36 | IHES Annual Report 2020
Olivia CARAMELLO Mathematics, associate professor, Università degli Studi dell'Insubria,
with the support of the Huawei Toposes Project at IHES.
OLIVIA CARAMELLO continued the development of her research program on the Grothendieck toposes as unifying 'bridges' in mathematics, working on several different themes: systematic study of the geometry of morphisms and equivalences of toposes (this is the subject of a research monograph in preparation); development, with her doctoral student Riccardo Zanfa, of relative topos theory through the language of stacks, and introduction of a higher-order parametric logic formalizing the structures classified by...
SCIENTIFIC ACTIVITY
Israel Gelfand Chair in Mathematics
DISTINCTIONS
AILA Prize (2011) L Oréal UNESCO fellowship for Women in Science (2014) "Rita Levi Montalcini" position from the Italian Ministry of Education, University and Research (since 2017)
Editor of: Logica Universalis
PUBLICATIONS
La « notion unificatrice » de topos, To be published in the proceedings volume of the conference series Lectures Grothendieckiennes, École normale supérieure.
Grothendieck Toposes as Unifying 'Bridges': a Mathematical Morphogenesis To be published in the Philosophy of Mathematics. Objects, Structures, and Logics, Springer (2021).
Denseness Conditions, Morphisms and Equivalences of Toposes Research monograph in preparation, pre-publication arXiv:1906.08737.
Comma Toposes In preparation.
A Unified Theory of Factorization Systems In preparation (with an appendix by Axel Osmond).
With Riccardo Zanfa On the Dependent Product in Toposes Accepted for publication in Mathematical Logic Quarterly.
Relative Topos Theory via Stacks and Higher order Parametric Logic Research monograph in preparation.
With Axel Osmond The Over topos at a Model In preparation.
CONFERENCES
Colombia Workshop in Honor of Alexander Grothendieck s Legacy, Universidad Nacional de Colombia, Bogotá (27 28 August) Toposes as Unifying Spaces: Historical Aspects and Prospects (video conference)
Topics in Contemporary Mathematics, Universidad Nacional de Colombia, Bogotá (25 30 October) The Geometry of Morphisms and Equivalences of Toposes (video lectures)
Italy Summer School of ScienzaNuova, Merano (July), Unità e molteplicità: l'estetica dell'oggetto in matematica (video conference)
Iran Mathematical Logic Weekly Seminar, IPM Institute for Research in Fundamental Sciences, Tehran (13, 20 et 27 May) An Invitation to Topos-theoretic Model Theory (video research lecture)
United Kingdom Spring School: Topics in Category Theory, International Centre for Mathematical Sciences, Edinburgh (11 13 March) Introduction to Grothendieck Toposes (video research lecture)
