User s lir - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T09:30:34Z http://mathoverflow.net/feeds/user/4089 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/15767/concerning-the-dimension-of-a-complex-variety-modulo-a-prime Concerning the dimension of a complex variety modulo a prime S Lir 2010-02-18T22:35:24Z 2010-02-28T08:27:59Z <p>Let V be a complex affine variety given as the vanishing set of a set of polynomials with integral coefficients. I have 3 questions.</p> <p>1)</p> <p>Under what assumption will the dimension of V over C remain the same as the dimension of V computed over some finite field like Z_P, assuming that the prime P does not divide any of the coefficients of the polynomials defining V?</p> <p>2)</p> <p>How can such a prime P be found if we have a set of polynomials whose vanishing set is V? </p> <p>3)</p> <p>Suppose that V has a singularity over Z_P. Can we conclude that V is singular variety? In other words. Does having a singularity over a finite field immediately imply the variety is not smooth? If not, what guarantees that having a singularity modulo p implies a singularity over C?</p> http://mathoverflow.net/questions/15915/how-do-you-become-a-good-listener/15975#15975 Answer by S Lir for How do you become a good listener? S Lir 2010-02-21T15:04:48Z 2010-02-21T15:19:22Z <p>Listening is a very broad topic. I will focus mainly on listening to a math talk with the hope of extracting something useful from it.</p> <p>I find taking notes during a talk helps. I simply write some key words. If the speaker emphasizes a point, I write it down, even if it does not make sense at the time. I might later google some of the key terms. So on... </p> <p>People who don't write fast enough, or who are new to attending math talks, might find useful a digital recorder running on a timer. Jot down the time when an important point or example was made and some of the ideas surrounding it, maybe also the notation; then go back later if needed. You may want to save both the recorded talk, and via a digital camera in text mode, digitize your notes and place them in a folder adding some key words easily searched later if needed. </p> <p>As Ravi puts it in these <a href="http://math.stanford.edu/~vakil/potentialstudents.html" rel="nofollow">Notes</a> (Thanks Kevin Lin for the link), one is never sure where new ideas are coming from, or where the seed of a solution to a problem one has been working on is going to come from. Sometimes, a new idea may come from listening to a talk on something seemingly disjointed from one's work. </p> http://mathoverflow.net/questions/27026/math-effect-on-intelligence Comment by S Lir S Lir 2010-06-04T13:02:36Z 2010-06-04T13:02:36Z Ummmmmm, I would try music lessons, or listening to serious music instead. Although, I am completely baffled by what the term smart means and my answer is probably based on my peculiar understanding of the term. Another thing you might try is engaging in regular discussions with people you think are smart. If by smart you mean people that score well on exams, then I take back what I said. http://mathoverflow.net/questions/15915/how-do-you-become-a-good-listener/15975#15975 Comment by S Lir S Lir 2010-02-22T00:20:32Z 2010-02-22T00:20:32Z Actually, people into digitizing notes might find the following technology interesting. <a href="http://en.wikipedia.org/wiki/Livescribe" rel="nofollow">en.wikipedia.org/wiki/Livescribe</a>