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Stream: community: our work

Topic: Ralph Sarkis

Ralph Sarkis (Mar 07 2021 at 16:32):

It won't be very long because I am a very young researcher but here's what I am working on.

1. I am working with monads and distributive laws to model the combination of non-determinism, probability and termination as quantitative algebraic effects (in the sense of Mardare, Panangaden and Plotkin - LICS2016) --- in an internship with Daniela Petrişan.
2. I am in the middle of my PhD applications.
3. I take part in a reading group on topos theory, we are reading Generic Figures and Their Glueings. This is a lot of fun, so I might want to start another group soon.

John Baez (Mar 07 2021 at 22:52):

Who wrote Generic Figures and Their Glueings?

Robert Seely (Mar 07 2021 at 23:02):

Marie and Gonzalo Reyes and Houman Zolfaghari ... the book itself is available online (just use Google).

Evan Patterson (Mar 07 2021 at 23:13):

One thing I like a lot about that book is that it works many concrete examples of topos-theoretic constructions, in the setting of presheaf categories where you can really calculate things. The running examples include sets, graphs, reflexive graphs, and discrete dynamic systems (or "evolutive sets," as the authors call them).

Fawzi Hreiki (Mar 07 2021 at 23:18):

Its a really nice book but I wish they had discussed that $PSh(C)$ is the free cocompletion of $C$. I feel like that fact is what justifies the 'generic figures' perspective.

Ralph Sarkis (Jun 25 2021 at 14:47):

Update for the end of my internship.

1. My internship with Daniela Petrişan resulted in this preprint (among other results).
2. I am currently preparing an oral presentation on this internship to complete my masters.
3. When I am done with 2, I will try to do a bit less maths and enjoy the last real summer holiday I will have for a long time (I am starting my PhD in September). Spoiler: I will probably not succeed.
4. I am still thinking about this question and the link with Dusko's recommended readings.
5. I am updating my lecture notes for an introduction course on category theory I want to give in September.

Tom Hirschowitz (Jun 26 2021 at 12:14):

So you'll be in Lyon, right?

Ralph Sarkis (Jun 26 2021 at 12:20):

Yes, working with Matteo Mio.

Ralph Sarkis (Oct 07 2021 at 08:54):

Update after a great first month of PhD.

1. I am working on quantitative equational logic and variants with Matteo Mio and Valeria Vignudelli.
2. I am working on semifree monads (defined here) with Aloïs Rosset.
3. I am preparing a talk for RAMiCS in November on the results mentioned here. I have given a talk to my team in Lyon and have received a lot of feedback that I will implement for RAMiCS. I will probably write a preprint before the talk.
4. I am teaching (well, for now, I am helping masters students teach) a category theory course to students in Lyon. I have made my notes available for them, so here they are. There are still lots of holes to fill and a big polishing step, but I am expecting to have a finished book by the end of next year.
5. I am part of this reading group on Sheaves in Geometry and Logic. We have only just started, so you can easily join if you are interested.

Leopold Schlicht (Oct 07 2021 at 17:24):

That's impressive! How do you manage to do that much?

Ralph Sarkis (Oct 07 2021 at 18:58):

I don't think I am being very productive on all fronts. I like to have many different projects so that whenever I lose focus on one, I can try to think about the others. Only 4 and 5 have real timing requirements so I can work on the first three at my own pace.

Ralph Sarkis (Jan 25 2022 at 11:05):

Update after a great first semester of PhD.

1. I have just submitted a paper on quantitative algebraic reasoning with Matteo Mio and Valeria Vignudelli. I am bit exhausted from the obligatory pre-submission rush, so I'll discuss this with you a bit later.
2. Project 2 and 3 from last time are stalled, but I'll try to revive them soon.
3. I am crossing my fingers for the ACT adjoint school, Fillipo Bonchi's project is in the perfect direction towards my dream thesis.
4. My category theory course last semester was great. I didn't end up teaching too much because I let younger students teach, but I enjoyed helping them prepare lectures, and we still covered the contents (up to Yoneda) of my book. I had very good feedback on the book, and also lots of ideas of new things to add.
5. I am a TA for a semantics class this semester. Not as cool as teaching a full course, but still very enjoyable.

