The regularity of difference divisors

We prove the regularity of difference divisors on unitary and GSpin Rapoport-Zink spaces.Comment: 12 page

IDENTITY AND SOCIAL RELATIONS: A CASE OF CHINESE GRADUATE STUDENTS IN THE U.S.

This dissertation research separates out the social relations implied in identity theory and empirically shows the interaction of identity and social relations. I conducted 60 interviews and one online survey with respondents at two public universities in two cities with distinctive sociocultural characteristics. The respondents were graduate students from mainland China pursuing their master’s or doctoral degrees in the U.S. The students’ lengths of stay in the U.S. varied, but all experienced a major life transition from China to the U.S. The qualitative interview data show that the adoption of a religious identity in the two places, defined as different social environments, impact the interaction of identity and networks. Where the community is small and homogeneous, the Chinese graduate students are quickly thrown into strong religious dyadic relationships and primary groups, and soon thereafter acquire a religious identity. Where the community is large and sparsely connected, the identity pool is large and the adoption of the religious identity becomes less constrained by dyadic relationships and primary groups. The interview data also show that within-person time spanning (the time span between prior to the respondents’ arrival in the U.S. and after the respondents’ coming to the U.S.), and between-person time spanning (the “newcomers” who have lived in the U.S. for less than one year versus the “old-timers” who have lived in the U.S. for over one year) are important in the identity network process. The transfer from China to the U.S. fosters the emergence of the Chinese ethnic identity. The Chinese network composition of the newcomers and the old-timers granted them a similar list of important identities. The quantitative findings confirm that place, time, and personal network function together to impact identity importance. Also, the classification of ties into “important people” and “time bound people” are effective predictors of identity importance. In conclusion, this dissertation research demonstrates empirically how social relations and identity impact each other. This research also provides a case study for the population – Chinese graduate students in the U.S

Arithmetic Siegel-Weil formula on X0(N)\mathcal{X}_{0}(N)

We establish the arithmetic Siegel-Weil formula on the modular curve $\mathcal{X}_{0}(N)$ for arbitrary level $N$, i.e., we relate the arithmetic degrees of special cycles on $\mathcal{X}_{0}(N)$ to the derivatives of Fourier coefficients of a genus 2 Eisenstein series. We prove this formula by a precise identity between the local arithmetic intersection numbers on the Rapoport-Zink space associated to $\mathcal{X}_{0}(N)$ and the derivatives of local representation densities of quadratic forms. When $N$ is odd and square-free, this gives a different proof of the main results in [SSY22]. This local identity is proved by relating it to an identity in one dimension higher, but at hyperspecial level.Comment: arXiv admin note: text overlap with arXiv:2106.15038 by other author

Arithmetic Siegel-Weil formula on X0(N)\mathcal{X}_0(N): singular terms

For arbitrary level $N$, we relate the generating series of codimension 2 special cycles on $\mathcal{X}_{0}(N)$ to the derivatives of a genus 2 Eisenstein series, especially the singular terms of both sides. On the analytic side, we use difference formulas of local densities to relate the singular Fourier coefficients of the genus 2 Eisenstein series to the nonsingular Fourier coefficients of a genus 1 Eisenstein series. On the geometric side, we study the reduction of cusps to compute the divisor class of the Hodge bundle and the heights of special divisors. When $N$ is square-free, this gives a different proof of the main results in the works of Du, Yang and Sankaran, Shi, and Yang.Comment: 46 pages. arXiv admin note: text overlap with arXiv:2106.15038 by other author

Efficient evaluation of accuracy of molecular quantum dynamics using dephasing representation

Ab initio methods for electronic structure of molecules have reached a satisfactory accuracy for calculation of static properties, but remain too expensive for quantum dynamical calculations. We propose an efficient semiclassical method for evaluating the accuracy of a lower level quantum dynamics, as compared to a higher level quantum dynamics, without having to perform any quantum dynamics. The method is based on dephasing representation of quantum fidelity and its feasibility is demonstrated on the photodissociation dynamics of CO2. We suggest how to implement the method in existing molecular dynamics codes and describe a simple test of its applicability.Comment: 5 pages, 2 figure

Modeling dynamic volatility under uncertain environment with fuzziness and randomness

The problem related to predicting dynamic volatility in financial market plays a crucial role in many contexts. We build a new generalized Barndorff-Nielsen and Shephard (BN-S) model suitable for uncertain environment with fuzziness and randomness. This new model considers the delay phenomenon between price fluctuation and volatility changes, solves the problem of the lack of long-range dependence of classic models. Through the experiment of Dow Jones futures price, we find that compared with the classical model, this method effectively combines the uncertain environmental characteristics, which makes the prediction of dynamic volatility has more ideal performance

Patterned Fluidity of Chinese Ethnic Identity: Networks, Time, and Place

This study tests the salience/prominence of Chinese ethnic identity by applying identity theory, social identity theory, and social network analysis. Using survey data of Chinese graduate students in two universities in the United States, I show how Chinese ethnic identity salience varies with the percentage of Chinese in an individual’s ego network revolving around him or her. In addition, among newcomers to the United States, as the percentage Chinese in ego networks increases, the decline of Chinese identity salience/prominence declines, but for old timers in the United States, as the percentage Chinese increases, the decline of Chinese identity salience/prominence is reversed. The ethnic identity salience lapses with time unless the respondents keep a cohort of co-nationals. Moreover, a cosmopolitan sociocultural environment is conducive to the maintenance of ethnic identity when an individual has many co-nationals in his or her ego network while having many co-nationals does not stop the decline of ethnic salience in an isolated social environment