### Research Interest

Dr. Manat Mustafa received his Ph.D. in mathematics from Al-Farabi Kazakh National University in 2012 in Almaty. He is currently an assistant professor at the Department of Mathematics at Nazarbayev University. Prior to joining Nazarbayev University, he served in the School of Physics and Mathematics at Nanyang Technological University in Singapore as a research fellow.2003-2009 he was a high school math teacher at Republican Specialized Physics-Mathematics Secondary Boarding School for Gifted Students named after O.Zhautykov in Almaty. His research interests include Mathematical logic, computability theory, set theory, Algebra, and operator theory.

Rogers semilattices in the analytical hierarchy: The case of finite families

Nikolay Bazhenov, Manat Mustafa, **2020** In : ALC2019 Procceding

Bounded Reducibility for Computable Numberings

Nikolay Bazhenov, Manat Mustafa, Sergei Ospichev, **2019** In : Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings, p. 96-107

Computable isomorphisms of distributive lattices

Nikolay Bazhenov, Manat Mustafa, Mars Yamaleev, **2019** In : Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings, p. 28-41

Computable Isomorphisms of Distributive Lattices

Nikolay Bazhenov, Manat Mustafa, Mars Yamaleev, **2019** In : Theory and Applications of Models of Computation11436, p. 28-41

Classifying equivalence relations in the Ershov hierarchy

Nikolay Bazhenov, Manat Mustafa, Luca San Mauro, Andrea Sorbi, Mars Yamaleev, **2020** In : . , p. 1-30

Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

N. A. Bazhenov, M. Mustafa, L. San Mauro, M. M. Yamaleev, **2020** In : . 41 , p.2 , p. 145-150

Semilattices of punctual numberings

Nikolay Bazhenov, Manat Mustafa, Sergei Ospichev, **2020** In : . 12337 , p. 1

The algebraic and geometric classification of nilpotent right alternative algebras 1

Nurlan Ismailov, Ivan Kaygorodov, Manat Mustafa, **2020** In : .

Bounded reducibility for computable numberings.

Nikolay Bazhenov, Manat Mustafa, Sergey Ospichev, **2019** In : . , p. 1

Reductions between types of numberings

Ian Herbert, Sanjay Jain, Steffen Lempp, Manat Mustafa, Frank Stephan, **2019** In : . , p. 1-30

A generalisation of the exponential distribution and its applications on modelling skewed data

Manat Mustafa, Muhammad Zubair, Ayman Alzaatreh, M. H. Tahir, Muhammad Mansoor, **2018** In : . 2 , p.1 , p. 68-79

Elementary theories and hereditary undecidability for semilattices of numberings

Nikolay Bazhenov, Manat Mustafa, Mars Yamaleev, **2018** In : .

ELEMENTARY THEORIES AND HEREDITARY UNDECIDABILITY FOR SEMILATTICES OF NUMBERINGS

Manat Mustafa, Nikolay Bazhenov, Yamaleev Mars, **2018** In : .

Green-type identities for Rockland operators on graded Lie groups

Manat Mustafa, Durvudkhan Suragan, **2018** In : . , p. 1-8

Boolean algebras realized by c.e. equivalence relations

Nikolay Bazhenov, Manat Mustafa, Frank Stephan, Mars Yamaleev, **2017** In : . 14 , p. 848-855

On interpolation of noncommutative symmetric Hardy spaces

Turdebek N. Bekjan, Manat Mustafa, **2017** In : . , p. 1-11

Friedberg numberings in the Ershov hierarchy

Serikzhan A. Badaev, Mustafa Manat, Andrea Sorbi, **2015** In : . 54 , p.1-2 , p. 59-73

Families Without Minimal Numberings

K. Sh Abeshev, S. A. Badaev, M. Mustafa, **2014** In : . 53 , p.4 , p. 271-286

Positive undecidable numberings in the Ershov hierarchy

M. Manat, A. Sorbi, **2012** In : . 50 , p.6 , p. 512-525

Rogers semilattices of families of two embedded sets in the Ershov hierarchy

Serikzhan A. Badaev, Mustafa Manat, Andrea Sorbi, **2012** In : . 58 , p.4-5 , p. 366-376

1. M. Mustafa, A.Sorbi. Positive undecidable numberings in the Ershov hierarchy ; Algebra and logic ,-Vol. 50, N6, pp. 512-525, N January 2012.

