# All Questions

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### On the existence of a square root for a unitary modular tensor category

The centre $Z(\mathcal{C})$ of a fusion category $\mathcal{C}$, is a unitary modular tensor category. Question: What about the converse, i.e., can we characterize every unitary modular tensor ...
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I proposed my conjecture as follows: Let $f(x)$ is a real continuous function on $[m, M]$ and $f'>0, f''>0$ on $[m, M]$, let $m \le x_i \le M$, for $i=1, 2,..., n$. Then \frac{f(x_1)+f(x_2)+... 0answers 127 views ### What techniques are available for constructing D-modules over smooth projective varieties? I'm trying to learn about D-modules for computing intersection cohomology but I'm having trouble coming up with explicit constructions of D-modules on projective varieties. Since this is an involved ... 0answers 22 views ### Covering Number of a Positive Semidefinite Cone (Approximate the Objective of a SDP) I was wondering what the covering number of a positive semidefinite cone is. Consider the semidefinite optimization program \begin{align} \max\langle \mathbf{C}, \mathbf{X} \rangle~~\text{subject to}~... 0answers 126 views ### Research topics in Curves and Surfaces [on hold] I advance that I'm not a mathematician but I'm an undergraduate student of mathematics. In my courses at university I have studied a bit of Differential Geometry, in particoular differential geometry ... 0answers 132 views ### Where can I find basic “computations” of equivariant stable homotopy groups? I am new to this subject; so please correct me if I will say something wrong or if you don't like my notation. In particular, I don't know whether it is reasonable to consider an infinite group G (... 2answers 142 views ### Combinatorial identity involving number of cycles (of any length) in a permutation I am going through Phil Hanlon's paper and on page 127, right after the first paragraph, "It is well known that.." which boils down to the following identity: \prod_{i=0}^{n-1}(\beta-i) = \sum_{\...
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Composition Diamond lemma for Lie algebra over a field $F$ has already been investigated in several papers : L.Bokut and Y.Q.Chen Groebner-Shirshov bases for Lie algebras and A.I Shirshov, ...
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### ($\oplus$, $\otimes$) is a semiring. If $\otimes$ = +, what are the possible operators $\oplus$?

Assume that ($\oplus$, $\otimes$) is a semiring over the non-negative reals. If $\otimes$ is +, what are the possible operators for $\oplus$? So far I have proven that ...
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### Reference request for a well-known lemma in Parabolic Vector Bundle

In the paper- "Moduli Space of parabolic vector bundles on a curve" - Usha N Bhosle, Indranil Biswas-Beitr Algebra Geom (2012), 53:437-449, DOI: 10.1007/s13366-011-0053-7, Lemma $2.1$ is being ...
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### Poincaré–Bendixson theorem on the torus

I was reading the paper A Generalization of a Poincaré-Bendixson Theorem to Closed Two-Dimensional Manifolds by Arthur J. Schwartz which proves the following theorem: THEOREM. Let $M$ be a ...
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### An inequality in cyclic polygon and tangential polygon

I proposed my conjecture, it is strengthened version of the Erdős–Mordell inequality as following: Let $A_1A_2.....A_n$ be a cyclic polygon and $B_1B_2....B_n$ be the its tangential polygon. Let P be ...
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### Extending homomorphisms between ordered abelian groups

Let $\Omega$ be a linearly (i.e. fully) ordered set, and let $\Lambda_{\Omega}$ be the ordered abelian group consisting of those $(\lambda_\omega)_{\omega\in\Omega}\in\mathbb{R}^{\Omega}$ with well-...
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### Is a one-dimensional compact complex analytic space necessarily projective?

Let $X$ be a compact complex analytic space with singular locus $X^{\mathrm{sing}}$. Suppose that $X\setminus X^{\mathrm{sing}}$ is a Riemann surface. If $X^{\mathrm{sing}} = \emptyset$, then $X$ is ...
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### Group bundles for topological spaces without universal cover

I‘m currently writing my Bachelor Thesis on (Co-)Homology with local coefficients. Let me first describe the situation: There are two approaches in defining Homology with local coefficients of a ...
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### Hodge decomposition on open manifold

For the open manifold like $X\times \mathbb R$ or $X\times \mathbb R^+$, where $X$ is a closed manifold. Is there any decomposition like (Hodge Decomposition) of the Differential forms on it.
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### Cohen's model yet again

It has been discussed already whether a countable OD set necessarily contains an OD element. See e.g. A question about ordinal definable real numbers . A negative answer was obtained in Archive for ...
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### A generalization of Erdős–Mordell inequality [on hold]

I proposed my conjecture generalization of Erdős–Mordell inequality as following: Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point in $A_1A_2....A_n$. Let $d_i$ be the distances from $P$ ...
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### Hyperbola application [on hold]

A curved mirror is placed in a store for a wide angle view of the room. the right hand branch of x squared over one minus y squared over three equals one models the curvature of the mirror. a small ...
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### Algorithm for Longest Common Subtour

For a new kind of heuristic for the TSP I need to calculate the longest subtour, that is common to a set $T_1,\ ...,\ T_m$ of tours, that are "good" approximations of the optimal tour $T_{opt}$. By a ...
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### How many number of finite points exists inside the circle? [on hold]

I am doing project on Image processing dealing with circular images. So I need an approximate number of pixels present inside circle image of radius R and Circle center of (x,y). Please give me the ...
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### Computing canonical forms from orbit partitions

Suppose we know the orbit partition of the vertices of a graph (due to the action of its automorphism group). Is it easy (as in "polynomial time") to generate a canonical form (aka "canonical labeling"...
### How to compute $[CP^2, G/PL]$?
Let $E^4$ be the two stage Postnikov space appearing in the homotopy type of the classifying space $G/PL$. One of its properties is that it only has two nontrivial homotopy groups $\pi_2(E)=Z/2Z$ and \$...