Contributions of Women Political Scientists to a More Just World

This roundtable was originally presented as a panel at the 2003 Annual Meeting of the APSA in Philadelphia that was sponsored by the Committee on the Status of Women in the Profession

Queering Anarchism : Addressing and Undressing Power and Desire: preface

Queering anarchism? What would that mean? Isn’t “anarchism” enough of a bogeyman in this country that any effort to “queer” it would only make it appear even more alien and irrelevant to mainstream culture than it already is? Why do it? And why now? Because-- as this excellent anthology makes evident in its multifaceted exploration of the many dimensions of both anarchism and queer—we have only just begun to understand the many possibilities offered by a queered anarchism, both with respect to critiques of existing institutions and practices and with respect to imagining alternatives to them

Khintchine-type double recurrence in abelian groups

We prove a Khintchine-type recurrence theorem for pairs of endomorphisms of a countable discrete abelian group. As a special case of the main result, if $\Gamma$ is a countable discrete abelian group, $\varphi, \psi \in End(\Gamma)$, and $\psi - \varphi$ is an injective endomorphism with finite index image, then for any ergodic measure-preserving $\Gamma$-system $\left( X, \mathcal{X}, \mu, (T_g)_{g \in \Gamma} \right)$, any measurable set $A \in \mathcal{X}$, and any $\varepsilon > 0$, the set of $g \in \Gamma$ for which $$\mu \left( A \cap T_{\varphi(g)}^{-1} A \cap T_{\psi(g)}^{-1} A \right) > \mu(A)^3 - \varepsilon$$ is syndetic. This generalizes the main results of (Ackelsberg--Bergelson--Shalom, 2022) and essentially answers a question left open in that paper (Question 1.12). For the group $\Gamma = \mathbb{Z}^d$, we deduce that for any matrices $M_1, M_2 \in M_{d \times d}(\mathbb{Z})$ whose difference $M_2 - M_1$ is nonsingular, any ergodic measure-preserving $\mathbb{Z}^d$-system $\left( X, \mathcal{X}, \mu, (T_{\vec{n}})_{\vec{n} \in \mathbb{Z}^d} \right)$, any measurable set $A \in \mathcal{X}$, and any $\varepsilon > 0$, the set of $\vec{n} \in \mathbb{Z}^d$ for which $$\mu \left( A \cap T_{M_1 \vec{n}}^{-1} A \cap T_{M_2 \vec{n}}^{-1} A \right) > \mu(A)^3 - \varepsilon$$ is syndetic, a result that was previously known only in the case $d = 2$. The key ingredients in the proof are: (1) a recent result obtained jointly with Bergelson and Shalom that says that the relevant ergodic averages are controlled by a characteristic factor closely related to the quasi-affine (or Conze--Lesigne) factor; (2) an extension trick to reduce to systems with well-behaved (with respect to $\varphi$ and $\psi$) discrete spectrum; and (3) a description of Mackey groups associated to quasi-affine cocycles over rotational systems with well-behaved discrete spectrum.Comment: 28 pages. Changes and corrections after reviewer feedback. To appear in Ergodic Theory and Dynamical System

Counterexamples to generalizations of the Erd\H{o}s B+B+tB+B+t problem

Following their resolution of the Erd\H{o}s $B+B+t$ problem, Kra Moreira, Richter, and Robertson posed a number of questions and conjectures related to infinite configurations in positive density subsets of the integers and other amenable groups. We give a negative answer to several of these questions and conjectures by producing families of counterexamples based on a construction of Ernst Straus. Included among our counterexamples, we exhibit, for any $\varepsilon > 0$, a set $A \subseteq \mathbb{N}$ with multiplicative upper Banach density at least $1 - \varepsilon$ such that $A$ does not contain any dilated product set $\{b_1b_2t : b_1, b_2 \in B, b_1 \ne b_2\}$ for an infinite set $B \subseteq \mathbb{N}$ and $t \in \mathbb{Q}_{>0}$. We also prove the existence of a set $A \subseteq \mathbb{N}$ with additive upper Banach density at least $1 - \varepsilon$ such that $A$ does not contain any polynomial configuration $\{b_1^2 + b_2 + t : b_1, b_2 \in B, b_1 < b_2\}$ for an infinite set $B \subseteq \mathbb{N}$ and $t \in \mathbb{Z}$. Counterexamples to some closely related problems are also discussed.Comment: 8 page

It Takes More Than a Village!: Transnational Travels of Spanish Anarchism in Argentina and Cuba

Spanish anarchists travelled to and from both Argentina and Cuba in the late nineteenth and early twentieth centuries, bringing with them not only ideology, but press, pamphlets and organizing strategies. Spanish immigrants and visitors played important roles in the development of the labour movement and anarchist women’s movement in each country. It is true that the movement in Spain was unique, in the sense that it attained a massive following and played a prominent role in a profound social revolution. But it is also the case that ideas and practices from Spain found fertile ground and exercised a deep influence on labour movements in Cuba and Argentina. And the experiences of Spanish exiles in Argentina and Cuba, in turn, influenced the movements in Spain. The ‘travels’ of Spanish anarchism suggest that anarchist internationalism was a transnational reality, one critical to the development of movements on both sides of the Atlantic

Popular differences for polynomial patterns in rings of integers

We demonstrate that the phenomenon of popular differences (aka the phenomenon of large intersections) holds for natural families of polynomial patterns in rings of integers of number fields. If $K$ is a number field with ring of integers $\mathcal{O}_K$ and $E \subseteq \mathcal{O}_K$ has positive upper Banach density $d^*(E) = \delta > 0$, we show, inter alia: 1. If $p(x) \in K[x]$ is an intersective $\mathcal{O}_K$-valued polynomial and $r, s \in \mathcal{O}_K$ are distinct and nonzero, then for any $\varepsilon > 0$, the set of $n \in \mathcal{O}_K$ such that $$d^* \left( \{ x \in \mathcal{O}_K : \{x, x + rp(n), x + sp(n)\} \subseteq E \} \right) > \delta^3 - \varepsilon.$$ is syndetic. Moreover, if $\frac{s}{r} \in \mathbb{Q}$, then there are syndetically many $n \in \mathcal{O}_K$ such that $$d^* \left( \{ x \in \mathcal{O}_K : \{x, x + rp(n), x + sp(n), x + (r+s)p(n)\} \subseteq E \} \right) > \delta^4 - \varepsilon.$$ 2. If $\{p_1, \dots, p_k\} \subseteq K[x]$ is a jointly intersective family of linearly independent $\mathcal{O}_K$-valued polynomials, then the set of $n \in \mathcal{O}_K$ such that $$d^* \left( \{ x \in \mathcal{O}_K : \{x, x + p_1(n), \dots, x + p_k(n)\} \subseteq E \} \right)> \delta^{k+1} - \varepsilon$$ is syndetic. These two results generalize and extend previous work of Frantzikinakis and Kra on polynomial configurations in $\mathbb{Z}$ and build upon recent work of the authors and Best on linear patterns in general abelian groups. The above combinatorial results follow from multiple recurrence results in ergodic theory, which require a sharpening of existing tools for handling polynomial multiple ergodic averages. A key advancement made in this paper is a new result on the equidistribution of polynomial orbits in nilmanifolds, which can be seen as a far-reaching generalization of Weyl's equidistribution theorem.Comment: 34 pages. Title changed from previous version, more details added to proof of Theorem 3.7, minor changes and corrections throughout the tex