
Maryam Mirzakhani’s Pioneering Mathematical Legacy - anthotny
http://www.newyorker.com/tech/elements/maryam-mirzakhanis-pioneering-mathematical-legacy
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therajiv
I knew Maryam was incredible the first time I heard her give a talk at
Stanford. To my fellow cancer researchers out there: this is about as good
motivation as we'll ever have to keep plugging along.

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adrianratnapala
So I am trying to undesrstand what her work was about. It seems fields medal
was for "the _dynamics_ and geometry of Riemann surfaces and their moduli
spaces" (my emphasis).

What is dynamics to a geometer? Clearly it is important -- because it is
important in physics. But I want to understand what mathematicians are getting
excited about.

We can talk about a family of geometrical objects foo(t) where the parameter t
is a single real value, which stands in for time. But -- other than its
relation to the physical world -- why is that $t$ parametrisation important?
Why not complex parameters, or multiple parameters, or something completely
different?

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stonesixone
My memory may be a bit fuzzy on this. But I believe one way the term
"dynamics" is used in her work is in reference to the space of Riemann
surfaces (or equivalently, the space of hyperbolic geometries on a surface).
This space is called moduli space. Certain topological operations on the
surface (e.g. twisting a "handle") give rise to a corresponding transformation
on moduli space. So one of the things mathematicians in this area can study is
the dynamics of such operations on moduli space. This means, for example,
studying the behavior of these operations on moduli space, in the limit.

Also, to a mathematician, "dynamics" can often simply mean studying the
behavior of iterations of a single function from a space to itself. So the
parameter "t" in this case is over the positive integers (or all integers if
the function has an inverse).

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c517402
The article does a very poor job of describing her work. Does anyone have
links to something understandable?

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Mz
[http://micheleincalifornia.blogspot.com/2014/08/links-on-
mar...](http://micheleincalifornia.blogspot.com/2014/08/links-on-maryam-
mirzakhani-first-fields.html)

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wfunction
Still bothers me that we didn't get a black bar. Can someone explain what the
criterion is?

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tptacek
Stories and threads on HN are, for the most part, a sort of community
property. The bar at the top of HN is not: it belongs to the operators of HN.
Litigating how and when they use it to express grief is not an especially
polite thing to do.

The easiest way, then, to understand the "black bar" is to think of it as an
expression of sorrow that has a direct connection to HN's operators.

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wfunction
If it was a private thing I would be totally with you, but the black bar's
entire purpose is to send a public message to the community. It seems natural
for the public reading the message to wonder why it was sent (or omitted) on a
given occasion. It's not "why aren't you grieving?" but rather "what message
are you trying to send us through displaying or omitting it?"

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jeswin
The public message is that "someone who has had a profound impact on YC, or HN
and its members has passed away". That impact is up to the operators to
decide.

Much the same way a family remembers their loved ones, but doesn't grieve
every important person who has passed away irrespective of their stature. Like
parent was saying, it's a little discomfiting to see this discussed on
threads.

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racl101
"this is about as good motivation as we'll ever have to keep plugging along."

So, other people dying of cancer not as good motivation?

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dang
Please be charitable when commenting here. That means responding to the
strongest plausible interpretation of what someone might mean, instead of a
weaker one that's more offensive or ridiculous.

We detached this subthread from
[https://news.ycombinator.com/item?id=14794057](https://news.ycombinator.com/item?id=14794057)
and marked it off-topic.

