# All Questions

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### Expected summation of dropped intervals?

For each $n\in\mathbb{N}$, let $I_n$ be an interval of length $1/2^{n}$. We drop each $I_n$ onto the interval $[0,1]$ uniformly at random (so that there is "wraparound" if need be). What is the ...
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### Determining whether $k(x + x^{-1})$ is post-critically finite for $0 < |k| < 1$

My REU partner and I are working on a problem involving iterations of quadratic rational maps over an algebraically closed field $K$ that is complete with respect to a non-trivial non-archimedean ...
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### Is there a generalization of homotopy groups to fractional dimensions

Does there exist a reasonable candidate for such an object as $\pi_{\frac12}(X)$?
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### Showing that a sequence of random variables with increasing expected value converges to a Poisson random variable

Consider a sequence $\{X_n\}_{n \geq 1}$ of nonnegative, integer-valued random variables. For any random variable $Y$ and $k \geq 1$, let $(Y)_k = Y(Y-1)(Y-2)\dots(Y-k+1)$ be the $k^\mathrm{th}$ ...
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### Stacks with representable morphisms to algebraic stacks

If $Y$ is an algebraic stack over a scheme $S$ and $X$ is a stack such that there exists an $S$-morphism $X\to Y$ representable by algebraic spaces, then is $X$ an algebraic stack (in the sense that ...
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### An algebraic strengthening of the Saturation Conjecture

The Saturation Conjecture (proved by Knutson-Tao) asserts that $c_{n\mu,n\nu}^{n\lambda}\neq 0\Rightarrow c_{\mu,\nu}^{\lambda} \neq 0$, where $c$ denotes a Littlewood-Richardson coefficient and $n$ ...
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### On the global structure of the Gromov-Hausdorff metric space

This is a purely idle question, which emerged during a conversation with a friend about what is (not) known about the space of compact metric spaces. I originally asked this question at ...
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### Intersection Question of set theory [closed]

At an institute where students can opt more than one subject, of 300 students, 55 did not choose any of Mathematics, Physics or Social. 110 choose Mathematics, 130 choose Physics and 140 choose ...
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### Minimal number of intersections in a convex $n$-gon?

For a convex polygon $P$, draw all the diagonals of $P$ and consider the intersection points made by those diagonals. Let $f(n)$ be the minimal number of such intersections where $P$ ranges over all ...
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### Pure motives and compatible systems of $\ell$-adic representations

I am trying to understand the statement of the conjectures of Deligne on special values of certain $L$-functions, from his article titled, "Valuers de Fonctions L et periodes d'integrales" which ...
196 views

### A question on permutations

Given integers $1$ through $n$, let $S$ be set of ordering of integers that respect even alternating or reverse alternating permutations (https://en.wikipedia.org/wiki/Alternating_permutation) up to ...
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### Are periodic billiard trajectories stable on a manifold with strictly convex boundary?

Let $(M,g)$ be a compact Riemannian manifold with strictly convex boundary. Let $\gamma:S^1\to M$ be a periodic billiard trajectory (geodesic in the interior and reclects specularly at the boundary). ...
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### Class forcings and elementary embeddings

In the Hamkins-Kirmayer-Perlmutter paper "Generalizations Of The Kunen Inconsistency", they prove the following theorem: "Theorem 7: In any set forcing extension $V[G]$, there is no nontrivial ...
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### Why a cone/parabolic set for the nontangential maximal function?

Suppose $f\in L^p(\mathbb{R}^d)$. Then the Dirichlet BVP for the Laplace equation $\Delta u = 0$ in the upper-half plane $\mathbb{R}^d\times\mathbb{R}_{>0}$ with boundary value $f$ can be solved by ...
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### Vector inequation problem [closed]

{A_i} = \left( {\begin{array}{*{20}{c}}{{A_{i1}}}\\{{A_{i2}}}\\ \vdots \\{{A_{in}}}\end{array}} \right),{B_i} = \left( {\begin{array}{*{20}{c}}{{B_{i1}}}\\{{B_{i2}}}\\ \vdots ...
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### Characteristic Cycles and Nearby Cycles

Let $Y$ be a smooth algebraic variety over $\mathbb{C}$, let $X = Y \times \mathbb{C}$ and let $f: X \to \mathbb{C}$ be the projection. Let $M$ be a (not necessarily regular) holonomic $D_X$-module ...
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### Is any blow-up of smooth subvarieties always an extremal contraction?

Let $X$ be a smooth complex projective variety and $Z$ be a smooth subvariety of $X$. Take the blow-up $\pi: Y \to X$ of $X$ along $Z$. Then I want to know whether $\pi$ is the contraction of an ...
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### What is the minimum number of filled cells in a partial Latin rectangle with autotopism group $\cong C_2$ and autoparatopism group $\cong S_3$?

Definitions: a partial Latin rectangle is an $r \times s$ matrix containing symbols from $[n] \cup \{\cdot\}$ such that each row and each column contains at most one copy of any symbol in $[n]$. The ...
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### Essential surfaces in the Exterior of Montesinos knots

Hatcher and Oertel computed the boundary slopes of essential surfaces of Montesinos knots in this paper. But they do not consider surfaces that do not intersect the boundary of the exterior. An ...
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### optimization of quadratic over linear function [closed]

I'm a computer science student. Please I need a help in solving a constrained normalized quadratic function. I'm familiar with solving quadratic constrained optimization function with matlab by ...
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### Non strictly-singular operators and complemented subspaces

If $T$ is a bounded operator which is not strictly singular, acting on a separable Banach space $X$, can one always find an infinite dimensional, closed and complemented, subspace $Y$ such that $T$ ...
36 views

### Counting the k-factors of the complete graph on n vertices [closed]

I was originally trying to solve the following problem: 10 people are in a room, and you give them a task. Their task is for each person to shake hands with exactly 3 other people in the room. How ...
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### What does “control of a deformation problem” mean?

Is the expression "control of a deformation problem' ever defined? There are of course many examples relating a dg-Lie or L-infty algebra to a deformation problem, and the phrase is evocative. Is it ...
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### What are the problems with Logicism? [closed]

"Maybe" logicism is a ("philosophical") stand, posture in mathematics. My questions are: Why logicism is not a "absolute" posture in mathematics (what are your problems)? Are there some evidence for ...
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### Baire Category Theorem for complete uniform spaces

The version of the Baire Category Theorem I have in mind is the statement that a countable intersection of dense open subsets of a complete metric space is dense. The question is: is it likewise ...
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### Computer calculations in a paper

I think I can improve the current upper bound concerning an open problem. The ideas are purely combinatorial, but in the end I have to calculate the maximum of a really ugly, non elementary function ...
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### Time-stepping numerical scheme for the advection dispersion equation

I am facing a simple (at first glance) problem. I need to implement a numerical scheme for the solution of the first order wave propagation equation with chromatic dispersion included. My original ...
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### Is the complex structure on a del-Pezzo surface a regular complex structure?

Let $(X, \omega, J)$ be a compact symplectic manifold with an almost complex structure. Fix some homology class $\beta \in H_2(X, \mathbb{Z})$. An almost complex structure $J$ is said to be ...
Let $L$ be an complete lattice. A lattice homomorphism $f: L\to L$ is said to be join-incomplete if there is an infinite set $S \subseteq L$ such that $f(\bigvee_L S) > \bigvee_L f(S).$ How can ...
In constructive mathematics, several authors, including Bishop himself, use the term "locally non-constant" function. That is: A function $f: [a, b] \longrightarrow \mathbb{R}$ is called locally ...