Episode 9: Random Walks & Long Runs, with Elisabetta Mazzolari

00:00:03:

00:00:10: From Mathematics Minister, this is On a Tangent.

00:00:13: The podcast where we tell the stories behind mathematics and explore fascinating paths that lead early career researchers to Minster.

00:00:21: My name is Carlo Kaule.

00:00:23: I'm PhD student in Arithmetic Geometry And have the privilege of following in the months footsteps To bring new stories for you In the month to come.

00:00:31: For the second episode Of This New Season i am joined by Elisabetta Marzolari.

00:00:36: Elisabeta's academic journey began in Italy at the University of Pavia where she completed both her bachelor's and master's degrees.

00:00:43: During her master studies, a research study took her to TU Delft in the Netherlands Where She finished her thesis on large deviations And the Curie Weiss model.

00:00:53: In October of twenty-twenty five she moved to Münster To work as a doctoral student at the group of Matthias Löwe.

00:01:00: So it is great to have you Elisabetta.

00:01:01: Thanks

00:01:02: for having

00:01:03: me!

00:01:05: The first question always asks what your childhood mathematical memory

00:01:10: was.

00:01:10: So, I don't know if this is my first mathematical memory but... ...I have this picture of myself at the kitchen table in my parent's house.

00:01:21: While doing one of my first mathematics homework under the supervision from my mother and i guess that problem was something like if I have three apples and they give you one apple, then how many apples do we have left?

00:01:35: Yeah.

00:01:35: And yeah...I remember that i was liking a lot this type of problem because once you understand the mechanism there is behind them everything gets very easy and it's easier than in looks.

00:01:47: and yeah..i guess this my first

00:01:49: memory.

00:01:50: So your mother was a mathematically involved person or...?

00:01:54: No no actually but she liked a lot mathematics.

00:01:56: She still

00:01:56: likes a lot Mathematics.

00:01:58: So I think she kind of influenced us a bit.

00:02:02: Great, and this was in Pavia.

00:02:04: or where did you grow up?

00:02:05: No so i grew up In small city north of Italy.

00:02:09: it's very close to Pavia.

00:02:10: The city is called Cremona.

00:02:12: It

00:02:12: has a very pretty city

00:02:14: Very nice.

00:02:17: Then you went to your school and high school, so at what point did you realise that it was more than like a kitchen table hobby for you?

00:02:27: And really something which you have lot of interest in doing.

00:02:32: Wanted maybe do study also later.

00:02:36: Yes well I was very indecisive between options.

00:02:41: At first, I was very oriented towards physics.

00:02:45: Then at some point... ...I wanted to do medicine and then even philosophy And the end mathematics of course.

00:02:53: So one day when speaking with my team-mates.. ..I was doing basking.

00:02:58: at that time She told me she was studying mathematics in university And i found it interesting!

00:03:07: But from this moment on doing mathematics at university started to become a concrete option.

00:03:16: So also, this was I think my last year or second-to-last year of high school and that time i had very good teacher in

00:03:26: my class...

00:03:27: And not so good teacher with physics if can say!

00:03:31: Of course!

00:03:34: Those factors led me to choose mathematics at the end.

00:03:39: Did you have any concept of what studying math would be like?

00:03:43: No, actually I was attracted in high school.

00:03:46: that it's good but not just because there is a particular talent... ...I think he wanted to learn and study new things But then no!

00:03:57: I didn't had many ideas about it.

00:04:00: It was my right choice.

00:04:02: So then you decided at some point that you want to study mathematics.

00:04:06: And so how did you choose to go to Pavia?

00:04:11: and what was it like for you this time?

00:04:14: I don't know, i chose...I feel a lot of things in my academic part were led by chance.

00:04:22: I don' t want me be misunderstood but really I wanted to go to university in Favilla because also some of my friends were studying there.

00:04:34: It's a very good University that we have here, and it is kind-of close to my hometown.

00:04:40: so this was the perfect solution.

00:04:44: And then yes...I decided both for my Bachelor and Master to do a general curriculum Because they didn't want to specialize on only one topic in mathematics.

00:04:56: So, for instance I did my bachelor thesis in algebra and it was about the construction with straight edge and compass.

00:05:03: And connection to Galois theory... ...I liked that a lot!

00:05:07: Then during my master's I kind of shifted my interest towards probability but i didn't see as cut.

00:05:16: It is just more natural changing of my interests.

00:05:22: So yeah, then I decided to write my master thesis in probability.

00:05:28: But actually it was also very fed up with the city because i studied in same city both for Bachelor and Master.

00:05:36: And a lot of friends they left at some point.

