Dr Rauan Akylzhanov

Pure Mathematics  ·  Machine Learning Research  ·  Almaty, Kazakhstan

[email protected] Google Scholar ra312.github.io github/ra312 +7 701 211 4844

›Current Research

Active question
Under what conditions do synthetic data-generating priors enable a tabular transformer pre-trained on synthetically generated distributions to generalise to unseen real-world data without task-specific fine-tuning?

At HighSky I am pre-training transformer models on synthetic data generated from varied Bayesian priors and structural causal graphs, with the goal of achieving state-of-the-art performance on unseen real-world tabular datasets. I investigate how diverse prior sampling strategies during pre-training enable foundation models to generalise across heterogeneous tabular distributions. In parallel, I continue work in harmonic analysis on non-commutative spaces — extending Hörmander–Mikhlin multiplier theory to general von Neumann algebras.

Note: Compressing long contexts with log-signatures (March 2026)

›Publications

12 peer-reviewed articles, 2 preprints; 220+ citations; h-index 7 (Google Scholar, 2026). This list follows my Global Talent visa CV; for live metrics see Google Scholar.

2025

1. Hörmander–Mikhlin type theorem on non-commutative spaces
R. Akylzhanov, M. Ruzhansky, K. Tulenov
arXiv preprint arXiv:2503.01240

2022

2. Norms of certain functions of a distinguished Laplacian on the ax+b groups
R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang
Mathematische Zeitschrift, 302(4):2327–2352

2020

3. Contractions of group representations via geometric quantization
R. Akylzhanov, A. Arnaudon
Letters in Mathematical Physics, 110(1):43–59
4. Lp–Lq multipliers on locally compact groups
R. Akylzhanov, M. Ruzhansky
Journal of Functional Analysis, 278(3):108324
5. Re-expansions on compact Lie groups
R. Akylzhanov, E. Liflyand, M. Ruzhansky
Analysis and Mathematical Physics, 10(3):33

2019

6. Hardy–Littlewood, Hausdorff–Young–Paley inequalities, and Lp–Lq Fourier multipliers on compact homogeneous manifolds
R. Akylzhanov, M. Ruzhansky, E. Nursultanov
Journal of Mathematical Analysis and Applications, 479(2):1519–1548

2018

7. Smooth dense subalgebras and Fourier multipliers on compact quantum groups
R. Akylzhanov, S. Majid, M. Ruzhansky
Communications in Mathematical Physics, 362(3):761–799

2017

8. Net spaces on lattices, Hardy–Littlewood type inequalities, and their converses
R. Akylzhanov, M. Ruzhansky
Eurasian Mathematical Journal, 8(3):10–27

2016

9. Hausdorff–Young–Paley inequalities and Lp–Lq Fourier multipliers on locally compact groups
R. Akylzhanov, M. Ruzhansky
arXiv preprint arXiv:1510.06321
10. Fourier multipliers and group von Neumann algebras
R. Akylzhanov, M. Ruzhansky
Comptes Rendus Mathématique, 354(8):766–770
11. Hardy–Littlewood–Paley-type inequalities on compact Lie groups
R. Akylzhanov, E. D. Nursultanov, M. V. Ruzhanskii
Matematicheskie Zametki, 100(2):287–290
12. Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)
R. Akylzhanov, E. Nursultanov, M. Ruzhansky
Studia Mathematica, 234(1):1–29

2014

13. Well-posed solvability of functional-differential equations with unbounded operator coefficients
R. Akylzhanov, V. V. Vlasov
Differential Equations, 50(9):1161–1172

2008

14. On an inequality for the non-increasing rearrangement of a function
R. Akylzhanov
Eurasian Mathematical Journal, no. 3, 34–36

