Joachim Christian Kock

Joachim Christian Kock is a Professor in the Department of Mathematics at Universitat Autònoma de Barcelona, where he is affiliated with the Laboratori d'interaccions entre geometria, àlgebra i topologia (LIGAT). His research focuses on the intersection of category theory, algebraic topology, and combinatorics.

He received his Ph.D. (Doutor em ciências) from the Federal University of Pernambuco in 2000 and his Masters (Cand Scient) from Aarhus University in 1996. Following his doctorate, he held postdoctoral positions at prestigious institutions including Côte d'Azur University, KTH Royal Institute of Technology, and Caltech.

Professor Kock's research primarily centers on decomposition spaces, operad theory, and higher category theory. His work establishes connections between combinatorial structures and homotopy theory, with significant contributions to the understanding of polynomial functors, groupoids, and bialgebras. He employs advanced categorical methods to explore fundamental structures in mathematics.

His recent publications demonstrate a consistent focus on decomposition spaces and their applications across various mathematical domains. Kock has developed innovative approaches connecting combinatorial mathematics with higher categorical structures, particularly in the areas of operads and polynomial functors. His collaborative work spans multiple institutions and research groups across Europe.

Professor Kock has received research funding from the Spanish Ministry of Economy and Competitiveness (MINECO) and the European Regional Development Fund (FEDER) for multiple projects, including 'Teoría de homotopía de estructuras algebráicas' and 'TEORIA DE HOMOTOPIA DE ESTRUCTURAS COMBINATORIAS Y ALGEBRAICAS.'

He is actively involved in supervising graduate students and has mentored at least three students according to institutional records. His research group participates in international collaborations with institutions in France, Sweden, and the United States.