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Fei Cao's user avatar
Fei Cao's user avatar
Fei Cao's user avatar
Fei Cao
  • Member for 5 years, 3 months
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Currently a Visiting Assistant Professor at the University of Massachusetts Amherst . Hobbies: Naruto/Boruto, Detective Conan, NBA, Yu-Gi-Oh! (a trading card game, I am a semi-professional Yu-Gi-Oh! player by the way), etc. Email: [email protected]. I am glad to discuss mathematics and potential research collaboration possibilities with you via email. I am interested in partial differential equations, stochastic processes, interacting particle systems, and theoretical machine learning. I will be looking for a tenure-track position starting at 2025 Fall semester. Google scholar profile: https://scholar.google.com/citations?user=ev7IXh0AAAAJ&hl=en&authuser=1
Personal website: https://feicao1995.github.io/

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question
13
prove a challenging inequality or find a counterexample to it
Dec 30, 2020
question
8
A possible bug in a highly cited paper (Adam gradient descent)?
Oct 9, 2021
question
7
Modified Energy Method for Transformed Fokker-Planck Equation (Tricky Integration by parts...)
Aug 6, 2020
question
7
Prove that $0\le\int_0^1\log(u){\rm d}x+\frac1{2\pi^2}\int_0^1\frac1{u^2}\left(\frac{{\rm d}u}{{\rm d}x}\right)^2{\rm d}x$
Feb 28, 2021
question
7
A possible error in Villani's monograph “Hypocoercivity”
Mar 20, 2021
question
6
A tough definite integral using contour integration
Jul 15, 2020
question
6
Show that $\frac{1}{n}\sum_{j=1}^\infty \left( 1 - (1-p_j)^n\right) \to 0$ as $n \to \infty$
Dec 23, 2021
question
6
Showing $\frac{f(a+2b)+f(a-2b)}{2f(a)}\leq\sqrt{1-\left(\frac{b}{a(1-a)}\right)^2}$ for $f(x)=\sqrt{x(1-x)}$ with some constraints
Nov 20, 2020
question
6
Possibility of bounding $\sum_{n=0}^N |a_n|$ from above by $\sup_{z\in (0,1)} |\sum_{1\leq n\leq N} (1+z+\ldots+z^{n-1}) a_n|$
Feb 6
question
6
Proper linearization of ODEs of the form $\dot{x}(t) + f(x(t)) + \sigma(t) = 0$?
Aug 6, 2023
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Stack Overflow for Teams? How does it work?
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Modified energy method for transformed Fokker-Planck equation (tricky integration by parts…)
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Lower bound $\int_0^1 \frac{|f'(x)|^2}{f} \,\mathrm{d} x$ by $\int_0^1 |f-1|^2\, \mathrm{d} x$
8
Competitions in the applications for postdoc positions (Applied Math)
5
Random time change from Oksendal's SDE textbook