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  1. About
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Violeta Borges Marques

About

I am currently a post-doctoral researcher at the CRC 1624, in the University of Hamburg, working with Christoph Schweigert. I recently defended my PhD thesis, “Towards quantization of quasi-categories in modules”, done under the supervision of Wendy Lowen and Arne Mertens at the University of Antwerp. I started my PhD in 2021, as part of the ERC Project “Foundations for Higher and Curved Noncommutative Geometry”.
Before that, I was a MSc student of Mathematics at the University of Lisbon - IST, where I wrote my thesis under the supervision of Gustavo Granja.

Research Interests

My main interests are Homotopy Theory and Deformation Theory. My PhD project focuses on developing models for linear oo-categories and study their homotopical and deformation properties, with an eye towards applications in Derived Noncommutative Algebraic Geometry and Mathematical Physics. More broadly, I am also into Homological Algebra, Category Theory, Higher Structures and TQFTs.
My daily arXiv briefing is: math.AT, math.CT and math.KT.

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Publications

“The category of necklaces is Reedy monoidal”, with A. Mertens, Theory and Applications of Categories, 2024, Volume 41, 71 - 85.

We further the study of the interactions between Reedy and monoidal structures on a small category, building upon the work of Barwick.  In the second part, we study the category Nec of necklaces, as defined by Baues and Dugger-Spivak, showing that the category of A-valued presheaves on Nec is model monoidal when equipped with the Day convolution product, for any symmetric monoidal model category A.

“Deformation of quasi-categories in modules”, with W. Lowen and A. Mertens, Journal of Pure and Applied Algebra, 2025, Volume 229.

We initiate the deformation theory of templicial modules. In particular, we show that two important classes of templicial modules, quasi-categories in modules and deg-projective templicial modules, are preserved under levelwise flat infinitesimal deformation.

Preprints

“Templicial nerve of an A-infinity category”, with A. Mertens, 2024.

We construct a lift of Faonte's A-infinity-nerve which lands in templicial vector spaces. Further, we show that, when restricted to dg-categories, this nerve recovers the templicial dg-nerve and that the nerve of any A-infinity-category is a quasi-category in vector spaces.