I am currently an assistant professor in the mathematics and computer science department at Indiana State University.
I was previously a Research Fellow in the theory group
at the University of Birmingham, working on the EPSRC project "Nominal String Diagrams" with
Dan Ghica,
Fabio Zanasi, and
Alexandra Silva.
Before that, I was a project researcher at the
ERATO MMSD project
in Tokyo. This project aims to extend formal methods and software
verification techniques to
cyberphysical systems,
with particular emphasis on applications to automotive control and manufacturing.
I worked on developing mathematical perspectives on machine learning and neural networks based on coalgebra and category theory.
I also worked on on quantitative refinements of bisimulation and other coalgebraically defined structures.
I received a PhD in mathematics at Indiana University in August 2017 as a student of
Larry Moss.
My academic background is primarily in coalgebra, logic, and category theory.
For some automatically maintained lists, check out my
dblp and
Google Scholar pages.
Papers:
Final versions available from publisher, preprint may differ from published versions.

The differential calculus of causal functions,
with Bart Jacobs,
2019.
preprint

Differentiable Causal Computations via Delayed Trace,
with Shinya Katsumata,
LICS 2019.
preprint

Relational Differential Dynamic Logic,
with Jérémy Dubut,
Shinya Katsumata,
Ichiro Hasuo,
Juraj Kolčák,
and Akihisa Yamada,
2019.
preprint

Quantitative bisimulations using coreflections and open morphisms,
with Jérémy Dubut,
Shinya Katsumata,
and Ichiro Hasuo,
2018.
preprint

Fibrational Bisimulations and Quantitative Reasoning,
with Jérémy Dubut,
Shinya Katsumata,
and Ichiro Hasuo,
CMCS 2018.
preprint

Neural Nets via Forward State Transformation and Backward Loss Transformation,
with Bart Jacobs,
2018.
preprint

Precongruences and parametrized coinduction for logics for behavioral equivalence,
with Lawrence Moss,
CALCO 2017.
preprint

A complete logic for behavioural equivalence in coalgebras of finitary set functors,
CMCS 2016.
preprint

Eigenvalues and Transduction of Morphic Sequences,
with Lawrence Moss,
William Tune,
and Jörg Endrullis,
DLT 2014.
preprint

Eigenvalues and Transduction of Morphic Sequences: Extended Version,
with Lawrence Moss,
William Tune,
and Jörg Endrullis,
DLT Special Issue 2014.
preprint

Linearization of Automatic Arrays, Weave Specifications, and Variadic Sequences,
MFPS 2013.
preprint
Talks:

Rewriting for monoidal closed categories, FSCD 2022, 2022.
slides

Differentiation of Causal Functions, ISU, 2022.
slides

Functorial String Diagrams for ReverseMode Automatic Differentiation, PPLV Seminar, UCL, 2022.
slides

Functorial String Diagrams for ReverseMode Automatic Differentiation, Indiana University Logic Seminar, 2022.
slides

Differentiating Stateful Processes, Lo Seminar, LIPN Paris, 2020.
slides

Recurrent Neural Networks: A Categorical Perspective, University of Calgary, 2019.
slides

Differentiable Causal Computations via Delayed Trace, LICS, 2019.
slides

Neural Nets via Forward State Transformation and Backward Loss Transformation, MFPS, 2019.
slides

Differential Categories, Recurrent Neural Networks, and Machine Learning, SYCO 4, 2019.
slides

The differential calculus of causal functions, ERATO MMSD G0 Seminar, 2019.
slides

Differentiation of causal functions, IU Logic Seminar, 2019.
slides

Rewriting dataflow diagrams, TRS 50, 2019.
slides

Differentiation of stateful functions, ERATO MMSD Colloquium, 2019.
slides

Fibrational Bisimulations and Quantitative Reasoning, CMCS, 2018.
slides

Differentiation of stateful functions, Shonan #109: Diagrammatic Methods, 2018.
slides

Behavioural equivalence in coalgebras of finitary set functors, AMS Sectional Meeting, 2017.
slides

Parametrized coinduction for logics, CALCO, 2017.
slides

Bisimulation and Precongruence, ERATO MMSD Colloquium, 2017.
slides

Upto techniques in metric spaces, Shonan #97: Enhanced coinduction, 2017.
slides

A complete logic for behavioural equivalence in coalgebras of finitary set functors, CMCS, 2016.
slides

A logic of Laurent streams, Graduate Student Logic Conference, 2015.
slides

Projections of stream convolution products and a proof of Christol’s Theorem, IU Logic Seminar, 2015.
slides

Linearization of Automatic Arrays and Weave Specifications, MFPS, 2013.
slides