**fzalameatunal.edu.co**

Categorical Logic and the Logic of Sheaves: Foundations for a Synthetic Philosophy of Mathematics.

The presentation will include two parts. First, we will give a brief overview of the emergence of sheaves (1942-1950), Grothendieck and elementary toposes (1962-1970), Kripke models for intuitionism (1963) and Caicedo’s logic of sheaves (1995). Second, we will show how a synthetic philosophy of modern (1830-1950) and contemporary (1950-today) mathematics can be understood, building on an analogy with toposes of sheaves on Kripke models, and studying therein some main polarities of mathemati- cal thought (multiplicity/unity, continuum/discrete, along Galois, Riemann, Poincar ́e, Cantor, Gödel, Grothendieck, Connes, or Gromov, for example).

Fernando Zalamea obtained his PhD In categorical logic (University of Massachusetts, 1990, under the supervision of Ernest Manes). Professor of the Mathematics Department of the National University of Colombia. Director of the Research Division (1998-2000) of the National University. He has offered numerous courses and seminars in mathematical logic (non-classical logic, categorical logic) and in crosses with philosophy (history of logic, philosophy of contemporary mathematics).

He is editor of the magazine “Cuadernos de Sistemática Peirceana” (www.acervopeirceano.org), Peirce's only specialized magazine worldwide. He has published around twenty books. He has about a hundred articles on mathematics, logic and criticism of culture.

He has obtained some of the most important essays prizes Hispanic American context: Siglo XXI (Mexico 2013), Jovellanos (Spain 2004), Gil-Albert (Spain 2004), Kostakowsky (Mexico 2001), Andrés Bello (Colombia 2000).

He has been included in 100 Global Minds - The Most Daring Cross-Disciplinary Thinkers in the World (Roads, 2015). He is currently preparing (2016-2018) a monograph on the entire published work of Alexander Grothendieck: Grothendieck. A guide to his mathematical and philosophical work.