# Mathematics and Natural Sciences

## John Duncan, Phd

##### Associate Professor, ECAS, Mathematics

*Moonshine as a Bridge from Physics to Number Theory*

This proposal involves moonshine, physics and number theory. Number theory is home to some of the most challenging open problems known to humankind. Physics has—on the strength of theoretical advances over the last century—produced some of the most transformative of our modern-day technologies. Moonshine is a new field of mathematics that has arisen from surprising coincidences relating algebra to number theory. We propose to use mathematical moonshine to forge a new bridge between physics and number theory, and thereby produce new physical methods for tackling the most difficult unsolved number theoretic questions.

## Ajit Srivastava, PhD

##### Assistant Professor, ECAS, Physics

*Strongly interacting states of optical excitations in two-dimensional crystals*

A reductionist approach in physics has been very successful in uncovering the fundamental laws of nature at the smallest scale of elementary particles. Yet the same laws, applicable at all scales, are not very useful in explaining the collective behavior of a large number of elementary particles. In other words, it is hopeless to understand the properties of a solid, by a bottom-up approach which focuses on elementary particles. Condensed matter physics is the field of physics which deals with different phases of matter which emerge from a macroscopic number of constituents. The key feature which gives rise to di↵erent phases from the same constituents is the interaction amongst them. Interaction between electrons, which carry charge, are at the heart of many interesting and practically useful phenomena such as superconductivity. One way of increasing interactions amongst electrons is to confine them which makes them “see” each other more. Recently, atomically thin crystals, where electrons are confined to thickness of an atom, have been discovered. When two such “monolayers” are stacked together, the resulting sandwich structure can have remarkable electronic properties such as superconductivity or an insulating state where all electrons are arranged in a lattice. In this proposal, we try to answer the question of whether neutral (no net charge) optical excitations - which can also be considered as particles but are created only for a short time by shining light on such sandwich structures - can also spontaneously arrange in a crystal. Such crystals of optical excitations can have potential applications in quantum information processing which is much faster than traditional computation. We expect preliminary results from the proposed research to directly lead to competitive funding from federal agencies.

## Alessandro Veneziani, PhD

##### Professor, ECAS, Mathematics

*Aggregated Morphological and Computational Fluid-Dynamics Data Analysis of Type-B Aortic Dissections*

Type-B Aortic Dissection is a lethal disease afflicting 26 million patients annually worldwide. It occurs for a tear developing in the intimal layer of the aorta, causing the dissection of the aortic wall, creating a true and a false lumen. Therapy preventing the growth of the false lumen and possible lethal ruptures may consist of either medications or surgery. As surgery may be risky, it would be critical to anticipate the need for intervention vs. medical therapy. Computational patient-specific modeling may play a significant role in understanding the prognostic factors of the evolution of the disease and, ultimately, in supporting the clinical decision-making.

This project combines advanced tools of image processing, numerical partial differential equations, and statistical mining to answer the need to find more reliable and established risk indicators that may support doctors at the early stage of the pathology. We will work on a set of Emory retrospective data. The images of these patients will be analyzed, reconstructed and meshed to run a specifically developed computational fluid dynamics software so to combine an aggregate and complex set of data to correlate with the evolution of the pathology (“Growth” vs. “No Growth” of the false lumen) with the help of advanced Principal Component Analysis techniques. The successful accomplishment of this 1-year study will allow establishing a procedure to use in a much larger clinical trial (granted by external funds) and, ultimately, to support doctors' decision-making. The PI will work with a post-doc and a Ph.D. student (summer internship).