Ivan Di Liberti (Jan 25 2022 at 12:14):

Ralph Sarkis said:

Update after a great first semester of PhD.

1. I have just submitted a paper on quantitative algebraic reasoning with Matteo Mio and Valeria Vignudelli. I am bit exhausted from the obligatory pre-submission rush, so I'll discuss this with you a bit later.
2. Project 2 and 3 from last time are stalled, but I'll try to revive them soon.
3. I am crossing my fingers for the ACT adjoint school, Fillipo Bonchi's project is in the perfect direction towards my dream thesis.
4. My category theory course last semester was great. I didn't end up teaching too much because I let younger students teach, but I enjoyed helping them prepare lectures, and we still covered the contents (up to Yoneda) of my book. I had very good feedback on the book, and also lots of ideas of new things to add.
5. I am a TA for a semantics class this semester. Not as cool as teaching a full course, but still very enjoyable.

Hi Ralph, your work seems intriguing to me. I wonder whether you took into consideration Rosicky's work on metric monads and what would be the link between the two.

Ralph Sarkis (Jan 25 2022 at 12:53):

I have read this paper and this other related paper, but I am not comfortable with enriched categories, locally presentable categories and accessible categories, so I don't understand every detail. From my understanding, the solution we crafted to talk about operations which are not nonexpansive (see Second extension axis in the introduction) is not something either paper can deal with. That was my main motivation for writing this paper, every thing I read on (categorical) universal algebras deals with operations of type $X^n \to X$ or $[n,X] \to X$, where the product or function space is constructed categorically, i.e.: with the categorical product or its adjoint.

Now, our solution is to almost take a product (we take a lifting of the product) as the domain of the operation. It turns out, as our paper shows, this still leads to a nice theory (very close to Mardare et al.'s approach).

In order to really understand the link between our paper and Rosicky's, I would like to extend our solution to lift the function space too (i.e. have more general arities as in Ford et al.'s paper), and translate our work to the categorical language used in Rosicky's paper (the Lawvere-Linton way of doing universal algebra). I don't see how to do this right now, but I am looking for solutions, and I wanted to ask here at some point for some help.

Ivan Di Liberti (Jan 25 2022 at 12:56):

Ralph Sarkis said:

I have read this paper and this other related paper, but I am not comfortable with enriched categories, locally presentable categories and accessible categories, so I don't understand every detail. From my understanding, the solution we crafted to talk about operations which are not nonexpansive (see Second extension axis in the introduction) is not something either paper can deal with. That was my main motivation for writing this paper, every thing I read on (categorical) universal algebras deals with operations of type $X^n \to X$ or $[n,X] \to X$, where the product or function space is constructed categorically, i.e.: with the categorical product or its adjoint.

Now, our solution is to almost take a product (we take a lifting of the product) as the domain of the operation. It turns out, as our paper shows, this still leads to a nice theory (very close to Mardare et al.'s approach).

In order to really understand the link between our paper and Rosicky's, I would like to extend our solution to lift the function space too (i.e. have more general arities as in Ford et al.'s paper), and translate our work to the categorical language used in Rosicky's paper (the Lawvere-Linton way of doing universal algebra). I don't see how to do this right now, but I am looking for solutions, and I wanted to ask here at some point for some help.

Thanks Ralph. I also told Jiri about your work, I think that's a quite cool development.

Ralph Sarkis (Jan 25 2022 at 13:11):

That's awesome to hear!

Ralph Sarkis (Apr 17 2022 at 13:07):

Quick update.

1. My paper with Matteo Mio and Valeria Vignudelli was accepted at LICS 2022, I am implementing the reviewers' suggestions.
2. I was accepted at the adjoint school, so I have been working on this (on Fillipo Bonchi's project), and I am excited to go to Glasgow in July.
3. Next week, I am supervising an internship with a high school student. I will try to work with them on the graphical syntax for logic I discovered in Christian Williams' talk. I have no idea what to expect, but I think we will have fun anyways.
4. Next month, I am giving a talk for my whole CS department on diagrammatic reasoning. I am preparing some slides, and I even prepared a thumbnail respecting the codes of YouTube (see below).
5. If nothing goes wrong :fingers_crossed:, I should be going to Montréal for a whole semester starting in August to work on quantitative algebraic reasoning with Prakash Panangaden.
   .
   

