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Invited researcher Louis Hirsch Kauffman
Contract number
14.Y26.31.0025
Time span of the project
2018-2020

As of 15.02.2021

28
Number of staff members
39
scientific publications
General information

Name of the project: Geometrical and quantitative topology and dynamics

Strategy for Scientific and Technological Development Priority Level: а


Goals and objectives

Research directions:

- Geometry and topology of knots and three-dimensional manifolds

- Geometry and dynamics in classical and quantum magnetic fields on low dimensional materials

- Topological methods in natural sciences and robotics

Project objective: Conducting scientific research of the theory low dimensional manifolds by means of both topological and geometrical methods using methods of dynamics, applications of results in multidisciplinary research


The practical value of the study

  • We have established correlation between topology, quantum computing and qualities of fermions. In particular, we have studied the remarkable unitary braid group representations associated with Majorana fermions. (Kauffman L. H., Lomonaco S. J.). 
  • Our researchers have investigated integrable magnetic billiards. As a new application of algebraic technique we have studied the existence of polynomial integrals for the two-sided magnetic billiards introduced by Kozlov and Polikarpov. (Byaliy M., Mironov A. Ye.).
  • We have solved an open problem: an infinite family of 2-connected transmission irregular graphs aha been built (Dobrynin A. A.D.). It is known that almost all the graphs are not transmission irregular. Many invariants of molecular graphs that are called topological indices in applications are built on the basis of vortex transmission. Such indices are used for find correlations between structure and characteristics of organic compounds.

Education and career development:

  • The leading scientist delivered two lecture courses: «Knot theory» (2018) and «Combinatorial knot theory» (2019) for undergraduate and postgraduate students of the Faculty of Mathematics and Mechanics of the Novosibirsk State University (Russia).
  • 1 candidate dissertation has been defended.

Other results:

  • Employees of the laboratory have written and published 29 academic papers and 5 monograph chapters in the domain of the project.
  • Seven international conferences have been organised:

1. Russian-Chinese Conference on Integrable Systems and Geometry (18–26 August 2018, Euler International Mathematical Institute, Russia);

2. Interdisciplinary symposium «Topological structures in mathematics, physics and biology» (14–18 September 2018, Novosibirsk State University, Russia);

3. International conference «Geometry days in Novosibirsk – 2018» (19–22 September 2018, Novosibirsk State University and Sobolev Institute of Mathematics of the Siberian Department of the Russian Academy of Sciences, Russia);

4. 6th Russian-Chinese conference on knot theory and related problems (17-21 June 2019, Novosibirsk State University and S. L Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Russia);

5. Conference «Integrable Systems and Their Applications» (5–11 August 2019, Sobolinaya Gora Hotel  & Resort, Russia);

6. International conference «Geometry days in Novosibirsk – 2019» (26–30 August 2019, Novosibirsk State University and S. L Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences,Russia);

7. Conference «December readings in Tomsk» (10–15  December 2019, Tomsk State University, Russia).

Collaborations:

  • Russian-French Interdisciplinary Scientific Center. J.-V. Poncelet (Russia): joint organization of the multidisciplinary symposium «Topological structures in mathematics, physics and biology» (14–18 September 2018);
  • S. L Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Russia): joint organisation and staging of the international conferences «Geometry days in Novosibirsk – 2018» (19–22 September 2018), «Geometry days in Novosibirsk – 2019» (26–30 August 2019), «6th Russian-Chinese conference on knot theory and related problems» (17-21 June 2019);
  • International Laboratory for Mirror Symmetry and Automorphic Forms of the Higher School of Economics: joint staging of the conference «Geometry days in Novosibirsk – 2019» (26–30 August 2019);
  • Regional Mathematical Science and Education Center of the Tomsk State Univesity: joint staging of the conference «December readings in Tomsk» (10–15 December 2019);
  • Yeungnam University (South Korea): joint research, the «Graphs, Riemann surface, and their coverage» Russian-Korean Grant from the Russian Foundation for Basic Research.

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Kauffman L. H., Lomonaco S. J.
Braiding, Majorana Fermions, Fibonacci Particles and Topological Quantum Computing. Quantum Information Processing. 17(8): 201 (2018).
Bialy М., Mironov A.
Survey on Polynomial in Momenta Integrals for Billiard Problems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2131): 20170418 (2018).
Dobrynin A.A.
Infinite Family of 2-connected Transmission Irregular Graphs. Applied Mathematics and Computation 340(1): 1–4 (2019).
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