I am currently a researcher at INESC-TEC working on mathematical semantics of hybrid computation and effective equality via mathematical logic (e.g., game semantics, linear logic, dependent types, homotopy type theory, higher-order computability and complexity), category theory (e.g., monads, algebraic theories, internal/enriched and higher categories, fibrations), topology and analysis (e.g., constructive topology, algebraic topology, domain theory, functional analysis). More generally, I am trying to formulate how to develop a rich mathematical universe of partial maps, concurrency, probability, classical logic, etc. with nontrivial effective equalities inside a much simpler universe of intuitionistic linear logic and constructive mathematics, in which everything is total, sequential, deterministic, linear and constructive with only the trivial equality, and apply this mathematical framework to theoretical computer science.
Research interests. My research interests are in pure mathematics and theoretical computer science, specifically, mathematical semantics (esp. game semantics) of logic and computation (n.b., game semantics is far from game theory in economics), constructive mathematics, (higher-order) computability and complexity, (higher) category theory, topology and the connection between these fields as well as their applications to theoretical computer science.
Brief CV. Before coming to Braga, I was a postdoctoral research scholar at the University of Minnesota in 2019–2022. I also had short time positions at Kyoto University in 2019, and at Australian National University in 2022. I was a doctoral student at the University of Oxford in 2012–2018 (DPhil; logic, foundations & structures) advised by Samson Abramsky and Bob Coecke (cf. my mathematical genealogy), where my doctoral thesis is on a game-semantic foundation of logic, computation and constructive mathematics. Before going to Oxford, I was an undergraduate student at Hokkaido University (BEng; TCS) in 2007–2012, where I was fortunate enough to have Thomas Zeugmann as my mentor. My bachelor thesis is on computational group theory advised by Shin-ichi Minato. Meanwhile, in 2009–2010, I temporally left the undergraduate programme and had a one-year study at the University of Wisconsin-Madison (exchange program; pure maths), where I met another mentor Ken Ono who is also the vice president of the American Mathematical Society.