John Baez (Apr 17 2022 at 14:28):

Great! Let us know how it goes with that high school student. Good luck on your trip to Montreal. Prakash is a great guy. If nothing goes wrong I'll see you at ACT2022 in Glasgow.

Christian Williams (Apr 17 2022 at 20:56):

great! I'm glad you're trying it out - yes, let us know how it goes, and I'm available if you want to discuss any ideas.

Ralph Sarkis (May 07 2022 at 16:47):

I am getting back to you (especially @Christian Williams and @John Baez) on my internship.

I spent 4 days with a high school student (16 years old) trying to show him what research in maths/cs is. Out of those 4 days, around 1.5 days was spent on discovering the 2-dimensional syntax for relations described in Christian's talk. Every time I introduced a new piece of syntax, we spent a lot of time finding examples and asking simple questions before moving on, and by the end of the week, we were able to cover relations, composition of relations, implications, vertical and horizontal composition of implications. I am not sure what to think of the end result. On the one hand, he and I had fun exploring these ideas and I believe the graphical syntax definitely helped him throughout our work. On the other hand, on the last day, he was supposed to prepare a quick explanation of what he did during the week to share with other students who did a similar internship, but he told me he was not confident enough in his understanding of relations, so we switched to a more concrete subject.

Let me give a bit more details. It was really hard for him to find examples and questions by himself. I think the main problem is that he is not used to abstract reasoning, and I think I was bad at pointing out the relevant patterns. For instance, whenever we dealt with composition of two relations, he had to draw the points in the colors and links between them before understanding (that's I think the main good point about the syntax: the points and links picture for a relation embeds well in the syntax). This was easier when dealing with relations between a set and itself, in particular, familial relationships (dad, cousin, grandparent, etc.) between humans and the usual orders on integers. I found he was not very enthusiastic about our findings, so I'd like to look for better examples of things to prove (for me, the best thing we have proved is that if a relation is reflexive, then it is dense, we had lots of examples of dense and non-dense relations and we figured out all dense ones were reflexive, so we showed the implication (very easily) graphically).

TLDR: Teaching relations to a high school student is very hard, but I believe it is less hard when using a graphical syntax.

John Baez (May 07 2022 at 17:24):

Thanks for the report! Teaching is always hard, and it's harder when you're teaching something new... but it sounds like you both had fun and discovered interesting things.

Christian Williams (May 09 2022 at 17:04):

Thanks Ralph, this is interesting. Could you share some implications and composites that the student made?

Christian Williams (May 09 2022 at 17:06):

also, above it looks like you posted a screenshot of a video you made, but I'm having trouble finding the link.

Ralph Sarkis (May 10 2022 at 15:17):

We made lots of compositions with familial relations:

• sibling of sibling is sibling, but cousin of cousin is not cousin.
• father of father is paternal grandfather, father of parent is grandfather.
• father implies parent and father implies father so we get paternal grandfather implies grandfather.
• we looked at the chart of nth cousin nth removed and did a few of them.

We had person allergic to ingredient and ingredient inside recipe implies person shouldn't try this recipe.

When I tried doing more abstract things we looked at the empty, identity and full relation on a set, and we saw how they compose with each other and with an arbitrary relation.

Ralph Sarkis (May 10 2022 at 15:20):

Christian Williams said:

also, above it looks like you posted a screenshot of a video you made, but I'm having trouble finding the link.

This is not a video (the progress bar is from the screenshot I made of the Rick and Morty scene), it is the thumbnail for a (in person) talk I am giving next week.

Christian Williams (May 10 2022 at 16:26):

Okay, nice. Did you compose implications, in sequence and/or in parallel?

Ralph Sarkis (May 10 2022 at 20:42):

Not that much, that was the last thing we did and I don't remember the examples we came up with.

Ralph Sarkis (Nov 10 2022 at 13:44):

Update.

