to a special discussion between three interesting panelists. So we have Vinten Serf, the ACM Turing Award winner of 2004. We have Alessio Figali, the Fields Medalist, one of the Fields Medalists of 2018. And Efim Celmanov, who won the Fields Medal in 1994.

And the three of us will discuss among themselves and with us the scientific exchange and collaboration in the post-COVID era. So perhaps, Vinten, perhaps you could start and just say a bit about how you experienced the change of how a scientific collaboration works.

Well, certainly like everyone else, I haven't been traveling and I haven't been meeting anyone face to face. I've been here in my basement office for the last six months sitting in this chair doing a lot of video conferencing. And so the first thing I would observe is that post-COVID is an interesting term because I don't believe we will eradicate this particular disease.

It will be around like other coronaviruses. And so we will probably have to have periodic vaccine shots, which of course aren't yet even available. Although perhaps I guess there have been at least one announcement of a vaccine from Russia.

So we're at the beginning of a process for trying to get better control over the spread of this virus. I think also, like many other people, I've spent most of my time in the last six months online, either using the Internet for exchange of information or exchange of data or having

video conferences or doing email or just surfing the web looking for content of use. And I believe even in the post-COVID period, two things are going to happen. The first one is that people will have discovered they can work from home in many cases, whereas before they might not have been able to do that or their employers thought they couldn't.

And I think that will be a permanent shift. People will be flexibly able to work at home as well as in their offices. And the second thing is that the access to and exchange of information will continue to be extremely important in order to advance scientific progress.

And so as has been true in the past, sharing of information, getting access to current results is very important and the Internet has a role to play in that. So I'm curious to see what my two colleagues have to say about this same question.

So Alessio, you want to? Okay, then I will start. Yeah, I mean, I think we're all in the same situation. Like here in Switzerland, we are at least a bit back to normal, if you can say normal. We're back to the office at least a few days a week.

So interactions are restarting a bit and also with teaching, we do a bit of impressive teaching, even if few students can come and many are away. So I, of course, we've done a lot of collaboration online. Personally, I understand we need to find solutions.

It's not ideal for me, maybe everyone has his own way of doing mathematics, but I like a lot to interact in front of a blackboard and spend time with collaborators and chatting over sometimes nonsense. Because, you know, when you don't have a clear idea yet of how to prove mathematical theorem, sometimes you just stare trying, trying.

And I don't know, I don't like this. It's difficult to reproduce the same with a computer. I mean, being both in front of a screen with a collaborator doesn't work the same. So I think we're trying to find solutions. We need, of course, to find a compromise.

You know, very careful with masks and everything. But, I mean, the problem is going to be traveling, right? So traveling will not be easy, actually. And these effects on, I think, mostly the research part, it affects less, I think, this change of information research.

I mean, we are organizing a lot of online seminars, which is good. So it's very easy still to disseminate works and, you know, share ideas and particularly, you know, discuss new developments.

Still, as many of us know, when we go to conferences, not just listen to talk, it's also to have the chance to talk to the speaker and, you know, ask the details. That is difficult to ask just when you listen to the conference once or something, right? So it's really the atmosphere with that we are missing.

And we'll have to find compromises. This summer I organized the hybrid conference in Oberwolfolk. So 20 participants in presence and 25 online. And, you know, we'll do what we can. But, yeah, I agree with Veeam turning out that, you know, these videos will not go away like that.

I mean, we'll have to first find the good vaccine and then enough vaccinations for everyone. And then probably this new data, we have to get vaccinations over. We don't know the strength of the virus, how it will change over time. I mean, there are too many questions, but, okay, as mathematicians or computer

scientists or researchers in general, we need to go on and find solutions. We are lucky that technology is on our side, I think. I don't want to take too much time. Maybe we can move to the next. Well, I'm an optimist.

I think that this Zoom conferences and Zoom seminars will, of course, enrich scientific exchanges. And they will stay even when things more or less get back to normal. But I think that real conferences, when people meet each other, are still needed and there will be some conferences.

