User larry rolen - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T11:25:37Z http://mathoverflow.net/feeds/user/7998 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/5751/can-infinity-shorten-proofs-a-lot/94641#94641 Answer by Larry Rolen for Can infinity shorten proofs a lot? Larry Rolen 2012-04-20T13:37:55Z 2012-04-20T13:37:55Z <p>Using Eilenberg-Maclane spaces (namely $K(\mathbb{Z},2)=\mathbb{P}^{\infty}(\mathbb{C})$) and cellular approximation,one can show that any 3-fold with a positive Betti number has a map to the sphere $S^2$ which is not nullhomotopic. I am not sure how "down to earth" this example is, but it shows that even when studying finite dimensional objects it is natural to consider infinite-dimensional things. </p> http://mathoverflow.net/questions/94165/analogues-of-the-riemann-roch-theorem Analogues of the Riemann-Roch Theorem Larry Rolen 2012-04-16T00:30:15Z 2012-04-16T09:18:27Z <p>In his thesis, Tate derives a Poisson formula on the adeles and a theorem which he calls the "Riemann-Roch Theorem". More specifically, given a continuous, $L^1$ function $f$ on the adeles such that certain sums converge uniformly, then for all ideles $a$, we have</p> <p>$\frac{1}{|a|}\displaystyle\sum_{\xi\in k}\hat{f}(\xi/a)=\displaystyle\sum_{\xi\in k}f(a\xi)$.</p> <p>Tate further refers to this theorem as the "number theoretic analogue of Riemann-Roch". My question is how this relates to the geometric Riemann-Roch theorems and why this deserves to be called an analogue of these theorems. </p> http://mathoverflow.net/questions/20331/how-not-to-write-an-nsf-proposal-poster-does-any-one-know-where-to-find-it-onl/33722#33722 Answer by Larry Rolen for "How not to write an NSF proposal" poster: does any one know where to find it online? Larry Rolen 2010-07-28T22:08:58Z 2010-07-28T22:08:58Z <p>I don't know of this poster but there is a funny lecture by Serre: "How to Write Mathematics Badly" which may be of some relevance. <a href="http://modular.fas.harvard.edu/edu/basic/serre/" rel="nofollow">http://modular.fas.harvard.edu/edu/basic/serre/</a></p>