Home page of Tiago Cruz

Tiago Cruz

Current postal address

Universität Stuttgart

Institut für Algebra und Zahlentheorie

Pfaffenwaldring 57

D-70569 Stuttgart

Office: 7.321

Telephone: +49-(0)711 / 685 - 65352

E-mail: tiago[dot]cruz[at]mathematik[dot]uni-stuttgart[dot]de

Picture of Tiago Cruz
Research interests

  • Quasi-hereditary algebras and stratified algebras

  • Schur algebras, Schur-Weyl duality

  • Homological invariants, dominant dimension

  • Homological algebra, Representation theory and category theory

    Teaching

  • Winter Semester 2024/2025 - Lineare Algebra und analytische Geometrie I

  • Summer Semester 2024 - Mathematik für Informatikstudiengänge II

  • Winter Semester 2023/2024 - Mathematik für Informatikstudiengänge I

  • Winter Semester 2021/2022 - Lineare Algebra und analytische Geometrie I

  • Summer Semester 2018 - Höhere Mathematik 2 für Ingenieurstudiengänge

  • Winter Semester 2017/2018 - Höhere Mathematik 1 für Ingenieurstudiengänge

    CV

    Currently, I am a postdoc at the Institute of Algebra and Number Theory at the Department of Mathematics - University of Stuttgart.

    From November 2022 to September 2023, I was a postdoc at the Max Planck Institute for Mathematics in Bonn.

    Until October 2022 I was a research assistant in the field of representation theory at the Institute of Algebra and Number Theory at the Department of Mathematics - University of Stuttgart.

    In October 2021, I defended my PhD dissertation in the field of representation theory in Stuttgart.

    The title of my doctoral thesis is Algebraic analogues of resolution of singularities, quasi-hereditary covers and Schur algebras, supervised by Prof. Dr. Steffen Koenig.

    From September 2018 to August 2021 my research was funded by Studienstiftung des deutschen Volkes.

    In July 2017, I obtained my master's degree in pure mathematics at University of Coimbra.

    The topic of my master's thesis was Schur-Weyl duality (available online: here), supervised by Prof. Dr. Ana Paula Santana and Prof. Dr. Ivan Yudin.

    Here is my ORCID profile. Here is a list of conferences I have attended.

    Publications / Preprints

  • A new formula for the classical dominant dimension using bimodules (joint with René Marczinzik): in preparation

  • An Auslander-Buchsbaum formula for higher Auslander algebras and applications (joint with René Marczinzik): arXiv

  • A higher dimensional Auslander-Iyama-Solberg correspondence (joint with Chrysostomos Psaroudakis): arXiv

  • Higher torsion-free Auslander-Reiten sequences and the dominant dimension of algebras (joint with René Marczinzik): arXiv, Journal of Algebra - Free Access

  • Higher Morita-Tachikawa correspondence: arXiv, Bulletin of the London Mathematical Society - Free Access

  • Relative Auslander-Gorenstein pairs (joint with Chrysostomos Psaroudakis): arXiv

  • Quasi-hereditary covers of Temperley-Lieb algebras and relative dominant dimension (joint with Karin Erdmann): arXiv, Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Free Access

  • On split quasi-hereditary covers and Ringel duality: arXiv (extended version), Forum of Mathematics, Sigma - Free Access

  • On Noetherian algebras, Schur functors and Hemmer-Nakano dimensions: arXiv, Representation Theory of the American Mathematical Society - Free Access

  • Characteristic tilting modules and Ringel duality in the Noetherian world:pdf, arXiv

  • Cellular Noetherian algebras with finite global dimension are split quasi-hereditary: arXiv, Journal of Algebra and Its Applications

  • An integral theory of dominant dimension of Noetherian algebras:pdf, Journal of Algebra

  • On properly stratified Gorenstein algebras (joint with René Marczinzik): arXiv, Journal of Pure and Applied Algebra

  • A characterisation of Morita algebras in terms of covers: arXiv, Algebras and Representation Theory - Free Access

  • Schur-Weyl duality over commutative rings: pdf, arXiv, Communications in Algebra

  • Wheels for Staircases (joint with Fátima Silva Leite, Jorge Batista, Krzysztof Krakowski, André Carvalho, Eduardo Domingues, André Lizardo and Gonçalo Saraiva)

    Please notice that the arXiv versions might differ slightly from the published versions.

    Other activities

    Currently, I am a zbMATH reviewer.

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