Dario Alejandro Garcia Rico

Dario Alejandro Garcia Rico is a full-time faculty member (Docente de Planta) in the Department of Mathematics at the University of the Andes, Colombia. His research focuses on model theory with particular interest in ultraproducts of finite structures and their applications to combinatorics.

His educational background includes:

• PhD in Mathematics from the University of Los Andes (2015)
• Master in Mathematics from the University of Los Andes (2010)
• Bachelor's degree in Mathematics from the National University of Colombia (2008)

Dr. Garcia's research primarily centers on model theory, specifically examining the model-theoretic properties of ultraproducts of finite structures with potential applications to combinatorics. His work explores pseudofinite structures, asymptotic classes, and O-minimality. He has made significant contributions to understanding pseudofiniteness, measurability, and the connections between model theory and combinatorial structures through his investigations of random graphs (RG), r-regular infinite forests (Tr), and infinite-regular forests (Tinf).

Throughout his publications, Garcia has established important results in the model theory of pseudofinite structures, particularly in the areas of ultraproducts of finite graphs, asymptotic classes, and the relationship between pseudofinite dimension and forking independence. His work demonstrates how polynomial expressions can characterize definable sets in pseudofinite structures and how combinatorial cell decomposition techniques can be adapted to ordered asymptotic classes.

His notable scientific achievement includes:

• Marie Curie Research Fellowship at the University of Leeds (2016-2018) under grant agreement MODFIN 656422 on model theory of pseudofinite structures

Dr. Garcia has supervised graduate students working on topics related to model theory of finite structures. His research has been supported by prestigious grants including the Marie Curie Fellowship. He has collaborated with prominent researchers in the field including Alf Onshuus (University of the Andes) and Thomas Scanlon (UC Berkeley).

His work is centered in the Department of Mathematics at the University of the Andes, where he continues to advance research in model theory and its applications to combinatorial problems through the study of pseudofinite structures.