00:05:40: so...I applied for the Erasmus trainship.

00:05:45: go to Delphi in the Netherlands, write my master thesis.

00:05:48: What was for you like a strongest difference between studying in Italy and studying at the Netherlands?

00:05:54: In the Netherlands I did the Erasmus, it's called the Erasmus traineeship.

00:05:58: so i didn't have to attend lessons or give exams because just my masters thesis.

00:06:04: So I felt that I was more part of the academic environment not as student studying and then doing exams, attending lessons.

00:06:16: Would you say the hierarchies were flatter in Netherlands?

00:06:19: or what was your

00:06:20: main reason?

00:06:21: Exactly!

00:06:23: For sure their relationship is very less hierarchical than those I had in Italy with my professor And also when I spent in Netherlands.

00:06:33: it was first contact of academic environment because I had a weekly meeting with my supervisor and where there was discussing the doubts that I have, problems while writing my master thesis.

00:06:49: And also showing her progress.

00:06:52: in the meanwhile i could speak all day to her PhD student about what is fascinating for me and our research field.

00:07:02: And so yeah, it was my first contact with the academic environment.

00:07:06: So this is very interesting because you said that you did your bachelor's season algebra and of course I'm very attracted to Alra naturally from what i am interested in.

00:07:15: Do do remember how they shifted probability?

00:07:20: Was it like more appealing than its applyable?

00:07:24: I would say much more then algebra for example.

00:07:27: Yeah...I feel maybe I needed something that could be more applicable in some sense.

00:07:37: But also, it was very tailored by the professor there.

00:07:42: yet so i had a good professional capability and they stimulated my interest alot.

00:07:50: A real part of my interests in mathematics is due to Professor there.

00:07:56: yet How much students were you in your master's classes?

00:08:00: Master

00:08:01: very few, around ten.

00:08:02: Yeah we were super few

00:08:04: The same thing where I studied for a masters.

00:08:07: so there i had also close relationships with the professor because courses was small.

00:08:13: You just have good mentor

00:08:16: At least in the bachelor, it was super cold with my professor.

00:08:22: But then we were few so I got to know him a bit better...

00:08:28: How did you come up specifically with Delft?

00:08:30: Why not another university team?

00:08:32: My thesis is at first to be a professor of Pavia, where I studied.

00:08:39: And he had a contact with this professor in the Netherlands, and it was very interesting for me that there were statistical mechanics.

00:08:48: So I decided to go there basically... He has a contact so i could have done everything like living.

00:08:58: And so you didn't know your Delft master advisor before, but it was just a match?

00:09:06: Yeah

00:09:06: exactly.

00:09:07: It's also Italian

00:09:09: and

00:09:10: I liked their supervision very much!

00:09:13: She had a really nice group with two PhDs and they helped me a lot.

00:09:17: And how did this work?

00:09:19: In your meeting society, you talk in Italian or English...

00:09:21: No we were talking in English because also those meetings are attended by

00:09:26: two

00:09:27: PhD students.

00:09:29: Sometimes there was like zoom-meeting connection with my other supervisor in Italy but these meetings were very interesting Also super intense.

00:09:38: We spent the whole afternoon together on our own with Blackboard.

00:09:43: Ah, really?

00:09:45: Yeah it was very interesting.

00:09:46: So you just discussed everything that came to mind...

00:09:49: Exactly for the progress I made in one week.

00:09:52: of course the topic is also kind-of easy so not a big deal but yeah

00:09:58: Very cool!

00:09:59: Then were you deft.

00:10:01: and how did this happen after you came to Münster?

00:10:04: Basically deft was my first encounter with the academic world Because before, when I was in Italy... ...I didn't really know how to do a PhD.

00:10:16: But at the Netherlands it was much more attractive for this kind of environment.

00:10:23: So i decided to apply for my PhD And my supervisor in the Netherlands suggested to apply for a position here, because she visited some weeks before university and had very good impression.

00:10:40: Also there was this perfect match Because one of the main papers that I studied with my master thesis is written by my

00:10:50: current

00:10:51: supervisor.

00:10:53: So it's really cool!

00:10:54: You meet your heroes after?

00:10:56: I can also very much relate to that.

00:10:59: To me it was really cool.

00:11:01: finally meet the person, you read the papers from all time and like always see this name.

00:11:06: then there is a person behind them.

00:11:07: Exactly!

00:11:09: Yeah i really liked as well coming to Münster.

00:11:12: So, my office is right across from you through the window kind of and I see your like very studying a lot.

00:11:19: And so what does this process do?

00:11:22: You know that blackboard at Whiteboard...so i have Blackboard in My Office but you have whiteboard!

