Episode 12: On the purpose of studying Mathematics with Raquel Murat García

00:00:03:

00:00:10: From Mathematics Münster, this is on a tangent.

00:00:12: The podcast where we tell the stories behind mathematics and explore some fascinating plots that lead early career researchers to Münster.

00:00:20: My name is Carlo Kaule.

00:00:20: I'm PhD student in Arithmetic Geometry And i have the privilege of bringing new stories for you In the month to come For the fifth episode Of season.

00:00:28: ,I am joined by Raquel Murat-Garcia.

00:00:31: After earning her bachelor's degree in Computational Mathematics in Castello de la Plana She completed her master's at the University of Münster with ACESIS on the existence of vibrations over coset spaces.

00:00:43: Currently, she is an Ada Loveless Fellow and PhD candidate in Linus Kramer's research group.

00:00:49: Alongside her research, Raquel volunteers as a Phd representative for the Mathematics Minister Graduate Center – and mentors female master students nearing graduation!

00:00:59: The podcast always starts with question what your first mathematical memory

00:01:04: was?

00:01:04: So I was thinking about this when i heard the other podcasts and I don't know if these counts, but they think that first came to my mind.

00:01:11: is That one.

00:01:12: When?

00:01:13: Was a kid?

00:01:13: II liked so every time there was like a piece of paper And it had like something to write with.

00:01:19: I liked doing This drawing.

00:01:22: that was so.

00:01:23: first I started with a line and then at The end I drew two perpendicular lines and Then at the end of those two new lines I drew perpendicular lines and then continue, which is nothing but like too regulatory.

00:01:41: But of course I didn't know what this was...I just liked drawing it!

00:01:44: And i always think wow it's amazing no matter how much time spent on it..i can keep going!

00:01:50: It's incredible.

00:01:52: so i guess these were my first thoughts about Infinity.

00:01:57: I think that's so cool because it also connects with your research nowadays!

00:02:01: Exactly,

00:02:02: yeah when i realized this was already group theory in a way

00:02:08: Yeah Cool and how old were you then?

00:02:10: Like...

00:02:12: I don't know..I would say maybe like between ten to twelve something like these.

00:02:17: So where did you grow up in Spain

00:02:19: ?

00:02:19: I grew up in a city.

00:02:21: well at big town called Chiclana is the very south.

00:02:25: It's facing the Atlantic, so contrary to popular opinion it is not super hot there because there are oceans and not the sea.

00:02:34: So actually many times its hotter here in Münster than

00:02:38: elsewhere.

00:02:41: Oh wow!

00:02:41: Ok for your primary school or high school you were there?

00:02:47: that your interest in math becomes more serious.

00:02:49: I mean, you're high school or middle school where are just always good at math?

00:02:54: Or how did this develop for you?

00:02:56: So actually during my high school... ...I wanted to study something related to languages and I wanted to study linguistics.

00:03:03: Okay

00:03:04: This was the first idea.

00:03:05: then i thought about studying translation of German precisely

00:03:09: Yeah, because

00:03:11: I had German instead of English.

00:03:14: You could do this in Spain?

00:03:16: Yeah,

00:03:16: I mean...I was very lucky.

00:03:17: The school that i was assigned to because it's close to my house is not German.

00:03:21: the rest of them had English and

00:03:22: why were you so interested in German ?

00:03:24: I don't know..I liked it !

00:03:25: I also have a good teacher all time.

00:03:27: So yeah This way I

00:03:29: like it.

00:03:30: What Math wasn't on your mind at that time

00:03:32: ?

00:03:34: I think I liked physics more Because he always has same teacher for six years And he was amazing.

00:03:41: Really, he taught me how to think about hard problems and such.

00:03:44: It was a very good figure in my life And I never really thought of math In fact when i finished.

00:03:50: So this is the first idea Something related with two languages.

00:03:53: Then also like philosophy.

00:03:55: But then again there's no architecture jobs in Spain.

00:04:06: Also for linguistics.

00:04:08: it wasn't that great option if you want to have an actual job.

00:04:13: So then I shifted and started studying biomedical engineering...

