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.is the associated bundle whose structure group is Diff k (n).Let J reg k X denote the bundle of k-jets of germs of parametrised curves f : C → X in X which are regular in the sense that they have nonzero first derivative f ′ 0. After fixing local coordinates near p ∈ X, the fibre J reg k X p can be identified with J reg k (1, n) and J reg k X = Diff X × Diff k (n) J reg k (1, n).

Personality is a study of persons. However, persons exist within contexts, and personality coherence emerges from persons in contexts. But persons and environments bidirectionally influence each other, with persons selecting into and modifying their contexts, which also have lasting influences on personality. Thus, environmental change should produce changes in personality. Alternatively, environmental changes may produce few changes. This paradoxical viewpoint is based on the idea that novel environments have no predefined appropriate way to behave, which allows preexisting personality systems to stay coherent (Caspi & Moffitt, 1993). We test these two perspectives by examining longitudinal consistency idiographic personality coherence using a quasi-experimental design (N = 50; total assessments = 5,093). Personality coherence was assessed up to one year before the COVID-19 pandemic and again during lockdown. We also test antecedents and consequences of consistency, examining both what prospectively predicts consistency as well as what consistency prospectively predicts. Overall, consistency was modest but there were strong individual differences, indicating some people were quite consistent despite environmental upheaval. Moreover, there were relatively few antecedents and consequences of consistency, with the exception of some goals and domains of satisfaction predicting consistency, leaving open the question of why changes in coherence occurs.

Personality traits are relatively consistent across time, as indicated by test-retest correlations. However, person-centered ipsative consistency approaches suggest there are individual differences in this consistency. Despite this, it is unknown whether these differences are individual differences due to person-level characteristics (i.e., some people are just more consistent than others) or exogenous forces (i.e., lack of consistency is due to environmental changes). Moreover, it is unclear whether the processes promoting consistency are the same across people. We examine these two questions using item-level profile correlations across four to nine waves with four datasets (N = 21,616) with Bayesian multilevel asymptotic growth models. Results indicated that there were, on average, very high levels of profile consistency across time, highlighting the stable nature of person-centered personality. However, there were notable individual differences in initial profile correlations as well as in changes across time; indicating that some people are more consistently consistent than others, even over long-time frames. Moreover, the shapes of people’s trajectories indicated that the mechanisms responsible for reinforcing personality consistency vary across people. We discuss how these findings provide insights on what drives personality development.

Does deviancy or adjustment predict creativity? To address this question, we tested the association between personality profile normativeness (similarity between one’s personality profile and the average profile—a proxy for the deviancy-adjustment continuum) and creativity across four different samples (total N = 348,768). We used a wide range of creativity measures, including self-reported, informant-reported, behavioral, and occupational creativity, as well as several essential statistical controls (i.e., demographics, socio-economic background, intelligence, and life satisfaction). Furthermore, we employed both cross-sectional and longitudinal designs, including samples of college students and representative adult populations. We found that people who had more normative personality profiles were more creative. However, this association only held within modality (i.e., when both personality and creativity were either self-reported or informant-reported). We did not find robust associations between personality profile normativeness and laboratory-based behavioral measures or creativity, occupational creativity, or creative achievements. We discuss alternative explanations for the observed adjustment-creativity link, specifically, implicit theories of creativity and person perception biases (halo effects). Notably, the findings did not support the idea that deviancy breeds creativity, suggesting that the famed “mad genius” hypothesis might not hold among the general population.

Personality changes across the lifespan, but strong evidence regarding the mechanisms of personality change remains elusive. Studies of personality change and life events, for example, suggest that personality is difficult to change. But there are two key issues with assessing personality change. First, most change models optimize population-level, not individual-level, effects, which ignores heterogeneity in patterns of change. Second, optimizing change as mean-levels of self-reports fails to incorporate methods for assessing personality dynamics, such as using changes in variances of multivariate time series data that often proceed changes in mean-levels, making variance change detection a promising technique for the study of change. Using a sample of N = 388 participants (total N = 21,790) assessed weekly over 60 weeks, we test a permutation-based approach for detecting individual-level personality changes in multivariate time series and compare the results to event-based methods for assessing change. We find that a non-trivial number of participants show change over the course of the year but that there was little association between these change points and life events they experienced. We conclude by highlighting the importance in idiographic and dynamic investigations of change.