We will travel, maybe we'll travel less at the beginning because it will take time to persuade funding agencies that such conferences are needed.

But eventually we will get back to normal. So I'm an optimist. So I think that you make a very good point, Dafim, that people getting together is very different face to face, sharing a meal, having a break, taking a walk. Standing in front of a whiteboard, having a massive argument about some particular equation is my favorite mode

of operation is in front of the whiteboard drawing pictures or writing equations and having a big debate. Because out of that intensity, I think often comes some real insight. So I'm frankly looking forward to the time when we can get back together again.

But on the other side of this, as a technologist, I'm very interested in the possibility of creating devices that simulate this kind of interaction. For example, I agree that typing on a keyboard is not the same as writing on a whiteboard. But I wonder if we could have a kind of a shared whiteboard where anything you write is visible to me and anything I write is visible to you.

I've seen attempts at doing this and they've mostly been crappy. That's a technical term. But I think it might be possible to achieve that objective, but it still is not the same, I think, as feeling like you're right there with someone else having this debate.

So I have to ask you whether this in-person debate thing, from your experience, has made a big difference in terms of discovery and solution of problems. I want to stress the importance of human warmth in education.

The warmth between the teacher and the students, between two students, that's a way of inspiration. That's where we find inspiration. And human warmth on the screen of a computer is a problem.

So, Alessio, for your work, what's your conclusion about the importance of the face-to -face things and, of course, this wonderful presence, this inspirational presence that Efim is talking about? Certainly, I resonate with that. How about you? I completely agree. I mean, it's so important.

And I think we also, I see it myself when I watch the talks and also that it's not the same, the fact that you are online. First of all, it's more difficult to concentrate, usually. And second, you know, I remember myself when I was a student, maybe the professor writes something and

then you don't understand what's written on the blackboard, you talk to the guy next to you or whoever, and you start to say, oh, but what do you say, but I don't understand what he's doing, it's too complicated, whatever. I mean, you need bonding from the people around you and doing this at home, it's tricky, right? So, of course, I mean, we're lucky there is technology, otherwise probably we wouldn't even be able to teach.

But still, it's very important. And also one point that has been discussed, I mean, also the funding. You know, I'm the director of an institute in Zurich, and I was in a big meeting some months ago with all the institutes of research of Europe, the biggest, most of them.

And we are all in the situation where we got public funding to organize conferences, and now we're almost unable to do that. But then still you need to do something because if the funding are cut, then it's difficult to get the money back at some moment. So that's why I was very positively impressed by Oberwolf in Germany, the way they are operating, they've been extremely efficient.

So I'm trying to emulate them here in Zurich. But still, yeah, so there are a lot of ifs around, but yeah, we need to be strong and we need also to find compromises.

I think we need probably to work more local like we do with food, you know, zero kilometer food for environment. Probably we need to say, okay, you know, Europe is still a big continent, and then we can work more at the European scale or especially at some scale and then US more on their scale.

And then, you know, for intercontinental, we'll have to wait a moment. But I mean, we cannot completely avoid interactions. But you know, there is a lot of uncertainty right now. So I understand that people are also a bit scared. So it's been again, and I want to shift the conversation a little bit back to technology for a moment.

A lot of schools, whether it's colleges or high schools or even elementary schools have been forced into an online engagement in order to keep people safe. And I think the tools for teaching online are still fairly crude. And it raises some interesting questions from my point of view.

How does education change when we're forced into this online mode? And I will argue that one thing which is quite helpful is that if you record a lecture, then you can play it over and over again. It's hard to ask the professor to keep repeating himself or herself. But if you have it recorded, which is what many of the teachers now do, then the students have the opportunity to replay the lecture.

It's not quite the same as being able to ask somebody sitting next to you, what did that mean? But it does give you some control over the experience that you wouldn't normally have in a face to face setting. So that's one point. The second point, I think, is that I have experienced larger attendance in online events because people don't have to travel.