00:04:20: Why, baby?

00:04:21: Medical engineering?

00:04:21: Yeah exactly!

00:04:22: And

00:04:23: i cannot really explain it because very soon

00:04:28: became

00:04:29: obvious that it was not for me.

00:04:31: The first semester was all about computer science math and physics But then the second semester was all medicine and I hated it, so... Then I stopped.

00:04:43: And thanks to that first semester I actually realized how much I enjoyed math courses because they were actual maths not like in high school.

00:04:50: So I already had an introduction into analysis and linear algebra ...and liked it a lot!

00:04:57: Also I also liked computer science part.

00:05:01: So when found out there's another bachelor called Computational Maths That was like a mix of computer science and math.

00:05:10: And that's what it is.

00:05:11: So this was in Valencia?

00:05:13: Yeah, so very far from your home.

00:05:17: yeah I mean the biomedical engineering.

00:05:20: at that time It was possible in València Madrid and Barcelona.

00:05:23: okay

00:05:24: madrid and barcelona are extremely expensive.

00:05:26: yeah Okay,

00:05:27: so valencia was the only possible option.

00:05:29: any was the same for computational math.

00:05:32: He was only castellón Which is next to Valencia or Madrid and it's very expensive.

00:05:37: So

00:05:38: was that hard for you?

00:05:39: To be so like?

00:05:40: how many hours is it from your hometown to travel?

00:05:44: It depends I think by train probably eight.

00:05:47: Oh, so it's super fun

00:05:48: It's fine.

00:05:49: I didn't go over often

00:05:50: Was it wasn't hot for you.

00:05:51: or what did

00:05:51: I mean?

00:05:52: I guess at the first year he was hurt because I had never liked cooked clean Yes but not like taking care of a full house by myself.

00:06:03: But I don't really remember struggling very much, i think we became used to it first and i liked the freedom.

00:06:11: yeah so like a very good community around?

00:06:15: The university in Valencia or how would you describe social life there ?

00:06:19: I liked alot my bachelor's the computational math one because for some reason There's only like thirty slots to begin with, and then after a year of course.

00:06:33: It was twenty people.

00:06:33: by the end we are fifteen at most.

00:06:35: so it became super close friends.

00:06:39: So high school again...it was small class.

00:06:41: everyone were friends with each other.

00:06:43: this is really

00:06:43: nice.

00:06:44: Was that hard for

00:06:46: you?

00:06:47: Not when I did because back then no one interested in math now Enter a bachelor.

00:06:55: in Spain there's like a grade between five and fourteen And when I entered, i think it had six so everyone could get in.

00:07:05: Now its close to twelve or thirteen.

00:07:10: So now is very hard

00:07:12: Probably also because of the computer science part.

00:07:17: How much programming was involved in this?

00:07:19: So how much time did you spend on math, pure math and programming?

00:07:22: because he said also the passion for programming.

00:07:26: Yeah it was half-and-half.

00:07:27: I would say okay

00:07:28: but do they still enjoy programing as much?

00:07:31: during your bachelor's?

00:07:31: yeah i liked a lot.

00:07:32: um yeah well at some point i realized that like a lot pure maths.

00:07:39: so we wanted to continue

00:07:40: there.

00:07:41: But in your bachelor's, the kind of pure math you studied was more direction-of-dynamic systems right?

00:07:48: No.

00:07:50: Well okay yeah... This is what I did my bachelor thesis on but to be honest i don't remember anything.

00:07:56: it was analysis related and actually I chose this only because a professor that was guiding me.

00:08:08: It was the one that taught us the topology course.

00:08:13: And

00:08:13: I liked topology a lot, so if i go with him and do something like this in the end it would be something else... ...I also enjoyed but didn't really know what analysis is about topologies.. ..I just liked him as professor!

00:08:27: Then you decided to not pursue computer science part of it further?

00:08:30: Was it hard decision for your to stop doing this part or did you say it's

00:08:35: fifty-fifty?!

00:08:37: I don't know, at some point i got a little bit bored.

00:08:42: It's fun but maybe i can learn this on my own if still want to.

