Mathematics

12:06 AM

@TedShifrin I didn't express myself very well with what I wrote, but I was trying to say this is the relationship between the Lagrangian and the BH right? So the BH is a map from $\Bbb{R}^{n+1} \mapsto \Bbb{R}^{n+1}$ right? I'm just trying to make sure I understand the basic facts. Presumably then, my $F$ should involve $L$ and write $L$ in such a way that it includes $c$.

But something like $L(c,\lambda,\mathbf{x}) = f(\psi(c)) - \lambda g(\psi(c))$ doesn't make sense.

user147690

12:33 AM

@Paul Did you decide on your next post yet?

pjs36

Is it even worth giving a geometric answer to this post? There's already an answer, but it's pretty stuffy.

Paul Plummer

Lol, I was just thinking about that, I think it will be between a sketch of the free product three non trivial groups with an extra relation, is not the trivial group, and the marked group topology. @AlexClark

user147690

@PaulPlummer Oh hahaha, take the two votes and combine them. I take it Mike didn't vote then?

Ted Shifrin

@Stan, existence of $\psi$ is what you're trying to prove.

Paul Plummer

@pjs36 I would say so, nothing wrong with that, my eyes basically glazed over when I saw that answer

user147690

12:37 AM

@PaulPlummer Agreed

Paul Plummer

@AlexClark Well he did not ping me if he did

user147690

@PaulPlummer Nice introduction of tropical geometry I have only read a a little bit of it so far, but I will finish it off soon

Paul Plummer

@BalarkaSen Another application of the marked group topology, is that you can use the Baire category theorem to show the existence of some groups.

Looks nice @AlexClark

user147690

@PaulPlummer If you looked at it quickly the operations and the tropical additive identity are pretty fun

pjs36

Ah, Sturmfels, what a guy

user147690

12:49 AM

@pjs36 I haven't read any of his other work before

pjs36

If I'm not mistaken, he does some really cool geometric/combinatorial probability, for gene sequencing and that sort of thing

I could be mistaken though

user147690

That sounds right

user147690

Tropical mathematics has interests in phylogenetic trees

user147690

@pjs36 This might have been what you were thinking about?

pjs36

I actually had this in mind

I like the pair, Pachtor and Sturmfels, because they've found a use for graph associahedra, and I've worked with them a fair amount

Cᴏɴᴏʀ O'Bʀɪᴇɴ

12:54 AM

hi guys ~ quick combinatorial question: if I have $n$ slots, each of which could have any of $m$ possible values, do I have $nm$ distinct series? Or is it something like nCm or nKm? How many distinct series do I have?

user147690

@pjs36 Oh wow thanks for that. I will be doing a research project over the american summer on tropical geometry(although I know essentially none now)

pjs36

@AlexClark Interesting, and you are quite welcome! I know 0 about the subject as well, but I've seen the name a few places

user147690

@TedShifrin Were you referring to Eric Stucky?

Mike Miller

No, he's referring to Eric Auld, someone I don't think youu know.

user147690

1:22 AM

@MikeMiller I don't. I went back in the chat history to his first uses of Eric and Eric Stucky turned up

Cᴏɴᴏʀ O'Bʀɪᴇɴ

nevermind, I have $n^m$

user147690

@Paul So with $\Bbb R[x]/(x^2+1)$ I can see I get the form $a+bx\pmod{x^2+1}$ where $x^2\equiv -1$ so I can see how my quotient ring is isomorphic to $\Bbb C$. But As you said $x$ doesn't equal $i$, but has the same 'information' as $i\in\Bbb C$ would. Can I make that idea rigorous? How?

Paul Plummer

Show that there is an isomorphism between the two rings @AlexClark

user147690

1:37 AM

@PaulPlummer As in explicitly show it?

Paul Plummer

Yes :)

user147690

Will this be easy? Don't give me the answer though

Paul Plummer

Yah, it is pretty easy

user147690

Okay sweet, thanks

pjs36

So how'd the tropical geometry thing come about, @AlexClark ?

user147690

1:45 AM

@pjs36 The topic or me doing research on it over the american summer?

pjs36

hehe, American summer... yeah, the research

user147690

@pjs36 Well Eric Stucky is going to be doing research through CRP(Collabora‌tive Research Project organisation), and this is the topic they have given - and he has offered people to join him on it.

user147690

Well to make sure I am specific I could either say the American summer or the Australian winter, and American summer seems better communication haha.

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$Mathematics$ Mathematics