Contact Information
1409 W. Green Street
Urbana, IL 61801
Biography
After receiving my PhD in 2016 from the University of California, Davis, I moved to the University of Arizona, where I was a Postdoctoral Research Associate in the Department of Mathematics from 2016-2019. From 2019-2023, I was a postdoc at the Technical University of Munich. During this time, I was first a Distinguished Postdoc at the Munich Center for Quantum Science and Technology from 2019-2022, and then a postdoc supported by the multi-institution collaborative grant CRC TRR 352: Mathematics of Many-Body Quantum Systems and Their Collective Phenomena.
Research Interests
My research interests lie in mathematical physics. In particular, I use analytical methods to investigate questions related to the classification of quantum phases of matter. My research program focuses on questions related to spectral and dynamical properties of quantum lattice models, including:
- Developing methods for proving ground state energy gaps.
- Rigorously proving the existence of spectral gaps in key models.
- The stability of a spectral gap under sufficiently small perturbations of the model.
- Quasi-locality of quantum lattice models.
- Investigating low-lying excited states of gapped systems.
- Properties exhibited by gapped ground state phases.
Additional Campus Affiliations
IQUIST - member
Recent Publications
- A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs (with A. Lucia) - J. Math. Phys. 64, 041902 (2023) [journal] [arxiv]
- A bulk gap in the presences of edge states for a truncated pseudopotential (with S. Warzel) - Ann. Henri Poincaré, 24, 133–178 (2023) [journal] [arxiv]
- Quasi-locality bounds for quantum lattice systems, part II: Perturbations of frustration-free spin models with gapped ground states (with B. Nachtergaele and R. Sims) - Ann. Henri Poincaré, 23, 393–511 (2022) [journal] [arxiv]
- The spectral gap of a fractional quantum Hall system on a thin torus (with S. Warzel) - J. Math. Phys. 63, 041901 (2022)
- Spectral gaps and incompressibility in a ν=1/3 fractional quantum Hall System (with B. Nachtergaele and S. Warzel) - Commun. Math. Phys. 383, 1093-1149 (2021) [journal] [arxiv]
- Low-complexity eigenstates of a ν=1/3 fractional quantum Hall system (with B. Nachtergaele and S. Warzel) - J. Phys. A: Math. Theor. 54, 01LT01 (2020)[journal] [arxiv]
- A class of two-dimensional AKLT models with a gap (with H. Abdul-Rahman, M. Lemm, A. Lucia and B. Nachtergaele) - Analytic Trends in Mathematical Physics, Contemp. Math. 741, 1-21 (2020) [journal] [arxiv]
- Quasi-locality bounds for quantum lattice systems, part I: Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms (with B. Nachtergaele and R. Sims) - J. Math. Phys. 60, 061101 (2019) [journal] [arxiv]
- Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems (with B. Nachtergaele and R. Sims) - Contemp. Math. 717, 93-115 (2018) [journal] [arxiv]