00:08:46: But it was more curious about math Also...I liked alot the fact that pure maths is useless And Im very proud of saying that im doing something useless for society.

00:09:01: I think its nice have goal just expanding human knowledge Per se, without any goal.

00:09:08: So I wanted to do something like this.

00:09:10: It's a little bit like philosophy in my opinion so i always liked

00:09:13: it.

00:09:14: You just like.

00:09:14: the fact that Mars is super hard and you're always having new challenge which was not the same for community science Yeah can very much relate.

00:09:25: also doing something useless.

00:09:28: I feel super privileged by the fact that i can just do this thing, even though there is no direct application to it.

00:09:36: And yeah...I think its really something special That these kinds of math which seem to be useless are really pursued a lot for example in Germany.

00:09:47: Could you have also specialized in your area now same way with Spain?

00:09:54: I think yes, there's pure math in Spain as well.

00:09:57: The problem is that finding money is super hard like it isn't so very

00:10:02: good.

00:10:03: Finals?

00:10:05: I get the impression but i'm not an expert at all on this that in Spain... ...the money for pure maths is much worse than for applied maths

00:10:14: right?

00:10:14: It's not only for math and research generally.

00:10:18: a lot of people who do PhDs are completely unpaid.

00:10:22: Wow,

00:10:23: like.

00:10:23: so they either live with their parents or They have a second job and then of course it takes forever.

00:10:30: Or do you get paid?

00:10:31: Like our ridiculous amount.

00:10:33: So You said that the appeal to Mars was similar like the appeal two philosophy.

00:10:38: right yeah, so did you also continue pursuing your interest like in philosophy or also maybe linguistics during your bachelors?

00:10:47: Was there not much time for that.

00:10:49: Exactly,

00:10:50: I'm very sad that i lost kind of this...I mean the interest is still dead but

00:10:54: at some point my

00:10:56: time spent on it.

00:10:58: sometimes I read books like.

00:11:00: also linguistics have been written recently more yeah comes and goes

00:11:05: okay.

00:11:06: And then after you're a bachelor How how did you end up in Munster?

00:11:10: I mean, okay probably.

00:11:12: what was it related to the fact that you studied German and then came to Germany as well?

00:11:16: Yeah exactly.

00:11:17: So he was several facts.

00:11:19: so first of all Because I decided they wanted to do math And I knew I didn't have a strong A strong but math background precisely because i had spent half of time doing computer science.

00:11:33: The thing is in Germany the masters are two years, but in Spain they're only one year.

00:11:39: So I thought to make up for that fact... ...that I lost time doing computation and could do it once more a year.

00:11:49: And then also because the masters here are free In Spain they were pretty expensive.

00:11:54: Oh

00:11:54: wow Every master you have to pay?

00:11:58: Even the public ones.

00:11:59: Maybe math isn't so expensive.

00:12:01: It's maybe two thousand year, two thousand euros a one-year.

00:12:08: yeah

00:12:09: it's not so much compared to other degrees

00:12:12: but

00:12:12: sure.

00:12:12: So this was...so then I wanted to come to Germany and so then i simply googled master's math in Germany in English.

00:12:20: Munster was there.

00:12:21: also Göttingen was there.

00:12:22: I applied for both.

00:12:24: what about Bonn?

00:12:26: Bonn needed like a thousand requirements, like this letter of recommendation.

00:12:37: So Göttingen also accepted me but they complained that I didn't have enough math background.

00:12:42: then i would have to do extra courses and I said I won.

00:12:47: Munster did not complain.

00:12:48: so just

00:12:48: thank you!

00:12:49: Okay what?

00:12:50: You didnt know anything about the city or... No

00:12:52: actually no..I didn´t really do much research.

00:12:56: I remember you also applied to Norway and they also got me there.

00:13:01: It was a super pretty city, it wasn't very good You know between like a lot of mountains.

00:13:05: beautiful but its extremely expensive

00:13:09: cost-of living.

00:13:09: yeah But the minsters are quite expensive right?

00:13:12: Yeah!

00:13:12: And

00:13:13: i don´t think that is extremely expensive compared to Spain not

00:13:17: so much.

