# Priyaa Varshinee Srinivasan

I am a compassionate mathematician working as a post-doctoral researcher at the Tallinn University of Technology, Estonia. Along with research in category theory, I am interested in creating pathways to make math communication user-friendly and approachable – from math in school to mathematical research. I derive inspiration from the works of Tai Danae Bradley, Eugenia Cheng, John Baez, Pawel Sobocinski, Bob Coecke, David Spivak and many others in this area. My research experience includes categorical quantum mechanics, linearly distributive categories and currently polynomial functors.

I completed my Ph.D. under the supervision of Prof. Robin Cockett at University of Calgary. My PhD thesis was at the crossroads of computer science, mathematics and quantum theory and in an inter-disciplinary field called categorical quantum mechanics. Details on my thesis projects can be found in this page.

I am broadly interested in the interaction of concurrency and quantum computing. Details on a few of my projects are availabe in this page.

## Career Timeline

2023 - Present Postdoctoral Fellow Tallinn University of Technology, Estonia (Sep '24 - Present)

2023 - 2024 Postdoctoral Fellow Topos Institute, Berkeley, USA (Aug '23 - Jul '24)

2022 - 2023 International Research Associate National Institute of Standards and Technology, USA (Jan '22 - Jul '23)

2021 Sessional Lecturer University of British Columbia, Canada (Sep - Dec)

2015 - 2021 Ph.D. in Computer Science University of Calgary, Canada (supervised by Prof. Robin Cockett)

2012 - 2014 Masters of Mathematics in Computer Science University of Waterloo, Canada (supervised by Prof. Martin Karsten)

2009 - 2012 Software Engineer II Hewlett Packard India Software Operations, India

2005 - 2009 Bachelors in Computer Science Engineering Madras Institute of Technology, India

I am interested in communicating mathematics inclusively & accessibly. Below are a few materials based on my talks.

## Message passing logic

Linear actegories are a formal diagrammatic framework for reasoning about concurrent message passing systems. They are developed by Cockett and Pastro in 2009 in their paper Message passing logic. This talk explains the motivation and structure of the logic, linear actegories and a toy model.

## Dagger linear logic

Categorical quantum mechanics applies methods for category theory to develop a diagrammatic reasoning formalism for quantum processes. In my thesis, we extended the exisiting formalism from monoidal to linearly distributive categories (LDCs). These talks introduces LDCs and my thesis work.

## Blog series

The aim of this blog series is to provide an accessible, intuitive introduction to linearly distributive categories, functors, transformations, other associated structures and applications by assimilating information spread across multiple highly technical articles, and to encourage discussion.

## Publications

Author names are arranged alphabetically by their last name which is a standard practice in mathematics literature.

Book

Angeline Aguinaldo, Paul Dancstep, Brendan Fong, and Priyaa Srinivasan, “Relational Thinking: from Abstractions to Applications”. Mar 2024 Online Book

Refereed Journal publications

Robin Cockett, Cole Comfort, and Priyaa Srinivasan. “Dagger linear logic for categorical quantum mechanics”. Logical Methods in Computer Science, 17(5), Nov. 2021 (slides)

Srinivasan Arunachalam, Vlad Gheorghiu, Tomas Jochym-O’Connor, Michele Mosca, and Priyaa Srinivasan. “On the robustness of bucket brigade quantum RAM”. New Journal of Physics, 17(12), 123010, Dec. 2015

Peer-reviewed conference Proceedings

(Distinguished paper) Robin Cockett, Amolak R. Kalra and Priyaa Srinivasan, “Normalizing resistor networks”. To appear in the conference proceedings of 6th International Conference on Applied Category Theory, Maryland, USA, Aug. 2023 (slides)

Robin Cockett, Isabelle Jianing, Carlo Maria Scandolo and Priyaa Srinivasan, “Extending monotones as Kan extensions”. To appear in the conference proceedings of 4th International Conference on Applied Category Theory, Jul. 2022 (slides)

