Call for Participation -- Applied Category School 2019

Call for Participation -- Applied Category School 2019

[Daniel Cicala]

  CALL FOR PARTICIPATION -- APPLIED CATEGORY THEORY 2019 SCHOOL
Oxford, UK. 2019 July 22 – 26

Dear scientists, mathematicians, linguists, philosophers, and hackers,

        We are writing to let you know about a fantastic opportunity to
learn about the emerging interdisciplinary field of applied category theory
from some of its leading researchers at the ACT2019 School.   It will begin
in January 2019 and culminate in a meeting in Oxford, July 22-26.
       Applied category theory is a topic of interest for a growing
community of researchers, interested in studying systems of all sorts using
category-theoretic tools.  These systems are found in the natural sciences
and social sciences, as well as in computer science, linguistics, and
engineering. The background and experience of our community’s members are
as varied as the systems being studied.
       The goal of the ACT2019 School is to help grow this community by
pairing ambitious young researchers together with established researchers
in order to work on questions, problems, and conjectures in applied
category theory.

WHO SHOULD APPLY?
       Anyone from anywhere who is interested in applying category-theoretic
methods to problems outside of pure mathematics. This is emphatically not
restricted to math students, but one should be comfortable working with
mathematics. Knowledge of basic category-theoretic language—the definition
of monoidal category for example— is encouraged.
       We will consider advanced undergraduates, Ph.D. students, and
post-docs. We ask that you commit to the full program as laid out
below. Instructions
on how to apply can be found below the research topic descriptions.

SENIOR RESEARCH MENTORS AND THEIR TOPICS
       Below is a list of the senior researchers, each of whom describes a
research project that their team will pursue, as well as the background
reading that will be studied between now and July 2019.

Miriam Backens

-- Title: Simplifying quantum circuits using the ZX-calculus

-- Description: The ZX-calculus is a graphical calculus based on the
category-theoretical formulation of quantum mechanics.  A complete set of
graphical rewrite rules is known for the ZX-calculus, but not for quantum
circuits over any universal gate set.  In this project, we aim to develop
new strategies for using the ZX-calculus to simplify quantum circuits.

-- Background reading:

     1. Matthes Amy, Jianxin Chen, Neil Ross. A finite presentation of
CNOT-Dihedral operators. https://arxiv.org/abs/1701.00140

     2. Miriam Backens. The ZX-calculus is complete for stabiliser quantum
mechanics.  <https://arxiv.org/abs/1307.7025>
https://arxiv.org/abs/1307.7025


Tobias Fritz

-- Title: Partial evaluations, the bar construction, and second-order
stochastic dominance
-- Description: We all know that 2+2+1+1 evaluates to 6. A less familiar
notion is that it can *partially evaluate* to 5+1.  In this project, we aim
to study the compositional structure of partial evaluation in terms of
monads and the bar construction and see what this has to do with financial
risk via second-order stochastic dominance.

-- Background reading:
     1. Tobias Fritz, Paolo Perrone. Monads, partial evaluations, and
rewriting.
https://arxiv.org/abs/1810.06037

     2. Maria Manuel Clementino, Dirk Hofmann, George Janelidze. The monads
of classical algebra are seldom weakly cartesian.
https://link.springer.com/article/10.1007/s40062-013-0063-2

     3. Todd Trimble. On the bar construction.
https://golem.ph.utexas.edu/category/2007/05/on_the_bar_construction.html


Pieter Hofstra

-- Title: Complexity classes, computation, and Turing categories

-- Description: Turing categories form a categorical setting for studying
computability without bias towards any particular model of computation. It
is not currently clear, however, that Turing categories are useful to study
practical aspects of computation such as complexity. This project revolves
around the systematic study of step-based computation in the form of
stack-machines, the resulting Turing categories, and complexity classes.
This will involve a study of the interplay between traced monoidal
structure and computation. We will explore the idea of stack machines qua
programming languages, investigate the expressive power, and tie this to
complexity theory. We will also consider questions such as the following:
can we characterize Turing categories arising from stack machines? Is there
an initial such category? How does this structure relate to other
categorical structures associated with computability?

-- Background reading:

     1. J.R.B. Cockett, P.J.W. Hofstra. Introduction to Turing categories.
https://www.sciencedirect.com/science/article/pii/S0168007208000948

     2.  J.R.B. Cockett, P.J.W. Hofstra, P. Hrubes. Total maps of Turing
categories.
https://www.sciencedirect.com/science/article/pii/S1571066114000759

     3. A. Joyal, R. Street, D. Verity. Traced monoidal categories.
https://pdfs.semanticscholar.org/c232/37a187d026b8130d98c09187b8ba4f611c40.pdf


Bartosz Milewski

-- Title: Traversal optics and profunctors

-- Description: In functional programming, optics are ways to zoom into a
specific part of a given data type and mutate it.  Optics come in many
flavors such as lenses and prisms and there is a well-studied categorical
viewpoint, known as profunctor optics.  Of all the optic types, only the
traversal has resisted a derivation from first principles into a profunctor
description. This project aims to do just this.

