Research

                                                               Research interests:   

My research centers around algebraic K-theory, a branch of mathematics that studies objects like modules, vector bundles, and algebraic cycles through invariants defined by K-groups. Within this broad area, I am particularly interested in understanding the behavior of ideal class groups, Picard groups, and Brauer groups within the context of monoid algebras. The study of ideal class groups focuses on classifying ideals within a ring up to isomorphism, giving insight into the structure of divisors and factorization in these algebras. Picard groups, which classify invertible sheaves, and Brauer groups, concerned with central simple algebras, provide additional layers of information on divisibility, cohomology, and the structure of modules over the algebra.

     In addition, I explore the Picard groups and ideal class groups of monoid schemes. Monoid schemes, which extend classical schemes by incorporating monoids, offer a rich ground for studying algebraic and geometric properties in a more generalized setting. By investigating these groups in both monoid algebras and monoid schemes, I aim to gain a deeper understanding of how these fundamental algebraic structures behave under various conditions, and how they relate to concepts in algebraic geometry, topology, and arithmetic.

                                                                    List of publications/ preprints:

5. M. A. Raihan and H. P. Sarwar, Brauer groups of monoid algebras (In progress).

4. M. A. Raihan and H.P. Sarwar, Picard groups and invertible modules over Rees-Like algebras (In progress).

3. M. A. Raihan and H. P. Sarwar,  The group of invertible modules over monoid algebras (Submitted).

2. M. A. Raihan and H. P. Sarwar, Subintegrality and ideal class groups of graded integral domains (Submitted).

1. M. A. Raihan, Leslie G. Roberts and H. P. Sarwar, Subintegrality and ideal class groups of monoid algebras (Submitted).

                                                    Conference/Workshop/Meetings

• Conference on Topics Related to Projective Modules, at The Institute of Mathematical Sciences (IMSc), Chennai, India. (July 23-26, 2025)(Presented). Here is the link: Click!

• Commutative Algebra and Singularity Theory, Osaka Metropolitan University, Osaka, Japan (September 9-13, 2024) (online) (Participant). Here is the link: Click!

•  Lefschetz properties in algebra, geometry, topology and combinatorics, Krakow, Poland (June 23-29 , 2024) (Presented). Here is the link: Click!

•  International E-Conference of Young Researchers in Algebra and Number Theory  (online, Jan 12-13, 2023) (Participant). Here is the link: Click!

•  Advanced instructional course on Advanced Commutative Algebra, National Centre for Mathematics (online Jan 02-May 02, 2021) (Participant). Here is the link: Click!

• Online meeting on "Algebraic K-theory and its applications to commutative algebra and algebraic geometry" August 20-21, 2020)(Participant). Here is the link: Click!

• National Level Workshop on Graph Theory: Algebraic and Algorithmic Aspects (GT A3)-2016 (December 19-24, 2016 ) (Participant). Here is the link: Click!

                                                                            Talks

• Subintegrality and ideal class groups of monoid algebras,  at The Institute of Mathematical Sciences (IMSc), Chennai, India. (July 25, 2025).

• Subintegrality and ideal class groups of graded integral domains,at  Indian Institute of Technology Kharagpur, India.  (July 1, 2025).

• Subintegrality and ideal class groups of monoid algebras, at  Indian Institute of Technology Kharagpur, India.  (December 27, 2024 ).

• The ideal class group and the Picard group of monoids, at  Indian Institute of Technology Kharagpur, India.  (March 8, 2022).

• The divisorial class group and the Picard group Of monoid algebras, at Indian Institute of Technology Kharagpur, India.  (November 26 , 2021).