Robin Cockett and Priyaa Srinivasan, “Exponential modalities and complementarity”. Electronic Proceedings in Theoretical Computer Science 372, Proceedings on the 4th International Conference on Applied Category Theory, Cambridge, UK, pp. 207-220, Jul. 2021 (slides)

Robin Cockett, Cole Comfort, and Priyaa Srinivasan, “The category CNOT”. Electronic Proceedings in Theoretical Computer Science 266, Proceedings on 14th International Conference on Quantum Physics and Logic, Nijmegen, Netherlands, pp. 258-293, Jul. 2017

Pre-prints

Robin Cockett, Jean-Simon Pacaud Lemay, and Priyaa Srinivasan, “Drazin Inverses in Categories”. ArXiv:2402.18226 [math.CT] Feb. 2024

Robin Cockett and Priyaa Srinivasan, “Completely positive maps for mixed unitary categories”. ArXiv:1905.08877 [math.CT] Jun. 2019

Thesis

Priyaa Srinivasan, “Dagger linear logic for categorical quantum mechanics”. Doctoral thesis, Department of Computer Science, University of Calgary, Canada, Doctoral thesis, Sep 2021.

Priyaa Srinivasan, “Preserving data locality in applications using message passing”. Master's thesis, David R. Chertion School of Computer Science, University of Waterloo, Canada, Dec 2014.

## Research visits

Visiting researcher Tallinn University of Technology, Estonia May 7 - 11, 2024 hosted by Prof. Pawel Sobocinski

Visiting researcher Tallinn University of Technology, Estonia Feb 6 - 17, 2023 hosted by Prof. Pawel Sobocinski

Mitacs Globallink Research Intern University of Edinburgh, UK Dec 2018 hosted by Prof. Chris Heunen

Mitacs Globallink Research Intern University of Oxford, UK Sep - Nov 2018 hosted by Prof. Bob Coecke

## Invited talks

Communicating relational thinking, Berkeley Seminar, Topos Institute & Relatorium Seminar (online) Sep 2024 video

What kind of linearly distributive categories do Polynomial functors form? 31st Workshop in Foundations Methods in Computer Science, Kanaskis, Canada Jul 2024 slides

Communicating relational thinking 31st Workshop in Foundations Methods in Computer Science, Kananaskis, Canada Jul 2024 slides

Message passing logic Information and Technology Division, National Institute of Standards and Technology, Maryland, USA July 2023

Quantum message passing logic 30th Workshop in Foundations Methods in Computer Science, Sackville, Canada Jun 2023 part1 part2

Dagger linear logic for Categorical Quantum Mechanics Topos Institute, Berkeley, USA Apr 2023

Linearly distributive categories and structures Tallinn University of Technology, Estonia Feb 2023

Dagger linear logic for Categorical Quantum Mechanics 29th Workshop in Foundations Methods in Computer Science, Kananaskis, Canada Jun 2022 part1 part2

Dagger linear logic for Categorical Quantum Mechanics University of Bath, UK (online) Nov 2021

Preserving locality in parallel applications Institute of Quantum Science and Technology, University of Calgary, Canada Oct 2014

Hardware and Software Trend - A Computer Scientist Perspective Centre for Quantum Technologies, National University of Singapore Apr 2014

## Conference talks

Normalizing resistor networks 6th International conference on Applied Category Theory, Maryland, USA Aug 2023 video

Extending monotones as Kan extensions 5th International conference on Applied Category Theory, Glasgow, United Kingdom Jul 2022 video

Exponential modalities and Complementarity 4th International conference on Applied Category Theory, Cambridge, United Kingdom Jun 2021

Complete positivity for mixed unitary categories 16th International conference on Quantum Physics and Logic Jun 2019

Complete positivity for mixed unitary categories 27th Workshop in Foundations Methods in Computer Science, Kananaskis, Canada May 2019

Complete positivity for mixed unitary categories 2nd Symposium on Compositional Structures, Glasgow, United Kingdom Dec 2018

Dagger linear logic for categorical quantum mechanics 1st Symposium on Compositional Structures, Glasgow, United Kingdom Sep 2018

Quantum channels for mixed unitary categories 15th International conference on Quantum Physics and Logic, Halifax, Canada Jun 2018 (poster)

