# Dr. Mohammad Fozouni

### Assistant Professor of Mathematics, Harmonic and Functional Analysis

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## Biography

**Mohammad Fozouni**

Assistant Professor of Mathematics, Faculty of Basic Science and Engineering, Gonbad Kavous University

Harmonic and Functional Analysis

**Educations:**

- Ph. D. Harmonic Analysis, Kharazmi University (MGP link)

Thesis: Homological and Cohomological Properties of Banach Algebras Based on Characters

Supervisor: Dr. Javad Laali

Advisor: Dr. Morteza Essmaili.

- M. Sc. Mathematical Analysis, Kharazmi University, Tehran, Iran

Thesis: Generalized Notions of Amenability

Supervisor: Prof. Alireza Medghalchi.

- B. Sc. Pure Mathematics, Payamnour University, Gonbad Kavous Branch.

**Responsibilities:**

- Head of the Mathematics and Statistics Department (Spring 2017-In Progress).

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My **Erdos Number **is 4

- Mohammad Fozouni

- Javad Laali

- John. S. Pym

- Neil. B. Hindman

- Paul Erdos

Reference: MathSciNet

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**Contact Information:**

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**Other Things:**

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**Quotes:**

*"If you can't prove your theorem, keep shifting parts of the conclusion to the assumptions, until you can"*

## Reasearch Areas

1- General Theorey of Banach Algebra

2- Abstract Harmonic Analysis.

3- Functional Analysis.

4- Homological properties of Banach modules.

5- Locally compact quantum group.

**MSC:** 43A07, 43A10, 43A15, 43A20, 46H05, 46H25, 46M10, 22D15.

## Journal Papers

**Selected publications:**

1- Some properties of functional Banach algebras, * Facta Univ. Ser. Math. Inform.* Vol. 28, No. 2 (2013), 189--196.

2- On $(\sigma,\tau)$-module extension Banach algebras, * J. Linear. Topological. Algebra.* Vol. 03, No. 04 (2014), 185--194. (Unfortunately there is a corrigendum of this work that you can see here).

3- Generalized injectivity of Banach modules, * Sarajevo. J. Math.* Vol.11 (24), No.2, (2015), 197--204.

4- Hereditary properties of character injectivity with application to semigroup algebras,* Ann. Funct. Anal.* 6 (2015), No. 2, 162--172.

5- On $\Delta$-weak $\phi$-amenability of Banach algebras, * U. P. B. Sci. Bull. Series A.* Vol. 77 (4), (2015), 165--176.

6- Closed ideals with bounded $\Delta$-weak approximate identities in some certain Banach algebras, * Miskolc Mathematical Notes,* Vol. 17 (2016), No, 1, 413--420.

7- *n*-multipliers and their relations with n-homomorphisms, * Vietnam J. Math.*, (2017) 45: 451--457.

8- $\phi$-injectivity and character injectivity of Banach modules, * U. P. B. Sci. Bull. Series A,* Vol. 78, Iss. 3

(2016), 43--52.

9- On character space of the algebra of BSE-functions, ** Sahand Comminucations in Mathematical Analysis**, to appear.

**Submitted papers:**

1- Two types of approximate identities depending on the character space of Banach algebras.

2- BSE property for some certain Segal and Banach algebras.

3- *n*-Jordan multipliers.

4- On a question related to bounded approximate identities of ideals in Banach algebras.

**In preparation papers and recent works:**

1- I'm reading the locally compact quantum groups theory. It's wonderful, but very tough and complicated.

**Services for international communities:**

1- Reviwer for *MathSciNet*.

2- Referee for *Int. J. Nonlinear Anal. Apl*.

3- Referee for *Complex and Nonlinear Systems.*

**You can download and see my complete CV via the following link:**

**Notes: **

1- A Characterization of Amenable Locally Compact Quantum Group (**In Persian**).

## Research Projects

i- **BSE-property of some Banach algebras ****(In Persian).**

ii-** Generalized multipliers (In Persian).**

iii- **Notes on approximate identities of some Banach algebras (In Persian).**

## Theses

You can download my M.Sc thesis and Ph.D dissertation in Persian via the following two links:

M.Sc, Generalized Notions of Amenability

Ph.D, Homological and Cohomological Properties of Banach Algebras Based on Characters

## Weekly Schedule

In the summer semester, I don't have any class. For the coming fall semester I have the following courses:

i- History of Mathematics,

ii- Topics in Mathematics and Applications (I'm going to teach Game Theory),

iii- Real Analysis.

## Courses Taught

1- General Topology.

2- Algebraic Topology.

3- Calculus 1,2.

4- Foundation of Geometry.

5- Dynamical Systems.

6- Complex Functions.

7- Real Analysis 1.

## Lecture Notes

1- Hilbert Spaces in Functional Analysis (In Persian).