2. S.Badaev, M.Mustafa, A.Sorbi. Rogers semi lattices of families of two embedded sets in the Ershov hierarchy , Mathematical Logic Quarterly. -Vol. 58, issue 4-5.-P.366-376. -2012 August.

3.K. Abeshev,S. Badaev, M. Mustafa. Family without minimal numbering. Algebra and Logic, Vol. 53, No. 4, September, 2014

4. S. Badaev, M. Mustafa, A. Sorbi. Friedberg numberings in the Ershov hierarchy //Archive for Mathematical Logic February 2015, Volume 54, Issue 1, pp 59–73

5. T.N. Bekjan, M.Mustafa, On interpolation of noncommutative symmetric Hardy spaces, Positivity; , Volume 21, Issue 4, pp 1307–1317 https://doi.org/10.1007/s11117-017-0468-y

6. N.Bazhenov, M.Mustafa, F.Stephan, M.Yamaleev. Boolean algebras realized by c.e.equvivalence relations. Siberian electronic mathematical reports. V14, pp848-855. 2017.

7. M. Zubaira, A.Alzaatreh, M. H. Tahir, M. Mansoora and M.Mustafa. A generalization of the exponential distribution and its applications on modeling skewed data. the Journal of Statistical Theory and related fields. 16 May 2018. https://doi.org/10.1080/24754269.2018.1466099.

8.M.Mustafa, D.Suragan. Green-type identities for Rockland operators on graded lie groups.Complex Analysis and Operator Theory (2018). https://doi.org/10.1007/s11785-018-0824-3.

9. Bazhenov.N, M.Mustafa, M.Yamaleev, Elementary theories and hereditary undecidability for semilattices of numberings. Archive for Mathematical Logic (2019). https://doi.org/10.1007/s00153-018-0647-y

10.Bazhenov N., Mustafa M., Yamaleev M. (2019) Computable Isomorphisms of Distributive Lattices. In: Gopal T., Watada J. (eds) Theory and Applications of Models of Computation. TAMC 2019. Lecture Notes in Computer Science, vol 11436. Springer, Cham.

11. Bazhenov, N., Mustafa, M. and Sergei Ospichev. Bounded Reducibility for Computable Numberings. To appear in Lecture Notes in Computer Science**, (CIE2019, https://community.dur.ac.uk/cie.2019/ )**

12. I.Herbert, J.Sanjay Jain, M.Mustafa, L.Steffen and F.Stephan. Reductions between types of numberings.

Annals of Pure and Applied Logic. https://doi.org/10.1016/j.apal.2019.102716. 2019.

13. N.Bazhenov, M.Mustafa, L.S.Mauro, A.Sorbi, and M.Yamaleev, Classifying equivalence relations in the Ershov hierarchy, **Submitted for publication.**

14.M.Mustafa, D.Suragan. Hardy type inequalities for quaternion-valued functions. **Submitted for publication**.

15. Ardak Kashkynbayev; Manat Mustafa; Durvudkhan Suragan. Floquet theory for quaternion-valued ordinary differential equations. **Submitted.**

### In preparation

- Bazhenov.N, M.Mustafa, M.Yamaleev. Sigma-definable equivalences relations.
- Ardak Kashkynbayev; Manat Mustafa; Durvudkhan Suragan. Caccioppoli type inequalities for quaternion-valued functions.

The full list of publications can be found on google scholar page.

**Conferences: ****The 16th Asian Logic Conference** and Fourteenth International Conference on Computability, Complexity, and Randomness took the place at NU in Kazakhstan in June 2019. Please see more information about ALC2019 and CCR2019 by the following web pages: The Sixteenth Asian Logic Conference and Fourteenth International Conference on Computability, Complexity and Randomness

Discrete Mathematics, Linear Algebra with Applications, Abstract Algebra