1. I am in Montréal right now visiting Prakash Panangaden. It's fun being back here, and Prakash has so much to teach me. We are not making as much progress as I expected, but I am in no rush.
2. In meetings with Prakash, he told me that McGill has historically been very hostile to category theory (even if they had several stars who held lots of seminars in Montréal), and that is probably why the team didn't get renewed. As revenge, I have been introducing diagrammatic reasoning to anyone that would listen. I had good discussions when giving this talk a couple of times.
3. I participate in biweekly discussions on pedagogy in mathematics organized by Rosalie Bélanger-Rioux. It's quite informative and it confirms my slight preference of teaching over research.
4. I am trying to accelerate my progress on my category theory notes/book, because I am thinking of putting a first finished version in the appendix of my thesis, so I can link to definitions/results/notation from it using the knowledge package.
5. I miss the dynamics of my lab, my office mate, and especially my supervisors in Lyon (we still meet and talk online), but I am trying to make the most of my time alone to figure out what I want to do with my thesis (this is hard!).

Ralph Sarkis (Apr 03 2023 at 08:32):

Update.

1. I got back in Lyon in January, and started working more intensely with my supervisors, which resulted in a paper I am writing right now.
2. I am still meeting with Prakash, but I haven't been able to do what we want to do. In short, we are looking at another distance between probability distributions, and we want to show it leads to a monad lifting of the distribution monad on $\mathbf{Set}$ to a category of metric spaces.
3. I was TAing for two classes this semester Semantics and Verification and Proofs and Programs. The latter included an intro to CT up to cartesian closed categories (and the Curry-Howard-Lambek correspondence) but without doing a lot with functors and naturality (a bit like Steve Awodey's book). It is always nice to see students improving in categorical thinking throughout the semester.
4. I am going to Prakash's workshop in Barbados in a month. Many people have told me great things about it, and I am especially glad to go since the subject is exactly what my thesis should be about.
5. I am giving my diagrammatic reasoning talk once again, and this will be a warm-up for another research internship with high school student(s) I am doing next week. I plan to try teaching a diagrammatic language of relations again, but I am still not sure if I want to do Christian's version like last time or Bonchi et al's version (similar to graphical linear algebra). I want to keep better notes on what I do this time to better answer your questions.

Ralph Sarkis (Sep 07 2023 at 15:47):

Update for the start of term.

1. I am working on making our latest paper on Universal Quantitative Algebra fit the LMCS page limit to submit there.
2. I am preparing a presentation on this (focusing on section 7) for a seminar in Paris that Marie Kerjean kindly invited me to.
3. I have been working more intensely on the quotient stuff started here with Jean-Baptiste Vienney, but I think we will slow down now and postpone writing the paper for later.
4. I have to start structuring my thesis more carefully. I think I know the big picture of what I want to sell, but the details and some results are still missing from my game plan. My defense is planned for next September, so I believe my manuscript must be done by June.
5. I am organizing the introduction to category theory class this semester. I won't get to teach much (well I teach younger students how to teach the class), but I think I will have at least as much fun as last time (Fall 2021).
6. I did not take the time to write my experience report on the string diagrams internship. For some reasons, it does not feel good to think about writing it, so I haven't. I will probably do one again this year (in winter), but I am also trying to do other mediation activities (in particular, there is an exposition on maths and cooking in the maths/cs museum next to my school which I will get to animate).

Ralph Sarkis (Sep 07 2023 at 17:28):

7. (Had to leave in a hurry) I visited Fabio Zanasi to try to figure out quantitative diagrammatic reasoning. We have some interesting ideas, but not quite convincing still. I will keep thinking about this in case it can fit in my thesis.

Jean-Baptiste Vienney (Sep 08 2023 at 17:41):

What do you mean by quantitative reasoning? Does it have anything to do with graded linear logic?

Ralph Sarkis (Sep 08 2023 at 17:50):

Very briefly, instead of deriving equalities between terms we want to derive distances between terms. It has some interesting subtleties like the fact that the context (variables) may contain quantitative information as well, so the distance between terms depends on the distance between inputs.

