• Quantum computational complexity, Quantum algorithms, Quantum cryptographic protocols
• The transition from quantum to classical physics
• The notion of entanglement, and how it can be better understood via the study of quantum complexity
• Quantum Hamiltonian complexity and connections to condensed matter physics
• Connections between quantum computation and various other complexity topics such as Markov chains, lattices, and more

Nanoscience and Nanotechnology: Basic Science and Applications of Nanoparticles

• Synthesis and characterization of novel semiconductor nanocrystals and nanostructures and their assemblies
• Size dependent optical and electronic properties of nanocrystal
• Single nanostructure microscopy and spectroscopy
• Alternative energy solutions using nanoparticles
• Lasers and optical devices based on colloidal semiconductor nanostructures
• Biological, medical and sensing applications of nanocrystals
• Non linear optical properties of semiconductor nanocrystals and nanorods
• Electrical Transport studies on single nanorods and nanocrystal arrays

• Quantum coherence of NV centers
• Magnetic sensing and spectroscopy
• Quantum memory and control

Quantum devices in the nanoscale for quantum information processing:

developing novel quantum materials that can process quantum information by scattering of light, such as quantum mirrors.

• Conventionalism
• Conceptual foundations of statistical physics
• Quantum mechanics philosophy

• Quantum computation
• Distributed computation
• Fault tolerance
• Computational complexity and cryptography

• Quantum computation and algorithms
• The interstellar medium
• Genetic networks

• Quantum optics in complex media
• Multiple scattering of entangled photons
• Quantum imaging
• imaging in scattering samples
• Hanbury Brown-Twiss interferometry

• Multi-photon entanglement generation
• Projection of two biphoton qutrits onto a maximally entangled state
• Quantum key distribution with biphotons
• Photon enanglement with quasy-phase-matched crystals
• Photon enanglement with low-symetry crystals

• Nonequilibrium mode locking phase diagram
• Noise-activated transitions and entropic barriers
• Fluctuations, dispersive waves, and coherence
• Continuum-pulse and pulse-pulse interactions
• Entanglement generation in semiclassical wave packets
• Wave packet interferometry and geometric phases
• Scattering from classical singularities
• Self-interacting wave packets

• correlated quantum systems
• modern condensed matter physics
• devising new numerical methodologies such as quantum Monte Carlo, tensor networks, and machine learning inspired techniques that push this boundary

• Combinatorics of convex sets, convex polytopes, and Helly-type theorems
• Analysis of Boolean functions, influence, noise sensitivity, and threshold phenomena
• Algebraic and topological combinatorics
• Linear programming
• Combinatorial problems in theoretical computer science
• Quantum fault tolerance

• Coherent chemistry: light induced processes
• Coherent control and laser cooling
• Dynamical processes on surfaces
• Quantum thermodynamics
• Computational and teaching methods