00:13:19: How did you start at Mönster Lake could easily integrate into this student.

00:13:24: Yeah, because the year that I arrived... ...I think it was already a second one than the master.

00:13:29: It's fully in English so full of international people and all of them were equally lost.

00:13:36: So then we made friends easily And we survived together.

00:13:42: Great!

00:13:43: How did you come up with specializing your current research area?

00:13:48: Actually when i arrived here.. ..I wanted to do topology and maybe analysis but My advisor Linus Krammer was giving a lecture on geometric group theory.

00:14:00: And I remembered that he had enjoyed the group-theory part, I had him in Bachelors, so maybe it's his first semester and then we can do something else!

00:14:11: I liked it very much also because I thought he was good at lecturing... Also there were some friends who were doing it.

00:14:21: It became my main subject.

00:14:22: I was also doing algebraic topology at the same time with the same friends, so we were all like in this topology and group theory field And then i continued to do more of these just because I had enjoyed it.

00:14:35: Then I also tried some analysis but realized that didn't really enjoy them much.

00:14:40: So I kept on with topology.

00:14:46: Then you at some point had to write your master thesis and probably it was a very easy choice.

00:14:50: Yeah, yeah... Or what would you say?

00:14:52: But maybe it's the harder choice if you want to keep on doing math research or else its totally clear for you.

00:14:59: I decided that i wanted do research when in my last year of bachelor

00:15:05: Because

00:15:07: I saw an interview with Spanish mathematician called Maria Cumplido.

00:15:13: She is in Sevilla Okay.

00:15:15: And she's a group theorist, precisely and I read an interview of her because she had won some prize...I don't remember what exactly?

00:15:24: She was saying that math is not about doing useful stuff, but at least pure math is about like expanding my knowledge.

00:15:33: what I said before.

00:15:33: and And I thought wow this is so nice.

00:15:36: Yeah Now you also want to do these?

00:15:38: And she said that Coincidentally many times it has happened That precisely group theory has ended up having a lot of applications for computer science and coding on such But its never the aim To begin with yeah.

00:15:53: So then i thought This Is Nice and I wanted

00:15:57: Are you still interested in these kinds of applications?

00:16:00: The real application to

00:16:01: me.

00:16:02: To computer science, just because I have a background.

00:16:04: No not now...I mean i don't know how much longer it will be in academia but maybe we'll do that again and really enjoy coding so its never again when I do math.

00:16:17: thats what I think about.

00:16:19: Okay was there very easy progression from writing the master thesis into starting your PhD here?

00:16:26: How did this feel like for you?

00:16:28: I think at the beginning, it was a bit lost.

00:16:31: Did your only apply to Münster?

00:16:34: The application is very easy because I asked Linus if he could help me find a position anywhere else and he said that precisely He had three PhD students that were all about to finish.

00:16:49: Ah, okay!

00:16:51: It's all about chiming?

00:16:52: Yeah I was very lucky then Same...I mean it was possible for me to have financing from my position precisely because someone just got a permanent job at another institution.

00:17:02: and yeah..it's

00:17:04: a lot of luck.

00:17:05: In academia you have so much luck as crazy.

00:17:09: When your master sees this i think you did some research some proper research right?

00:17:14: Yeah, exactly.

00:17:15: Venus gave me a paper that was like... ...a certain proposition on someone's PhD thesis many years ago.

00:17:23: That was full of mistakes And so first I corrected the mistake and in the end The result is not as good as what he aimed to prove but of course didn't even prove it.

00:17:36: With this results we could apply something which had been done for compact groups two locally compact groups.

00:17:44: So then it was probably not so hard for you to transition into some research mode, because I think from my master's thesis this was mostly expository maybe very tiny extra but really doing research was quite hard at the beginning.

00:18:02: Yeah no...I mean also i spent a year only reading because I had to learn I didn't know group cohomology.

00:18:14: Is your project now related to your master's thesis?

00:18:17: No, no.

00:18:18: So this year I just read a book for like almost a year and then i also had to learn about condensed math... Oh

00:18:25: it was pretty

00:18:25: tough!

00:18:26: ...I knew the definitions but that's it.

