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bio website math.princeton.edu/directory/…
location Princeton, NJ
age 20
visits member for 5 years, 5 months
seen 3 hours ago

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
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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?
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28
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