My current mathematical interests lie in the mathematical theory and its applications in various fields, especially in biology.
During my Bachelor's degree, I mainly focused on commutative algebra and module theory. Under the supervision of Prof. Indah Emilia Wijayanti, I wrote a Bachelor thesis on some properties of certain maps between a collection of submodules of a module and a collection of ideals of a commutative ring. In particular, I studied some sufficient conditions for these maps to be lattice homomorphism or anti-homomorphism.
During my Master's degree, I studied some algebraic aspects of geometric objects. Under the supervision of Dr. Bram Petri, I wrote a Master thesis that mainly discusses hyperbolic manifolds. In particular, I studied the number of complete hyperbolic manifolds of certain dimension with volume less than a given positive number.
During my doctoral study, I was mainly interested in studying the application of algebraic methods in various fields. For instance, I was fascinated with the connections between algebra and phylogenetics, which is a branch in biology that studies the evolutionary relationships between some biological entities, particularly species. In this particular biological application, I combined many mathematical tools from algebra, geometry, combinatorics, graph theory, computer algebra and many more. Moreover, I was also greatly interested in applying algebraic methods to other statistical models which include factor analysis models and latent variable models. These two examples in applications hopefully will illuminate many more surprising connections between algebra and geometry and many real life problems.
During my postdoctoral research, I mainly focus on creating an effective denoising method for DNA sequences to correct errors in DNA sequencing data in order to be able to make better biological data analysis and better prediction of various biological phenomena.
Publications and Preprints
Puguh Wahyu Prasetyo, Adhy Kurnia Triatmaja, Fariz Setyawan, Muhammad Ardiyansyah, Angger Hafid Prabawa, Shafa Violeta Chaila Putri, Ayoudya Titan Widyasmara, Hafizh Naufal Azmi, and Samsul Arifin, ADEBOT1: revolutionizing educational robotics with Arduino and Lie algebra simulation. Submitted to a journal.
Puguh Wahyu Prasetyo, Adhy Kurnia Triatmaja, Fariz Setyawan, Angger Hafid Prabawa, Hafiz Naufal Azmi, Muhammad Ardiyansyah, and Samsul Arifin, Optimization of robotic movement: applying Lie algebra to improve the performance of mbot2, International Journal on Advanced Science, Engineering, and Information Technology, vol. 15, no. 2, pp. 376–386, Apr. 2025. https://doi.org/10.18517/ijaseit.15.2.20501
Puguh Wahyu Prasetyo, Joe Repka, and Muhammad Ardiyansyah. A note on the n-array unit graphs. Submitted to a journal.
Muhammad Ardiyansyah and Luca Sodomaco, Dimensions of Higher Order Factor Analysis Models, Algebraic Statistics 14-1 (2023), 91-108. DOI: 10.2140/astat.2023.14.91.
Muhammad Ardiyansyah, Dimitra Kosta, and Jordi Roca-Lacostena, Embeddability of centrosymmetric matrices capturing the double-helix structure in natural and synthetic DNA, J. Math. Biol. 86, 69 (2023). https://doi.org/10.1007/s00285-023-01895-8.
Muhammad Ardiyansyah, Distinguishing level-2 phylogenetic networks using phylogenetic invariants, Preprint arXiv:2104.12479. (Revision submitted to a journal)
Muhammad Ardiyansyah, Indah Emilia Wijayanti, and Puguh Wahyu Prasetyo, On a class of λ -modules, Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 3, Mar. 2021, pp. 329 -34. doi:10.37863/umzh.v73i3.513.
Muhammad Ardiyansyah, Kaie Kubjas, and Dimitra Kosta, The model-specific Markov embedding problem for symmetric group-based models, J. Math. Biol. 83, 33 (2021). https://doi.org/10.1007/s00285-021-01656-5.
Books and Dissertations
Burhanudin A Nugroho, Uswatun Khasanah, Puguh Wahyu Prasetyo, Muhammad Ardiyansyah. Permodelan Matematika . UAD Press.
Muhammad Ardiyansyah. Algebraic aspects of hidden variable models (doctoral thesis (2023)).
Puguh Wahyu Prasetyo and Muhammad Ardiyansyah. Teori Ring dan Aljabar serta Implementasinya. In progress.