<p>No one knows if there are connections between GoI and GCT. </p>

<p>It's quite plausible, since both are used to analyze complexity, and since GoI is formulated in terms of monoidal categories and GCT is based on representation theory. However, to my knowledge there aren't any researchers who understand both well enough to say for certain.  </p>

CC BY-SA 3.0
2015-05-12T08:42:50.520Z
I definitely agree.  I know nobody who understands both well enough to be able to tell whether there is a connection or not.  In fact, I'd be surprised to meet a GCT expert who has even heard about the GoI.  People of the opposite kind exist, Neel and I are examples (I can consider myself a GoI expert vaguely knowing what GCT is about).  In any case, we won't be able to do much more than speculate.  Personally, I am pessimistic about the existence of a meaningful connection.
Damiano Mazza
CC BY-SA 3.0
2015-05-11T08:38:25.403Z
2015-05-11T08:38:25.403Z
Neel Krishnaswami
<p>I'm very much a novice in these subjects, but Geometry of Interaction and Geometric Complexity Theory seem to speak similar language and have vaguely similar goals. Am I not mistaken? Are there any links between them?</p>

CC BY-SA 3.0
2015-05-10T17:18:36.693Z
It might help if you spelled out what geometry of interactions and geometric complexity theory mean to you, and more explicitly pointed out the overlap in language and goals that you are seeing. This would make this question more valuable for other novices (since they can see some definitions and connections) and show to the experts due dillegence on your part of having a basic grounding.
Artem Kaznatcheev
CC BY-SA 3.0
2015-05-12T08:54:59.423Z
@ArtemKaznatcheev: even an expert like me would find it hard to explain to a complexity theorist (or somebody who knows what GCT is about) what the geometry of interaction (without "s") is.  It was introduced in the late 80s by J-Y. Girard as a proof-thoeretic research program whose goal was (roughly) to overcome the traditional syntax/semantics divide.  Today, the term denotes a collection of recipes and techniques that turned out to be useful for studying quantitative properties of programming languages (optimal evaluation, execution time/space, compilation into hardware circuits...).
Damiano Mazza
CC BY-SA 3.0
2017-11-19T11:35:50.013Z
It seems that I'm 2 years late but doesn't [Thomas Seiller](https://www.seiller.org/Research.html) work on both Geometry of Interaction and Geometric Complexity Theory ? Maybe you should take a look at his work.
Boris
<cc.complexity-theory><gct><linear-logic>
Are there links between Geometry of Interaction and Geometric Complexity Theory?
valya
# Are there links between Geometry of Interaction and Geometric Complexity Theory?

(Asked by: username_0 on 2015-05-09)

I'm very much a novice in these subjects, but Geometry of Interaction and Geometric Complexity Theory seem to speak similar language and have vaguely similar goals. Am I not mistaken? Are there any links between them?

**Tags:** cc.complexity-theory, gct, linear-logic
> **Comments:**
> **username_1**: It might help if you spelled out what geometry of interactions and geometric complexity theory mean to you, and more explicitly pointed out the overlap in language and goals that you are seeing. This would make this question more valuable for other novices (since they can see some definitions and connections) and show to the experts due dillegence on your part of having a basic grounding.  
> **username_2**: @ArtemKaznatcheev: even an expert like me would find it hard to explain to a complexity theorist (or somebody who knows what GCT is about) what the geometry of interaction (without "s") is.  It was introduced in the late 80s by J-Y. Girard as a proof-thoeretic research program whose goal was (roughly) to overcome the traditional syntax/semantics divide.  Today, the term denotes a collection of recipes and techniques that turned out to be useful for studying quantitative properties of programming languages (optimal evaluation, execution time/space, compilation into hardware circuits...).  
> **username_3**: It seems that I'm 2 years late but doesn't [Thomas Seiller](https://www.seiller.org/Research.html) work on both Geometry of Interaction and Geometric Complexity Theory ? Maybe you should take a look at his work.  

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## 1 answers

### Answer by username_4 on 2015-05-11. Score: 6

No one knows if there are connections between GoI and GCT.

It's quite plausible, since both are used to analyze complexity, and since GoI is formulated in terms of monoidal categories and GCT is based on representation theory. However, to my knowledge there aren't any researchers who understand both well enough to say for certain.

> **Comments:**
> **username_2**: I definitely agree.  I know nobody who understands both well enough to be able to tell whether there is a connection or not.  In fact, I'd be surprised to meet a GCT expert who has even heard about the GoI.  People of the opposite kind exist, Neel and I are examples (I can consider myself a GoI expert vaguely knowing what GCT is about).  In any case, we won't be able to do much more than speculate.  Personally, I am pessimistic about the existence of a meaningful connection.  

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