I began my formal research career as an undergraduate studying weak lensing and dark matter with George Smoot at LBNL. Dark matter is an invisible form of matter which is known to make up roughly 27% of our universe. Its only interaction we know of so far is gravitational, which means it can pull things inward the way the Earth pulls us down to the ground. This also implies that it doesn't interact with light, which is why we call it dark. We can see ordinary matter, like the chair you are sitting on or your bright, shiny smartphone companion, because it interacts with light. This kind of ordinary matter only makes up 5% of our universe. Pretty pathetic, right? For those keeping a tally, stay tuned to read about what makes up the other 68% of our universe.
But let's get back to dark matter! As I said, it can pull things inward, including light. This means that light coming from distant galaxies can be distorted as it travels through nearby dark matter. This is what it looks like when that happens. By tracking this distortion very carefully, scientists can infer the amount of dark matter that must have existed along the way. This allows them to produce beautiful maps of the dark matter distribution, like the one created by some of my former summer research supervisors at Caltech and JPL.
I entered graduate school at Stanford planning to continue with astrophysics, but became interested early on in learning more about the theoretical side of the subject. I completed a research rotation in theoretical astrophysics and began veering toward more purely theoretical subjects. After rotations with Vahe Petrosian and Michael Peskin I ended up as a student of Leonard Susskind.
Most of what I worked on as a Ph.D. student was in the subject of holography. Before getting into this I should say a few words about the problems occupying theoretical physicists. In one class of physicists are low-energy physicists, which work on the physics of systems at low energies, like metals, window glass, crystals, etc. In another class are high-energy physicists, which work on the physics of systems at high energies, like in the early universe when things were really hot and at very high energies. The primary tool which both fields use is known as quantum field theory, which provides a synthesis between the fields of quantum mechanics and special relativity. Quantum mechanics describes things like atoms and quarks, while special relativity is necessary to describe objects moving at near the speed of light. Both fields have amazing implications for the world we live in, such as entanglement and time dilation. Quantum field theory has so far been successful in uniting three of the four fundamental forces of nature: the weak force, the strong force, and the electromagnetic force. The fourth force, gravity, does not seem to cleanly fit in the structure of quantum field theory. Finding a way to unite gravity with the other three fundamental forces is the subject that many high-energy physicists, including myself, spend their time thinking about.
Holography is an idea, originally proposed by Gerard 't Hooft and my advisor Leonard Susskind, which claims that a theory of quantum gravity in three spatial dimensions can be rewritten as a quantum theory without gravity in two spatial dimensions. That would be great, because as I mentioned above we think we more or less understand quantum theories that do not involve gravity! All this was rather speculative until some very concrete breakthroughs, due to string theory, showed that this idea is correct in certain instances. Unfortunately, the instances in which it seemed to be correct were not accurate descriptions of our universe. Most of my work has been dominated by trying to adapt these tools to contexts which more closely resemble our universe and the things in it. One of the primary problems, which I tend to return to frequently, is how to incorporate the accelerated expansion that our universe underwent in its infancy (and is currently undergoing) into a comprehensive holographic theory. This current accelerated expansion is caused by what we call dark energy, although we do not really know much about it other than it makes up the remaining 68% of our universe. This is partly why the stakes are so high in understanding it!
I had many distinct interests in graduate school, so I also worked
on novel descriptions of exotic materials, glassy dynamics and
chaos in string theory, observational signatures of our universe colliding with other universes
in a purported multiverse, quantum entanglement as
a probe of quantum gravity, and ultrametricity as a probe of quantum cosmology.
I also had a wild paper about our universe colliding with other
lower-dimensional universes in a way we could observationally detect. That paper was a blast, and I am still waiting patiently for observers
to measure our predictions :)
UC Santa Barbara
At Santa Barbara my two primary mentors were Mark Srednicki and
Joe Polchinski. Both were deep and original thinkers from whom I learned lots of
physics that I applied to my own work. While I did not collaborate with them, I did collaborate with
Gary Horowitz, who my advisor used to call the President of Gravity. My intuition for
gravitational dynamics was greatly sharpened by this collaboration, and I could see why the President of Gravity moniker was so accurate. I was
also able to collaborate with some brilliant young graduate students, who are all currently pursuing a range of interesting questions in theoretical physics.
I spent most of my time in Santa Barbara thinking about symmetries in quantum field theory. Symmetries in physical laws are -- and have been for over a hundred years -- one of the most profound ways to probe and understand nature. Much of the
utility of understanding symmetries is due to Emmy Noether. In one of the most brilliant works
of mathematical physics in the 20th century, she showed that continuous symmetries in the laws of physics lead to quantities that are conserved in time.
For example, the fact that the laws of physics do not change in time leads to energy conservation. The fact that they do not change in space leads to
momentum conservation. Given that physical systems are messy, with lots of components colliding and interacting, the fact that we can isolate
some quantities that remain unchanged in all of this is incredibly useful.
One of the consistency conditions of holographic duality is that the symmetries of the two systems match. After all, if they are the
same system in a different physical guise, they had better have the same symmetries in one form or another! I studied symmetries of quantum field theory
at finite temperature, discovering various ways in which the physics at high temperature is equivalent to the physics at low temperature. For example, we used
one of these equivalences to prove that the energy (and its derivatives with respect to the system's
spatial size) of many critical systems at low temperatures is negative. I also illustrated how
these symmetries appeared in a gravitational dual description, and argued that there were important physical implications for black holes. Throughout this work
I became particularly obsessed with understanding the fundamental ingredients behind what makes holographic duality possible. After all, a quantum field theory
and a quantum theory of gravity look very different! I eventually argued for a particular context in which they are actually very similar, and -- spoiler alert --
the main tool used was a symmetry and the particular way it was violated. (Thanks Emmy!) This symmetry is known as center symmetry and was historically used in an attempt
to understand how quarks confine in atoms. Using center symmetry, one can begin to see
the guts of a geometric description akin to that of gravity emerge
from the quantum field theory, primarily through something known as the Eguchi-Kawai mechanism.
I came to Cornell University as a member of the Simons Bootstrap Collaboration under
Tom Hartman. This privately funded collaboration primarily aims to use consistency
principles of quantum field theories to constrain their properties and compute their parameters. Through holographic duality, the techniques are applicable to
quantum gravity, which is the focus of much of my work on the bootstrap. I have also begun focusing
on the simplest physical models that capture the
features of a quantum theory of gravity. These are theories of quantum mechanics, a la the old days of Heisenberg, Bohr, and the heroes of early 20th
century physics. Remarkably, quantum mechanics -- without the added complications of special relativity -- seems to have the structure of quantum gravity
built into it. Special relativity, gravity, and black holes are all emergent features of simple theories of quantum mechanics.