Mahmood Alaghmandan
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office: 419-348-9710 (4042)

malaghma[at]fields.utoronto.ca

Ph.D. in Mathematics



The Fields Institute for Research in Mathematical Sciences
222 College Street, Second Floor
Toronto, Ontario M5T 3J1


Academic Biography:

I am a postdoctoral fellow in Fields institute (the thematic program of Abstract Harmonic Analysis, operator and Banach algebras).


I recently graduated from my Ph.D. program under the supervision of Yemon Choi and Ebrahim Samei. In the main project of my Ph.D. program (which I am still pursuing), I studied hypergroups and their applications to locally compact groups. The main part of the project concerns different amenability notions of hypergroup algebras, in particular, I am considering these concepts for different classes of examples. I have also studied different properties of hypergroup algebras for weighted discrete commutative hypergroups. Further, I have studied the Fourier algebra of hypergroups, its examples, and its relations to different amenability notion of hypergroups.

I have also done some research in questions on projections of locally compact groups. Applying Non-commutative Harmonic Analysis, we are considering idempotents of wider classes of group algebras. This study is a joint project with Mahya Ghandehari, Keith Taylor, and Nico Spronk. The ultimate goal of this joint project is to understand fully the nature of all projections (self-adjoint idempotents) in L1(G) for any locally compact group G. Our result for unimodular groups is a significant step in this program. We are to generalize our initial result to non-unimodular groups. There is an intimate connection between projections in L1(G) and generalized continuous wavelet transforms.

Following my interest in Banach algebra, I have done some research on separating maps on Banach algebras, approximate and character amenability of (abstract) Segal algebras. Also pursuing a question from my Ph.D. program, I studied amenability properties of centre of group algebras for discrete groups. This project on class functions on groups led to a new one on the class function subalgebra of Fourier algebras for compact groups.

Studying some interesting papers by Wildberger, I recently became interested to know more about finite hypergroups. The wide variety of examples from group theory to graph theory makes any result very interesting.


You can see my detailed accademic curriculum vitae for more information.



I spend my leisure time enjoining literature, philosophy, cinema, and music. Here you can read more about my hobbies. Sometimes, when I feel that there is something that I should write down, I blog it here!

Papers:

Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim. ZL-amenability constants of finite groups with two character degrees. Canad. Math. Bull. (to appear)

Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim. ZL-amenability and characters for the restricted direct products of finite groups, J. Math. Anal. Appl. 411 (2014), no. 1, 314-328.

Alaghmandan, Mahmood. Approximate amenability of Segal algebras. J. Aust. Math. Soc. 95 (2013), no. 1, 20ñ35.

Alaghmandan, Mahmood; Nasr-Isfahani, Rasoul; Nemati, Mehdi. Character amenability and contractibility of abstract Segal algebras. Bull. Aust. Math. Soc. 82 (2010), no. 2, 274-281.

Alaghmandan, Mahmood; Nasr-Isfahani, Rasoul; Nemati, Mehdi. On $\phi$-contractibility of the Lebesgue-Fourier algebra of a locally compact group . Arch. Math. (Basel) 95 (2010), no. 4, 373-379.

Alaghmandan, Mahmood. Amenability notions of hypergroups and some applications to locally compact groups. (Submitted).

Alaghmandan, Mahmood; Nasr-Isfahani, Rasoul; Nemati, Mehdi. Lebesgue-Fourier algebra of a hypergroup. (Submitted).

Alaghmandan, Mahmood; Nasr-Isfahani, Rasoul; Nemati, Mehdi. Separating maps between commutative Banach algebras. (Submitted).

Alaghmandan, Mahmood; Mehdi, Ghasemi. Structure of seminormed $*$-subalgebras of $\ell^\infty(G)$ and their amenability notions (In preperation)

Alaghmandan, Mahmood, Ghandehari, Mahya; ; Spronk, Nico; Taylor, Keith F., Projections of L1(G); unimodular groups. (In preparation)

Alaghmandan, Mahmood; Nico Spronk. Amenability notions of $ZA(G)$. (In preparation)

Alaghmandan, Mahmood, Ebrahim Samei, Weighted hypergroup algebras. (In preparation)

Talks:

Hypergroups and their amenability notions, Workshop on Operator Spaces, Locally Compact Quantum Groups and Amenability, Fields institute, Toronto, Canada, summer 2014.

Hypergroups and weighted hypergroup algebras, Banach algebras and applications 2013, Gothenburg, Sweden, summer 2013.

Hypergroups, Workshop on Banach Algebras and Harmonic Analysis, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Iran, spring 2013.

Hypergroups and some questions in harmonic analysis, Analysis Seminar, Department of Pure Mathematics, University of Waterloo, winter 2013.

The amenability property of the center of some specific discrete group algebra, Saskatchewan Analysis day, University of Regina, fall 2011; CMS summer meeting, Regina, summer 2012.

Matrix Lie groups and their Lie algebras, University of Saskatchewan, spring 2012.

Approximate amenability of Segal algebras, Saskatchewan Analysis day II, University of Saskatchewan, spring 2012.

Similarity problem for locally compact groups, University of Regina, Saskatchewan, Canada, spring 2011 Isfahan University of Technology, Iran, summer 2011.

Fourier Algebra, Isfahan University of Technology, Isfahan, Iran, fall 2008 ( 25 parts).

Other manuscripts:

Weighted hypergroups and some questions in Abstract Harmonic Analysis, Ph.D. dissertation, University of Saskatchewan, Canada, 2013.

Matrix Lie groups and their Lie algebras, University of Saskatchewan, Spring 2012.

Notes on similarities,University of Saskatchewan, Spring 2011.

Fourie Algebra (in Persian), M.Sc. Thesis, Isfahan University of Technology, Winter 2010.


 

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