PhD Woooooooooo

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MartianInvader
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PhD Woooooooooo

Postby MartianInvader » Fri Apr 09, 2010 10:34 pm UTC

Dissertation? Written and edited.
Thesis defense? Scheduled and completed.
Mountain of paperwork? Filled out and submitted.

...And that's a Math PhD, baby! This is a hell of a rush to finally be done.

As a bonus, I managed to work the phrase "Phase 3: Profit!" meaningfully into my defense. Boo-ya.
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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majikthise
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Re: PhD Woooooooooo

Postby majikthise » Fri Apr 09, 2010 10:45 pm UTC

Congratulations! I now have even more respect for PhD students after experiencing a big rise in headfuckery for masters year.

Which field are you working in (wild stab in the dark- does it involve lots of free groups)?
Is this a wok that you've shoved down my throat, or are you just pleased to see me?

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Cleverbeans
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Re: PhD Woooooooooo

Postby Cleverbeans » Sat Apr 10, 2010 12:55 am UTC

Congratulations, you must be very proud. :D
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Matterwave1
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Re: PhD Woooooooooo

Postby Matterwave1 » Sat Apr 10, 2010 4:32 am UTC

Did you also manage to incorporate: "phase 2: ???????"

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BlackSails
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Re: PhD Woooooooooo

Postby BlackSails » Sat Apr 10, 2010 4:09 pm UTC

Matterwave1 wrote:Did you also manage to incorporate: "phase 2: ???????"


I believe that is most of the PhD program.

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MartianInvader
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Re: PhD Woooooooooo

Postby MartianInvader » Mon Apr 12, 2010 3:48 pm UTC

Gee, majikthise, how ever did you guess? I do geometric group theory, which is sort of the offspring of geometric topology and combinatorial group theory. There's a lot of group presentations, Cayley graphs, and other things that let you deal with groups as though they're metric spaces.

"Phase 2:????" wasn't in there verbatim, though it was basically a question about whether you could do this three-step process on graphs, so maybe I should have put more question marks in. It was basically this:

Phase 1: Each vertex starts with N dollars.
Phase 2: Each vertex gives some or all of its dollars (in whole dollar amounts) along edges to its adjacent neighbors (how, though, is the big question????)
Phase 3: Profit! (Each vertex ends up with more money than it started with.)
Last edited by MartianInvader on Mon Apr 12, 2010 3:50 pm UTC, edited 1 time in total.
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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Re: PhD Woooooooooo

Postby Natty » Mon Apr 12, 2010 3:49 pm UTC

Congrats!!!

Maybe I should get off my lazy butt and go get mine.
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jestingrabbit
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Re: PhD Woooooooooo

Postby jestingrabbit » Mon Apr 12, 2010 3:59 pm UTC

MartianInvader wrote:Gee, majikthise, how ever did you guess? I do geometric group theory, which is sort of the offspring of geometric topology and combinatorial group theory. There's a lot of group presentations, Cayley graphs, and other things that let you deal with groups as though they're metric spaces.


Do you know Caroline Series?
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EstLladon
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Re: PhD Woooooooooo

Postby EstLladon » Mon Apr 12, 2010 5:53 pm UTC

Congrats! I recently (December) became one too.
From Russia with math.

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MartianInvader
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Re: PhD Woooooooooo

Postby MartianInvader » Mon Apr 12, 2010 6:04 pm UTC

jestingrabbit wrote:
MartianInvader wrote:Gee, majikthise, how ever did you guess? I do geometric group theory, which is sort of the offspring of geometric topology and combinatorial group theory. There's a lot of group presentations, Cayley graphs, and other things that let you deal with groups as though they're metric spaces.


Do you know Caroline Series?


