bio | website | math.princeton.edu/directory/… |
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location | Princeton, NJ | |
age | 20 | |
visits | member for | 5 years, 5 months |
seen | 3 hours ago | |
stats | profile views | 3,281 |
I am a second year graduate student in pure mathematics at Princeton University.
Aug
26 |
awarded | Good Question |
Aug
12 |
comment |
Intuition behind the following theorem of Reeb?
A Morse function on a smooth manifold $M$ gives rise to a handlebody decomposition of $M$, with an $i$-handle for each index $i$ critical point. In the case of Reeb's theorem, there is one index $0$ critical point (minimum) and one index $n$ critical point (maximum), and so $M$ is obtained by attaching an $n$-handle to a $0$-handle, i.e., gluing two $n$-balls by identifying their boundary $\mathbb{S}^{n-1}$'s. However, this is simply $\mathbb{S}^n$ (Alexander's trick). |
May
26 |
comment |
What's the name of this branched covering?
Dear @paul, thank you for your comment! :) I guess in that case one can also state that the genus of the surface will be the ceiling of $\frac{\text{deg}(f)-2}{2}$. |
May
25 |
comment |
What's the name of this branched covering?
Hi @Balarka, is that true? For example, you can exhibit any Riemann surface as a branched double cover of $\mathbb{CP}^1$ (to exhibit this geometrically, put a skewer symmetrically through the surface and let $\mathbb{Z}/2$ act as rotation by 180 degrees about the skewer). |
May
22 |
awarded | Famous Question |
Mar
29 |
comment |
What is the $L^p$-norm of the (uncentered) Hardy-Littlewood maximal function?
Thank you so much for your answer, Mark! (I'm very sorry I didn't see it until now.) I really, really appreciate that you took the time to write such a detailed answer. Thank you! |
Mar
29 |
accepted | What is the $L^p$-norm of the (uncentered) Hardy-Littlewood maximal function? |
Mar
28 |
awarded | Enthusiast |
Mar
23 |
awarded | Yearling |
Dec
23 |
awarded | Autobiographer |
Nov
29 |
awarded | Favorite Question |
Jul
2 |
awarded | Curious |
Mar
20 |
awarded | Popular Question |
Feb
17 |
awarded | Necromancer |
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24 |
awarded | Popular Question |
Sep
30 |
awarded | Caucus |
Sep
2 |
awarded | Civic Duty |
Sep
2 |
awarded | Vox Populi |
Aug
18 |
awarded | Citizen Patrol |
Aug
9 |
awarded | Suffrage |