Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...
The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numer ...
In this thesis, we consider an anisotropic finite-range bond percolation model on Z2. On each horizontal layer {(x,i):x∈Z} for i∈Z, we have edges ⟨(x,i),(y,i)⟩ for 1≤∣x−y∣≤N with $N\in\mathbb{N ...
Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum ...
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their critical behavior— ...
Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.
Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineer ...
This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
Coupled dynamical systems are omnipresent in everyday life. In general, interactions between
individual elements composing the system are captured by complex networks. The latter
greatly impact the way coupled systems are functioning and evolving in time. ...
Mutations in nuclear-encoded mitochondrial genes are responsible for a broad spectrum of disorders among which Leigh syndrome is the most common in infancy. No effective therapies are available for this severe disease mainly because of the limited capabili ...
Collective tunneling is a ubiquitous phenomenon in finite-size spin clusters that shows up in systems as diverse as molecular magnets or spin clusters adsorbed at surfaces. The basic problem we explore is to understand how small flipping terms can cooperat ...
We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite progr ...
