WEBVTT
Kind: captions
Language: en

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[Music]

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It makes you feel like your brain is
able to do something big, and it's also

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a very very happy moment, and it's just
like... the reason why I keep doing the job

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that I have, and the reason why I accept
the defeats that often happen in this

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kind of work, and I think over the years
what I notice is that the feeling of

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finally being able to finish the proof,
it is as intense as the first time when

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I started my research. My goal was not to
be employed in one of the best

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universities in the world or proving the
most important theorem, but I had been

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very lucky. I happened to be somehow in
the right place at the right moment. So I

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grew up in a small town in Italy, in a
very rural part of Italy, and all my

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family, they were all farmers - so there
was no math people at all. In fact, I had

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no idea that you could have a career as
a mathematician. And unfortunately, my

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father died when I was 10, and it was a
very chaotic moment. Working on math

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problems was somehow a way of bringing
into my life some kind of logic order,

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which I always felt like I needed. I need
things to be pretty organized so that

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was just a way of coping: a coping
mechanism with the situation. In Italy at

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that time, high school was not mandatory,
but my brother, luckily for me he's 10

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years older, and being a boy he was the
one who was supposed to improve the

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the situation. So he was already assigned
as the first that will go to college and

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convinced my mother that I need to go to
high school. And this high school I went

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to, it was a very rigorous science school
with a lot of emphasis on math and

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physics. And so that worked out well for
me because I really liked math,

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and at the end of the high school was
again the question what I will do.

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There was not much money at home, but I
had a great math teacher in high school,

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and he convinced my mom to send me to
college and study math, so then I would

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become a high school teacher like
himself, and it would be a great job for

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a woman. And I picked University of
Bologna as a college without really

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telling anybody, because I had friends
that went there, but in particular

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because there was a boy who really
liked me [laughing]. So I was very lucky because

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University of Bologna is actually an
excellent place to study mathematics, but

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when I started learning more sophisticated
mathematics, I just decided: This

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is what I like to do, I would like to do this
for as long as I can. And I realized that

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there is a way of doing it beyond
college which is doing a PhD which I

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didn't know what it was, or why
people would do that. I just wanted to

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keep doing research, so I started my
research on my PhD thesis in a field

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that at that time was just at the
beginning. So, by default, I became an

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expert in the field. So if I had started
my PhD two years before or three years

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later, maybe this would not have happened.
I work on the pure side of partial

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differential equations, which is a branch
of analysis. And within this field I

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study something called dispersive
partial differential equations. So, these

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equations come from physics and they had
a long history very often. I do not make

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up the equations, but since they cannot
be solved directly, with abstract tools

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we try to figure out what are the
properties and qualities of the solutions

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without really being able to write
them down, by inventing or discovering

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certain elements in abstract mathematics
that will give us answers to questions

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that originally might come from physics
and in practice are solved in this more

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abstract setting. So what I like about
that is not really giving the physical

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answer, but actually discovering the
invention of the tools that will bring

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us to those answers.

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[Music]

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So there has been a
defining moment in a sense in my research, and this sort of started in a
negative way.

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I was at Institute for Advanced Study and I
was supposed to give a talk, and the

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night before I reviewed my talk and was
ready to give that talk the day after, but at

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the same time I got an email from a
Japanese mathematician who said that he

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actually wasn't sure about a step in a
certain paper which was the same paper I

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was presenting the day after. And so it
turned out that I wasn't sure about that

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step either at that point, so I couldn't
really give that talk. It was a very

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negative moment, let's put it that way,
but what happened is that from

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investigating further this particular
step in the proof of that particular

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theorem, I started a collaboration with
this Japanese mathematician and at the

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same time a collaboration with two other
Americans. All of our names are Colliander,

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Keel, myself,
Takaoka and Tao, and now we are called as the

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"I team", so we worked a lot together. We have
a lot of very good papers together, we

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are now known as a team somehow, and that
was a very important moment for the

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evolution of my research. So I started
from a negative thing, but it ended up to be

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probably the most fruitful path to my
career so far.

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[Music]

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So, to explain it in a simple way, it basically says the following: Since the
equations that I studied come from

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physics and in physics if a system is
closed and there is no interaction from

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outside, you expect there are certain
things that remain the same, constant in

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time. For example, the energy, the total
energy of the system. But in order to be

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able to write mathematically what
energy is... Usually the energy is

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composed of the kinetic part and the
potential part, so you have to write a

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certain integral. To make sense of them,
the function that you are integrating

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has to be a sort of certain regularity,
or else you cannot write it down. In our

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invention of this "almost conservation
law" what we did was, well, the solution of

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the equation that we are looking at didn't
have enough regularity to be able to

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write those integrals, and hence you
cannot even talk about the conserved

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quantity. But what we did was: We modified
the function a certain way to give it a

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little bit more regularity, and then
being able to write the same formula for

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the conserved law. But since what you
have doesn't have the right regularity

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it's not quite conserved - but it's
almost conserved, and that

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still gives you a lot of information. And
then, we're trying to make the object

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which is not as nice nicer to be able to
use something which is physical, but of

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course because you made an approximation
to start with, what you have is not

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something that remains constant in time
but almost does, and that helps.

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[Music]

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I actually feel like I have been very
lucky to grow up in Italy, because in

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high school, girls were supposed to be
better than boys and that's the message

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I got, so I didn't really worry about
being good in math and I didn't feel

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like it was something that will make me
less attractive in high school. So in

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college I guess it was even better somehow,
maybe because you already start with

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a cohort of people that just like math,
and you spend most of the time with

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that cohort. But a big difference came
when I moved to the United States and

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that was something that I was not
expecting, you know. I wasn't aware or I haven't

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had any idea that there was an issue. And
again, when I was doing my PhD

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I had a lot of issues at the beginning: I
didn't speak any English, there was a

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very different way of learning math,
there was a lot of homework that I was not

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used to. So at the beginning, I didn't pay
attention to anything, it was just kind of

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survival mode. It was more towards the
end of my PhD that when there was the

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process of looking for a job for the
next step like a postdoc, that I started

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realizing how mean somehow the
environment was for women, and in

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particular the first time of
understanding of this issue

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unfortunately came from my colleague
grad students. In fact, when I

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received my offer to spend a year at the Institute
for Advanced Study and two years at

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Stanford University, well, a couple of my
male colleagues said: "Oh yeah, that's

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because these are women jobs, that's why
you've got these positions" and I was

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completely taken aback by that
observation. And then I have started looking

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more into this issue, and it's true - there
are positions that are

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specifically set up for women in order
to increase the diversity of the various

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departments, and although I had no proof
that these positions that I obtained

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were for women, there was none of that
written, then I start doubting and this

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somehow stayed with me and stays with me
until now unfortunately, so...

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[Music]

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Maybe it's a good idea to ignore what usually the voice tells you,

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like: "Women
cannot do math, women are not good at science

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and women don't have the same kind of
brain". It worked for me to try to know

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them, and if you are witty or you
find some kind of cute and good way of

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responding, say that that's not the
truth. But it never worked for me:

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engaging in a very stubborn manner
to fight this kind of biases.

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I always did it in practice, like: I proved
theorems, I showed that I could do it,

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more than just talk and trying to dissuade
these people from thinking in this way,

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so I would say just go ahead. If you like
it, you will always find along the way

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people that will appreciate you. Maybe
not everybody, obviously, but you don't need

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everybody. You just need somebody who really
takes you under his or her wing and

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believes in you, and you will be going. So
just look for that person and do what

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you like.

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[Music]