Intersection Theory Research Articles

Shifted Witten classes and topological recursion

The Witten r r -spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin–Frobenius manifold using the Givental–Teleman reconstruction theorem. We show that the R R -matrix and the translation of these two specific shifts can be constructed from the solutions of two differential equations that generalise the classical Airy differential equation. Using this, we prove that the descendant intersection theory of the shifted Witten classes satisfies topological recursion on two 1 1 -parameter families of spectral curves. By taking the limit as the parameter goes to zero, we prove that the descendant intersection theory of the Witten r r -spin class can be computed by topological recursion on the r r -Airy spectral curve. We finally show that this proof suffices to deduce Witten’s r r -spin conjecture, already proved by Faber, Shadrin and Zvonkine, which claims that the generating series of r r -spin intersection numbers is the tau function of the r r -KdV hierarchy that satisfies the string equation.

Bertini theorems for differential algebraic geometry

We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the differential analogue of Bertini’s theorem, namely that for an arbitrary geometrically irreducible differential algebraic variety which is not an algebraic curve, generic hypersurface sections are geometrically irreducible and codimension one. Surprisingly, we prove a stronger result in the case that the order of the differential hypersurface is at least one; namely that the generic differential hypersurface sections of an irreducible differential algebraic variety are irreducible and codimension one. We also calculate the Kolchin polynomials of the intersections and prove several other results regarding intersections of differential algebraic varieties.

“If you're strung out and female, they will take advantage of you”: A qualitative study exploring drug use and substance use service experiences among women in Boston and San Francisco

BackgroundSignificant disparities in substance use severity and treatment persist among women who use drugs compared to men. Thus, we explored how identifying as a woman was related to drug use and treatment experiences. MethodsThe study recruited participants for a qualitative interview study in Boston and San Francisco from January–November 2020. Self-identified women, age ≥ 18 years, with nonprescribed opioid use in the past 14 days were eligible for inclusion. The study team developed deductive codes based on intersectionality theory and inductive codes generated from transcript review, and identified themes using grounded content analysis. ResultsThe study enrolled thirty-six participants. The median age was 46; 58 % were White, 16 % were Black, 14 % were Hispanic, and 39 % were unstably housed. Other drug use was common with 81 % reporting benzodiazepine, 50 % cocaine, and 31 % meth/amphetamine use respectively. We found that gender (i.e., identifying as a woman) intersected with drug use and sex work practices and exacerbated experiences of marginalization. Violence was ubiquitous in drug use environments. Some women reported experiences of gender-based violence in substance use service settings that perpetuated cycles of trauma and reinforced barriers to care. Substance use services that were women-led, safe, and responsive to women's needs were valued and sought after. ConclusionWomen reported a cycle of trauma and drug use exacerbated by oppression in substance use services settings. In addition to increasing access to gender-responsive care, our study highlights the need for greater research and examination of practices within substance use service settings that may be contributing to gender-based violence.

Cultural Globalization and Transnational Cinema: On Intersectionality and Ethnoscapes in Hermine Huntgeburth’s Die weiße Massai

This article is an interdisciplinary critique of Hermine Huntgeburth’s Die weiße Massai (The White Masai; 2005)—a transnational film—as a text that enables a reflection on the peculiarity of North-South cultural globalization. The juxtaposition of Swiss and Masai cultures in this film using marriage as a space of global encounter, it is argued, uniquely gives agency to the significance of cultural incompatibility as a requisite binder in a globalized world. In this process I use cultural intersectionality and ethnoscapes theories to rethink the volatility of transnational cultural units. I also use a visual anthropological methodological and theoretical basis in its semiotic critique of the film’s narrative arc of cultural dispersion. The article proposes the utility of cultural incongruity in rethinking sustainable cultural units in a globalized context.

Versatile Black Female Identity in Olympia Vernon’s Eden

Political movements of racism and feminism during the late twentieth and early twenty-first centuries included monolithic approaches to identity that treated each category of race and gender exclusively. As a result, these movements fail to serve the black feminist liberation project because they do not treat blackness and gender as interlocking aspects that shape their experience. Therefore, this article aims to examine how black women’s intersectional position is represented in Eden(2003), a novel about the American South by Olympia Vernon, and how this examination enhances a powerful, versatile black female identity. Drawing on theories of intersectionality and gendered subjectivity as positionality, this study highlights how black Maddy Dangerfield, the protagonist, navigates women’s racial and gender suppression in the novel. In doing so, Maddy acquires consciousness that problematic racial and gender configurations throughout history do not necessarily hold deterministic powers over her subjectivity. In this sense, versatility as a form of radical black female subjectivity is an outcome of a simultaneous positioning as part of a historical context and detached from the determinism of that context. Maddy uses her positional perspective to create new meanings about blackness and femaleness. This process exposes how values attached to race and gender hold no deterministic power over a woman’s subjectivity. The significance of this study lies in shedding light on how versatile black female identity is part of a non-traditional way of resisting racial and gender domination that enacts engaging intersectionality and positionality

