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285G, Lecture 8: Ricci flow as a gradient flow, log-Sobolev inequalities, and Perelman entropy
It is well known that the heat equation (1) on a compact Riemannian manifold (M,g) (with metric g static, i.e. independent of time), where is a scalar field, can be interpreted as the gradient flow … more »
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285G, Lecture 8: Ricci flow as a gradient flow, log-Sobolev inequalities, and Perelman entropy
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Terence Tao wrote 2 weeks ago: It is well known that the heat equation (1) on a compact Riemannian manifold (M,g) (with metric g s … more »
Quantitative Borel-Cantelli Lemma
Pietro wrote 2 months ago: Everyone knows and loves the Borel-Cantelli lemma: it is widely used, intuitive and has a cute proof … more »
Something Certain About Uncertainty
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Peter Luthy wrote 2 months ago: I was motivated by a comment on Jim Pivarski’s recent post to speak about the Heisenberg Uncer … more »
Kleiner's proof of Gromov's theorem
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Terence Tao wrote 2 months ago: This week there is a conference here at IPAM on expanders in pure and applied mathematics. I was an … more »
Singular Integral Operators and Convergence of Fourier Series
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Peter Luthy wrote 3 months ago: I’m Peter “Viking” Luthy, a journeyman graduate student at Cornell. I’m an … more »
254A, Lecture 11: Compact systems
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Terence Tao wrote 3 months ago: The primary objective of this lecture and the next few will be to give a proof of the Furstenberg re … more »
Length and Area I
Pietro wrote 4 months ago: This is a topic which has fascinated me for years, and on which I’ve spent many (fortunately u … more »
PCM article: Phase space
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Terence Tao wrote 4 months ago: I’m continuing my series of articles for the Princeton Companion to Mathematics with my article on … more »
The Walsh model for M_2^* Carleson
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Terence Tao wrote 5 months ago: Ciprian Demeter, Michael Lacey, Christoph Thiele and I have just uploaded our joint paper, “Th … more »
Distinguished Lecture Series III: Charles Fefferman, "Interpolation of functions on R^n"
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Terence Tao wrote 5 months ago: Today, Charlie wrapped up several loose ends in his lectures, including the connection with the clas … more »
Distinguished Lecture Series II: Charles Fefferman, "Interpolation of functions on R^n"
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Terence Tao wrote 5 months ago: On Thursday, Charlie Fefferman continued his lecture series on interpolation of functions. Here, he … more »
Distinguished Lecture Series I: Charles Fefferman, "Interpolation of functions on R^n"
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Terence Tao wrote 6 months ago: The first Distinguished Lecture Series at UCLA of this academic year is being given this week by my … more »
Analysis & PDE
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Terence Tao wrote 6 months ago: I’ve joined the inaugural editorial board for a new mathematical journal, Analysis & PDE. … more »
PCM article: The Fourier transform
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Terence Tao wrote 6 months ago: I’m continuing my series of articles for the Princeton Companion to Mathematics by uploading … more »
PCM article: Harmonic analysis
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Terence Tao wrote 8 months ago: I’d like to begin today by welcoming Timothy Gowers to the mathematics blogging community; Tim … more »
Amplification, arbitrage, and the tensor power trick
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Terence Tao wrote 8 months ago: It occurred to me recently that the mathematical blog medium may be a good venue not just for exposi … more »
(Gil Kalai) The entropy/influence conjecture
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Gil Kalai wrote 9 months ago: [This post is authored by Gil Kalai, who has kindly “guest blogged” this week’s “open proble … more »
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