And so setting aside time zone problems like being awake at three o'clock in the morning for a lecture that's many time zones away, I've seen more participation in these online conferences or the online classes.

And so there may turn out to be some benefit to using these online techniques. But I'm curious to hear what Efim and Alessio have to say about that. In general, I was very impressed by all this online machinery, the scientific life stopped.

And then we found out that it did not stop. Seminars go on and indeed, as Efim said, the participation went up. Still, you know, I have two grandchildren who study online. I teach online.

To say the truth doesn't work very well. Humans are warm blooded animals. We need a personal interaction cannot be replaced.

You know, all these years of wonderful lectures are available online. Please, from the best teachers. Still, it does not replace real education and in-person. So I hope that our university authorities found an authority to understand.

So just as a response, I resonate with what Efim is saying. I mean, I'm a warm blooded human being too. On the other hand, Georgia Tech in the US has initiated some years ago now,

six or seven years ago maybe, an online class for computer engineering or electrical engineering. Which costs far less than the in-residence classes do. And it seems to be working in terms of just testing people and seeing what they know.

So the experience may not be quite as pleasant perhaps. But I think it's very important for us to recognize that at least some places have managed to produce college level educational courses and successful graduations. Even if the experience doesn't have quite the same flavor to it.

And I see Alessio has unmuted, so you must have a reaction too. Oh, no. Yeah, I unmuted after Efim. Yeah, I mean, I think I said on computer Efim in any case, I mean, I think it's extremely complicated to do things online.

It's not the same. There is nothing. Actually, it will actually be interesting also if the audience, even if they don't have questions, if they could kind of comment since they are, most of them are students. They could give us some feedback on their perspective.

But on my side, yeah, I feel it's just extremely complicated. And I think, as you know, online teaching has been around for a while now. There are really online universities in several years. The role of the university is not just to give knowledge, it's also to, you know, promote these interactions, to give something, you know, some kind

of, you know, you give projects to students, they work together and then maybe also the fact that, as I said, asking questions to your neighbors. And if you cannot do it, you go to the assistant and then the professor.

And also one thing that, you know, one thing that sometimes happens, and I think it's extremely useful when you teach in front of an audience, sometimes you make a mistake and students correct you. And that's extremely useful because as a student, you need to see that the professor make mistakes and you can correct the person and that's fine.

I think it's, but when usually it's done online, especially if it's recorded, there is a tendency to do perfect lectures because you are very well prepared to have something recorded, you don't want to record a mistake. And that's not good, right? Because it is like something immutable and too well

prepared. I don't know. I think we need a human touch also in the lecture. So this is missing. I think, as I say, at ETH now we are lucky because we do some in-person teaching as well. Essentially, what we do is that we rotate a fraction of the students that they can come into

class. So maybe one fifth of the students come and then they rotate. It's better than nothing, right? But yeah, it's not ideal. So let me shift again to another observation.

Some disciplines like mine, computer science, have the feature that they can be taught easily in a remote way because an awful lot of the interfaces are just what you would see on the screen of a laptop or a desktop that could be anywhere. And so the classes that involve learning how to configure something or run a computer program that's

doing computational linguistics or computational chemistry or computational physics, those are all quite feasible to do remotely. And so at least for certain kinds of disciplines and certain kinds of applications, the online space works very well. And because it's sort of forced on us by the fact that computers have become so central to a great deal of scientific research.

But you guys are mathematicians. And so my question for you is whether computational methods have made any difference at all in terms of the kinds of progress that you can make in proving new theorems or discovering new kinds of mathematics.

Well, mathematicians work on problems that are very abstract and sometimes detached from reality. How can they keep inspiration? How are they able to concentrate on them for so long?

And here they find inspiration in each other. Sometimes people need co-authors just to inspire them, to keep interest. It's much easier and more natural to do it if you meet people personally.

