Are Yui and Fuyutsuki on a hike or something in ep 21?

[Monk Ed]

The scene where Fuyutsuki (in a flashback) reacts to Yui mentioning that she's seeing Gendo. They seem to be on some kind of hiking trail in autumn. It seems like it would be improper for a male professor to go on a hike with one of his female students alone. Is it possibly just one of those subtle hints that he's into her, or is there a broader cultural context that I may be missing? For example, maybe it's common for trails leading up to university campuses to go through such beautiful areas so they're not so much hiking an isolated wilderness trail together as they are encountering each other on the way to class.

(I ask such details for fanfic-related reasons. Having any possible unseen/unspoken context that may exist in that scene would be nice, but is far from necessary.)

[valshon]

I backpack/hike often and looking at the scene they seemed well geared, perhaps they were venturing into the back country to do some type of research?

[EvangelionFan]

I never had any reason to think they were doing anything other than hiking for some occupational-related reason

[boyfrand]

i thought it was implied that they were just really good friends because of their unique but shared insight into some biological field

[Na7e]

They are good friends, but Fuyutsuki holds deeper emotions that Yui doesn't reciprocate due to her relationship with Gendo.

[Monk Ed]

It says a lot to me, then, that they'd be hiking together alone, one-on-one as opposed to with a group of more students. I felt pretty chummy with a lot of my professors, and my Dad (who is a professor now) has been pretty chummy with a lot of his students, but something like that is more than an extra mile. I had no idea they had become that close.

[Reichu]

Was Fuyutsuki ever actually one of Yui's professors? All we know is that she was a bioengineering major, Fuyutsuki read her paper and met with her because some faceless professor thought it would be a good idea, and then... they're hiking together and she's calling him "sensei".

[valshon]

Was Fuyutsuki ever actually one of Yui's professors? All we know is that she was a bioengineering major, Fuyutsuki read her paper and met with her because some faceless professor thought it would be a good idea, and then... they're hiking together and she's calling him "sensei".

she probably got taken on as a research associate or department aide.

[Ceimoa Nan]

perhaps they were venturing into the back country to do some type of research?

But what could they find on a hike related to their research?

"Role of Microscopic A.T. Fields in the Embryogenesis of Pinus pentaphylla," Fuyutsuki et. al, Journal of Metaphysical Biology, October 1999.

[Kendrix]

They are biologists, they might've been collecting some plants.
Certainly not everything they ever did research on is related to the fate of humanity.

[Ceimoa Nan]

Well, I imagine it was something in between the two. All this "metaphysical biology" stuff that Fuyutsuki, Yui, and Dr. Katsuragi were involved in served as the basis for all the fate of humanity stuff post-2I, yet before 2I, they didn't have any clue (well, maybe a clue) about Adam or Lilith or the Angels. So where did they get the idea for Super Solenoids and A.T. Fields? Well, I guess it's a possibility that they developed these theories during the Katsuragi Expedition, but maybe they somehow gained evidence for A.T. Fields and stuff by collecting ordinary plants. That's what I was getting at with my fanfictitious scholarly article title.