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# MathOverflow : Recent Questions and Answers

I have a $2n times 2n$ block symmetric matrix that in the simplest case ($n=2$) looks like: $$M_2 = begin{bmatrix}a_1 & 0 & b_{1,2} &... Asked on 11/29/2021 1 answer ## Canonical forms for block-positive-definite matrices Suppose we are given a block 2times 2 matrix that is positive-definite, and let's suppose for simplicity that the blocks along the main diagonal are the identity. So... Asked on 11/29/2021 by Laurent Lessard 0 answer ## Form of a block upper triangular matrix of finite order If I take a diagonalizable block upper triangular matrix whose diagonal blocks are of finite order, is it true that away from the leading block diagonal, the matrix is zero?... Asked on 11/29/2021 by user44128 1 answer ## Determinant of block tridiagonal matrices Is there a formula to compute the determinant of block tridiagonal matrices when the determinants of the involved matrices are known? In particular, I am interested in the case ... Asked on 11/29/2021 2 answer ## Full measure properties for Zariski open subsets in p-adic situation Let F be a p-adic field and let X be a smooth integral variety over F (I am chiefly interested in the case when X... Asked on 11/29/2021 by Alex Youcis 0 answer ## Prove int_{0}^{infty} cos(omega x) exp(-x^{alpha}) , {rm d} x ge {alpha^2 sqrt{pi} over 8} exp left( -frac{omega^2}{4} right) I would like to prove that$$int_{0}^{infty} cos(omega x) exp(-x^{alpha}) , {rm d} x ge{alpha^2 sqrt{pi} over 8} exp left( -frac{omega^2}{4} right) for any $omega >... Asked on 11/29/2021 0 answer ## Prove of the shape-derivative identity relating the shape and material derivative of a shape-dependent function I've started reading about shape optimization. Most of the concepts I've encountered so far (such as the shape derivatives of domain and boundary integrals and the corresponding) seem to be... Asked on 11/29/2021 1 answer ## Example of an intersection complex not concentrated in a single degree I'm having trouble finding references for in-depth examples of perverse sheaves, so answers in the form of such a reference would be most helpful. I want to construct an example... Asked on 11/29/2021 1 answer ## Is every proper regular relative algebraic space curve over a Dedekind domain projective? This question is in some sense a follow up to a related question Is a normal proper relative curve over a DVR projective? Let$R\$ be a Dedekind domain,...

Asked on 11/26/2021 by Lisa S.

## Examples of residually-finite groups

One of the main reasons I only supervised one PhD student is that I find it hard to find an appropriate topic for a PhD project. A good approach, in...

Asked on 11/26/2021 by Yiftach Barnea