Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.

Globalizing the Sculptural Landscapes of the Sarapis and Isis Cults in Hellenistic and Roman Greece

“Globalizing the Sculptural Landscape of Isis and Sarapis Cults in Roman Greece,” asks questions of cross-cultural exchange and viewership of sculptural assemblages set up in sanctuaries to the Egyptian gods. Focusing on cognitive dissonance, cultural imagining, and manipulations of time and space, I theorize ancient globalization as a set of loosely related processes that shifted a community's connections with place. My case studies range from the 3rd century BCE to the 2nd century CE, including sanctuaries at Rhodes, Thessaloniki, Dion, Marathon, Gortyna, and Delos. At these sites, devotees combined mainstream Greco-Roman sculptures, Egyptian imports, and locally produced imitations of Egyptian artifacts. In the last case, local sculptors represented Egyptian subjects with Greco-Roman naturalistic styles, creating an exoticized visual ideal that had both local and global resonance. My dissertation argues that the sculptural assemblages set up in Egyptian sanctuaries allowed each community to construct complex narratives about the nature of the Egyptian gods. Further, these images participated in a form of globalization that motivated local communities to adopt foreign gods and reinterpret them to suit local needs.

I begin my dissertation by examining how Isis and Sarapis were represented in Greece. My first chapter focuses on single statues of Egyptian gods, describing their iconographies and stylistic tendencies through examples from Corinth and Gortyna. By comparing Greek examples with images of Sarapis, Isis, and Harpokrates from around the Mediterranean, I demonstrate that Greek communities relied on globally available visual tropes rather than creating site or region-specific interpretations. In the next section, I examine what other sources viewers drew upon to inform their experiences of Egyptian sculpture. In Chapter 3, I survey the textual evidence for Isiac cult practice in Greece as a way to reconstruct devotees’ expectations of sculptures in sanctuary contexts. At the core of this analysis are Apuleius’ Metamorphoses and Plutarch’s De Iside et Osiride, which offer a Greek perspective on the cult’s theology. These literary works rely on a tradition of aretalogical inscriptions—long hymns produced from roughly the late 4th century B.C.E. into the 4th century C.E. that describe the expansive syncretistic powers of Isis, Sarapis, and Harpokrates. This chapter argues that the textual evidence suggests that devotees may have expected their images to be especially miraculous and likely to intervene on their behalf, particularly when involved in ritual activity inside the sanctuary.

In the final two chapters, I consider sculptural programs and ritual activity in concert with sanctuary architecture. My fourth chapter focuses on sanctuaries where large amounts of sculpture were found in underground water crypts: Thessaloniki and Rhodes. These groups of statues can be connected to a particular sanctuary space, but their precise display contexts are not known. By reading these images together, I argue that local communities used these globally available images to construct new interpretations of these gods, ones that explored the complex intersections of Egyptian, Greek, and Roman identities in a globalized Mediterranean. My final chapter explores the Egyptian sanctuary at Marathon, a site where exceptional preservation allows us to study how viewers would have experienced images in architectural space. Using the Isiac visuality established in Chapter 3, I reconstruct the viewer's experience, arguing that the patron, Herodes Atticus, intended his viewer to inform his experience with the complex theology of Middle Platonism and prevailing elite attitudes about Roman imperialism.

Throughout my dissertation, I diverge from traditional approaches to culture change that center on the concepts of Romanization and identity. In order to access local experiences of globalization, I examine viewership on a micro-scale. I argue that viewers brought their concerns about culture change into dialogue with elements of cult, social status, art, and text to create new interpretations of Roman sculpture sensitive to the challenges of a highly connected Mediterranean world. In turn, these transcultural perspectives motivated Isiac devotees to create assemblages that combined elements from multiple cultures. These expansive attitudes also inspired Isiac devotees to commission exoticized images that brought together disparate cultures and styles in an eclectic manner that mirrored the haphazard way that travel brought change to the Mediterranean world. My dissertation thus offers a more theoretically rigorous way of modeling culture change in antiquity that recognizes local communities’ agency in producing their cultural landscapes, reconciling some of the problems of scale that have plagued earlier approaches to provincial Roman art.

These case studies demonstrate that cultural anxieties played a key role in how viewers experienced artistic imagery in the Hellenistic and Roman Mediterranean. This dissertation thus offers a new component in our understanding of ancient visuality, and, in turn, a better way to analyze how local communities dealt with the rise of connectivity and globalization.

Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.