Key Skills

Mathematics

Advanced Calculus and Optimization – Multivariable functions, constrained optimization, and sensitivity analysis for physical and engineering systems.
Linear Algebra and Functional Analysis – Diagonalization, spectral theorem, and applications to dynamical systems and quantum mechanics.
Probability and Stochastic Modeling – Random processes, convergence laws, and stochastic simulations for physics and biological modeling.
Differential Equations and Modeling – Analytical and numerical resolution of ODEs/PDEs applied to transport, thermodynamics, and control systems.
Numerical Methods and Computational Physics – Finite element and finite volume methods for complex systems and data-driven simulations.

Classical and Continuum Mechanics – Newtonian and Lagrangian formulations, conservation laws, rigid-body dynamics, and central-force orbital motion.
Thermodynamics and Statistical Mechanics – State functions, thermodynamic potentials, equations of state, phase transitions, and microscopic derivation of macroscopic laws.
Electromagnetism and Wave Physics – Maxwell’s equations, electromagnetic induction, field interactions, optics, and wave propagation at material interfaces.
Quantum and Modern Physics – Schrödinger equation, quantum states and operators, atomic orbitals, spin, and introduction to solid-state and semiconductor physics.
Geophysics and Fluid Dynamics – Fundamental equations of hydrodynamics and thermodynamics applied to natural systems; transport and diffusion in fluids and porous media.

Quantum Chemistry and Molecular Reactivity – Orbital theory, electronic structure, and predictive modeling of molecular reactivity using frontier orbitals and catalytic cycles.
Thermodynamics and Chemical Kinetics – Energy transformations, reaction equilibria, rate laws, and catalytic efficiency in energy and industrial systems.
Electrochemistry and Energy Storage – Design and optimization of batteries, fuel cells, and electrolyzers; current–potential curve analysis for reaction kinetics.
Synthetic and Supramolecular Chemistry – Multi-step synthesis, stereochemical control, and molecular design for advanced materials and polymers.
Analytical and Physical Chemistry Techniques – Spectrophotometry, calorimetry, and chromatography for quantitative system characterization.

Cellular and Molecular Biophysics – Quantitative study of motility, cytoskeleton dynamics, and force generation; fluorescence imaging (actin, vinculin).
Systems Biology and Network Modeling – Analysis of signaling networks, stochastic gene expression, and modeling of regulatory motifs from omics data.
Microfluidics and Bioengineering – Droplet-based quantification of E. coli, enzymatic assays, PDMS chip fabrication via lithography, and plasma bonding.
Synthetic Biology and Bioelectronics – Electronic modeling of genetic circuits (toggle switch, repressilator); integration of feedback control and synchronization systems.
Biomaterials and Biointerfaces – Surface functionalization and fluorescent probes for biosensing and bioimaging applications.

Analog and Digital Electronics – Circuit design, filtering, oscillators, VHDL/Verilog implementation, and embedded system control.
Signal and Image Processing – Advanced feature extraction, computer vision, and real-time analysis.
Applied Instrumentation – Semiconductor physics, photonics, and experimental instrumentation.
Scientific Computing and Data Science – Strong programming foundation in Python, SQL, C, C++, MATLAB, LabVIEW, with experience in simulation, modeling, and data processing.