User john - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T16:20:57Z http://mathoverflow.net/feeds/user/18503 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/127627/tropicalization-of-the-grassmannian Tropicalization of the Grassmannian john 2013-04-15T14:40:32Z 2013-04-15T20:13:07Z <p>Let $Trop(Gr(m,n))$ denote the tropicalization of the grassmannian $Gr(n,m)$. Let $\phi^m : \mathbb R^{n \choose 2} \rightarrow \mathbb R^{n \choose m}$ such that $X_{i,j} \rightarrow X_{i_1,...,i_m}$ and $$X_{i_1,...,i_m}= \mathrm min \frac {1}{2}( X_{i_1, i_{\sigma(1)}}+ X_{ i_{\sigma(1)},i_{\sigma^2(1) }} + \ldots X_{ i_{\sigma^{m-1}(1)},i_{\sigma^m(1) }} )$$ where $\sigma$ represents a cyclic permutation. So, basically $\phi^m$ takes a dissimilarity vector of a tree to a m-dissimilarity vector of that tree.</p> <p>For what values of $m \gt 3$ and $n$ is it known that $$\phi^m (Trop(Gr(2,n)) = Trop(Gr(m,n)) \cap \phi^m (\mathbb R^{n \choose 2})$$ ? For what values it is known they can't be equal?</p> http://mathoverflow.net/questions/99352/important-open-questions-in-the-field-of-tropical-geometry Important open questions in the field of Tropical geometry john 2012-06-12T09:44:37Z 2012-07-29T07:32:01Z <p>What are some of the important unanswered questions in the field of tropical geometry?</p> http://mathoverflow.net/questions/78037/video-lectures-for-algebraic-geometry Video lectures for Algebraic Geometry john 2011-10-13T17:42:53Z 2012-05-08T10:37:48Z <p>Are there any good video lectures for studying Algebraic geometry ?</p> http://mathoverflow.net/questions/84629/learning-tropical-geometry Learning Tropical geometry john 2011-12-31T07:01:34Z 2011-12-31T18:20:35Z <p>I'm interested in learning tropical geometry. But my background in algebraic geometry is limited. I know basic facts about varieties in affine and projective space, but nothing about sheaves, schemes etc.</p> <p>I wanted to know how much algebraic geometry does one need to understand the research literature in tropical geometry.</p> <p>What are the other subjects which I must know before starting tropical geometry? </p> http://mathoverflow.net/questions/78247/consequences-of-the-langlands-program Consequences of the Langlands program john 2011-10-16T04:57:27Z 2011-10-17T02:23:55Z <p>In the one-dimensional case the Langlands program is equivalent to the class field theory and the two-dimensional case implies the Taniyama-Shimura conjecture.</p> <p>I would like to know are there any other important consequence of the Langlands program?</p> http://mathoverflow.net/questions/127627/tropicalization-of-the-grassmannian Comment by john john 2013-04-16T10:25:18Z 2013-04-16T10:25:18Z @quim Yes, he did it. http://mathoverflow.net/questions/127627/tropicalization-of-the-grassmannian/127653#127653 Comment by john john 2013-04-15T22:06:22Z 2013-04-15T22:06:22Z @David Speyer Will the dimensional arguement still hold since I'm intersecting $Trop(Gr(m,n))$ with $\phi^m (\mathbb R^{n \choose 2})$? We know that$$\phi^m (Trop(Gr(2,n)) = Trop(Gr(m,n)) \cap \phi^m (\mathbb R^{n \choose 2})$$ is true when $m =3$ and $n \geg 5$. http://mathoverflow.net/questions/45802/undergraduate-math-research/45866#45866 Comment by john john 2013-01-05T07:07:31Z 2013-01-05T07:07:31Z @Timothy Wagner. How did you join a pure math graduate program, even though you were an engineering undergraduate. I thought that was not possible or at least very difficult. http://mathoverflow.net/questions/78037/video-lectures-for-algebraic-geometry/90672#90672 Comment by john john 2012-04-01T16:28:16Z 2012-04-01T16:28:16Z is any knowledge of physics is required for understanding these lectures? http://mathoverflow.net/questions/54430/video-lectures-of-mathematics-courses-available-online-for-free/54676#54676 Comment by john john 2011-12-30T12:02:19Z 2011-12-30T12:02:19Z how do I view these lectures? I'm unable to open them. http://mathoverflow.net/questions/78037/video-lectures-for-algebraic-geometry Comment by john john 2011-10-13T18:48:00Z 2011-10-13T18:48:00Z Something similar to that covered in Hartshorne.