Gabriel Goren-Roig
Hi there! I’m Gabo, a PhD student in Mathematics at Universidad de Buenos Aires in Buenos Aires, Argentina, working at the intersection between Category Theory, Logic and Computer Science.
I am part of the Logic, Language and Computability Research Group (GLyC). My advisor is Santiago Figueira. My research is funded by CONICET, Argentina’s National Research Council.
Below you will find a description of the main motivations behind my research, current and otherwise. I am always happy to discuss these topics, so please get in touch if you are so inclined.
You can find my list of publications here.
Research Interests
Computational Category Theory
I am interested in Computational Category Theory for both applied and theoretical reasons.
On the applied side, being able to compute answers to categorical questions algorithmically seems fundamental to making Category Theory more applicable in the sciences. Categorical database theory is an excellent example of application where it is crucial—if the idea is to make any sense at all—to not only develop a mathematical theory at a semantic level but also explicitly develop its syntactic and algorithmic counterpart.
On the theoretical side, I am interested in how syntax refines semantics, in the sense that new phenomena arise when we become more strict with our notions of mathematical equivalence. For instance, once we have focused on syntactic descriptions we can narrow the scope even further to the finite ones and analyze the classes of finitely presentable objects that arise.
In my work, an interesting example of this phenomenon came up when trying to understand the syntactic representations for profunctors, which is an important point for categorical database theory. In particular, the fundamental equivalence between functors $\mathcal{C}^\text{op} \times \mathcal{D} \to \sf{Set}$ and functors $\mathcal{C}^\text{op} \to \sf{Set}^\mathcal{D}$ does not carry over to the world of finite syntactic descriptions. This is the main observation that led to the paper Presenting Profunctors.
Applications of Category Theory to Finite Model Theory and Databases
Categorical logic can be understood as the perspective that logics, understood as inductively defined syntax for well-formed formulas and well-formed proofs, constitute syntactic presentations for categorical structures in a similar sense as the one described above.
Although the field has a long history and a deep connection with type theory and the theory of programming languages, traditionally it has been disconnected from other areas of logic more connected with combinatorics and computational complexity, as is the case of finite model theory and the theory of databases.
An intersection between these two traditions, Structure and Power, has begun to take form owing greatly to the research program of game comonads. Currently, I am particularly interested in using this framework to understand what kinds of logics are possible near the lower end of the expressive power spectrum as exemplified by Basic Modal Logic. In this context I have worked on a variation of Basic Modal Logic with (non-unary) relations instead of propositional variables and developed its fundamental model theory using the framework of game comonads and arboreal categories.
In the past I have studied a bit of coalgebraic modal logic and I would be interested in exploring the connection with this topic as well.
Emergence
I am interested in developing a rigorous understanding of the concept of emergence. Currently, I am trying to understand the relationship between emergence and failure of the glueing axiom as formalized by sheaf theory. Computationally, this can be seen as local consistency of data that fails to imply global consistency, as it happens in topics such as dynamic programming, constraint satisfaction and data integration.
I am also interested in emergence from the perspective of information loss through coarse-graining. This perspective partly contributes to my interest in logical indistinguishability of models as a form of logical or language-based coarse-graining.
Finally, going back to my Physics training, I also have a perennial interest in dynamical systems and the coarse-graining of dynamics, as exemplified by center manifolds and Crutchfield et al.'s fascinating predictive states/computational mechanics framework. Although these topics are not part of my current research, I intend to reconnect with them eventually.
News
| Dec 31, 2024 | Another year in my PhD adventure has gone by. As part of my PhD coursework, in 2024 I have taken the following classes: Differential Topology, Homological Algebra and Algebraic Geometry. |
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| Nov 28, 2024 | Good news: our paper Modal Logic with Relations over Paths: a Theoretical Development through Comonadic Semantics has been accepted into JLC. |
| Jul 04, 2024 | I gave a talk at Topology, Algebra and Categories in Logic in Barcelona, Spain, titled Generalised Unions of Conjunctive Queries in the Algebraic Data Model. abstract pdf |
| Jun 28, 2024 | This week I attended the TACL 2024 Summer School, including tutorials on quantum contextuality by Samson Abramsky, categorical automata theory by Daniela Petrisan and the theory of polymorphisms for constraint satisfaction problems by Michael Pinsker. |
| Jun 17, 2024 | I gave a talk at Applied Category Theory in Oxford, UK, titled Presenting Profunctors. recording |
| May 04, 2024 | Our paper Presenting Profunctors has been accepted to ACT 2024. This means it will be published in the Proceedings and I will give a talk about it! This is joint work with Emilio Minichiello and Joshua Meyers. |
| Jul 28, 2023 | This week I took an intensive course titled Algorithmic aspects of minor-closed graphs by Ignasi Sau. |
| Jul 08, 2023 | This semester I took Algebraic Topology towards the fulfillment of my PhD coursework. |
| Mar 28, 2023 | Gave a flash talk on the concept of comonads at the local event Día del ICC (one-day internal workshop of the Computer Science Institute). |
| Jul 04, 2022 | I gave a talk at the Structure Meets Power Workshop at ICALP 2022, titled Path Predicate Modal Logic and its Comonadic Semantics. slides |
| Jun 02, 2021 | I gave a remote talk at Applied Category Theory 2021 in Cambridge, UK, titled Stochastic game logic, coalgebraically. recording |
| Feb 10, 2021 | Excellent news: I have been selected for participation in this year’s Applied Category Theory Adjoint School! |
| Aug 07, 2019 | I gave a talk at the Santa Fe Institute in Santa Fe, New Mexico, USA, in the context of the REU program. Title: Inferring Finite State Machines from Time Series. recording |