The uniqueness theorem for Gysin coherent characteristic classes of singular spaces

AbstractWe establish a general computational scheme designed for a systematic computation of characteristic classes of singular complex algebraic varieties that satisfy a Gysin axiom in a transverse setup. This scheme is explicitly geometric and of a recursive nature terminating on genera of explicit characteristic subvarieties that we construct. It enables us, for example, to apply intersection theory of Schubert varieties to obtain a uniqueness result for such characteristic classes in the homology of an ambient Grassmannian. Our framework applies in particular to the Goresky–MacPherson ‐class by virtue of the Gysin restriction formula obtained by the first author in previous work. We illustrate our approach for a systematic computation of the ‐class in terms of normally nonsingular expansions in examples of singular Schubert varieties that do not satisfy Poincaré duality over the rationals.

“Why am I here?”: A phenomenological exploration of first‐generation college student experiences in STEM majors within a predominantly white institution

AbstractFirst‐generation college students (FGCSs) are a growing population in undergraduate education. Research on FGCS primarily focuses on the challenges and barriers they encounter in college. While important, this literature offers a limited view of FGCS as learners. Moreover, minimal literature has examined these students' lived experiences within sciences, technology, engineering, and mathematics (STEM). This study explores the learning experiences of FGCS (N = 17) in undergraduate STEM programs at a mid‐sized, private, predominantly white institution. Guided by the frameworks of intersectionality and social cognitive career theory, the researchers utilized a qualitative, phenomenological research methodology to hear the perspectives of FGCS to and to identify problematic higher educational structures in STEM. Findings point to an elitist stance underlying STEM programs based in general disciplinary norms that restricted FGCS access to STEM majors and careers across social, academic, and professional elements of the academic experience. FGCS who were multiply minoritized based upon race, gender, and social class experienced the compounding of marginalization, and academic success and persistence came at a personal cost. Students also reported relying predominantly on personal strengths and motivations to overcome elitism in STEM rather than on institutional supports. Findings also highlight the variation in the first‐generation experience and identify the unique barriers FGCS encounter within STEM fields. Implications for dismantling inequitable structures for higher education in STEM attending to the social, academic, and professional inclusion of FGCS.

Lorentzian Fans

Abstract We introduce the notion of Lorentzian fans, which form a special class of tropical fans that are particularly well-suited for proving Alexandrov–Fenchel-type inequalities. To demonstrate the utility of Lorentzian fans, we prove a practical characterization of them in terms of their two-dimensional star fans. We also show that Lorentzian fans are closed under many common tropical fan operations, and we discuss how the Lorentzian property descends to the underlying tropical variety, allowing us to deduce Alexandrov–Fenchel-type inequalities in the general setting of tropical intersection theory on tropical fan varieties.

The interplay of gender and perceived sexual orientation at the bargaining table: A social dominance and intersectionalist perspective

Prior research suggests that female negotiators often obtain worse outcomes than male negotiators. The current research examines whether this pattern extends to the large subset of men and women who identify as gays and lesbians. In particular, we interweave scholarship on gender stereotypes with work on intersectionality and MOSAIC theory to develop a theoretical model that anticipates how male and female negotiators will be treated at the bargaining table based on whether they are perceived to be heterosexual or homosexual. This model predicts that homosexual women, like heterosexual men, will receive more beneficial negotiation offers and outcomes than heterosexual women and homosexual men. Additionally, it suggests that this will happen because people hold markedly different behavioral expectations for male and female heterosexual and homosexual negotiators. The results of five experimental and audit studies involving diverse samples of participants including Masters Students in the U.S. and India, individuals selling items on Craigslist, and street vendors in India provide robust support. Collectively, these findings highlight the importance of considering gender and sexual orientation in tandem when studying negotiation.

The Conundrum of Identity in the Omani Higher Education: A Case Study of an English Language Teaching (ELT) Context

The developing status of the Omani higher education has made this sector subject to both national and global influences. Such influences created inconsistencies between the demands of the local context and those of the increasingly globalizing context, which resulted in a nationally diverse faculty body. This paper draws on the Social Identity Approach (SIA) and the intersectionality theory to argue that identity in the workplace could be understood better through focusing on processes rather than individual narratives since processes reveal much of the complexity of prototypes especially when applied to workgroups. The paper reports the findings of a qualitative case study conducted in an English language-teaching department in Oman. The study explored identity intersectionalities within a workgroup by analyzing the data generated through 16 interviews, eight meeting observations and document analysis. The thematic analysis reveals that identities are constructed based on intersections of language, nationality, contract and professional identity. Such intersections were evident in relation to the process of recruitment, employment security and retention, staff inclusion, and professional identity enactment. These findings demonstrate that analyzing identity at the intra-categorical level sheds light on its effects at the individual level. The paper concludes by highlighting theoretical and practical implications that are relevant to ELT contexts internationally.