Well, I'm nodding my head because most of my favorite work is done with someone else so that we kind of bang ideas against each other. Alessio, I'm sorry, I saw you were going to react. Well, no, no, I was just... Yeah, I mean, again, I'm completely effing.

I mean, it's, you know, sometimes you think about some, I mean, in my case, sometimes I think about something and I'm completely stuck most of the time. And then what they start to do is working maybe in the corridors and just seeing people that are doing something different.

Maybe students are in the corridors or whatever, just thinking, moving and not being stuck. And now, you know, the lockdown here at home all day, you can just walk in the same room over and over. I mean, and you don't see anyone.

That's the part, of course, that doesn't work. I mean, we need inspiration and sometimes it's just from other people or just maybe walk in and say, oh, today there is this seminar, let me go and sit. Because also the good thing, if you are, you know, it's true that when seminars are online, many people can access it.

But usually then you only go to the seminars that you really want to attend. You're not going to sit in front of your screen for a seminar. Vice versa, maybe, you know, there is a seminar in your topic just going on every week and you just go, whoever is the speaker. And sometimes you go to one which was very far from your area and that's one time out of maybe 100

you get a super inspiration out of a talk you would never have attended if it had not been in presence. So, you know, it's difficult to realize where there are ideas, but here is much more regulated. You only talk to people when you have to talk to people.

And then, you know, you talk with someone, you already know what to talk about. It's not like, as I said, sitting in front of a blackboard for three hours and just, you know, at some moment just talking about something else because you have no clue how to go on. And this part, it's very weird, very bizarre, right?

Difficult to do online. I see there are questions actually. Yeah, so I would like to pick up a question which was asked by one of the young researchers, Maria, who sometimes agrees with what Vin said that there's more attendance in conference and she was able to go to conference, she would not have been able to attend otherwise.

Isn't it necessary that we don't go back to normal, but to a new normal, which is more inclusive and let more people participate in events by making them online, for example. So how do you think about that? Yeah, I actually resonate with that point.

It's often the case that people who can afford to travel, you know, go to the conferences and people who cannot afford to travel don't. And you end up with sort of a repeating group of people who are funded adequately to participate and a collection of people who can't. So inclusion is pretty important, even if it's not a perfect arrangement.

And so I think I like the point of this question is for us to pay more attention to inclusion than perhaps we have in the past. And even if it's not a perfect solution, it's better to have more people involved.

I absolutely agree. I hope we will go to a new normal with online participant component. So people, some people could come to the conference, some people couldn't, but they should be able to participate online. But I don't want only online.

Yeah, I also think these are very good point. I think we learned some lessons from this. One thing we learned is that, you know, before it seemed that even for some talks, it was worth to, you know,

take a plane, run, spend 24 hours trip, give a talk and then run back because we had to teach the day after. And maybe now you're like, yeah, perhaps if it's just to give a talk and not spend a whole week there, it's not that worth it to just travel, right? Maybe you can do it online. And the moment you do it online, it's true that also you open this to many more people.

So people will not be able to be there. And I think this is, of course, a big advantage, right? So for many people from many countries where there are maybe less events now that they can benefit from this because they will never have attended, had the possibility to attend so many talks.

So perhaps, yeah, we have to go to a new normal. I agree. So we need the events like a nice one week conference, we're all together and we can chat. But probably, you know, if it's just one quick seminar between two lectures in our place, we don't need to catch a plane and just be there for two hours, give the talk and run back.

So just to reinforce that, I have been in London and now Heidelberg today and I will be home in time for dinner and that's a big deal. But I can ask you one of the things. So, I mean, since you, unless you mentioned that it's, I mean, there

are not these encounters by chance if you always have to somehow set up meetings and you know what you're talking about. Another one of the young researchers, in some sense, also wrote something in the chat which resonates in that that after class, there's no exchange between students. But we also see, I mean, in the, for example, now with the virtual H&F, there's this app where you can somehow

walk around in your avatar and meet people and there are some other, I mean, other kind of apps or technology like that. Did any one of you use that or use other things to make more chance encounters in the online world?