00:18:29: so then i think i started doing new things by end of first year only.

00:18:35: Yeah.

00:18:35: When did you start to become so active in student life, like being the representative and organizing something?

00:18:40: You think that being a mentor was always clear... Did you already do it before in your master's or...?

00:18:45: No!

00:18:46: Was this like the PhD community here?

00:18:48: The motivating factor for you?

00:18:50: Yes

00:18:50: exactly because Simone convinced me to say one thing about his podcast Before you Because he is really very active.

00:18:57: I'm involved with him And i was kind of office-made within I don't know.

00:19:04: He became friends and he told me, ''I'm going away someone has to do this you could do

00:19:09: it.''.

00:19:09: And then i said yeah okay why not?

00:19:14: Then also thought that's nice too... I always complain about the way things are organized but finally have an opportunity to do so.

00:19:25: About being a mentor This is what I wanted because when I was in the master thesis I was the mentee and it actually helped me a lot.

00:19:37: Marga is my mentor, we have like group of female students.

00:19:42: so then i thought its also nice to give something back.

00:19:46: Nowadays how does typical day of research look?

00:19:50: Is there a typical or everyday different?

00:19:54: It's more-or less every week differently... I get tired of working in the same place more or less within a week.

00:20:04: So, sometimes i wake up at eight go to the gym and then work.

00:20:08: Sometimes i wake-up Go to the Gym and Then Work again.

00:20:12: Yeah, sometimes I work here some times I work In my house sometimes I'm working At Cafeteria yeah...

00:20:19: I think..I also kind of related that like Especially if you have to do something creative, it's really hard to be in the same place all the time because we just get stuck and circled.

00:20:30: I

00:20:31: also like having people around.

00:20:33: so sometimes i go into a common room or library.

00:20:36: Yeah of course!

00:20:37: I mean...I love the common rooms for example but I feel like in the common room, i can't really get work done.

00:20:43: No!

00:20:44: Yeah you have to be very focused on it and when i have a certain goal that i know exactly what i need to do then there i work amazingly.

00:20:51: Like if i had to type something also

00:20:53: doesn't

00:20:54: require too much thinking... Common Room

00:20:56: is perfect.

00:20:58: But yeah.. Also i really liked being at the library with other people and co-working because i love co-workers.

00:21:03: And

00:21:04: we also felt pressure about

00:21:05: not

00:21:06: wasting too much time cause they will

00:21:08: judge you.

00:21:08: Exactly.

00:21:10: But if you want to have a day where your mind is more free, what do you do to relax?

00:21:17: What places do you like maybe.

00:21:21: I mean in summer... Yeah!

00:21:23: ...I go into the canal

00:21:24: alot

00:21:24: and i also like open swimming pool close here of fifty meters because i like swimming alot Otherwise just going for walks or gym running.

00:21:38: I like doing physical activities, so anything like this works.

00:21:43: Now that we've gotten to know Raquel We will come the second part of his podcast So-called A or B game.

00:21:50: For this game which consists of roughly eight thirty a or b questions i would ask Raquel To answer as quickly as possible in order to get an idea about her intuitive thoughts.

00:21:59: The first question is zero or one?

00:22:04: Zero

00:22:06: Coffee or tea?

00:22:07: Coffee

00:22:08: Beach or mountains?

00:22:09: Beach

00:22:10: Spring or autumn?

00:22:13: Running of swimming.

00:22:15: Snooze, getting up.

00:22:20: Order or chaos?

00:22:23: Disconnected or

00:22:25: connected?

00:22:27: Geometric or algorithmic?

00:22:30: Program or calculation?

00:22:33: Proof or count example?

00:22:36: Topology or geometry?

00:22:39: Condensed or classical?

00:22:43: I think i have to say condense.

00:22:46: Yeah, what is hard?

00:22:51: Mentoring or teaching?

00:22:54: Co-homology or homotopy?

00:22:57: Aida loveless or amenuita?

00:23:01: Blackboards and slides?

00:23:04: Post our talk!

00:23:06: Work at home or work in the office?

00:23:08: Office

00:23:10: Mensa-mring or home cooking?

