Research

Motivation: Protons and neutrons (collectively, hadrons) are the building blocks of everything around us, yet their internal structure remains an enigma. We can pull an atom out of a molecule and from that atom isolate a proton, but inside that proton, quarks and gluons are almost inextricably confined, making them challenging to study. 

Objective: I devise theory techniques that help us uncover the intricate inner quark and gluon structure of hadrons, including through first-principles calculations and formulating equations to interpret experimental data.

Relevant experiments:

• Electron-Ion Collider (EIC), under construction

• Large Hadron Collider (LHC) 

Motivation: Everyday substances come in three phases: solid, liquid, and gas. Quark/gluon matter also comes in phases. We typically see quarks and gluons confined in hadrons. However, under extreme temperatures or pressures, quarks and gluons can break free from hadrons and form new phases of matter like quark-gluon plasma. 

Objective: I develop mathematical tools to determine what phases of quark and gluon matter appear in nature, and to map out how these phases transition into one another as we vary temperature and pressure. 

Relevant experiments:

• Facility for Antiproton and Ion Research (FAIR), under construction

• Relativistic Heavy Ion Collider (RHIC)

Motivation: When you turn on a flashlight, a beam of white light illuminates the wall in front of you. When you shine that same light through a glass prism, a rainbow comes out. The field of optics explores the principles behind how light waves propagate through various materials and are impacted by electromagnetic forces. 

Objective: I develop techniques that help us better harness the power of time-periodic (Floquet) driving forces to control wave systems in optics and condensed matter.

Relevant experiments: 

• This work can inspire potential tabletop optics and condensed matter experiments

Motivation: In a diffractive process, two colliding particles forward-scatter off of one another at high energy, producing a spray of new particles but mysteriously leaving large ​“rapidity gaps” of the detector empty. Diffraction plays a key role in many phenomena across nuclear, particle, and astrophysics -- ranging from the nature of forward (Regge) physics, to the behavior of cosmic ray showers, to the saturation of nuclear matter.

Challenge: Even though diffraction comprises nearly 50% of the LHC and a projected 20% of the EIC cross section, it had long defied a systematic first-principles description.

Contributions and impact: We have developed a rigorous field theoretic framework to describe diffraction from first principles, utilizing the technique of effective field theory. Our framework makes new predictions and opens up novel frontiers for exploration at the dawn of the EIC, High-Luminosity LHC, and FAIR accelerators.

Links:

• Article on factorization of diffraction

• Seminar slides for high-energy theorists, May 2025

Motivation: In the coming years, the FAIR accelerator will come online, opening up a new window into the phases of quarks and gluons. Now is the time to develop a better understanding of what FAIR may find, with particular attention to signals of new physics. 

Challenge: At high density, the equation describing QCD loses features that make low-density QCD tractable. Specifically, the Dirac operator loses Hermiticity, inducing a sign problem, a major barrier to lattice (numerical) simulation. 

Contributions and impact: Non-Hermitian systems are widely studied in optics and condensed matter. We have imported insights from these fields into QCD, allowing us to develop new analytic and numerical tools for studying QCD at nonzero density. Using these tools, we showed that non-Hermiticity can give rise to an exotic phenomenon called a "moat" regime (a condensed matter term) near a critical point. We have proposed experimental signatures for this new "moatonic" phase of nuclear matter at FAIR.

Links:

• Article on experimental moat signatures

• Article on exotic phases in Z3 models

• Article on moat formation

• Recorded talk for non-Hermitian theorists, February 2024

• Seminar slides for high-energy theorists, September 2025

Motivation: Energy correlators (EECs) are a class of collider observables that are of wide interest due to their compelling theoretical properties, novel features for experimental studies, and the breadth of physical information they encode, ranging from the value of the QCD coupling αs to TMDs. 

Challenge: Extracting high-precision physical information requires high-precision theoretical knowledge of EECs.

Contributions and impact: We showed that the two-point EEC exhibits renormalons, singularities that cause poor perturbative convergence. We removed the leading renormalon, significantly improving predictions. Our results also provided information on nonperturbative corrections and the broader trans-series structure of energy correlators. This opens a path to extracting higher-precision physics from EECs, and improving predictions of related observables. 

Links

• Article on renormalons in the EEC

Motivation: Transverse momentum distributions (TMDs) encode the 3D momentum structure of quarks and gluons inside hadrons. Extractions of TMDs from experimental data exhibit large uncertainties for non-perturbative quark/gluon momenta, a kinematic region which lattice QCD is typically well-positioned to probe.

Challenge: TMDs are defined in terms of Wilson lines that carry time dependence. We cannot calculate time-dependent objects with lattice QCD (numerics) because of an obstacle called a sign problem. To circumvent this issue, one can define a new lattice-calculable "quasi-TMD" by making a time-independent projection of the Wilson lines. However, it is not a priori clear that quasi-TMDs encode the same physics as TMDs.

Contributions and impact: We have derived a factorization formula connecting quasi-TMDs to physical TMDs, establishing that lattice and physical TMDs share the same underlying physics. Our formula also opens up a path to computing gluon TMDs.

Links

• Article on lattice TMD factorization

• Seminar for high-energy theorists, October 2022

Motivation: In Floquet engineering, we apply a time-periodic modulation to change the effective behavior of a wave system. 

Contributions: We expanded the scope of Floquet engineering to more fully exploit spatial degrees of freedom. By utilizing time-periodic but spatially non-uniform driving fields, we showed that we could approximately transform broad classes of tight-binding systems into one another, using a perturbative procedure. 

Impact: We have proposed several optics applications, including removing disorder, undoing Anderson localization, and enhancing localization to an extreme in waveguides. This approach is applicable in broader contexts, and we foresee its use in a range of atomic, optical, and condensed matter systems. 

Links

• Article on Floquet engineering