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Construction of $K(Gal(bar{k}/k), 1)$

Take any field $k$. Is there a construction of the Eilenberg-MacLane space $K(Gal(bar{k}/k), 1)$ as a CW complex in terms of $k$?...

Asked on 12/05/2021 by jog

0 answer

Forcing as a tool to prove theorems

It is often mentioned the main use of forcing is to prove independence facts, but it also seems a way to prove theorems. For instance how would one try to...

Asked on 12/03/2021

9 answer

The determinant of the sum of normal matrices

Given two normal matrices $A,Bin M_n({mathbb C})$whose respective spectra are $(alpha_{1},ldots,alpha_{n})$ and$(beta_{1},ldots,beta_{n})$, is it true that $det(A+B)$ belongs tothe convex hull of the set of numbers$$prod_{i=1}^n(alpha_i+beta_{sigma(i)}),$$...

Asked on 12/03/2021 by Denis Serre

1 answer

The Fock space vs the Hilbert space in the context of quantum field theory

Mathematically the definitions are as follows : if $H_n$ is a $n$-dimensional complex Hilbert space then its two different corresponding ``Fock space"(s) are often denoted as $F_{1}$...

Asked on 12/03/2021 by gradstudent

2 answer

Block matrices and their determinants

For $ninBbb{N}$, define three matrices $A_n(x,y), B_n$ and $M_n$ as follows: (a) the $ntimes n$ tridiagonal matrix $A_n(x,y)$ with main diagonal all $y$'s, superdiagonal all $x$'s and subdiagonal all $-x$'s....

Asked on 12/03/2021 by T. Amdeberhan

1 answer

Extending submodular functions from a sublattice

This came about when I was studying the connection between matroids and stronggreedoids, but it has broken through into a subject I am not particularlyfamiliar with: submodular functions...

Asked on 12/03/2021 by darij grinberg

1 answer

Regularity properties of Minakshisundaram–Pleijel zeta function

Let $(M,g)$ be a closed (compact, no boundary) smooth $n$-dimensional Riemannian manifold. The Laplace–Beltrami operator $Delta_g$ on $M$ has discrete spectrum $(lambda_j)_j$ (indexed without multiplicity)...

Asked on 12/03/2021 by AlephBeth

0 answer

On proving the absence of limit cycles in a dynamical system

I'm studying this classical paper in nonlinear dynamics in biophysics and I want to understand it properly. I'm stuck at this two-variable problem which I've struggled with for too long...

Asked on 12/03/2021 by Norregaard

1 answer

Computing the infinite dimensional Lebesgue measure of "cubes"

There is no Lebesgue measure in infinite dimensions—this slogan is familiar to every student interested in analysis. One possible, precise statement of this result may be as follows: if ...

Asked on 12/03/2021

0 answer

Why do Todd classes appear in Grothendieck-Riemann-Roch formula?

Suppose for some reason one would be expecting a formula of the kind $$mathop{text{ch}}(f_!mathcal F) = f_*(mathop{text{ch}}(mathcal F)cdot t_f)$$ valid in $H^*(Y)$ where$f:Xto Y$ is a proper morphism with...

Asked on 12/01/2021 by Ilya Nikokoshev

4 answer

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