# Dr. Rauan Akylzhanov

Research Associate, School of Mathematical Sciences
School of Mathematical Sciences
Qyeen's Building: CB203
+447510473201
r.akylzhanov@qmul.ac.uk
github
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Application Materials:
CV, Research Statement, Teaching Statement, Graduate Teaching Certificate , Doris Chen Merit Award .
Research Teaching Conferences Blog

I obtained my PhD in Pure Mathematics from Imperial College London. Currently, I am a research associate in Geometry and Analysis group at Queen Mary University of London. Before that, I was a math postdoc in Pure Analysis and PDE group at Imperial College London. Broadly speaking, in the interface between (harmonic) analysis and operator algebra theory. The long-term aim is to build theory of partial differential operators starting from a fixed noncommutative differential geometry.

My current project aims at bringing modern techniques of von Neumann algebras into the study of dispersive estimates for wave, Schrödinger, Klein-Gordon equations on different backgrounds. In my current working paper, I obtained a version of Hörmander-Mihlin $L^p$-multiplier theorems on semi-finite von Neumann algebras. The project is supported by the EPSRC grant EP/R003025/2. I expect 4 preprints in the coming months from different projects.

This work build on my dissertation, “$L^p$-$L^q$ Fourier multipliers on locally compact groups,” which used von Neumann algebra theory to obtain extensions of numerous theorems of Fourier analysis to general unimodular and separable topological groups. Specifically, it analyses $L^p$-$L^q$ Fourier multipliers considering them as linear operators affiliated with the group von Neumann algebra. I use the theory of noncommutative integration to establish the sufficient condition for the $L^p$-$L^q$ boundedness in terms of the noncommutative Lorenz spaces on the von Neumann algebras. I discovered that the norm of the operator is controlled by the decay rate of the semi-finite trace on the spectral projections and conclude that the growth of the spectral projections is the only essential information to derive the bounds.

Apart from these topics, I am now interested in mathematical foundations of artificial intelligence. Together with Shahn Majid, I am exploring the generating functional and n-point correlation functions arising from 0+1 quantum field theory on the lattice line.

## Education:

Imperial College London
London, UK
PhD in Pure Mathematics

Eurasian National University
Astana, Kazakhstan
Master of Science in Mathematics. Training in theory and practice of university education.

Lomonosov Moscow State University
Moscow, Russia
Specialist in Applied Mathematics and Computer Science

## Professional Appointments:

Since 2018 Research Associate(EPSRC EP/R00302/1)
School of Mathematical Sciences
Queen Mary University of London

2017-2018 Pure Research Associate(EPSRC EP/R00302/1)
Department of Mathematics
Imperial College London

2012-2014 Faculty Teaching Assistant
Department of Mathematics and Computer Science
Moscow State University, Kazakhs Branch, Astana.

## Papers

Rauan Akylzhanov
Research Associate
Queen Mary University of London