Dr Rauan Akylzhanov

Pure Mathematics · Machine Learning Research · Almaty, Kazakhstan

[email protected] 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

14 papers (12 peer-reviewed + 2 preprints)

220+ citations

h-index 7

Hörmander–Mikhlin type theorem on non-commutative spaces

R. Akylzhanov, M. Ruzhansky, K. Tulenov

arXiv:2503.01240 · 2025
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 · 2022
Contractions of group representations via geometric quantization

R. Akylzhanov, A. Arnaudon

Letters in Mathematical Physics, 110(1):43–59 · 2020
L^p–L^q multipliers on locally compact groups

R. Akylzhanov, M. Ruzhansky

Journal of Functional Analysis, 278(3):108324 · 2020
Re-expansions on compact Lie groups

R. Akylzhanov, E. Liflyand, M. Ruzhansky

Analysis and Mathematical Physics, 10(3):33 · 2020
Hardy–Littlewood, Hausdorff–Young–Paley inequalities, and L^p–L^q Fourier multipliers on compact homogeneous manifolds

R. Akylzhanov, M. Ruzhansky, E. Nursultanov

J. Math. Analysis and Applications, 479(2):1519–1548 · 2019
Smooth dense subalgebras and Fourier multipliers on compact quantum groups

R. Akylzhanov, S. Majid, M. Ruzhansky

Communications in Mathematical Physics, 362(3):761–799 · 2018
Fourier multipliers and group von Neumann algebras

R. Akylzhanov, M. Ruzhansky

Comptes Rendus Mathématique, 354(8):766–770 · 2016
Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)

E. Nursultanov, R. Akylzhanov, M. Ruzhansky

Studia Mathematica, 234(1):1–29 · 2016
Well-posed solvability of functional-differential equations with unbounded operator coefficients

R. Akylzhanov, V. V. Vlasov

Differential Equations, 50(9):1161–1172 · 2014

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: L^p–L^q 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 L^p–L^q 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)