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Mohammad Abdulrahim

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Mohammad Abdulrahim

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Mathematics & Computer Science

mna@bau.edu.lb

07 985080 Ex: 3306

Debbieh

Mohammad Abdulrahim

Head of Mathematics & Computer Science Department

Professor Mohammad N. Abdulrahim has a Bachelor degree in mathematics in 1990 and an MS degree in mathematics in 1992 from American University of Beirut. He then completed his Ph.D. in Mathematics (Algebra) from The Pennsylvania State University- USA in 1995 where he had a position at the Department of Mathematics at the Altoona campus as well as the university park campus from 1995-1998. Beside teaching at Lebanese American University in Beirut, Professor Abdulrahim has been an assistant professor at the Department of Mathematics & Computer Science at Beirut Arab University since 1998. He got promoted to an associate professor in 2005 and a professor in 2011. During his position at Beirut Arab University, he paid many visits to The Pennsylvania State University which was essential in triggering his research in the field of braid group representations, which was his main scope of research. He is also a reviewer at the American Mathematical Society (AMS) since 2015. Currently, he is the chairman of the Department of Mathematics & Computer Science at the Faculty of Science at Beirut Arab University since 2008. He has several publications in group representations and his main interest is to study irreducible representations of the braid group and its normal subgroup, pure braid group. Open questions as of whether or not such representations are faithful are always of great significance to his research. Research. He has more than 59 publications in this field.
 

Teaching

Fall 2023/2024

  • Abstract Algebra II
  • Topology
  • Calculus(Engineering)
  • Topics in Mathematics
  • Advanced Topics in Mathematics
  • Research Techniques
  • Modules & Rings
  • Representation Theory
  • Galois Theory
  • Universal Algebra

Spring 2022/2023:

  • Real Analysis I
  • Real Analysis II
  • Int. to Complex Analysis
  • Topiics in Linear Algebra
  • Abstract Algebra I
  • Algebraic Topology
  • Advanced Topics in Abstract Algebra
  • Universal Algebra
  • Representation Theory
  • Individual Studies
  • Senior Project

Fall 2022/2023

  • Topology
  • Discrete Mathematics
  • Special Functions
  • Number Theory
  • Abstract Algebra II
  • Modules & Rings
  • Representation Theory

Spring 2021/2022

  • Real Analysis I
  • Real Analysis II
  • Abstract Algebra I
  • Int. to Complex Analysis
  • Set Theory
  • Senior Project
  • Individual Studies
  • Advanced Topics in Abstract Algebra
  • Homological Algebra
  • Algebraic Topology

Fall 2021/2022:

  • Topology
  • Discrete Mathematics
  • Special Functions
  • Topics in Mathematics
  • Abstract Algebra II
  • Modules & Rings
  • Representation Theory

Spring 2020.2021:

  • Real Analysis II
  • Real Analysis I
  • Abstract Algebra I
  • Topics in Linear Algebra
  • Senior Project
  • Universal Algebra
  • Algebraic Topology

Fall 2020/2021

  • Abstract Algebra II
  • Real Analysis I
  • Number Theory
  • Topology
  • Modules & Rings
  • Representation Theory

 

 

Research

Research Interests

The braid group, Bv, has a well- known representation due to Artin in the group of automorphisms of the free group with n generators. Applying the Fox derivatives and Magnus representation, we get the classical Burau representation which is of degree n. D.D. Long gave a new derivative of the Burau representation by using an action of the automorphism group of the group of a free group with n generators on the representation variety of the free group and the group G, where G is a compact semi simple Lie group . We say that a group is linear if it admits a faithful representation into the general linear group for some natural number n and some field K. The question of faithfulness of the braid group has been the subject of research for a long time. It has been shown that the Burau representation is faithful for values of n smaller than 4 and non faithful for values on larger than 4. However, the faithfulness of the Burau representation in the case n=4 is still unknown. Our target then is to construct possible linear irreducible representations of the braid group and hope we could find one that is proved to be faithful. We need also to mention that the concept of faithfulness plays an important role in the field of cryptography, where there is an undergoing significant research in that field.

 

Activities

1. Colloquium Lecture at The American University of Beirut, Lebanon, 2009 . Title of the talk: Tensor Product of Specializations of the Burau Representation.

2. Colloquium Lecture at The American University of Beirut at the conference of Lie Groups and Related Topics, April 23rd, 2014.

3. Organized a workshop in mathematics in March 2009 (Workshop on Representation Theory and Number Theory ) as a partner with American University of Beirut in the LSMS conference in April 26th, 2012.

4. Organized a workshop on Partial Differential Equations in April 22nd, 2015

5. Organized A workshop on Mathematical Analysis on March 15th, 2016.

Membership:

  • A reviewer of American Mathematical Society  (Member since 2015)
  • A reviewer of Journal of Mathematics & Statistics (Since 23/12/2021)|