Description:
Discussion of current mathematical research. (Moderated)
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Unique solution to system of generalized eigenvector problems
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Suppose we have the following sequence of equations: Fi k = alpha_i Ai k where we know that alpha_i > 0, all Fi and Ai are 6x6 having rank 3 and the column space of both Fi and Ai is the same for all i. All Fi and Ai are known. All alpha_i and k are unknown and we are interested in finding k. Each equation represents an instance of the generalized... more »
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symplectic group Sp(p,q) and reduction modulo a prime
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Hi! Does anyone know a book or a reference where one can find something about the reduction modulo a prime of certain algebraic groups, i.p. f.e. if we have a group G defined over a totally real number field F, with the help of a quaternion division algebra D/F and a hermitian form on D^{n+1} s.t. G(R) ~ Sp(n,1) (\times ...),... more »
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Positions at Penn State
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Tenure and Tenure Track Faculty Positions The Department is seeking to fill two or more positions; dependent on the qualifications and experience of the appointee, these may be at the assistant, associate or full professor level. One position is preferably to be filled in the area of probability theory/stochastic... more »
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K-dimensional subspaces of GF(p)^{2k} with zero intersection
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I am trying to construct a set of k-dimensional subspaces of GF(p)^{2k} such that all of the subspaces are disjoint except for the zero vector. I know that such a set can always be constructed with three subspaces contained in it, and have established an upper bound of p^{k} + 1 subspaces. I currently believe that this upper bound can always be achived for... more »
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OEIS A004664 related conjecture: n! + n^2 != m^2 for n>=1, m>= 0
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Hi, In addition to previously posted conjecture (unfortunately I have not seen any responses yet ;-) ) I came up with OEIS A004664 related conjecture: n! + n^2 != m^2 for n>=1, m>= 0 I checked using PARI that indeed n! +n^2 doesn't yield perfect square up to n=30,000 Is this conjecture known (could one on this list point me to the... more »
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Why "Borel" in Borel calculus?
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I looked through several "standard books", and could not find an answer: When one considers Borel calculus of a (bounded) normal/self-adjoint operator, one can apply any function which is l-infinity w.r.t. the spectral measure of the operator [*]. So, in principle, one could restrict attention to functions which are... more »
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Mapping Class Group computations
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Where can I find a rigorous proof that the (orientation-preserving) MCG(R^n)={1}? Also, is MCG(S^4)={1}? What about MCG(S^n), n>1?
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SOCG 2009 Call for Papers
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CALL FOR PAPERS, VIDEOS, AND MULTIMEDIA 25th Annual ACM Symposium on Computational Geometry June 8-10, 2009 Aarhus, Denmark [link] In cooperation with ACM SIGACT and SIGGRAPH The Twenty-fifth Annual Symposium on Computational Geometry will be held at the University of Aarhus, Denmark, and will be organized by... more »
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Combinatorial (?) assignment problem
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Greetz. I am looking at a problem, probably a simple enough one, for which I don't know a solution. Here's how it goes. Any help appreciated. Let s_i(a) and r_i(a) be two groups of functions, that each take one of two values, 0 or \sigma_i in the case of s_i, and 0 or \rho_i in the case of r_i,... more »
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