Violeta Borges Marques

Violeta Borges Marques https://violetaborgesmarques.com Violeta Borges Marques Sat, 04 Nov 2023 15:33:41 +0000 https://violetaborgesmarques.com en Front page https://violetaborgesmarques.com/Front-page Fri, 03 Nov 2023 12:45:21 +0000 Violeta Borges Marques https://violetaborgesmarques.com/Front-page AboutI 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 InterestsMy 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. Next ...  a.about-link {color: rgb(255, 170, 0)!important;} Mobile nav https://violetaborgesmarques.com/Mobile-nav Fri, 03 Nov 2023 12:45:21 +0000 Violeta Borges Marques https://violetaborgesmarques.com/Mobile-nav AboutPublications and PreprintsTeachingTalksCVContact Talks https://violetaborgesmarques.com/Talks Sat, 04 Nov 2023 15:33:41 +0000 Violeta Borges Marques https://violetaborgesmarques.com/Talks Conference TalksOct 2024 “Deformations of quasi-categories in modules” At the Higher structure in Noncommutative Geometry and Quantum Algebra conference. Seminar TalksDec 2024 “Deformations of quasi-categories in modules”At the Higher Structures Seminar.  Nov 2024 “The category of necklaces is Reedy monoidal” At the Séminaire de l’équipe TA. Dec 2023 “Infinitesimal deformations of templicial modules”At the Séminaire d'Homotopie et Géométrie Algébrique. Dec 2023 “Enriched Segal categories”At the Young Homotopy-theorist Online Meeting; slides. Nov 2023 “Deformation of quasi-categories in modules”At the Algebra Colloquium of the University of Antwerp. Nov 2023 “The category of necklaces is Reedy monoidal”At the Purdue Topology Seminar; (less interactive) slides. Oct 2023 “Deformation of quasi-categories in modules”At the Algebra and Topology Seminar of the University of Strasbourg; slides. Nov 2022 “Enriched Segal categories as models for weakly enriched categories”At the Algebra Colloquium of the University of Antwerp; video.Expository Talks Mar 2023 “A visual proof about higher homotopy groups”At the Mathematics Research Day of the University of Antwerp; slides. Reading Seminars Fall 2023 “Deformations of categories of coherent sheaves via quivers with relations”, S. Barmeier, Z. WangReading seminar with Lander Hermans, Alessandro Lehmann, Arne Mertens, Julie Symons and Carl Philipp Mazzanti. Spring 2023 “Deformation Theory: Lecture Notes”, M. Doubek, M. Markl, P. Zima Reading seminar with Lander Hermans, Alessandro Lehmann, Arne Mertens and Julie Symons. Fall 2022  “Kerodon”, J. Lurie Reading seminar with Matt Booth, Lander Hermans, Francesco Genovese, Alessandro Lehmann, Arne Mertens, Piergiorgio Panero and Julia Ramos-González. Mini-talks and Poster presentations             Sept 2024 “Deformation theory of quasi-categories in modules”5 min talk at the Tale of Geometries; slides. May 2024 “Infinitesimal deformations of quasi-categories in modules”Based on the homonymous preprint and presented at the PhD Day of the Belgian Mathematical Society (BMS); pdf. Apr 2024 “Hochschild cohomology for quasi-categories in modules”5 min talk at the Oberwolfach Workshop: Hochschild Cohomology and Applications; slides. Jan 2023 “Infinitesimal deformations of quasicategories in modules”Based on the homonymous preprint and presented at the SLMath Introductory Workshop: Noncommutative Algebraic Geometry; pdf. Publications and Preprints https://violetaborgesmarques.com/Publications-and-Preprints Fri, 03 Nov 2023 12:45:22 +0000 Violeta Borges Marques https://violetaborgesmarques.com/Publications-and-Preprints 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. Teaching https://violetaborgesmarques.com/Teaching Fri, 03 Nov 2023 12:45:22 +0000 Violeta Borges Marques https://violetaborgesmarques.com/Teaching TeachingSummer 2026 Seminar on Hochschild CohomologySeminar for Master’s students at the University of Hamburg. Spring 2025 Homological AlgebraExercise sessions for Master’s students at the University of Antwerp. Spring 2024 Homological AlgebraExercise sessions for Master’s students at the University of Antwerp. Spring 2023 Homological AlgebraExercise sessions for Master’s students at the University of Antwerp.  