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Stream: community: our work

Topic: Nicolas Blanco

Nicolas Blanco (Apr 23 2021 at 20:03):

I love this idea of sharing what we are doing. I will have a go.
Right now my main focus is to:

• Find a (hopefully interesting) story to structure my thesis around. It will most likely be to perform the following strategy on different examples:
  • To choose a (fragment of a) logic
  • To identify a sequent calculus for it where all the structural rules are encoded in the shape of the sequents (without mentioning any connective)
  • To define a generalised structure (multicategory/polycategory) that has morphisms of the same shape
  • To get a notion of representable objects/universal properties that captures the connectives/logical rules
  • To prove that such a structure with all the representable objects is equivalent to the usual categorical models of the logic
  • (optionally) To show that the universal properties are in fact specific fibrational properties

I am trying to make this intuition more convincing by:

• Writing down the details of well-known cases:
  • Intuitionistic multiplicative linear logic -> symmetric multicategories -> symmetric monoidal closed categories
  • Intuitionistic logic -> symmetric cartesian multicategories -> cartesian closed categories
• Clean up the MFPS paper with Noam Zeilberger on
  • Classical multiplicative linear logic -> symmetric polycategories -> *-autonomous categories (the original part is really the fibrational perspective here)
• Testing this on a new example inspired by some recent work by Christine Tasson and Martin Hyland
  • Linear-non-linear logic -> LNL-multicategory -> LNL-adjunction
• Wondering if something similar could be done for some notion of polarised/focused logic

Other things that I need to do

• Preparing my semestrial thesis group report/meeting
• Potentially submitting on the non-proceeding track of some conference(s)
• Starting to think about organising the future (graduation early 2022 hopefully): writing up process, listing potential external jury members, informing myself about postdocs/jobs...
• Preparing my talk about categorical semantics of linear logic at our PhD seminar on Monday

John Baez (Apr 23 2021 at 22:43):

Sounds like good stuff! Where are you, and whom are you working with?

Nicolas Blanco (Apr 23 2021 at 23:09):

Thanks! I am a PhD student at the uni of Birmingham although I am currently living in Paris. My supervisors are Noam Zeilberger and Paul Levy. I also started to collaborate with Alexander Gietelink Oldenziel, who will start a PhD will Paul-André Melliès soon.

Mike Shulman (Apr 23 2021 at 23:20):

I've also been thinking recently about LNL-multicategories (and LNL-polycategories). Maybe we can chat about them sometime.

Nicolas Blanco (Apr 23 2021 at 23:31):

@Mike Shulman I would love to! LNL-polycategories was also something I wanted to consider at some point. I am a PhD student so I always have something to do while simultaneously always being available for having a chat about research! Let me know when you have any availability.