Dr Rauan Akylzhanov

Noncommutative harmonic analysis & spectral theory · Mathematics of deep learning · Almaty, Kazakhstan

Endorsed by the Royal Society under the UK Global Talent route (Exceptional Promise, April 2026)

akylzhanov.r@gmail.com Google Scholar ra312.github.io github/ra312 +7 701 211 4844

›Research

Core question

How far can the spectral decay of a single Dirac-type operator carry analysis, on groups, quantum groups and von Neumann algebras, and in the geometry of neural-network training?

My research is about how the spectrum of an operator controls analysis where classical Fourier analysis is not available: non-abelian and non-unimodular groups, compact quantum groups, and general von Neumann algebras. Multipliers are the operators affiliated with the algebra, and the decay of the spectral projections of one Dirac- or Laplace-type operator is enough to prove sharp L^p–L^q estimates, Hardy–Littlewood–Paley inequalities and Hörmander–Mikhlin multiplier theorems. Key collaborations include work with Michael Ruzhansky on spectral multipliers and with Alexis Arnaudon on contractions of group representations via geometric quantization.

I am developing two linked programmes, set out in grant proposals prepared with Michael Ruzhansky: (i) regularity of spectral and Fourier multipliers in affiliated von Neumann algebras, with heat and Klein–Gordon decay estimates governed by an intrinsic spectral dimension; and (ii) a global pseudo-differential calculus directly on von Neumann algebras, combining compatible Fourier structures, quantum Riemannian geometry and Safarov's connection-based calculus, with L^p regularity, Gårding-type inequalities and applications to nonlinear evolution equations. The test cases are quantum tori, quantum Euclidean spaces, quantum groups and symmetric spaces.

A second strand applies the same spectral and geometric toolkit to the mathematics of deep learning: the geometry of loss landscapes, degenerate minima and the training dynamics of neural networks, and the structure of learned representations. As one probe, I use log-signature representations of sequences to study how transformers compress and organise contextual information. Recent work explores bridging byte-latent transformers with Qwen bodies through representation re-alignment, combining subword tokenization with continuous latent representations.

Alongside research I work in industry. I am currently at Kaspi Bank (AI strategy and statistical modelling), and before that worked on tabular foundation models and LLM evaluation at HighSky (2024–2026).

Note: Log-signatures as structured compression and probes of representation geometry (March 2026)

›Publications

12 peer-reviewed articles, 2 preprints; 220+ citations; h-index 7 (Google Scholar, 2026). 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.	L^p–L^q 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 L^p–L^q 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 L^p–L^q 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

2026 – present

Managing AI Strategy Expert

Kaspi.kz (Kaspi Bank), Data Factory, Almaty

AI strategy and hands-on statistical modelling: hypothesis-testing library and prediction pipelines for IT-monitoring alerts.

2024 – 2026

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.

2019 – 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.

2020 – 2021

Associate Professor, Computer Science

Suleyman Demirel University, Almaty

Taught data science and machine learning.

2018 – 2019

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 – 2018

PhD in Pure Mathematics

Imperial College London

Thesis: L^p–L^q Fourier multipliers on locally compact groups (awarded 1 July 2018). Advisor: Prof. Michael Ruzhansky. Examiners: Prof. Fulvio Ricci, Prof. Ari Laptev. Novel analytical frameworks bridging Connes' noncommutative geometry with Drinfeld's quantum group theory. Funded by an EPSRC Doctoral Studentship.

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–Mikhlin multiplier theorems on noncommutative spaces

Quantum Algebras Seminar, Queen Mary University of London

Apr 2018

Smooth dense subalgebras and Fourier multipliers on compact quantum groups

Laboratoire de Mathématiques de Besançon

May 2017

Multipliers on locally compact groups

Recent Developments in Harmonic Analysis, MSRI (now SLMath), Berkeley

Sep 2016

L^p–L^q bounds for pseudo-differential operators on quantum groups

Analysis and PDE seminar, Imperial College London

Apr 2015

Hardy–Littlewood, Hausdorff–Young–Paley inequalities and L^p–L^q Fourier multipliers

10th ISAAC Congress, University of Macau

Sep 2014

Hardy–Littlewood inequalities and Fourier multipliers

International Conference on Generalized Functions, University of Southampton

›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, extending the Paley, Hausdorff–Young and Hardy–Littlewood inequalities to noncommutative spaces, with applications to heat semigroups and abstract Klein–Gordon equations. Planned visits to Oxford and London.

2017 – 2020

EPSRC Research Grant EP/R003025/1 — PI: M. Ruzhansky

£500K

I wrote the research proposal, which Prof. Ruzhansky submitted as PI. The grant funded my postdoctoral positions at Imperial College London and Queen Mary University of London (harmonic analysis in semi-finite von Neumann algebras and quantum groups).

2017

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.

2020 – 2021

Associate Professor, Computer Science

Suleyman Demirel University

Data science and machine learning courses.

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).