No. After working out that you were talking about a person and not a mathematical concept, I checked out her webpage - it looks like she does a lot of stuff with Teichmuller space and mapping class groups. That's certainly geometric group theory, though it's not quite the same as what I do (group amenability and CAT(0) groups). It's always nice to hear about people working in the same sub-field as you!
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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jestingrabbit
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Re: PhD Woooooooooo

Postby jestingrabbit » Mon Apr 12, 2010 6:16 pm UTC

MartianInvader wrote:
jestingrabbit wrote:
MartianInvader wrote:Gee, majikthise, how ever did you guess? I do geometric group theory, which is sort of the offspring of geometric topology and combinatorial group theory. There's a lot of group presentations, Cayley graphs, and other things that let you deal with groups as though they're metric spaces.


Do you know Caroline Series?


No. After working out that you were talking about a person and not a mathematical concept, I checked out her webpage - it looks like she does a lot of stuff with Teichmuller space and mapping class groups. That's certainly geometric group theory, though it's not quite the same as what I do (group amenability and CAT(0) groups). It's always nice to hear about people working in the same sub-field as you!


I wrote my honors thesis on stuff she did (with Joan Birman mostly) ages ago on Fuchsian groups in the hyperbolic plane. All of the keywords in your post sparked fond memories. You only missed word metric.
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EmilyR
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Re: PhD Woooooooooo

Postby EmilyR » Mon Apr 12, 2010 6:48 pm UTC

Congrats! :)
Though I *loved* mine at the time, there's no way I'd go back and do it all again.

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Yakk
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Re: PhD Woooooooooo

Postby Yakk » Mon Apr 12, 2010 10:25 pm UTC

Must.... not ... name ... a ... series ... after ... Caroline Series ....
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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Re: PhD Woooooooooo

Postby DavCrav » Mon Apr 12, 2010 11:42 pm UTC

MartianInvader wrote:Gee, majikthise, how ever did you guess? I do geometric group theory, which is sort of the offspring of geometric topology and combinatorial group theory. There's a lot of group presentations, Cayley graphs, and other things that let you deal with groups as though they're metric spaces.

"Phase 2:????" wasn't in there verbatim, though it was basically a question about whether you could do this three-step process on graphs, so maybe I should have put more question marks in. It was basically this:

Phase 1: Each vertex starts with N dollars.
Phase 2: Each vertex gives some or all of its dollars (in whole dollar amounts) along edges to its adjacent neighbors (how, though, is the big question????)
Phase 3: Profit! (Each vertex ends up with more money than it started with.)


Yes, an infinite Ponzi scheme works... Everyone ends up with infinity dollars.

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MartianInvader
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Re: PhD Woooooooooo

Postby MartianInvader » Tue Apr 13, 2010 6:03 pm UTC

Well, it depends what kind of graph you're looking at. If you have an infinitely long string of vertices, each connected to its two neighbors by an edge, you still can't make a Ponzi scheme work, even though the graph is infinite. So the question becomes, "What sort of graphs admit a Ponzi scheme?"
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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Yakk
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Re: PhD Woooooooooo

Postby Yakk » Tue Apr 13, 2010 6:43 pm UTC

The whole dollar amounts thing makes it awkward. (otherwise, there is a ponzi 2-adjacent infinite graph)

Without that restriction, and the profit goal being "uniformly richer" (ie, you can bound the amount that a given vertex is richer), (which also rules out the infinite vertex chain), I'd expect it would ... have to do with the macroscopic shape of the graph being somehow 2+ dimensional? (so the ratio of incoming $ to volume in a growing sub graph doesn't collapse) Choke points also become interesting.

Oh, and congratulations, Dr Invader!!
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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BlackSails
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Re: PhD Woooooooooo

Postby BlackSails » Wed Apr 14, 2010 1:53 am UTC

MartianInvader wrote:Well, it depends what kind of graph you're looking at. If you have an infinitely long string of vertices, each connected to its two neighbors by an edge, you still can't make a Ponzi scheme work, even though the graph is infinite. So the question becomes, "What sort of graphs admit a Ponzi scheme?"