Simonas Tutlys (Sep 11 2023 at 08:56):

In the process of reading your paper and it seems very exciting so far.I'm interested in more specific things related to combining fuzziness and logic/algebra/"Theory B".For example,i'm interested in a structure similar to a generic category with product of homsets equipped with some partial fuzzy relation (a metric or mutual information of ouput for example) so instead of strict morphism equality we have a metric that we can optimize.I'm also interested in theretically analyzing (and then using those results in practice) the case of adding a unary fuzzy relation (idk what to call it,too many terms.a statistic?a real-valued function?) to homsets inspired by The Category Theoretic arithmetic of information where generalized axioms are derived from information theory for a function I:Hom(C)->R so that it would be a 'measure of information' and then some really interesting examples are given.I wonder if there would be any interesting relationship between the unary I operator and the binary 'distance' of morphisms if for example both are some information theretic functions,like the connection between kolmogorov and statistical complexity. Basically i'm intrested in quantitative generalized algebraic theories with a special case being categories,mostly the use case being using those structures as a way of knowledge representation and an architectural principle for AI.If there's any papers like that I would love to hear about them.

Also,it feels validating that this whole combination of fuzziness and Theory B stuff is coming back into vogue when I was thinking about it for years :)

Ralph Sarkis (Sep 11 2023 at 09:19):

I haven't thought too much about the multisorted case yet. I am guessing if if you want all the morphisms to form a metric space, it will not be too hard to adapt our results, but making every hom-set a metric space on its own will be more difficult with something like algebraic theories (the hom-sets are dependent types).

Your description made me think of normed or weighted categories which I learned about here.

I believe we are probably rediscovering some things known to the fuzzy logic community, but also probably providing new insights. I witnessed an inspiring discussion about this at a talk given by Radu Mardare on this paper.

Simonas Tutlys (Sep 11 2023 at 09:32):

Generalized algebraic theories are basically dependent types as far as i understand and im interested in exploring fuzzifying commutativity and see what would happen to universal constructions in that case.i have a few intuitions specific to (co)limits but in general i think a strict definition of a universal construction could be seen as a target of optimization for a fuzzy predicate of commutativity. the limit of zero entropy (perfect commutativity/match) would coincide with equality.thanks for the references!

Ralph Sarkis (Oct 30 2023 at 12:35):

Update (to motivate myself).

1. We submitted that paper to LMCS. I was able to remove enough stuff without hurting the paper (even improving it in some places).
2. I gave my talk last month in Paris, and I gave the same talk last week in Chambéry where Tom Hirschowitz kindly invited me. Here are the slides.
3. I have started to write my thesis :partying_face:. In the last month, I have mostly been procrastinating on starting to write, but it was kind of a productive procrastination. Since I have already written 80% of a book on category theory, I want to make it so that whenever I use basic CT notions in my thesis there is a link to the appropriate part of my book. It would be just like the knowledge package except between two pdf files (I will also use knowledge inside my thesis). I only needed to fix the chapter on adjunctions which was not satisfactory to me for a first draft, but I got carried away when writing and added more and more stuff. I didn't start working on making this knowledge links between files work.
4. We have already got a few people confirmed for my defense in September (the most important ones), so I am starting to feel the pressure.
5. The CT class I am teaching to teach is going great. I am very happy with my students, but I don't get to interact too much with my grand-students which is a bit sad.
6. I have been trained for the various mediation activities I will do this semester. They start in November and I am very excited (also scared I won't like working with a class of younger (high school) students).

Jean-Baptiste Vienney (Oct 30 2023 at 14:31):

I like that you feel the need to write a book on category theory rather than doing only research :sweat_smile:

Jean-Baptiste Vienney (Oct 30 2023 at 14:35):

Very cool that you want to link every basic notion to the definition in your book. Looks like a quite futuristic way to present math. I mean it's like on the wikis, but implementing at the level of research is very nice because it's supposed to make the material accesible to anyone with enough motivation

Ralph Sarkis (Oct 30 2023 at 16:10):

Thanks for the validating kind words Jean-Baptiste :smiling_face_with_hearts:

Patrick Nicodemus (Oct 30 2023 at 16:22):