Spring 2022 Homological AlgebraExercise sessions for Master’s students at the University of Antwerp. Other Academic ActivitiesWinter 2025 Junior ZMP SeminarCo-organizer.Spring 2025 Homoclinic Points and Category TheoryMedelezer (Master Thesis Jury Member) for the Master Thesis of Louis Van Gaelan “Homoclinic Points and Category Theory” CV https://violetaborgesmarques.com/CV Fri, 03 Nov 2023 12:45:23 +0000 Violeta Borges Marques https://violetaborgesmarques.com/CV EducationOct 2025 - Current Post-docAt the University of Hamburg, in the CRC 1624 porject. Sep 2021 - May 2025 PhD in MathematicsAt the University of Antwerp, under the supervision of Wendy Lowen and Arne Mertens. Sep 2018 - Jun 2021 MSc In Mathematics and Applications At the University of Lisbon - IST, under the supervision of Gustavo Granja; thesis. Sep 2015 - Jun 2018 BSc in Physics Engeneering At the University of Lisbon - IST. Reseach Stays and VisitsNov 2024 Université Sorbonne Paris Noord One week visit to work with Francesca Pratali.Jan 2024 Université Toulouse III - Paul Sabatier One month stay to work with Bertrand Toën.May 2023 Université Toulouse III - Paul Sabatier One week visit to work with Elena Dimitriadis-Bermejo.Organization Fall 2025 - Current Junior ZMP Seminar Co-organizer July 2025 SLMath Summer School "Noncommutative Algebraic Geometry"Local organizer and teaching assistant.Fall 2024 - Current UA Mathematics Research Day Co-organiser.Sept 2022 Noncommutative Shapes Local organizerHonors and Awards Dec 2024 Invitation to the Oberwolfach Workshop: Hochchild Cohomology and Applications. Oct 2023 Invitationby SLMath for the SLMath Connections & Introductory Workshops: Noncommutative Algebraic Geometry Oct 2023  Short Research Stay in Europe Grant Awarded by the Fonds Wetenschappelijk Onderzoek (FWO). 2020 Initiation to Research Grant Awarded by the CAMGSD - IST; I developed a project, under the supervision of Gustavo Granja, on the Cobordism Hypothesis. 2019 Initiation to Research Grant Awarded by the CAMGSD - IST; I developed a project, under the supervision of José Mourão, on Geometric Quantization and Imaginary Time Evolution. 2019 Jaime Campos Ferreira AwardAward given to Master’s degree students who show academic excelence in Mathematics. Other Academic Activities Mar 2023 Grow your Network: from the perfect pitch to lasting relationsWorkshop from the Antwerp Doctoral School (ADS). Sep 2023 - Current  Quarterly Internal NewsletterI write the Quarterly Internal Newsletter of the Department of Mathematics of the University of Antwerp. Jan 2023   ImaginaryGuide at "Imaginary", an exhibition for popularising Mathematics. Apr 2021 École de Printemps d’Informatique Théorique (EPIT) 2020Online School on Homotopy Type Theory. Conferences and Workshops Dec 2025 Geometry, higher structures, and physics ICSM Sep 2024 School on Deformation Theory IVSapienza Univeristy of RomeFev 2024 Introductory Workshop: Noncommutative Algebraic GeometrySLMath Fev 2024 Connections Workshop: Noncommutative Algebraic Geometry SLMath Oct 2023 Categories and stacks in algebraic geometry and algebraic topologyCIRM Sep 2023 Hopf Days in Brussels 2023 Université Libre de Bruxelles Jul 2023 Young Topologists Meeting 2023EPFL Jun 2023 A Panorama of Homotopy TheoryUniversity of Oxford Dec 2022 Journées HomotopiquesUniversity of Nice Sep 2022 Non-Commutative ShapesUniversity of Antwerp Jun 2022 Barcelona Conference on Higher StructuresUniversity of BarcelonaFull CV  Contact https://violetaborgesmarques.com/Contact Fri, 03 Nov 2023 12:45:24 +0000 Violeta Borges Marques https://violetaborgesmarques.com/Contact Contact Violeta Borges Marques (she/her) Department of Mathematics - GeomatikumUniveristy of HamburgOffice 1518Bundesstraße 55, 20146 Hamburgvioleta.borges.marques (at) uni-hamburg.de my ORCiD profile <img width="818" height="818" width_o="818" height_o="818" data-src="https://freight.cargo.site/t/original/i/6fbb2b31ae8a584d870217892a1534ce462eb69aef80d13f1c3d1c678a886b11/IMG_6538.jpg" data-mid="239396062" border="0" src="https://freight.cargo.site/w/818/i/6fbb2b31ae8a584d870217892a1534ce462eb69aef80d13f1c3d1c678a886b11/IMG_6538.jpg" /> me being awarded my PhD