Continuum of Trauma: Fear and Mistrust of Institutions in Communities of Color During the COVID-19 Pandemic

Historical, cultural, and social trauma, along with social determinants of health (SDOH), shape health outcomes, attitudes toward medicine, government, and health behaviors among communities of color in the United States (U.S.). This study explores how trauma and fear influence COVID-19 testing and vaccination among Black/African American, Latinx/Indigenous Latin American, and Native American/Indigenous communities. Leveraging community-based participatory research methods, we conducted 11 virtual focus groups from January to March of 2021 with Black/African American (n = 4), Latinx/Indigenous Latin American (n = 4), and Native American/Indigenous (n = 3) identifying community members in Inland Southern California. Our team employed rapid analytic approaches (e.g., template and matrix analysis) to summarize data and identify themes across focus groups and used theories of intersectionality and trauma to meaningfully interpret study findings. Historical, cultural, and social trauma induce fear and mistrust in public health and medical institutions influencing COVID-19 testing and vaccination decisions in communities of color in Inland Southern California. This work showcases the need for culturally and structurally sensitive community-based health interventions that attend to the historical, cultural, and social traumas unique to racial/ethnic minority populations in the U.S. that underlie fear and mistrust of medical, scientific, and governmental institutions.

The Right to Cyberbully? A Gendered Analysis During COVID-19 in Malaysia

This paper explores the rhetoric of cyberbullying with a focus on Malaysian female influencers during the COVID-19 pandemic. The research objectives entailed identifying various critical rhetoric and attacks against female influencers on digital platforms, understanding diverse levels of cyberbullying experienced by influencers from different backgrounds, and analysing reasons behind online aggressive behaviours. The study's theoretical framework contributes to intersectionality theory by examining how the COVID-19 context shapes nuances in Female Cyber Victimisation. Methodologically, the research employs critical discourse analysis to study language in online comments and responses reflecting cyberbullying against Malaysian female influencers. The analysis covers social media platforms (YouTube, Instagram, Facebook, TikTok) and forums (Hardware Zone, Lowyat.net, Cari.com.my), focusing on cyberbullying content over two years. Three prominent Malaysian female influencers targeted by cyberbullying namely Cathryn Li, Veveonah and Ain Husniza were selected for their distinct demographics and contexts, showcasing varying cyberbullying rhetoric. Findings reveal male internet commenters' presumptions about female influencers are shaped by religion and modesty perceptions. Influencers challenging gender norms face escalated negativity. Cathryn Li, perceived as less modest and non-Muslim, faced extensive derogatory comments affecting her mental health. Ain Husniza faced mockery due to her Malay Muslim background, while Veveonah was targeted for political motives. Rooted in conservative gender roles, societal expectations contribute to targeting female influencers, resulting in ridicule and harassment. These cases underscore the intricate interplay of gender, cultural norms, and online harassment, highlighting the necessity for comprehensive interventions to combat cyberbullying and safeguard the well-being of female influencers. Keywords: COVID-19, cyberbullying, gender, influencers, female cyber victimization.

Retrieving Materialism: The Continued Relevance of Dorothy Smith

In this article, I argue that Smith’s continued relevance coincides with more recent retrievals of Marx-inspired materialism. This materialism and the associated understanding of human beings—the social, language, and world people share in common—certainly do not capture all there is to say about Smith’s eclectic and expansive social theory. However, the material dimension distinguishes her work from many other feminist sociologies and results in her continued relevance as a thinker who brings to the table another way of doing feminist sociology. I illustrate this by showing how Smith’s Marx-inspired materialism and its associated understanding of language offer a productive and timely alternative to the feminist social theory of anti-categorical intersectional theory and new materialist theory.

Non-reductive geometric invariant theory and hyperbolicity

The Green–Griffiths–Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and Yang.

Isovariant homotopy theory and fixed point invariants

An isovariant map is an equivariant map between G-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein–Williams equivariant intersection theory for a finite group G. We prove that under certain reasonable dimension and codimension conditions on H-fixed subspaces (for H≤G), the fixed points of a self-map of a compact smooth G-manifold can be removed isovariantly if and only if the equivariant Reidemeister trace of the map vanishes. In doing so, we study isovariant maps between manifolds up to isovariant homotopy, yielding an isovariant Whitehead's theorem. In addition, we speculate on the role of isovariant homotopy theory in distinguishing manifolds up to homeomorphism.

"I don't have the energy": Racial stress, young Black motherhood, and Canadian social policies.