Ralph I mentioned this recently on another thread but I have recently discovered and started using a LaTeX package called "Semantic Tex" or sTeX which I use to add nice markup to mathematical documents (hyperlinks between definitions)
It facilitates breaking up a long document like a book into many small pieces which can be assembled together, in a more sophisticated way than just using \input or \include, in the sense that cross-references still work right between different files.
You can also reuse pieces more easily (a long definition you want to include somewhere else with the same notation)
And it exports to html in a fairly readable way, they have a simple webserver app that they supply with the semantic tex package that basically turns your paper or book into an interlinked wiki with things split up / arranged the same way you arrange your tex files.

Patrick Nicodemus (Oct 30 2023 at 16:24):

It's not perfect, it's a research project under continuing evolution. There are new features being added regularly and they don't always work right. But the core features of the library that have been there for a whlie work.

Ralph Sarkis (Jan 11 2024 at 09:01):

Update (before the start of term).

1. I think I am writing my thesis at an ok pace, not quick but not slow either. Here is a draft of the second chapter on "generalized metric spaces" which is closest to being done. It is missing a lot of english like the introduction and stuff betwen definitions and results, but should be readable on its own (I really enjoyed coming up with examples).
2. I quickly gave up on using the knowledge package between two files because I realized it would probably be very hard to make it work with hovering (some pdf viewers allow you to hover a link and display a small excerpt of the destination without clicking it). So now my appendix will contain a whole intro to CT book.
3. My jury is confirmed, modulo unexpected cirucmstances, for the last week of August/first week of July, which means I should finish my manuscript in May.
4. This semester I am a TA for a course on Proofs and Programs and a course on Semantics and Verification, should be fun as always.
5. I am enjoying the mediation activities I am doing at the math museum, and I will keep doing it (about one or two half-days a month).

Ralph Sarkis (Feb 18 2024 at 17:00):

Update.

1. I set myself some deadlines throughout the semester to keep track of my progress on writing the thesis. I was supposed to finish the two background chapters on Feb 15, but I am already late... Here they are, 90% done I would say, but I was pretty slow this last month for some personal reasons (I think, it is hard to pinpoint what makes my motivation levels change). I will move on to writing the main results now which (according to my next deadline) should take me a month.
2. The courses I am TAing for are taking a bit more time than I would like, but I am still having fun.
3. I have some possibly good news for a post-doc.
4. I have been doing a very little bit of actual research with my supervisors Matteo and Valeria as well as Paolo Pistone who joined our group recently.
5. Still enjoying the mediation stuff. I also had lots of fun participating in some kind of hackathon to create new activities (the ones I am animating right now were created by other people). I will also host an internship with two high school students in April, I will probably show them a diagrammatic language for relations like the previous two years.

David Egolf (Feb 18 2024 at 20:24):

I love it when people include a lot of examples and explanations at the start of their thesis. I think introductory chapters like that can be a great stand-alone resource, while also facilitating easier understanding of the main results. What you have already looks useful and interesting to me, so I've saved a copy for my future reference! :smile:

Ralph Sarkis (Feb 18 2024 at 20:35):

🙏🏼 I did try to write both chapters independent of each other and of the thesis, and the 10% missing is mostly about making that even more true. I am also planning to have a chapter devoted to examples/applications of our work, but that will inevitably require reading (at least skimming) the main chapter.

Ralph Sarkis (Mar 20 2024 at 21:10):

Update.

1. I had a (self-assigned) deadline on March 15th to finish writing the third chapter on the main results, and today I just finished writing the bare minimum :grimacing: I reviewed a paper and I had a 2-day workshop, so let's say I am late because of that. I wanted to spend the next couple of weeks on the "applications" chapter, but I think I will instead spend it on polishing chapters 1-3 to make better use of the kindness of my supervisors who agreed to read a first draft (I believe feedback on stuff that is almost done is more impactful). After that, I will do as much as I can on "applications", and write the introduction and conclusion. My official deadline is May 15th, and my viva is on September 3rd.
2. My courses are less time-consuming these days, and they will be done in a couple of weeks. I think the quality of my tutorials this year has been quite low because I didn't put enough time into them.
3. Even better news for a post-doc (still not 100%).
4. Every Monday I spend a very fun day in an office with my supervisors and Paolo Pistone doing research. I put almost 0 time on that the rest of the week.
5. I still love doing the mediation stuff and the people I do the mediation stuff with. Although I am afraid the internship in April I am hosting will make me even more late...

