Our research focuses on the development of non-perturbative and background-independent approaches to quantum gravity, with particular emphasis on loop quantum gravity, spin foam models, and asymptotic safe approach. This includes investigations into their mathematical foundations (e.g., quantum geometry, discrete spectra of geometric operators) and the derivation of effective descriptions that bridge the quantum theory with classical physics. A major goal is to apply these frameworks to address long-standing problems in cosmology, such as the nature of the big bang singularity, and in black hole physics, including the resolution of singularities and the information paradox. Additionally, I explore connections between these quantum gravity models and foundational questions in quantum information theory (e.g., entanglement entropy in gravitational contexts) and quantum foundations.

Quantum field theory serves as a fundamental framework and a source of inspiration in my research. I am particularly interested in its non-perturbative aspects, which encompass phenomena like strong coupling regimes, instanton effects, and other situations where perturbative expansions break down. This interest extends to the pursuit of rigorous mathematical constructions for QFT (e.g., axiomatic approaches) and a deep engagement with the renormalization group (RG) and its fixed-point flows. These endeavors are not only of intrinsic foundational importance but also provide crucial insights and methodological tools for addressing related issues in quantum gravity, such as ultraviolet completeness and potential correspondences between statistical models and gravitational theories.

Given the intrinsically non-perturbative nature of many central questions in quantum gravity and quantum field theory, the development and application of advanced computational techniques are essential. Our work involves employing numerical methods on classical computers, such as lattice field theory approaches, Monte Carlo simulations, and numerical relativity, to investigate non-perturbative dynamics, phase structures, and the evolution of specific physical processes within these theories. In parallel, We actively explore the potential of quantum simulators, to emulate the dynamics of target quantum gravity models or lattice gauge theories. These computational endeavors aim to provide numerical checks for theoretical predictions, uncover physical phenomena inaccessible to analytic methods, and ultimately advance our understanding of quantum spacetime and fundamental interactions.

A firm grounding in, and application of, classical general relativity forms the bedrock of my research. This involves delving into its predictions under extreme conditions, such as black hole interiors and the very early universe, as well as grappling with its implications for cosmological observations like dark energy and dark matter. To address these challenges and explore possible extensions of GR, we actively investigate a wide range of modified gravity theories. Moreover, we view these modified theories not merely as extensions of GR, but also as potential low-energy effective descriptions of candidate quantum gravity theories. Studying them provides a valuable bottom-up pathway towards understanding the possible ultraviolet completions of gravity. These include scalar-tensor theories, higher-derivative gravities (e.g., f(R) theories, DHOST theories), and mimetic gravity formulations. Our focus lies in analyzing their dynamical properties, constructing exact solutions (especially black hole solutions), and examining their consistency with both theoretical principles and astrophysical/cosmological observations, aiming to assess their viability as alternatives or extensions to the standard gravitational framework and to uncover hints about the underlying quantum theory of spacetime.