00:11:29: I think it's like a different culture between different fields of math..I feel like in mine field people hate whiteboards.

00:11:37: maybe it's also me and everyone only wants.

00:11:41: I also get why it's annoying, because you'd see my red blackboard is quite full and when i write always white things.

00:11:47: I have to wash my hands because my hand is clogged.

00:11:49: The

00:11:50: problem with that too like when you cancel things or try to erase then the chalk still on board.

00:11:58: so its not very practical.

00:12:00: You prefer practical things?

00:12:05: Other than writing about white boards.

00:12:08: how does researching look for your?

00:12:10: So I don't know, in this...I just started.

00:12:14: so i started a couple of months ago.

00:12:16: So I'm still in these grey area where I really do not what am doing but hope that it will lead sometimes to something.

00:12:24: Yes!

00:12:26: But now im studying a lot of literature and reading some paper and my supervisor just proposed me this first project that I'm working on.

00:12:38: so either i have a meeting with him where I discuss mainly the things, which can not be understood.

00:12:45: And sometimes they also show progress!

00:12:50: The other day basically I studied these papers... ...and started to borrow some books from the library.

00:12:59: They are super interesting.

00:13:01: So you use someone who uses the library and not very few people do that.

00:13:05: That's great!

00:13:05: Recently, but yeah it is really nice.

00:13:08: so basically I try to learn as much as i can.

00:13:10: Yes The goal for this period

00:13:13: Yeah...I think its a good idea.

00:13:15: at least I also tell myself because I am in similar periods of my PhD.

00:13:19: now Other than being at university or common room what do like most about city?

00:13:26: Oh..so My favorite part of the city is that there's a very bike-friendly city.

00:13:34: So I think i'm emotionally attached to bikes because also in my city, where I was born and where I lived There is Cremona.

00:13:44: It's a small town so we go everywhere by bike.

00:13:50: Is it as flat?

00:13:53: We are in this flat that is Canura Padana, so basically zero months.

00:13:58: That's good!

00:14:00: So yeah it my favorite means of transportation and only the one I use.

00:14:07: And also you have a beautiful bike.

00:14:08: I have to say Thanks for saying because

00:14:12: yes i think its super pretty bike But please that like alot on city Saturday market.

00:14:21: There is in Domplatz.

00:14:23: So one of my favorite activity, it's going there And go for a walk and then buy some Vegetables some fresh vegetables.

00:14:32: Wow you really buy vegetables?

00:14:33: Yeah I feel like most people i know go there to eat and grab something to

00:14:37: eat.

00:14:37: That the second part before

00:14:38: they

00:14:39: got here to eat this stand.

00:14:40: that is incredible.

00:14:41: It´s a Greek stand.

00:14:42: Okay...I like it alot.

00:14:43: Then They give you these...it´s called student box.

00:14:48: No, no it's great.

00:14:49: It was amazing!

00:14:51: I didn't know that i have to look for the next time.

00:14:54: yeah a great idea.

00:14:56: and if you're like not biking to work or at the market what do you like to do?

00:15:00: For coming down relaxing after full day of thinking about probability?

00:15:08: So these last two years i guess i developed this very strong passion in running And it is an activity that often clears my mind, but also just fun.

00:15:22: I go for a run and maybe the sun is shining there's very nice wind.

00:15:28: so after death life feels perfect you know?

00:15:33: There isn't any more chaos.

00:15:35: So i like running alot and started almost two years ago In Germany during the winter.

00:15:45: it's kind of hard but now there is starting like spring season to be back on track.

00:15:54: The day of recording the podcast is like, it's a very beautiful day again after winter.

00:15:59: so I think we are almost through.

00:16:02: We made it!

00:16:03: Exactly What do you recommend?

00:16:07: Where to go running best in Münster?

00:16:08: So...I

00:16:10: live on a neighborhood that was given back and there were many fields But also, I guess it's going to be very interesting running in the promenade.

00:16:21: And i was doing this calculation at end of day.

00:16:24: we are mathematicians

00:16:25: and that is

00:16:26: what we do!

00:16:28: The promenades plus ase should be like around ten kilometers.

00:16:33: so would like to prepare an half marathon.

00:16:35: Wow impressive.

00:16:37: And if I follow this route and to run around the promenade as they are, there should be enough marathon.

00:16:41: Yeah

00:16:45: great!

00:16:46: Very impressive.

00:16:50: Now that we've gotten to know Elisabetta We will come to second part of his podcast The so called A or B game.

00:16:56: For this game which consists roughly thirty A orB questions i'll ask Elisabeta To answer quickly As possible In order get an idea about her intuitive thoughts.