Two things. First of all, there was an old application called Second Life, which had an avatar and you could go around visiting people and there are lots of other ones like that, multiplayer games. At Google, we have in our buildings which are unoccupied right now, we have a place called a

micro kitchen. It's a place where there's coffee and other kinds of, you know, snacks and things like that. And people encounter each other there in sort of an unplanned way. We just started to think about an experiment where we would keep online micro kitchens available. Literally, if you went to

your office, you would see several different places in the virtual space where you could meet with somebody who is there. And we haven't turned this on yet. We're just exploring the possibility of having these incidental encounters. Alessio, I think you were about to react as well. So what do you think?

Well, I don't know exactly. No, I mean, I don't have too much to say on this point. I think we're all, yeah, there are these things. I don't know. I'm still on the virtual side, I have big problems, even with avatars and everything.

So, no, it's so difficult. There was actually a moment looking at some other comments of students and I said, I was just looking at the last one who says it's so difficult to attend a lecture because there are so million distractions on your computer that

make complicated, right? Actually, I had the same feeling of this student when I was watching some talk in the sense that it's so easy to get distracted also online. You know, it's because there is an email popping up and, you know, at least if you're in presence, you have,

you know, if you're in presence, at least there, you cannot just open your computer stuff to reply to mail or whatever. But then in the end of the screen, no one can check exactly what you're doing and then you can get easily distracted. So, I don't know, I would have been my university if I had to do it,

you know, online. I'm lucky that I didn't have this COVID, you know, 18 years ago. Do you think it will change how talks are prepared? I know that some online seminars don't take one hour talks anymore,

which is the standard thing in mathematics, but do half an hour or half an hour with a break and another half hour. So do you think with online seminars, the way we give talks will change? I think it's better actually. Yeah, I don't know. I attended two online conferences.

Again, it's very difficult to be concentrated for a long time. Actually, I think even the way of teaching should be different. I think one hour lecture is too long. I mean, we should think of lectures, maybe split in blocks of 20, 25 minutes where then you can take a small pause.

And, you know, you did some subjects, you say, okay, I proved this theorem, let's take a pause. You can relax a moment and then we start again. But even, you know, by splitting blocks, it helps. And also seminars, I think it will be better because maybe in half an hour, you pass a message. All the talks now, you know, before mathematics, it was useful to have also an hour

because we had the chance to give Blackboard talks and there you really can take the time. But if you go online, most likely you will do slides and then you go faster. And then, you know, one hour of quick talk, maybe it's better to half where the first half is more, you know, generic for many people to attend.

And then you give another half an hour for those who are really interested in the details of the proof. And people can kind of skip instead of pretending to be there and then just, you know, muting everything. I don't know, maybe there are solutions. But, you know, I think one hour concentration in front of a screen, it's a lot to ask, especially if you do it for more than one time during the day. That's my view.

I may say a few words, you know, it's all relative. The typical lecture in Europe, at least it was in the Soviet Union, was two hours. And when it came to the United States and 50 minutes, it was a cultural shock.

Was it too long? I think it's an online part that I find it long. I mean, in presence, also in Italy, you know, many professors were skipping the break. So in the end, it was, at least in my end, we were also going on for, you know, they would arrive when they wanted and leave when they wanted.

So it could be two hours without break. That was also common. But, you know, if you're there in person is really different. But I don't know, two hours in front of a screen, no break. Yeah, that's tough. You know, one thing I would point out is that you remember this phenomenon called MOOC, you know, massive open online courses.

And although I think the hyperbolic description of it has dissipated now, there are people who are still doing online lectures, but they aren't just lectures that go on for an hour or even two. A lot of them are broken into smaller pieces. And then a kind of question is, or

set of questions are asked in order to figure out whether the recipient is actually understanding the content. And I've been told by people who prepare lectures like that, that it's actually hard work, harder work than giving an in person lecture.

