# All Questions

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### Normalizing factor in Reciprocity of traces of Frobenius with solutions of equations mod p

One kind of Reciprocity tells us that we can count solutions to polynomial equations over finite fields and relate them to traces of Galois Representations with some normalization factor. For ...
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### Do the normal forms for braid groups really conceal information about better than randomly applying the braid relations?

In braid based cryptography, one typically wants to conceal the way a certain braid $b$ has been obtained. One therefore puts $b$ into some normal form. Since every braid has a unique normal form, the ...
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### Basic Definition and Notations in RWRE [on hold]

From the definition of Zeitouni's lecture notes on RWRE: $(V, E)$ is a special graph, and $N_v:= \{k \in V: (v,k) \in E\}$ is the neighborhood of $v \in V$. $\Omega = \prod_{v \in V} M_1(N_v)$ ...
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### Ring structure on cohomology of groups

Assume that $G$ is a finite group and that $A$ is an arbitrary $G$-module. Then we know that can define the cohomology groups of $G$ with coefficients in $A$ in the usual way and we denote the latter ...
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### Closed form formula for fill rate given a discrete distribution? [on hold]

I'm wondering whether there is a closed form way to obtain good estimates for fill rate given a discrete distribution of demand. I created a simple monte carlo simulation to see if I could see any ...
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### A rash guess about distribution of primes based on meager empirical evidence?

Elementary number theory is a field in which imbeciles can ask questions that experts cannot answer (and I wonder if discrete geometry is a similar subject in that respect?) and herewith I submit ...
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### Resolution of the ideal of the Abel-Jacobi image of a curve?

Let $C$ be a complex curve of genus $g\ge 2$ and let $a\colon C\to J(C)$ be the Abel-Jacobi map. Is there a finite resolution of the ideal $\mathcal I_{a(C)}$ whose terms are sums line bundles of the ...
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### function mapping odd numbers to counting numbers [on hold]

Mapping even numbers to counting numbers is straight forward. Without introducing any other variable: i = 0, 2, 4, 6, . . . if i > 0: count = i/2 what about ...
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### similarity metric for geometries [closed]

I'm searching for a method to calculate the degree of similarity of two given geometries. These geometries can be of any type and can have an arbitrary shape. For the sake of simplicity, I primarily ...
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### Can some exotic sphere be diffeomorphically embedded into some $R^n$?

Can some (or perhaps every) exotic sphere be diffeomorphically embedded into some $R^n$? How does such an embedding (if it exists) look like? I.e., what are the equations for a particular embedding? ...
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### Measures on a unit sphere of a Hilbert space

Consider a real separable infinite-dimensional Hilbert space $H$. Let $S=\{h\in H\mid \|h\|=1\}$ be a unit sphere in $H$. What are the most natural measures on $S$? Is there a (Borel) measure $\mu$ on ...
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### Reference quest: variety of lines and variety of planes

Let $X\subset \mathbb P_{\mathbb C}^n$ be a smooth projective variety, $F(X)\subset G(2,n+1)$ its Fano variety of lines and $$I_F=\left\{([l],[l'])\in F(X)\times F(X), l\cap l'\neq \emptyset\right\}$$ ...
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### Ellipticity of Bott-Chern Laplacian

I want to prove that Bott-Chern Laplacian \tilde{\Delta}_{BC}^{p,q}=(\partial\bar\partial)(\partial\bar\partial)^*+(\partial\bar\partial)^*(\partial\bar\partial)+(\bar\partial^*\partial)(\bar\...
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I'm looking for any graduate programs related to graph theory or combinatorics in canada like in waterloo or simon fraser universities. any other suggestions?
In Nakahara's Geometry, Topology and Physics on page 375, he constructs a Lie-algebra-valued one-form $\omega$ on a principal bundle $P$ by "lifting" a Lie-algebra-valued one-form $\mathcal A_i$ on an ...