We prove the existence of a power structure over the Grothendieck ring of geometric dg categories. We show that a conjecture by Galkin and Shinder (proved recently by Bergh, Gorchinskiy, Larsen and Lunts) relating the motivic and categorical zeta functions of varieties can be reformulated as a compatibility between the motivic and categorical power structures. Using our power structure, we show that the categorical zeta function of a geometric dg category can be expressed as a power with exponent the category itself. We give applications of our results for the generating series associated with Hilbert schemes of points, categorical Adams operations and series with exponent a linear algebraic group.

This article provides an empirical overview of federal lobbying in Canada, examining lobbying contacts by field and sector from 2011 to 2022. We track shifts in lobbying representation over this period, including across Harper Conservative and Trudeau Liberal administrations. The study reveals the dominance of business interests in lobbying in Canada and a high level of lobbying concentration. By sector, export-oriented industries with high environmental and climatic impacts—namely, agriculture, fossil fuel and manufacturing industries—predominate. With the transition to Trudeau, we find a significant increase in overall rates of lobbying and a modest increase in the ratio of public interest representation. Overall, the lobbying industry is characterized by greater access but unequal voice.

We define a Grothendieck ring of varieties with actions of finite groups and show that the orbifold Euler characteristic and the Euler characteristics of higher orders can be defined as homomorphisms from this ring to the ring of integers. We describe two natural λ-structures on the ring and the corresponding power structures over it and show that one of these power structures is effective. We define a Grothendieck ring of varieties with equivariant vector bundles and show that the generalized (‘motivic’) Euler characteristics of higher orders can be defined as homomorphisms from this ring to the Grothendieck ring of varieties extended by powers of the class of the complex affine line. We give an analogue of the Macdonald type formula for the generating series of the generalized higher-order Euler characteristics of wreath products.

In this article, we propose a causal relationship between a region's communist revolutionary legacy before 1949 and the variation in private sector development after 1949. In the case of Zhejiang, the pre-1949 revolutionary experience led to the power struggle between two elite groups, the guerrilla cadre group and the southbound cadre group, in the province after 1949. As the weak side, guerrilla cadres were willing to protect local economic interests in exchange for local popular support, which improved their odds of political survival. As a result, in contrast with counties where the guerrilla forces were historically weak, counties with strong guerrilla forces before 1949 saw significantly more robust private sector development throughout much of the Mao and post-Mao periods. In this article we provide preliminary historical and statistical evidence to support this hypothesis.