# Tagged Questions

This tag is used if a reference is needed in a paper or textbook on a specific result.

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### Algebraic Geometry for Topologists

As someone who is familiar with algebraic topology, say, at the level of Hatcher's book, and familiar with homological algebra and categories and applications in topology but has no idea what a ...
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### Induced structure of topological group [on hold]

If we consider a closed Jordan curve $\mathcal{C}$, I know that it's homeomorphic to the circle $S^1$. Now I take an homeomorphism $\phi:S^1\longrightarrow\mathcal{C}$ and this homeomorphism induces a ...
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### Is the category of prederivators cartesian closed?

The question is in the title. ${\bf PDer} = Fun({\bf Cat}^\text{op}, {\bf CAT})$ is obviously cartesian since $\bf CAT$ is. The usual argument for presheaf categories does not apply directly since 1-...
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### Follow-up to Steinberg's problem (12) in his 1966 ICM talk?

Steinberg's lecture at the 1966 ICM in Moscow here surveyed his work on regular elements of semisimple algebraic groups, while also formulating a number of then-open questions as "problems" (with ...
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### The number of monotone Boolean functions

In the paper "The number of monotone Boolean functions" A. D. Korshunov calculates an asymptotic number of the number of monotone Boolean functions (see https://en.wikipedia.org/wiki/Dedekind_number)...
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### A question on indefinite binary quadratic forms

Let $f(x,y) = ax^2 + 2bxy + cy^2$ be an irreducible, indefinite (so that $b^2 - ac > 0$) binary quadratic form. Put $d = b^2 - ac$. We say that two pairs of integers $(x_1, y_1)$ and $(x_2, y_2)$ ...
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### Irreducibility of family of polynomials

Consider the following family of polynomials over $\mathbb{Q}$: $$f_n = x^n - x^{n-1} - \dots - 1$$ Notice that these polynomials satisfy the recurrence $$f_{n+1} = x f_n - 1$$ I would like to ...
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### Numbers divisible only by primes of the form 4k+1

Let $A(N)$ denote the number of positive integers $n\le N$ composed of prime numbers $p\equiv 1\pmod 4$ only. Is there an asymptotic formula for $A(N)$ (as $N$ tends to infinity)?
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### Higgs fields whose determinant have only simple zeros

Is the following property true for every stable holomorphic bundle of rank 2 with trivial determinant on a compact Riemann surface: The space of trace-free Higgs fields, whose determinant have only ...
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### Examples of algorithms requiring deep mathematics to prove correctness

I am looking for examples of algorithms for which the proof of correctness requires deep mathematics ( far beyond what is covered in a normal computer science course). I hope this is not too broad.
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### Regularity for a div-curl system

Let $Q = [0,1]^3$ be the unit cube in $\mathbb{R}^3$, and let $U \subset Q$ be a simply-connected subdomain with smooth boundary. Suppose $g \: \colon Q \to \mathbb{R}^3$ is a non-negative smooth ...
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### Equivalence of algebraic and topological monodromy representations?

Does anyone know of a reference for the following fact? Let $M_g$ denote the moduli stack of genus g curves, let $A_g$ denote the moduli stack of abelian varieties, and let $U_g \rightarrow A_g$ ...
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### First eigenvalue for strictly convex domains

Let $M^n$ be a compact Riemannian manifold with boundary, suppose 1). $Ric(M)\ge (n-1)$ and 2). the principle curvatures of the boundary is bounded from below by $h\ge 0$. Is there any results on the ...
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### level sets portrait near a critical point

Let $f:\mathbb{R}^{2}\rightarrow\mathbb{R}$ be a smooth ($C^{\infty}$) function and $O$ be an isolated critical point of $f$. I am looking at the local level sets diagram near $O$ from topological ...