Alen Đurić

Forthcoming post

Postdoctoral researcher (starting in October 2024) at the Institute of Mathematics, Physics and Mechanics

Postdoctoral student in the Inria project team Picube, within the department PPS of IRIF, a research laboratory of the CNRS and Université Paris Cité

Funding: the FSMP and Inria
Host: Pierre-Louis Curien

Doctorat en Mathématiques

Thesis defended on 13 April 2023

Funding: laureate of the COFUND MathInParis PhD fellowship program (the European Union’s Horizon 2020 research and innovation programme under a Marie Skłodowska-Curie grant)
University: Université Paris Cité
Laboratory: Institut de Recherche en Informatique Fondamentale (IRIF)
Teams: πr² (Inria project team within the PPS), Algebra and computation (thematic team within the PPS)
Thesis directors: Pierre-Louis Curien and Yves Guiraud
External advisor: Viktoriya Ozornova

Areas of interest

Interested in interplay between algebraic structures and their interpretations from different perspectives (e.g. combinatorial or topological), particularly in their category-theoretic and homotopical aspects
Very fond of higher-dimensional rewriting, eager to find out more about its applications to other branches of mathematics, especially to algebra, e.g. in combinatorial group theory and in effective algebra
Curious about higher category theory and interested in working in the domain from the combinatorial angle
Increasingly enthusiastic about formalisation of mathematics using The Coq Proof Assistant
Topics around my PhD thesis work: normalisations in monoids, Garside theory, Artin-Tits monoids and groups, Coxeter groups, plactic monoids, word problem, theory of collapsing schemes (aka discrete Morse theory), homology of monoids, geometric group theory

Publications

Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size (with Duško Bogdanić, Sara Koljančić, Polona Oblak, and Klemen Šivic)
Linear Algebra and Its Applications, Vol. 690 (2024)
(doi)
Coherent presentations of monoids with a right-noetherian Garside family (with Pierre-Louis Curien and Yves Guiraud)
Journal of Homotopy and Related Structures, Vol. 18, issue 1 (2023)
(doi)
Compressed zero-divisor graphs of matrix rings over finite fields (with Sara Jevđenić and Nik Stopar)
Linear and Multilinear Algebra, Vol. 69, issue 11 (2021)
(doi)
Categorial properties of compressed zero-divisor graphs of finite commutative rings (with Sara Jevđenić and Nik Stopar)
Journal of Algebra and Its Applications, Vol. 20, No. 05, 2150069 (2021)
(doi)
The total zero-divisor graph of a commutative ring (with Sara Jevđenić, Polona Oblak, and Nik Stopar)
Journal of Algebra and Its Applications, Vol. 18, No. 10, 1950190 (2019)
(doi)

Submitted article under revision

Correspondence between factorability structure and quadratic normalisation in monoids
Submitted for publication in International Journal of Algebra and Computation
(arXiv:2206.01672)

E-mail: djuric@irif.fr