# Mabud Ali Sarkar

PhD Student

The University of Burdwan

Burdwan-713104, India

"Wipe out every tear from every eye"-Mahatma Gandhi

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Current Status: I have submitted my PhD thesis and looking for jobs (postdoc etc).

Research Topic: Algebraic Number Theory, Arithmetic Geometry, and Arithmetic Dynamics. In particular, my favourite research object is formal group. I am interested in the application of formal groups in (algebraic and analytic) number theory, algebraic geometry, and dynamics.

PhD Thesis Title: Studies on Formal Group Laws over Local Fields

Date of Submission of PhD Thesis: May 29, 2024

Date of Defending of PhD Thesis: November 2024 (expected)

Research Papers:

M. A. Sarkar & A. A. Shaikh, Rigidity and Unlikely intersections for stable p-adic dynamical systems, published in "p-adic Numbers, Ultrametric Analysis and Applications", Volume 14, Issue 2, 2022.

M. A. Sarkar & A. A. Shaikh, On the bases of 2-adic logarithm on the group of principal units, published in "Graduate Journal of Mathematics", Volume 8, Issue 1, 2023.

M. A. Sarkar & A. A. Shaikh, On the Image of p-adic logarithm on the group of principal units, 32 pages, 2021. (under revision in Houston Journal of Mathematics)

R. Abdellatif & M. A. Sarkar, Constructing 2-dimensional Lubin-Tate formal group over Z_p (I) 34 pages, 2024. (Under revision in Journal of Algebra)

M. A. Sarkar & A. A. Shaikh, Unlikely intersection for higher-dimensional formal groups. 20 pages, 2024. (submitted)

M. A. Sarkar & A. A. Shaikh, Unlikely intersection for higher-dimensional stable p-adic dynamical systems, 13 pages, (submitted)

M. A. Sarkar & A. A. Shaikh, Properties of Breuil-Kisin modules inherited by p-divisible groups, 10 pages, 2024. (submitted)

R. Abdellatif & M. A. Sarkar, Constructing 2-dimensional Lubin-Tate formal group over Z_p (II). 2024 (forthcoming)

Conference/Seminar Talks Given:

PhD Seminar of LAMFA, October 2, 2024, hosted by University of Picardie Jules Verne, Amiens, France

(Title of the talk: Local class field theory via Lubin-Tate formal groups)

The Early Number Theory Researchers Workshop, September 10-20, 2024, University of Duisburg-Essen, Germany

(Title of the proposed talk: Construction of 2-dimensional Lubin-Tate formal group over ZZ_p)

Equidistribution and Arithmetic Dynamics, Oklahoma State University, USA, 20/06/2022 to 24/06/2022.

(Title of the Talk: Rigidity and Unlikely Intersection in Stable p-adic Dynamical System)

International Webinar on Mathematics and Application, The University of Burdwan, 25/09/2020 to 27/09/2020.

(Title of the talk: Higher dimensional Lubin-Tate formal group).

National seminar on mathematical sciences (NSMS-2020), The University of Burdwan, India, 09/01/2020 to 11/01/2020.

(Title of the Talk: p-adic Hodge Theory and Breuil-Kisin Module).

p-adic Langland's correspondence conference, Henri Lebesgue Centre, Rennes, France, 02/09/2019 to 06/09/2019.

Elliptic curves and modular forms in arithmetic geometry, Università degli studi di Milano, Italy, 12/09/2022 to 16/09/2022.

Workshop/Summer School Attended:

"CIMPA school on “Group Action in Arithmetic and Geometry", Yogyakarta, Indonesia, 17/02/2020 to 28/02/2020.

Modular form and Galois representation, IISER Tirupati, India, 11/12/2019 to 17/12/2019.

Hodge theory and p-adic Hodege theory, CIMPA Research School, Centro de Investigación en Matemáticas A.C. (CIMAT), 02/08/2021 to 10/08/2021.

Automorphic Forms Summer School, Erdos Center, Budapest, Hungary, 29/08/2022 to 02/09/2022.

Summer School in Arithmetic Geometry, University of Duisburg-Essen, Germany, 05/09/2022 to 09/09/2022.

Heights and Model theory, Preliminery Arizona Winter School 2022, University of Arizona, 03/10/2022 to 11/11/2022.

An introduction to p-adic method in arithmetic, AIS, SRM University, Andhrapradesh, 26/07/2023 to 15/08/2023.

Hida Theory and Iwasawa Main Conjecture over Q, Chennai Mathematical Institute, Siruseri, India, 04/12/2023-09/12/2023.

Research Entrance Exam. Qualified:

NET (National Eligibility Test), conducted by CSIR, Government of India.

GATE (Graduate Aptitude Test in Engineering), conducted by IIT Guwahati, India.

SET (State Eligibility Test), conducted by West Bengal Government, India.

Awards: CSIR Research Fellowship for 5 years with File No.- 09/025(0249)/2018-EMR-I