# Raphael Bennett-Tennenhaus

### About me.

I completed my PhD at the University of Leeds in 2018, under the supervision of Prof. William Crawley Boevey. The title of my PhD thesis is Functorial Filtrations for Semiperfect generalisations of Gentle Algebras. I am currently doing a post-doc at Aarhus University, working with Peter Jørgensen.

Arxiv | Google Scholar | Email: raphaelbennetttennenhaus[at]gmail.com

### Research Interests.

I work in the representation theory of algebras. In my research so far I have taken methods from the world of finite-dimensional algebras, and adapted them to new contexts. These adaptations employ machinery from diverse areas such as commutative and noncommutative algebra, homological algebra and (logical) model theory. Lately my focus has broadened to: Auslander-Reiten theory; singularity theory; surface algebras and tiling algebras; higher homological algebra; purity and model-theoretic algebra in triangulated categories; and persistent homology.

### Papers and Preprints.

Functorial filtrations for homotopy categories of some generalisations of gentle algebras (2016) 1608.08514

(with W. Crawley-Boevey) Sigma-pure-injective modules for string algebras and linear relations (2018) Journal of Algebra, 513: 177-189

Sigma-pure injectives in homotopy categories for gentle algebras (2019) 1911.07691

(with A. Shah) Transport of structure in higher homological algebra (2021) Journal of Algebra, 574: 514-549

Classification of modules for complete gentle algebras (2021) 2107.09529

(with W. Crawley-Boevey) Semilinear clannish algebras (2022) 2204.12138

(with J. Haugland, M. Sandøy and A. Shah) The category of extensions and a characterisation of n-exangulated functors (2022) 2205.03097

Corner replacement for Morita contexts (2023) 2301.09518

Characterisations of ∑-pure-injectivity in triangulated categories and applications to endocoperfect objects (2023) Fundamenta Mathematicae (online)

(with D. Labardini-Fragoso) Semilinear clannish algebras arising from surfaces with orbifold points (2023) 2303.05326

(with J. Haugland, M. Sandøy and A. Shah) The category of extensions and idempotent completion (2023) 2303.07306

String algebras over local rings: admissibility and biseriality (2023) 2305.12885