Quantum channels for mixed unitary categories 26th Workshop in Foundations Methods in Computer Science, Ottowa, Canada Jun 2017

Resource reflecting functor and its application to non-uniformity 20th International Conference on Quantum Information Processing, Seattle, USA Jan 2017 (poster)

Structure of quantum information resource theories 25th Workshop in Foundations Methods in Computer Science, Vancouver, Canada Jun 2016

On the Robustness of Bucket Brigade Quantum RAM 19th International Conference on Quantum Information Processing, Banff, Canada Jan 2016 (poster)

On the robustness of bucket brigade quantum RAM Quantum Information Processing and Applications, Allahabad, India Dec 2015 (poster)

On the robustness of bucket brigade quantum RAM 15th Asian Quantum Information Science Conference Aug 2015

## Teaching and Mentorship

Content development and communication Relational Thinking: from Abstractions to Applications Nov - Mar 2024

Lead a pilot project to develop online content on relational thinking (category theory) based on the Algebraic Julia library for STEM-oriented audience interested in applied category theory. The book leverages on illustrations, and live coding to communicate formal concepts intutitively. The goal of the book is not just to teach mathematical but also to explore the hows and whys of mathematical thinking, more specifically, category theory.

Blog posts on the technology and the story-telling style of this book - https://topos.site/blog/2024-06-28-fantastic-book-four-months-i/

Communication Relatorium Seminar series Apr 2024

As a team project at our research group on compassionate mathematics, launched the Relatorium series with the support of the Topos Insititute. The aim of the monthly seminar series is to discuss math and math-related topics that we do not get to hear in traditional math talks. The seminars are designed to be somewhere in between a technical talk and a podcast. The aim is to create a safe space for the speaker to explore new ideas as well as the audience to engage with the speaker, and with one another.

The talks are live-casted YouTube at the Relatorium channel. The talks are also announced at the researchseminars.org.

Research Mentor Adjoint School of 6th International conference on Applied Category Theory Feb - Jul 2023

Project: Message passing logic for categorical quantum mechanics

Teaching Assistants: Rose Kudzman-Blais (University of Ottowa), Amolak Ratan Kalra (University of Waterloo)

Mentees: Brandon Baylor (Systems Engineer, Chevron Corporation), Durgesh Kumar (Senior undergraduate, Asoka University, India), Fabian Wiesner (Ph.D. student, Technische Universität Berlin), Isaiah Hilsenrath (Senior undergraduate, University of Maryland USA), Paige Frederick (Software Engineer, Super.tech)

Sessional Lecturer University of British Columbia, Canada Sep - Dec 2021

CPSC 213 - Introduction to Computer SystemsTeaching Assistant University of Calgary, Canada Jan 2015 - Apr 2021

CPSC 457 – Operating systems for Dr. Jalal Kawash, and Dr. Pavol Federl

CPSC 313 – Computability theory for Dr. Joel Reardon, Dr. Wayne Eberly, and Dr. Renate Scheidler

CPSC 411 – Compiler construction for Dr. Robin Cockett

CPSC 449 – Programming Paradigms for Dr. Robin Cockett

In Winter 2016, I was the Head Teaching Assistant of CPSC 457 and effectively trained fellow teaching assistants in kernel programming.Teaching Assistant University of Waterloo, Canada Sep 2012 - Dec 2014

CS 452 – Real time programming for Dr. Bill Cowan

CS 454 – Computer networks for Dr. Martin Karsten

CS 343 – Concurrent and parallel programming for Dr. Peter Buhr

## Committees

Programme Committee, 7th International Conference on Applied Category Theory, 2024

Member, ITL Diversity Committee, National Institute of Standards and Technology, Feb 2023 - Aug 2023

Sponsorship Chair, 6th International Conference on Applied Category Theory, July 31 - Aug 4, 2023

Co-chair, NIST workshop on Compositional structures for Systems Engineering and Design, Nov 3 - 4, 2022

Co-organizer, 27th Foundational Methods in Computer Science Workshop, May 28 - June 2, 2019