My name is Nataliya Balabanova, and I am a Postdoctoral Fellow in Mathematical Analysis at the University of Birmingham, working with Dr. Hong Duong. My research interests include Hamiltonian and Dynamical systems, symplectic and contact geometry and evolutionary game theory.
Email: n.balabanova@bham.ac.uk
I graduated from Faculty of Mechanics and Mathematics of Moscow State University in 2017 and completed a PhD in Pure Mathematics at the University of Manchester (supervised by James Montaldi) in 2021. I held the position of a Visiting Assistant Professor at the University of Toledo from 2021 to 2023, and my current position is Research Fellow in Mathematical Analysis at the University of Birmingham.
Newcastle, 2019. I am on the right.
My ongoing projects are dedicated to applications of dynamical systems to various problems in evolutionary game theory. We are investigating adaptive dynamics for donation games with finite and infinite memory and dynamical properties of mutator-replicator equations with incentive. I have also worked with Hamiltonian systems, as well as symplectic and contact geometry, for example in application to the restricted three-body problem.
For a more concise description, please have a look at my CV
Two body problem on a sphere in the presence of a uniform magnetic field, with James Montaldi, http://arxiv.org/abs/2101.07170 , Regular and Chaotic Dynamics, 26(4):370–391, 2021
Collision trajectories and regularisation of two-body problem on S2, with Alessandro Arsie, https://arxiv.org/abs/2210.13644 , Journal of Geometry and Physics, page 104883, 2023.
A note on the geometry of the two-body problem on S2, with Alessandro Arsie, https://arxiv.org/abs/2310.02659, Journal of Geometry and Physics, volume 198, page 105111, 2024
A Hamiltonian Approach to Vortex Dynamics on Non-Orientable Manifolds I: the Möbius Band, with James Montaldi, https://arxiv.org/abs/2202.06160
A Hamiltonian Approach to Vortex Dynamics on Non-Orientable Manifolds II: the Klein Bottle, https://arxiv.org/abs/2202.06175
Adaptive dynamics of direct reciprocity with N rounds of memory, with Manh Hong Duong and Christian Hilbe, https://arxiv.org/abs/2411.09535
Adaptive dynamics for individual payoff game-theoretic models of vaccination, with Manh Hong Duong, https://arxiv.org/abs/2411.09519
Replicator-mutator dynamics for public goods games with institutional incentives, with Manh Hong Duong and The Anh Han
Dynamics of infinite memory games and Hölder functions, with Sabrina Kombrink and Manh Hong Duong
Double bracket Brockett equation and rotating ellipses, with Alessandro Arsie
Fundamental constraints on tube invariants, with Shane Ross and Alessandro Arsie.
Seminar presentation at Contemporary Methods in Geometry Seminar, Lomonosov Moscow State University, March 2014, April 2016
Contributed short talk at Lomonosov Young Researchers Conference, Lomonosov Moscow State University, April 2015
Seminar presentation at Manchester Geometry, Topology and Mathematical Physics Seminar, November 2018, February 2020, October 2022
Contributed talk at 15th International Young Researchers Workshop on Geometry, Mechanics, and Control, organized by University of Utrecht, December 2020
Seminar presentation at Analysis and Geometry Seminar, University of Antwerp, February 2021
Seminar presentation at BGSU-Toledo joint Geometry and Topology Seminar, November 2021
Seminar presentation at Hamiltonian Systems Online Seminar, Canada, October 2022
Contributed talk at Geophysical Fluid Dynamics, 4th meeting of the LMS Network Applied Geometric Mechanics, June 2023
Contributed talk at Postdoctoral Symposium, University of Birmingham, November 2023
Seminar presentation at Birmingham Analysis Seminar, November 2023
Contributed talk at Vietnam-UK mathematics meeting, University of Edinburgh, December 2023
Contributed talk at Dynamics in Pure and Applied Mathematics conference, University of Birmingham, April 2024
Guest speaker at CSMM conference, University of Coventry, May 2024
Tutorials for a Computer Geometry course
Teaching Assistant for the courses
”Symmetry in Geometry and Nature”
”Fractal Geometry”
”Sequences and Series”
”Essential Partial Differential Equations”
Postgraduate Demonstrator for
OJ2, OD2, OB1, ON1, OF2 (Faculty of Science and Engineering foundation year Mechanics, Calculus, Logic and Combinatorics modules)
1M2, 2M1 (Calculus for first and second year Engineering students, respectively),
”Linear Algebra” (delivered online)
MATLAB Mathematical Workshop (delivered online)
MATH 1320 ’College algebra’
MATH 2450 ’Calculus for Engineering Technology’
MATH 1750, 1760 ’Calculus for Life Sciences I & II’
MATH 2850 ’Multivariable Calculus’
MATH 1180 ’Mathematical Reasoning’
MATH 2890 ’Linear Algebra’
LM Advanced Topics in Analysis (Complex Analysis, 4ATAn) 33871
2015-2016: Organising the Contemporary Methods in Geometry Seminar, Lomonosov Moscow State University
2014: Participation in Nauka 0+ popular science festival
2018-2019: Faculty of Science and Engineering PGR Student Representative, University of Manchester
2022, 2023: Organising and participating in yearly University of Toledo Maths Quiz
2024: Participation in organising University of Birmingham Big Maths Quiz