October 2023 talk at NYU i2i meeting: https://www.youtube.com/watch?v=jbmB2ZFu_48Magnetic Resonance Imaging (MRI): - Related time-dependent diffusion coefficient to permeability and surface area of membranes [Nature Physics 2011]. Application: in vivo quantification of fiber diameter and membrane permeability in muscle- Introduced structural universality classes and related the dynamical exponent of diffusion to the structural exponent characterizing these classes [PNAS 2014]. Applications: identified effectively one-dimensional diffusion along the neurites in tissues; explained diffusivity decrease in acute stroke in terms of an increase in the one-dimensional structural disorder; currently probing axonal structure in humans with time-dependent diffusion tensor imaging- Introduced the Standard Model of diffusion in white matter, for mapping intra- and extra-axonal volume fractions, diffusion coefficients, and free water fraction, and derived its parameter estimation degeneracies [NeuroImage 2018]- Pioneered random matrix theory-based denoising of MRI signals that has led to the widely-used MPPCA algorithm [MRM 2016, NeuroImage 2016, InvestRadiol 2023]- Mapped higher-order cumulant tensors of the diffusion propagator onto the addition of angular momenta. Used representation theory of SO(3) to classify all rotational invariants of the cumulant expansion up to 4th order [2023-]- Suggested Zero Shell Imaging [2023-] to map diffusion propagator with heavily undersampled directions in the q-space Condensed Matter Physics: - Formulated elastic scattering theory for 2+1-dimensional Dirac fermions; exactly solved scattering off a Coulomb potential. Applications: Determined conductivity of graphene'e electrons due to Coulomb impurities [Phys Rev B 2007, Appl Phys Lett 2007]- Suggested quantized adiabatic charge pumping of a fractional charge due to electron interactions in a Carbon nanotube [Phys Rev Lett 2005, Phys Rev B 2005]- Related 1/f type noise to collective fluorescence and transport in quantum dot arrays [Phys Rev B 2005, Nano Lett 2008, Nature Communications 2011]Specialties: Modeling of classical and quantum transport in interacting and/or disordered systems. Scattering theory, Green's functions, random matrices, renormalization, restricted Brownian motion, numerical simulations