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 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

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

  • 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

  • On split quasi-hereditary covers and Ringel duality: arXiv, to appear in Forum of Mathematics, Sigma

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

  • 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

  • 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)

    Other activities

    Currently, I am a zbMATH reviewer.

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