Why not? You could do something like Hilbert's grand hotel.

Lets say each vertex has 3 connections, and we can order them, sort of like an infinite tree. Each vertex gives 1 dollar to the vertex "upstream" and gets 2 dollars from the verticies "downstream"

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Re: PhD Woooooooooo

Postby Yakk » Wed Apr 14, 2010 2:51 am UTC

BlackSails wrote:
MartianInvader wrote:Well, it depends what kind of graph you're looking at. If you have an infinitely long string of vertices, each connected to its two neighbors by an edge, you still can't make a Ponzi scheme work, even though the graph is infinite. So the question becomes, "What sort of graphs admit a Ponzi scheme?"
Why not? You could do something like Hilbert's grand hotel.

Lets say each vertex has 3 connections, and we can order them, sort of like an infinite tree. Each vertex gives 1 dollar to the vertex "upstream" and gets 2 dollars from the verticies "downstream"

Some graphs admit a Ponzi scheme, others don't. The infinite binary tree admits a Ponzi scheme. The infinite string does not!
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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MartianInvader
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Re: PhD Woooooooooo

Postby MartianInvader » Wed Apr 14, 2010 2:32 pm UTC

Yeah, the point is you can only give money along edges that are already in the graph. So if you have an infinite 3-valent tree, then yes, there's a Ponzi Scheme, but other graphs (for example, take the integer lattice in the plane and connect each vertex to its 4 neighbors) don't have any way to set one up.

It turns out to be equivalent to the concept of Group Amenability and Folner sequences (those are both on wikipedia if you're interested).
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

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Re: PhD Woooooooooo

Postby Jumble » Wed Jun 23, 2010 7:00 am UTC

Congratulations, MartianInvader!

It's a real high, isn't it? I'll never forget the feeling (after 9 years of guilt), waking up and realising that I didn't need to worry about my bloody thesis ever again! And, 2 years later, that feeling is still there in the background. My recommendation would be to change your title with your bank and a few other services, so that in years to come when they phone up and ask to speak to Dr MartianInvader, you can enjoy that moment of thinking 'who's that - oh, it's me!'. Still gets me every time.

Are you going to stay in research?
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Re: PhD Woooooooooo

Postby BlackSails » Wed Jun 23, 2010 11:52 am UTC

Yakk wrote:
BlackSails wrote:
MartianInvader wrote:Well, it depends what kind of graph you're looking at. If you have an infinitely long string of vertices, each connected to its two neighbors by an edge, you still can't make a Ponzi scheme work, even though the graph is infinite. So the question becomes, "What sort of graphs admit a Ponzi scheme?"
Why not? You could do something like Hilbert's grand hotel.

Lets say each vertex has 3 connections, and we can order them, sort of like an infinite tree. Each vertex gives 1 dollar to the vertex "upstream" and gets 2 dollars from the verticies "downstream"

Some graphs admit a Ponzi scheme, others don't. The infinite binary tree admits a Ponzi scheme. The infinite string does not!


What about: Each node takes money from all the neighbors on the left, and passes one dollar to the right. Infinite money for everyone!

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Yakk
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Re: PhD Woooooooooo

Postby Yakk » Wed Jun 23, 2010 2:16 pm UTC

You can only take money in natural number amounts from neighbors, and the money each node starts with is a bounded natural number of some kind.

So you cannot take money from "all of the nodes on your left", because you are only connected to one of them. And regardless of how high the bounded amount of money each node starts with is, eventually the infinite string will be passing that much along (if it tries to pass along more each step), and the ponzi scheme breaks down.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

B.Good
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Re: PhD Woooooooooo

Postby B.Good » Wed Jun 23, 2010 9:18 pm UTC

My sincerest congratulations. I hope one day I can earn a PhD.

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Re: PhD Woooooooooo

Postby masher » Wed Jun 23, 2010 11:51 pm UTC

It's a good feeling, isn't it?


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