User jeff breeding - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T09:11:33Z http://mathoverflow.net/feeds/user/4544 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63967/cubic-polynomial-mapping-primes-to-primes Cubic polynomial mapping primes to primes Jeff Breeding 2011-05-05T02:15:11Z 2011-06-13T08:20:49Z <p>Let $f(n)=a_3n^3+a_2n^2+a_1n+a_0$, with $a_i\in\mathbb{Z}$, $a_3>0, a_0\neq 0$ such that $f(n)>0$ for all positive integers $n$.</p> <p>Given a prime $p$, when is $f(p)$ again prime?</p> <p>For example, let $f(n)=7n^3-50n+30$. Then, $$f(7)=2081\quad {\rm (prime)},$$ $$f(11)=19\cdot463,$$ $$f(13)=14759\quad {\rm (prime)}.$$</p> <p>Are there conditions on the $a_i$'s that guarantee that $f(p)$ is prime for all primes $p$?</p> http://mathoverflow.net/questions/30610/what-matrix-groups-can-be-embedded-in-sp-4/60887#60887 Answer by Jeff Breeding for What matrix groups can be embedded in $Sp_4$? Jeff Breeding 2011-04-07T05:20:05Z 2011-04-07T05:34:29Z <p>You can embed the direct product of two copies of $SL_2(\mathbb{R})$. One embedding sends the entries to the center $2\times2$ block, the other sends the entries to the corners with the $2\times2$ identity matrix in the center block. Here, the $J$ matrix is the standard anti-diagonal matrix</p> <p>For embeddings of other groups, you could look at the Bruhat decomposition of Sp(4) and write a decomposition of each cell. Some explicit information is given on the decomposition for GSp(4) in a <a href="http://www.math.ou.edu/~rschmidt/papers/NF.pdf" rel="nofollow">book</a> by Ralf Schmidt and Brooks Roberts, which is available on Ralf's website.</p> http://mathoverflow.net/questions/17821/steinberg-representations-of-finite-groups-of-lie-type Steinberg Representations of Finite Groups of Lie Type Jeff Breeding 2010-03-11T04:26:28Z 2010-10-30T01:37:06Z <p>Let G be a finite group of Lie type. Assume G is also of universal type. Is the Steinberg representation of G generic, i.e., does the Steinberg representation admit a Whittaker model? </p> <p>A Whittaker model for a representation of G is defined in a similar fashion as in the case of GL(2, F) in Bump's "Automorphic Forms and Representations." I am interested in the genericity of the Steinberg representation of a group of matrices over a finite field. </p> http://mathoverflow.net/questions/5499/which-mathematicians-have-influenced-you-the-most/19375#19375 Answer by Jeff Breeding for Which mathematicians have influenced you the most? Jeff Breeding 2010-03-26T01:12:07Z 2010-03-26T01:12:07Z <p><strong>Benedict Gross</strong>. I saw him lecture a few times on BSD. His enthusiasm and mastery were very inspirational. It reminded me why I want to be a professional mathematician. I had just finished my general exams the previous semester and felt tired from taking so many classes and preparing for exams. It had put a haze over the beauty of mathematics. Professor Gross made it clear again.</p>