›Experience

2024 – present
Senior Research Engineer
HighSky (highsky.io)
Tabular foundation models; per-feature transformer architecture with novel attention mechanisms for mixed-type data; synthetic data generation from structural causal graphs with diverse Bayesian priors; LLM evaluation (MMLU, GSM8K, HellaSwag, HumanEval); agentic multi-step reasoning systems.
2022 – 2024
Senior Machine Learning Engineer
Delivery Hero SE
Transformer-based representation learning for structured product data; retrieval-augmented generation (RAG) for natural language interfaces over large-scale product catalogues. Awarded "Most Advanced Project" at Global Search Domain Project Week, January 2023.
2020 – 2022
Machine Learning Engineer
KCell JSC
Sequential modelling of behavioural time series at population scale (15M+ users); RNN/LSTM architectures for socio-economic forecasting; representation learning for heterogeneous customer data; churn prediction and lifetime value estimation.
2018 – 2020
Postdoctoral Research Associate (EPSRC EP/R003025/1)
Queen Mary University of London
Harmonic analysis for Dirac-like operators affiliated with semi-finite von Neumann algebras. Established Paley-type inequalities yielding a proof of the Hörmander multiplier theorem via quantum group Pontryagin duality.
2017 – 2018
Research Associate (EPSRC EP/R003025/1)
Imperial College London
Characterised Connes spectral triples on compact quantum matrix groups; established Schwartz kernel theorems and global pseudo-differential calculus on compact quantum groups.

›Education

2014 – 2019
PhD in Pure Mathematics
Imperial College London
Thesis: Lp–Lq Fourier multipliers on locally compact groups. Advisor: Prof. Michael Ruzhansky. Examiners: Prof. Fulvio Ricci, Prof. Ari Laptev. Novel analytical frameworks bridging Connes' noncommutative geometry with Drinfeld's quantum group theory.
2012 – 2014
MSc in Mathematics
Eurasian National University
2007 – 2012
Specialist in Mathematics & Computer Science — With Honours
Lomonosov Moscow State University
Diploma: Well-posed solvability of functional-differential equations with unbounded operator coefficients.

›Selected Invited Talks

Jul 2025
Hörmander-Mikhlin type theorem on non-commutative spaces
15th ISAAC Congress, Nazarbayev University, Astana
Nov 2018
Hörmander-Mihlin multiplier theorems on noncommutative spaces
Quantum Algebras Seminar, Queen Mary University of London
May 2017
Multipliers on locally compact groups
Recent Developments in Harmonic Analysis, MSRI, Berkeley
Apr 2018
Smooth dense subalgebras and Fourier multipliers on compact quantum groups
Laboratoire de Mathématiques de Besançon
Apr 2015
Hardy-Littlewood, Hausdorff-Young-Paley inequalities and Lp–Lq Fourier multipliers
10th ISAAC Congress, Macao University

›Awards & Funding

2026 – 2028
Kazakhstan Ministry of Science Grant — Principal Investigator (under review)
£175K · 36 months
Fourier multipliers on non-commutative spaces and applications. Hörmander-type multiplier theorems on general von Neumann algebras with applications to stability of abstract Klein–Gordon wave equations. Planned visits to Oxford and London.
2017 – 2020
EPSRC Research Grant EP/R003025/1 — Co-investigator
£500K
Harmonic analysis in semi-finite von Neumann algebras and quantum groups. Imperial College London & Queen Mary University of London.
2016
Doris Chen Merit Award
Department of Mathematics, Imperial College London
Awarded for exceptional early promise and achievement in mathematical research.
2014 – 2018
EPSRC Doctoral Studentship
Imperial College London

›Teaching & Service

2019
LTCC Intensive Course Lecturer
Methods of Noncommutative Analysis · UCL, London
8-hour graduate course covering semi-finite von Neumann algebras, noncommutative geometry, Hörmander multiplier theorems via quantum group duality.
2015 – 2018
Graduate Teaching Assistant
Imperial College London
High Performance Computing (M3C), Data Science (M3A50), Multivariable Calculus, Analysis I & II, Algebra, Real Analysis. Joint Maths & Computing Tutor.
2018 – present
Reviewer
zbMATH Open  ·  Junior Member, Newton Institute, Cambridge

Academic collaborations

Prof. Michael Ruzhansky (Imperial / Ghent); Prof. Shahn Majid (QMUL); Prof. Yulia Kuznetsova (Franche-Comté); Prof. Terry Lyons FRS (Oxford); Dr Alexis Arnaudon (Imperial); Prof. Fedor Sukochev (UNSW, planned).