00:17:07: Zero or one?

00:17:08: Zero

00:17:09: Analysis or algebra?

00:17:11: Algebra

00:17:12: Coffee or tea?

00:17:12: Coffee Beach or mountains?

00:17:15: Mountains

00:17:16: Snus, or getting up?

00:17:19: I would like to say getting up

00:17:21: and then in his nose.

00:17:22: I agree.

00:17:23: Order or chaos?

00:17:24: Chaos Summer or winter?

00:17:27: Summer.

00:17:28: Conceptual proofs or technical proofs?

00:17:31: Technical proof

00:17:33: James Blunder one republic?

00:17:36: One Republic IID or not When the random walk or brawnian motion?

00:17:43: Random Walk.

00:17:44: Cycling in Delft, or cycling in Münster?

00:17:46: I think...cycling

00:17:51: in Münstern!

00:17:52: You have to say that

00:17:52: right?!

00:17:55: The law of large numbers are the central limit theorem.

00:17:59: Blackboarder's lights?

00:18:01: Blackboard.

00:18:02: PDF for physical copy?

00:18:03: Physical copy.

00:18:03: I'm

00:18:04: sorry

00:18:06: for the trees, but... I also agree.

00:18:07: It's such a nice idea if you can write things like that.

00:18:10: Delft or The Hague?

00:18:12: Delft!

00:18:13: Italy or Netherlands?

00:18:15: Italy!

00:18:16: Pavia o Milano.

00:18:21: Great.

00:18:22: Pavia or Cremona?

00:18:23: Cremone.

00:18:25: The Ligurian Sea of the Adriatic Sea?

00:18:27: Ah, Liguria.

00:18:27: For

00:18:28: sure.

00:18:29: The North or South?

00:18:33: South.

00:18:34: Paris or Rome

00:18:35: Room.

00:18:36: Microscopic or macroscopic?

00:18:40: Microscopy.

00:18:41: Qualitative or quantitative?

00:18:44: Qualitive.

00:18:46: Biking or running?

00:18:48: Running.

00:18:49: Medlab or R?

00:18:52: R. Okay,

00:18:53: ruler or compass?

00:18:56: Compass.

00:18:58: Discrete or continuous?

00:19:00: Discrete.

00:19:01: Way for a particle

00:19:04: Wave of particles.

00:19:06: Paris or Normandy?

00:19:08: Paris

00:19:09: Sicily or Sardinia?

00:19:11: Sicily.

00:19:12: Probability theory or statistical mechanics?

00:19:15: Probability theories, in general

00:19:17: Exact or asymptotic?

00:19:19: Asymptotic

00:19:21: Calculation or proof?

00:19:22: Proof.

00:19:23: Physics or chemistry?

00:19:24: Physics Constant external fields or random external fields?

00:19:29: Random external

00:19:30: fields.

00:19:31: Clapping and knocking

00:19:33: clapping.

00:19:34: To be or not to be?

00:19:35: Too good!

00:19:36: Great, that's already it so you didn't need any skips here.

00:19:40: Yeah but actually I'm not very sure about someone's answer they're gonna

00:19:44: give

00:19:44: because there was...I mean i was thinking fast because of the pressure.

00:19:47: That's great Because uh..you should always just say this is first thing that comes to mind.

00:19:52: So was Pavia or Krimona hard for you to decide?

00:19:54: Yeah,

00:19:55: it's very hard.

00:19:56: Because I guess that some years ago i would have said pavia.

00:20:00: so I kind of escaped from pavia and from krimona To study in pavia also.

00:20:04: I lived with two my best friends.

00:20:07: It is the ideal setting But now that Im abroad I feel like that Krimonah is my true home because also My parents are here And now Some of them are there.

00:20:18: You said you were living with two of your friends, so do like to live with other people more?

00:20:23: Like flatmates forever.

00:20:26: I think that i really enjoy my self-presence for the presence of myself but it's very nice when we share our flatmates.

00:20:36: So you said, do like technical proofs more but don't like calculations as much right?

00:20:42: Yeah exactly.

00:20:42: This is the point I mean...I really liked the rigor that's behind a technical proof But i hate calculation.

00:20:50: and also maybe it was because of trauma now Because im getting through a lot of calculations And Im having nightmares with

00:20:59: them.

00:21:01: So you have to sort of like big integrals?

00:21:03: Yeah,

00:21:04: exactly.

00:21:05: To me this is a nightmare but I guess i have go through them.

00:21:11: You also don't play as much around with the computer and programming things?

00:21:16: No, zero.

00:21:16: I'm pretty terrible With technology in general.