Significant socio-economic, health, and mental health disparities due to highly entrenched and systemic anti-Black racism in Canadian institutions, policies, and practices are now well documented in research and policy reports. Yet, few in-depth studies have addressed the mental health impacts of anti-Black racism on Canadian populations. This article is rooted in a community-based, qualitative research project with young first and second-generation Black Caribbean-Canadian mothers and is informed by Black Feminist epistemologies and intersectional theories and methodologies. Our research demonstrates how participants' childhood experiences with xenophobic and racist immigration policies and educational, child welfare, and childcare systems caused their future mental health challenges as young Black mothers, and how these struggles were exacerbated by their encounters with the racist, ageist, xenophobic medical, social, and mental health services they had to access as young mothers. Based on these findings, we recommend enhancements to current social policies to minimize the differential mental health impacts on young Black Canadian mothers.

Exploring Environmental Inequalities among Marginalized Communities across the World

Purpose: The main objective of this study was to explore the pervasive issue of environmental inequalities that disproportionately impact marginalized communities.
 Methodology: The study adopted a desktop methodology. Desk research refers to secondary data or that which can be collected without fieldwork. Desk research is basically involved in collecting data from existing resources hence it is often considered a low cost technique as compared to field research, as the main cost is involved in executive’s time, telephone charges and directories. Thus, the study relied on already published studies, reports and statistics. This secondary data was easily accessed through the online journals and library.
 Findings: The findings revealed that there exists a contextual and methodological gap relating to issues of environmental inequalities that impact marginalized communities. The empirical review revealed the stark reality that marginalized communities, often characterized by low socioeconomic status and limited access to resources, bear the brunt of environmental hazards and injustices. These disparities are not only detrimental to the health and well-being of these communities but also perpetuate cycles of poverty and hinder their ability to thrive. The findings of this study emphasize the significance of formulating targeted policies and interventions to rectify the environmental injustices faced by marginalized communities. Addressing these disparities requires a multifaceted approach that takes into account the complex intersections of race, class, and environmental well-being.
 Unique Contribution to Theory, Practice and Policy: The Critical theory, Environmental Racism theory and the Intersectionality theory may be used to anchor future studies on environmental justice and marginalized communities. The study recommends that there is need for inclusive decision making that involves community members, there is need for investing in sustainable infrastructure and promoting environmental awareness among others.

At the Intersections of Gender Inequality and State Fragility in Africa

ABSTRACT Intersectionality has become a widely used theoretical lens through which scholars examine women’s political and economic participation. Intersectional frameworks analyze the ways in which formal state structures produce gender inequalities. It is precisely this conceptual and empirical strength that make a theory originally rooted in the experiences of Black women in the United States, applicable to other groups of women in a range of national contexts. Extensive debates surround the generalizability of intersectional theory. Using my work on gender inequality as a predictor of state fragility in the African region, this piece addresses these questions both conceptually and methodologically. My larger project is a cross-national study; however, I will use original country case study datasets from women’s local civil society organizations in Nigeria and Ghana to illustrate the relationships between institutionalized inequalities and the mobilization efforts of different groups of women. First, I begin by defining intersectionality. Next, I combine African feminists and African Muslim feminists’ theoretical contributions which extend and expand intersectionality. This piece contributes to conversations about the ways in which intersectionality can be applied to other groups of Black women outside of the United States. Third, I demonstrate how intersectionality is used to capture the range of priorities and strategies activists used to define and promote gender equality within formal state structures.

Confronting Anti-Muslim Racism and Islamism: An Intersectional Perspective on Muslim Women’s Activism in Germany

ABSTRACT This article explores how Muslim women’s activism unfolds in the context of anti-Muslim racism and Islamism in contemporary Germany. In particular, it identifies both gendered forms of anti-Muslim racism and Islamism encountered by Muslim women’s organizations and ways they respond to it. Drawing on theories of intersectionality and boundary making, this study identifies the most common strategies used to confront anti-Muslim racism and Islamism and their implications for intersectional boundary making. For this purpose, six expert interviews with representatives of major Muslim women’s organizations were conducted and supplemented by data from internet research and participatory observation. Based on a Grounded Theory-inspired approach, the findings show that the responses of Muslim women’s organizations to anti-Muslim racism and Islamism reconfigure group boundaries. They create more inclusive spaces in which boundary formations by religion, race, and ethnicity and gender are transcended.

“Walking between the raindrops”: The hybrid and Intersecting Identities of Arab women with a PhD in Israel

This study examines Palestinian-Arab women with a PhD in Israel. Arabs represent about one-fifth of the country’s population, and despite significant modernization, Arab society remains largely conservative. The study relies on gender and ethnic identity development theories, as well as intersectionality theory. Based on interviews with Arab women who combine an academic career with family life, the findings highlight the barriers they have overcome, as well as opportunities that have promoted their career. It concludes that despite barriers that impede women’s progress, particularly in conservative societies, Arab women academics have realized their ambitions and become role models.