00:23:12: Home cooking.

00:23:14: Castellou, Valencia?

00:23:18: Castellon.

00:23:20: Valentiano and Castellano?

00:23:22: Castella.

00:23:23: Tragedy of comedy?

00:23:25: Tragedily.

00:23:26: Improvised or rehearsed?

00:23:28: Improvised.

00:23:30: Piano or guitar?

00:23:32: Guitar.

00:23:33: Clapping or knocking?

00:23:34: Clapping!

00:23:36: To be or not to be?

00:23:38: To

00:23:38: be?!

00:23:39: Great so that's already it.

00:23:42: okay

00:23:43: great job.

00:23:45: So, for the final part of our podcast I always ask specific set-of questions where i want you to answer with like one or two cents even though the question might be very hard.

00:23:56: The first question traditionally is what your favorite mathematical theorem?

00:24:01: Oh my god!

00:24:03: The Seifert-Bankampfen theorem.

00:24:07: To be honest don't remember this statement But I always, it comes up.

00:24:13: It's always useful or... Okay actually no!

00:24:17: I don't want to say this

00:24:19: change.

00:24:20: My favorite one is the Yoneda Lema because you never expect that these stupid little things are gonna be useful but its always there

00:24:30: Especially also in condensement.

00:24:35: Which of your results and achievements are most proud?

00:24:37: I only have one result

00:24:39: No, but it can also be general achievements.

00:24:41: General

00:24:42: achievements?

00:24:43: Like managing to go to Germany without fear for example... Can mean everything!

00:24:48: Or you could also as a result

00:24:52: I would say staying in Münster for such long time even though its hard sometimes.

00:24:59: Why is that hard?

00:25:01: It was hard from the master's point of view because literally everyone knew left.

00:25:07: So then i thought maybe I won't find France again.

00:25:10: But

00:25:12: it did!

00:25:13: Yeah, yeah... I understand that very well.

00:25:17: Which Mathematica field might you have chosen if not your current

00:25:20: one?

00:25:22: I guess topology.

00:25:24: Kind of doing topology with condensed math or other right?

00:25:26: Not really..

00:25:27: It's a

00:25:30: very group theoretical

00:25:31: idea.

00:25:34: Is there something in your professional life which would've done differently from the point of view today?

00:25:41: Yeah, okay.

00:25:41: So I always regret not talking to people that should talk too like.

00:25:45: I know there's people Why could benefit from talking to but I'm too shy to say hello Can ask you something.

00:25:54: so I never do it and I think in the end they waste a lot of time.

00:25:58: Yeah, it's always tough.

00:26:00: Especially if you don't have like very clear cut questions.

00:26:02: Exactly!

00:26:03: Like everyone tells me yeah just go ask this question.

00:26:05: they know and I'm like yeah but what am i gonna say?

00:26:08: my research?

00:26:08: And why should they be interesting?

00:26:10: maybe they don't care

00:26:12: Okay...and finally What advice would you give a student-like a bachelor student early bachelors maybe considering math research today?

00:26:22: So I think the most valuable thing that you need to have in order to do a PhD is motivation.

00:26:28: Like, uh...I don't think it matters so much whether you are super smart or super dumb like.. I don't- I dont' think this is something to begin with.

00:26:36: yeah what makes you smart and Is wanting to spend enough time working on it?

00:26:43: So if you have enough motivation i think You're gonna be successful

00:26:46: and probably you also have to love it, right?

00:26:48: Yeah.

00:26:48: This is what I mean

00:26:49: with

00:26:49: motivation because if you like them then we will spend enough

00:26:54: time on that.

00:26:55: Yes!

00:26:55: And this is one of the most underestimated factors.

00:26:59: It's

00:26:59: always when i meet someone who says they are doing a PhD in Maths They say oh you must be a genius and I always say no its just...I like it.

00:27:08: so then it easy for

00:27:09: me.

00:27:09: That sounds nice Amazing.

00:27:13: So thanks alot.

00:27:14: Thank You

00:27:15: and we will see each other in the second part, where you tell us a bit about your

00:27:43: research.