And the reason for this is that if you make use of the response to the test, and you discover based on that the student is not understanding something, instead of having them go back and just listen to the same thing you said before, sometimes you want to prepare remedial material based on what you now know the student doesn't understand.

And so the preparation actually is harder and longer, because you record substantially more information than simply a standing lecture would include, but it might actually result in better understanding by the student. So, once again, another exploration, not the same, I think, as a student and a professor on either

end of a log, where the professor is asking the student questions and the student is asking the professor questions and the two of them are discovering what it is that the student needs to know. Maybe Anna, there are many questions. So, I can see just my chat moving quickly.

Yes, so there have been some so about, I mean, online teaching, online lecturing, and I think one which is interesting, which we, I mean, shows a bit different aspect is that

some students might actually perform better with online classes and others might like more physical interaction. And so if you want to leave no one behind how you strike a balance between the two.

Well, Alessio, both of you look like you're about to react. Go ahead. I've been thinking about that. I think that, you know, one aspect that I was wondering, and I think this will be a social aspect, I thought that maybe now girls will perform better.

Because in our discipline, very often, like at ETH Polytechnic School, you have a lot of boys, like 90% of boys in the class, who are always more aggressive. And sometimes, you know, they kind of, you know, if you put some pressures, and you know, then maybe girls have a tendency to be a bit more shy and they're less likely to ask questions and always have to encourage them to ask questions.

So now, at least, you know, the advantage of online is that it creates, you know, there is no name, essentially, you can ask questions with a chat often, and then this creates a bit more balance.

And so some of my colleagues, what they do to keep interaction, so that's why I think it's not bad to split also the classes that, you know, you can be teaching online, maybe with your tablet or something. And then you can have the chat open like now. And perhaps, you know, you do 20, you can start to ask questions. Sometimes in class, we do that, right?

We do a theorem, and maybe we don't say everything we asked to the audience, okay, now, what do you think about this? Do you think this question is a lithic or whatever, you know, some math question? And the reality is that very often, either the ones who will reply are always the same, or no one replies to the questions.

But the online part makes it easier for people to say, okay, let me try. Anyhow, I mean, the professor doesn't know who I am, it's just a list of... And then you see these tons of, you know, 50, 60, 80 people will reply the answer. You cannot check all of them, but it's nice, right? At least if you played well, I think you can make it more interactive. Still, you need both. I don't know, I think we have to learn.

It's difficult for us as well. I think it's new for, you know, it's new for the students, it's new for us, the professors. And then where is the perfect balance between how to include more people and create more equality and more balance inside the classes and at the same time not feel people excluded?

Because for some people it's very difficult to, as I say, to work, to study from home. That's something we still, I don't know, we're still trying to figure out. But I think it's right that, you know, some people of the class will benefit more. So maybe we need to do some in one way, some in the other. I don't know. I think we're still discussing this a lot and I hope we'll do our best.

We'll be, we'll have to finish soon. So I want to make two points. First, we already have a combination, we have had it for some time, a combination of real courses and online courses.

At the University of California, all lectures are recorded and students can watch them as many times as they need. Second, as Vint quite correctly mentioned, there are open online courses, MIT courses, wonderful courses given by wonderful professors.

So far, I never met any mathematician who was educated in this way. That's it. So let me, let me shift again to a technology question.

Over 45 years ago, and bear us to say, I used to be a member of the faculty at Stanford. It just seems like forever. But during the time that I was lecturing, I had several television cameras, one of them in the back of the room so that you got a face to face shot and another one was in the ceiling.

And so you could take a picture of me drawing on a piece of paper that had two benefits. First, it's like being an online, you know, in real time kind of lecture equivalent to writing on a blackboard or a whiteboard, except it was more convenient because I could sit down and I would just draw on a piece of paper. And at the end of the lecture, I had the paper which I could reproduce and send out as augmentation of notes.

