Algebra enthusiast, Mindanawan, researcher, teacher, currently studying Leavitt Path algebras and Talented monoids

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Contact me

Email: alfilgen(at) alfilgen.org, alfilgen.sebandal(at) g.msuiit.edu.ph

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About me

I’m a PhD student in my last year at Mindanao State University, Iligan Institute of Technology (MSU-IIT) in the Philippines under the supervision of Jocelyn Vilela (MSU-IIT) and Roozbeh Hazrat (Western Sydney University, Australia). Last July 2022, I started my 6-month research fellowship at Western Sydney University, Australia. Before this, I completed my Master’s at MSU-IIT, supervised by Jocelyn Vilela.

Broadly, my research lies in the areas of Leavitt Path Algebras and Monoids with group action. In particular, I’m interested in answering questions about the relationship of representation of the talented monoid and the representation of the corresponding Leavitt Path Algebra, especially the graded isomorphism conjecture. Indeed, as of now, in all of my research, I make use of a graded version of the graph monoid, the so-called talented monoid. But I am open to learn new techniques and methods. You can read more about my work in my current research section.

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Awards

Gordon Preston Prize for 6th Australia Algebra Conference (Nov. 28-30, 2022) held at Sunshine Coast University, Queensland, Australia for the talk “A Confirmation on the Finite Graded Classification Conjecture for Leavitt Path Algebras”.

Seminar and Lecture Series in Algebra

I am currently co-organizing the monthly online “Seminar in Algebra” at MSU-IIT, where international experts talk about recent developments in their field.

In addition, I introduced a series of short lectures from Ph.D. students (national and international) and professors with special beginner topics in algebra. The lectures are held twice a month. Click here to view previous talks and a schedule of future ones.

Feel free to contact me if you are interested to participate or give a talk.

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Current research topics (December 2022)

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List of Publications

W. Bock, C.G. Canto, I.R. Campos, D. Martin Barquero, C. Martin Gonzalez and Sebandal, A. (2022). Algebraic Entropy and A Complete Classification of Path Algebras over Finite Graphs by Growth. preprint: http://arxiv.org/abs/2212.10912

Bock, W., Sebandal, A. (2022). An Adjacency Matrix Perspective of Talented monoids and Leavitt path algebras. preprint: https://arxiv.org/abs/2212.08227

Bock, W., Sebandal, A., & Vilela, J. (2022). A talented monoid view on Lie bracket algebras over Leavitt path algebras. Journal of Algebra and Its Applications, 2350170. https://doi.org/10.1142/S0219498823501700

Hazrat, R., Sebandal, A. N., & Vilela, J. P. (2022). Graphs with disjoint cycles classification via the talented monoid. Journal of Algebra, 593, 319-340. https://doi.org/10.1016/j.jalgebra.2021.11.022

Sebandal, A., & Vilela, J. (2022). The Jordan–Hölder theorem for monoids with group action. Journal of Algebra and Its Applications, https://doi.org/10.1142/S0219498823500883.

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Teaching Experience

I worked as a non-permanent faculty at MSU-IIT. Last term I taught the lectures:

• Abstract Algebra for undergrad
• Calculus I for Engineers
• Mathematics in the Modern World

Where you might see me 🙂

——- Conferences and Talks ————————————————————–

2022

March 23, Methusalem Junior Seminars Pure Mathematics, Ku Leuven, Belgium (online) Invited Talk: Leavitt path algebras and graph monoids

November 28-30, 6th Australia Algebra Conference, Sunshine Coast, Queensland, Australia, Talk: A Confirmation on the Finite Graded Classification Conjecture of Leavitt Path Algebras

August 2, Webinário PPGM-UFAM, Universidade Federal do Amazonas, Brazil (online) Invited Talk: Linking Leavitt Path Algebras, Talented Monoids and Lie Bracket Algebras

June 13-17, GABY: Groups and Algebras in Bicocca for Young Algebraists, University of Milano-Bicocca, Italy. Poster: Graph Aperiodicity and Computations of the Gelfand-Kirillov Dimension of a Leavitt Path Algebra

May 21, Mathematical Society of the Philippines Annual Conference, online event, Talk: Simplicity, Solvability, Nilpotency: A Talented Monoid View on Lie Bracket Algebras over Leavitt Path Algebras

March 28-31, International Conference on Semigroups, Algebras, and Operator Theory (ICSAOT 2022), CUSAT, India (online), Talk: Composition Series of a Talented Monoid and Applications to the Gelfand-Kirillov Dimension of a Leavitt Path Algebra

February 7-18, Cimpa School — From Dynamics to Algebra and Representation Theory and Back, Universidade Federal de Santa Catarina, Florianopolis, Brazil, Invited talk: A Talented Monoid view on Lie Bracket algebras arising from Leavitt Path algebras

February 2, Seminar in Mathematics, Technische Universität Kaiserslautern, Germany, Invited Talk: The Gamma-monoid Jordan-Hölder Theorem and the Talented Monoid and Leavitt Path Algebra Classification of Graphs with Disjoint Cycles

—– Research Visits and Talks ————————————————————-

2023 and Ongoing

June 12-16 (upcoming) Victoria University of Wellington, New Zealand

July 16, 2022 – present Western Sydney University, Australia

February 12-14 University of the Philippines Diliman, Manila, Philippines

February 15-17 University of the Philippines Cebu, Cebu, Philippines

2022

November 2-4 Universitat Politècnica de Catalunya, Barcelona

November 7-11 Universidad de Málaga, Malaga, Spain

November 14-16 Vrije Universiteit Brussel, Brussels, Belgium

November 17-18 Université de Picardie Jules Verne, Amiens, France

June 6-17 Technische Universität Kaiserlautern, Kaiserlautern, Germany

January 6-30 Technische Universität Kaiserlautern, Kaiserlautern, Germany

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