-- Background reading:

     1. Bartosz Milewski. Profunctor optics, categorical View.
https://bartoszmilewski.com/2017/07/07/profunctor-optics-the-categorical-view/
     2. Craig Pastro, Ross Street. Doubles for monoidal categories.
https://arxiv.org/abs/0711.1859


Mehrnoosh Sadrzadeh

-- Title: Formal and experimental methods to reason about dialogue and
discourse using categorical models of vector spaces

-- Description: Distributional semantics argues that meanings of words can
be represented by the frequency of their co-occurrences in context. A model
extending distributional semantics from words to sentences has a
categorical interpretation via Lambek's syntactic calculus or pregroups. In
this project, we intend to further extend this model to reason about
dialogue and discourse utterances where people interrupt each other, there
are references that need to be resolved, disfluencies, pauses, and
corrections. Additionally, we would like to design experiments and run toy
models to verify predictions of the developed models.

-- Background reading:

     1. Gerhard Jager.  A multi-modal analysis of anaphora and ellipsis.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.7214

     2. Matthew Purver, Ronnie Cann, Ruth Kempson. Grammars as parsers: Meeting
the dialogue challenge.
http://www.eecs.qmul.ac.uk/~mpurver/papers/purver-et-al06rolc.pdf


David Spivak

-- Title: Toward a mathematical foundation for autopoiesis

-- Description: An autopoietic organization—anything from a living animal
to a political party to a football team—is a system that is responsible for
adapting and changing itself, so as to persist as events unfold. We want to
develop mathematical abstractions that are suitable to found a scientific
study of autopoietic organizations. To do this, we’ll begin by using
behavioral mereology and graphical logic to frame a discussion of
autopoiesis, most of all what it is and how it can be best conceived. We do
not expect to complete this ambitious objective; we hope only to make
progress toward it.

-- Background reading:

     1. Fong, Myers, Spivak. Behavioral mereology.
https://arxiv.org/abs/1811.00420

     2. Fong, Spivak. Graphical regular logic.
http://arxiv.org/abs/1812.05765
     3. Luhmann. Organization and Decision, CUP. (Preface)


SCHOOL STRUCTURE
       All of the participants will be divided up into groups corresponding
to the projects.  A group will consist of several students, a senior
researcher, and a TA. Between January and June, we will have a reading
course devoted to building the background necessary to meaningfully
participate in the projects. Specifically, two weeks are devoted to each
paper from the reading list. During this two week period, everybody will
read the paper and contribute to a discussion in a private online chat
forum.  There will be a TA serving as a domain expert and moderating this
discussion. In the middle of the two week period, the group corresponding
to the paper will give a presentation via video conference. At the end of
the two week period, this group will compose a blog entry on this
background reading that will be posted to the n-category cafe.
       After all of the papers have been presented, there will be a two-week
visit to Oxford University from 15 – 26 July 2019.  The second week  is
solely for participants of the ACT2019 School. Groups will work together on
research projects, led by the senior researchers.
       The first week of this visit is the ACT2019 Conference, where the
wider applied category theory community will arrive to share new ideas and
results. It is not part of the school, but there is a great deal of overlap
and participation is very much encouraged. The school should prepare
students to be able to follow the conference presentations to a reasonable
degree.

HOW TO APPLY
     The application due date is 30 January 2019. To apply please send the
following to act2019school@gmail.com


-- Your CV

-- A document with:

-- An explanation of any relevant background you have in category theory or
any of the specific projects areas

-- The date you completed or expect to complete your Ph.D. and a
one-sentence summary of its subject matter.

-- Order of project preference

-- To what extent can you commit to coming to Oxford (availability of
funding is uncertain at this time)

-- A brief statement (~300 words) on why you are interested in the ACT2019
School. Some prompts:

-- how can this school contribute to your research goals?

-- how can this school help in your career?


     Also, have sent on your behalf to act2019school@gmail.com a brief
letter of recommendation confirming any of the following:

-- your background

-- ACT2019 School's relevance to your research/career

-- your research experience


QUESTIONS?
       For more information, contact either

- - Daniel Cicala. cicala (at) math (dot) ucr (dot) edu

-- Jules Hedges. julian (dot) hedges (at) cs (dot) ox (dot) ac (dot) uk


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]