# Research Interests

My research focuses on the theoretical, computational, and experimental aspects of searching for axion dark matter candidates. Currently, I am leading an effort to solve the extent to which axion dark matter candidate can form structure unique from a classical pressure-less fluid. I also have several other topics that I find fascinating, which you can read some about below. Most generally, I would classify my research interests as searching for novel approaches to unresolved problems.

If you would like to learn more about my work, collaborate, or have questions about the banner equations~~ ~~pictured at the top of this page, then please contact me.

**Axion Dark Matter:**

Axions are a proposed fundamental particle that are suspected to be the dark matter, and possibly also solve other lingering issues in fundamental physics. Axions are light, expected to weigh less than a billionth of an electron apiece. But, to be the dark matter and to seed the formation of galaxies and other structures in modern cosmology, axions must exist in great density; at least a trillion would be flowing through your screen right now! As a result of this tight packing, axion dark matter is expected to form a "Bose-Einstein condensate", meaning that the axions are overlapping on a quantum level.

There has been a great deal of effort to determine if our universe has axions, and their type. Techniques range from looking at indirect evidence in astrophysical sources like stars, black holes, galaxies, and even the cosmic microwave background, to direct detection in the laboratory. I am currently a collaborating PI at the premier axion dark matter experiment, ADMX. We search for axion dark matter with masses in the range of single to tens of micro-eV using resonant inverse-Primakov heterodyne detection, which is essentially a fancy AM radio that we use to try to tune in to the "axion station". I have taken roles in data-taking management and development, data analysis, and other computational roles.

Searches like ADMX need to know what the axion signal looks like in order to distinguish the axion channel from other sources of microwaves. To approximate the axion "song," we can use large simulations depicting the formation of our galaxy, which are performed on supercomputers. Simulations that I and others have performed can not only tell us what to look for, but conversely after an axion signal is detected tell us a great deal about the formation of the Milky Way.

Perhaps most exciting, I am trying to determine if this condensed matter can impact the way galaxies and other structures in our universe form and different ways we could possibly observe those differences. I perform much of this research using both analytical and numerical methods, which I run. A powerful new model of axion dynamics has already produced some impressive results, suggesting quantum nature of axion dark matter can span our Milky Way. You can see a selection of my recent results in my CV page and the Gallery (coming soon). This work may be applicable to other systems of tightly-packed atoms and sub-atomic particles, such as cold gases, electrons in solids, and the degenerate matter in white dwarf and neutron stars.

**Superluminal Travel within Relativity Theory:**

Hyper-fast (as in faster than light) solitons within modern theories of gravity have been a topic of energetic speculation for the past three decades. One of the most prominent critiques of compact mechanisms of superluminal motion within general relativity is that the geometry must largely be sourced from a form of negative energy density, though there are no such known macroscopic sources in particle physics. I was recently able disprove this position by constructing a new class of hyper-fast soliton solutions within general relativity that are sourced purely from positive energy densities, thus removing the need for exotic negative-energy-density sources. This is made possible through considering hyperbolic relations between components of the space–time metric’s shift vector. Further, these solutions are sourceable by a classical electronic plasma, placing superluminal phenomena into the purview of known physics. This is a very exciting breakthrough that I hope to have more report on soon.

**Gravity-Media Dualities:**

I also have interests in the interplay between media and fundamental forces. For instance, Einstein's theory of general relativity with media had a rich set of solutions, most of which we know almost nothing about. Standard theoretical explorations and simulations cover only a fraction of sought-after solutions. Novel techniques inspired by a similarity in description between two theories, called a duality, can help expand this scope and reveal new solutions, some of which could be quite powerful. Currently, I am considering a classical duality between matter, gravity, and internal gauge theories in order to explore exotic solutions with a wide range of potential uses.

**Physically-Motivated Action Principles:**

The action principle is a cornerstone of modern physics, providing a concise means of expressing classical and even quantum dynamics. This principle is made even stronger by the consideration of symmetries. Emmy Noether's two theorems revolutionized our consideration of fundamental physics a century ago, and there is still much to be learned from them now.

This simple pairing of symmetry and action may be able to tell us a great deal. The action principle, given the proper environment, and physical symmetries, may be capable of describing physical forces and their relation to the nature and existence of matter. Ultimately, I would like to determine if such a theory can capture gravity, electromagnetism, and the Yang-Mills theories of the weak and strong nuclear forces, and the observed sources of matter. Such a theory would provide more succinct, and hopefully useful, description of fundamental physics than currently exists.

**Ultra-Hyperbolic Equations:**

The field of partial differential equations can be broken down into four different classes: elliptic, parabolic, hyperbolic, and ultra-hyperbolic. The first three are seen in situations like electrostatics (Poisson's: elliptic), non-relativistic quantum mechanics (Schroedinger's: parabolic), and the motion of sound waves in media (hyperbolic). These classes are well posed as boundary value or initial value problems. The last class, ultra-hyperbolic, are not well posed as they have multiple time-like charcteristic directions and may have many solutions arising about a given set of initial data. The task of describing dynamics modeled by such equations could be seen as significantly disadvantaged. However, I am interested in the structure of these equations *because* of their solution degeneracies. I would like to better understand the structure of these degeneracies with the aim of finding a novel approach to quantum theory.

(Side note: relativity theory on space with multiple time and multiple space dimensions would circumvent the constancy of the speed of light, permitting superluminal travel without a warp drive.)