00:21:22: yeah...I am not very much Gen Z. Really

00:21:26: I'm terrible.

00:21:26: You never need to use your computer for any calculations or something.

00:21:29: No, zero.

00:21:30: Thankfully it's zero.

00:21:32: So you would also say your research topic is more pure math?

00:21:36: Yeah

00:21:36: actually its not very applied.

00:21:40: It's probability theory that

00:21:43: you can apply but... You don't want to be the person applying it

00:21:46: right?!

00:21:48: Exactly!

00:21:49: I actually like it because sometimes what i'm doing really isn't applied.

00:21:58: But sometimes I feel like if you could apply it, that would be nice.

00:22:02: You can tell people this is why i'm doing this.

00:22:06: You do these because in the talk then we say okay and we can apply them to a very good setting but of course don't do those things.

00:22:14: Just study very few concepts which are really nice.

00:22:17: Another

00:22:18: thing I was curious about... You talked about German winters, so would you say that?

00:22:25: Do you miss the weather in Italy a lot or do like have you settled?

00:22:29: and already because he went there Hague before and Delft.

00:22:34: So I think in general.

00:22:35: I miss it Italy a Lot Because there is where my friends and family

00:22:39: of course

00:22:39: this is the main reason.

00:22:41: um i Think easily adapt to every situation.

00:22:46: Yeah feel like disease now my my own.

00:22:50: And actually I come from the north part of Italy.

00:22:54: So there, weather in winter is not very nice and it's almost like this.

00:22:59: but now my mother is sending me a lot of pictures... Of the sun that is now in Cremona with twenty degrees.

00:23:07: The other day here was raining and i was super jealous.

00:23:12: So for the final part, I always want to ask five questions.

00:23:16: Try to answer like in one or two sentences but like... The five things that i wanna know of every everyone im interviewing.

00:23:22: so first thing is what's your favorite theorem?

00:23:28: I don't know.

00:23:29: I don't know if this is my favorite theorem, but we mentioned it also in the A or B game.

00:23:34: I think... I'm attached to the central limit theorem because It's one of the first theorems that you study The First Probability Course That You Take at University And Also Its Extremely Super Recurring Because i am now studying In different settings.

00:23:49: But Central Limit Theorem So yeah!

00:23:52: I would say the Central Limits Theorem Yeah

00:23:54: there are a lot of them right?

00:23:57: Great.

00:23:57: Which of your results are you most proud off?

00:24:03: I don't know, but so far i would say my master thesis like having the opportunity to do my master's thesis in depth and like...I applied for the traineeship project then scholarship and then I also think having the position here is a thing that i should not take for granted.

00:24:23: Certainly, it's very tough!

00:24:26: I agree yeah great what mathematical theory would you have gone into?

00:24:30: Oh this was also really interesting to me in the A or B game.

00:24:33: he said algebra not analysis.

00:24:35: how can?

00:24:39: So would it have been algebra?

00:24:41: I guess so.

00:24:42: And i also know that you can kind of work in the intersection between probability and algebras, some people here in mincer are doing this... ...and..I think its very interesting!

00:24:52: It could be a perfect mix.

00:24:56: Very nice!

00:24:58: What is what do say should u or what you've done differently with experience today during all your time until you came here?

00:25:08: So I don't have a lot of regrets actually.

00:25:11: Great!

00:25:12: But maybe, i would've enjoyed doing the whole master abroad because they really enjoy my time in Delft and it was very little...I mean..i only stayed there for some months but maybe during the whole Master Abroad It will be nice experience both professionally also like personally.

00:25:33: Yes sure cool.

00:25:36: Finally What advice would you give a high school student who is now thinking about if she should go into math or what she should pursue?

00:25:45: Would be your one advise with all the experience that we have today.

00:25:50: Very tough question I know!

00:25:52: Yeah exactly!

00:25:55: Don't be afraid of math, i know that math could sound intimidating.

00:26:00: it actually is,

00:26:02: but

00:26:02: often like a hard work and true commitment really pays off.

00:26:07: This is very meritocratic... this is a very meritocratical word.

00:26:12: so I guess yes don't be afraid of doing

00:26:14: it!

00:26:14: And workout!

00:26:17: Great.

00:26:18: thank you very much for coming here today and was very nice talking to you.

00:26:22: we will see each other in the video part.

00:26:27: if you enjoyed the conversation with Elisabeth as much Please consider sharing this episode with a friend or colleague.

00:26:34: In the show notes you can also find link to video part of my conversation with Elisabeth, where she shows her probability.

00:26:41: theory can be used to explain why meta suddenly changes behavior.

00:26:46: I'm Carlo and i will catch on next tangent.