Ralph Sarkis (Apr 18 2024 at 16:01):

Update.

1. Last week, I finished the main body of the thesis which now consists of only 3 chapters (because I will not have time to write chapters 4 and 5...). I will now start to write the introduction, conclusion and abstract. In parallel, my supervisors are reading the main body and they will give me feedback when they are done.
2. Last Friday, I saw my supervisor Matteo do what is essentially a grown-up version of my thesis defense in September (it is a French thing called HDR which allows him to officially supervise PhD students). I had a good time talking with the members of the jury, especially Ana Sokolova, about maths and not maths.
3. My courses are done! Research is at a halt probably until I am done writing my thesis.
4. This week, I took a "break" from writing the thesis as I had two high school (16yo) interns with me. We studied the string diagrammatic syntax for relations (Figure 2 here) and proofs by induction. I will not promise to write-up a report this time, but I can answer any question you may have, the soonest the better (so I remember stuff more vividly). A brief summary: it was very fun again, we did relations, then compositions, then identities, then implications, then parallel compositions (monoidal products), we explained some of the axioms of Figure 2 in loc. cit. and discussed lots of examples. Then, we did some proofs by induction for the standard series, 1+...+ n, 1² + ...+ n², and so on to explain induction, and we combined it with diagrammatic reasoning to do all the proofs in this post of GLA.
5. Oh, and I decided to use the following title for my thesis: Lifting Algebraic Reasoning to Generalized Metric Spaces. Hopefully it follows John Baez's advice. (I had another shorter/punchier but overzealous title.)

Jean-Baptiste Vienney (May 01 2024 at 02:32):

The paper that you link in 4. looks so cool! I remember that Nathan Haydon made a talk about the calculus of relations of Peirce (from 1897!) at FMCS 2022 which was more like a philosophy talk (he talked about the history of this calculus in the work of Peirce if I remember correctly) and Paweł Sobociński seemed not very convinced about this stuff because the talk wasn't like an usual math talk. This is so cool that they ended writing a paper together (and with the two other authors) improving this mysterious calculus of Peirce into a graphical language for first-order logic! By the way for the anecdote the slides of Nathan from summer 2022 are here.

Jean-Baptiste Vienney (May 01 2024 at 02:45):

Well, they had already written a paper together in 2020 so it seems my psychological skills are not very good :sweat_smile:. Anyway, I love this paper.

Jean-Baptiste Vienney (May 01 2024 at 02:52):

In fact it looks like Pawel is the supervisor of Nathan. Perhaps that why he was talking to him in a critical way :sweat_smile: Sorry, now I stop poluting your thread.

Ralph Sarkis (May 01 2024 at 04:47):

Filippo Bonchi is scheduled to talk about this for Topos tomorrow.

Jean-Baptiste Vienney (May 01 2024 at 07:02):

Thanks! I was scared I could not attend the talk because I'll be travelling from Ottawa to my parents near Bayonne in France tomorrow, but it looks like the talk will start just one hour after I'll arrive at their home. I hope they will not be angry at me if I go away some time to listen to the talk :)

Ralph Sarkis (May 01 2024 at 07:19):

:joy: I think it will be available on YouTube after it is livestreamed.

Jean-Baptiste Vienney (May 01 2024 at 07:24):

Yes, that's the other option :joy:

Ralph Sarkis (May 11 2024 at 11:18):

Update.

1. I am done. All in all, I really enjoyed writing this, although I would have liked 2-3 more years to work on it and make it :sparkles: perfect :sparkles:.
2. I will now start doing research again, maybe go to ACT+MFPS in Oxford, figure out how to move to London for my postdoc, and take some holidays.
3. My defense is in September, so I will prepare for that in August. Hopefully, I will be a doctor for the next update.