The reason I bring this up is that we don't have a convenient way of doing the same thing at home or, you know, in a remote way. I'm predicting that we should have a device which you could fit to the top of your laptop when it's open

that can look down on a place where you can draw and write. That would be easier than trying to do a shot of a blackboard, which you're standing in front of, which is, you know, invariably frustrating. And that way we might actually be able to emulate some of the dynamics of an

online rather of a face to face talk and think about working together with someone else. You know, you're writing the equations down and having a big argument about it. The other guy can show his or her alternatives. So I think we're missing at least one piece of technology that we ought to add to the things that we already use for online classes.

So I don't know who to turn to to suggest that, but I bet you that that would be a big help. So the existing technology is not, you're not satisfied with that. So for example, hooking up an iPad and share the screen on Zoom or something like that.

Well, that might work too. I mean, the slight kind of thing that you can sketch on. You can tell how old fashioned I am. It didn't occur to me to do that. But if it works, yes, no disagreement there. If you have a stylus and high enough resolution, that would work too. I mean, that's actually for both for me working with collaborators or also for some of the classes we teach.

Here online we use that because it's the, I mean, the emulates in some sense writing on a board. So we have five minutes left. I would like to pick up one other question which goes in a completely different direction from the audience.

Which deals with the two body problem, which many academics face. And some other question statement is, isn't it with remote working actually alleviate some of the difficulties and could one perhaps envision even a fully remote academic job?

Like a remote tenure track job where you teach online and you are in place X and higher by university B in a different place. How do you think about that? If I may? Yes. The problem is that I see with that, I mean, this would work if you had a full teaching job, then I could see the something remotely.

I mean, in some sense, but I don't, the point is that I don't believe we will remain, you know, 100% remote teaching. But let's say even if teaching remain 100% remote, still there are things that you need to do in place.

So of course it can help, you know, that if I live in a city and I only have to go maybe once a week, I can be more flexible. So of course it could help with some flexibility because it means you're not so terrible. You know, if you have an academic couple that don't live in the same city

anymore, as long as the community is doable, because really now we need to commute less. But, you know, fully remote. I don't think it's doable. I mean, just for the simple reason that we still need to go to the department when there are some meetings still that, you know, you have to have some conversation in person.

Right now we're back to in person meetings every time we have a large enough room. I mean, that's how we do meetings in our department and I'm meeting my students, my postdocs. So, you know, when you have a faculty job, you also have people that work with you, PhD students, postdocs. You need to meet them and I cannot just supervise them all the time, just online.

So I think it depends on the position, but I doubt this will help the two-body problem. But it will help, as I say, the fact that we need to commute less. So, I mean, we probably need to go any hour bit less to the department and this could help if you're not to be commute.

Do you have an opinion about that? I mean, you said Google headquarters is... Yeah, it's been a long time since I've been on the campus in a teaching position. I'm going to disagree a little bit with Alessio and the only reason for that is that I'm seeing enough,

historically, enough correspondence courses and online MOOCs and other things to believe that it is possible to fulfill a faculty position. There may be some things that you aren't able to do conveniently, but if the primary

position has to do with lecturing and teaching, I think the remote online position is feasible. So I guess I would argue that we'll see some of that, but I think in many other cases, you'll want to have the ability to see and interact directly with students.

But I see no reason why at least some positions might be of that kind, especially if they're primarily focused on teaching. I agree that there might appear remote jobs, but very few.

Probably the university offers online courses, somebody has to do it and that's more or less remote. Also research position is practically remote now because one has to get some results, publish papers and where he did it at home or in his office doesn't matter.

But if you have a teaching job, would a university hire somebody who intends not to come? That's a negative. So we are at the end of our time. I would like to thank you, the three of you very much for this very interesting and I think enjoyable discussion.

So hope to see you at a different occasion. We look forward to that. Thanks so much. Thank you very much. Thanks to you. Thanks to the other forum for organizing this.