.
• Jan 2013, Dec 2011 - Jan 2012 and Sept-Oct 2010, Visiting Scholar, Department of Mathematics, University of California, San Diego, U.S.A.
• Nov 2011, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Prague.
• July-Dec 2006, Visiting Fellow in the Programme on Noncommutative Geometry at the Newton Institute, U.K.
• July - Aug 2005, Visiting Scholar, Department of Mathematics, University of California, San Diego, U.S.A.
• April 2004, University of Lille, France.
• April 2003, Visiting Professor, Tunghai University, Academia Sinica, National Tsing Hua University, National Cheng Kung University, Taiwan.

Research students:

• Nujood Mued J Alshehri
• Connor Evans

Former Research students:

• David Cushing (PhD 2015) Thesis: Homological properties of Banach and C*-algebras of continuous fields, http://theses.ncl.ac.uk/jspui/handle/10443/3024/
• David Brown (PhD 2016) Thesis: A rich structure related to the construction of holomorphic matrix functions, http://theses.ncl.ac.uk/jspui/handle/10443/3532/
• Amos Ajibo (PhD 2019) Thesis: Interpolation problems, the symmetrized bidisc and the tetrablock, http://theses.ncl.ac.uk/jspui/handle/10443/4507
• Omar Alsalhi (PhD 2019) Thesis: Algebraic aspects of rational tetra-inner functions http://theses.ncl.ac.uk/jspui/handle/10443/4836
• Hadi Alshammari (PhD 2019) Thesis: The Construction of Rational Tetra-Inner Functions, http://theses.ncl.ac.uk/jspui/handle/10443/4819
• Dimitrios Chiotis (PhD 2020) Thesis: Superoptimal analytic approximation and exterior products, http://theses.ncl.ac.uk/jspui/handle/10443/4911

Recent Roles and Responsibilities:

• Degree Programme Director Year 3, 2011 - 2019
• MAGIC representative for Newcastle node 2016 - 2019
• Member of the School Postgraduate Committee, 2016 - 2019
• Member of the School Executive Committee, 2017 - 2019
• Research group leader, Pure Maths Group, 2012 - 2019
• Member of the School Research Committee, 2012 - 2019
• Member of the School Management Committee, 2012
• Degree Programme Director Year 2, 2007-2010
• DPD of MSc in Financial Mathematics with Management, 2004-2006
• Chairman of Board of Studies for MSc in Financial Mathematics with Management, 2004-2006
• Handbook for MSc in Financial Mathematics with Management, 2004-2006
• Treasurer of the British Mathematical Colloquium in Newcastle, 2006
• Member of the School Postgraduate Committee, 2004-2006

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School of Mathematics and Statistics WWW http://www.ncl.ac.uk/maths