Michael Ren

• Researched and presented on nonlinear optics. Specifically on the process of second harmonic generation. Derived the Manley Rowe relations for the electromagnetic energy of an optical photon traversing a non-centrosymmetric medium starting from a nonlinear dielectric response for the nonlinear maxwell equations.
• Employed quantum bootstrap to determine the eigenstates of the bosonic creation and annihilation operators on the harmonic oscillator, as well as through degenerate and nondegenerate perturbation theory. Also solved the Schrodinger equation for the Hydrogen atom, both in terms of algebraic methods and series expansions of the Bessel functions.
• Measured the transverse resistivity of a copper sample by applying a Hall voltage. Vibrating sample magnetometer option to measure the saturation moment. Last experiment of personal choice included measuring the critical temperature and magnetic field of a YBCO superconductor. Included a presentation and question and answer session afterwards. Had a detailed one-one session with the professor, and derived the London equations for superconductivity and the London penetration depth from the assumption of the Drude model of conductivity.
• Presented on superfluid helium IV. Studied its property of carrying zero entropy, and its thermal wave property, and the underlying two fluid theory for its inviscid flow. Also compared and referenced Feynman's original papers on liquid helium, especially the discussion of the trial wavefunction for liquid helium which predicts the existence of quantum vortices and elementary excitations.

• Analytical and problem solving skills
• Proficiency in communication and presentation
• Independent research skills
• Adept at technical writing
• Hands on experience with Laboratory equipment

• MAE 8 (MATLAB Programming for Engineering Analysis)
• CSE 11 (Introduction to Programming and Computational Problem-Solving: Java)
• CSE 12 (Basic Data Structures and Object-Oriented Design)
• MATH 20D (Introduction to differential equations)
• MATH 31AH-CH (Honors Linear Algebra and Multivariable Calculus)
• MATH 140 A-C (Foundations of Real analysis)
• MATH 150A-B (Differential Geometry)
• PHYS 100A-C (Physics for Physics Majors-Electricity and Magnetism)
• PHYS 110A-B (Lagrangian and Hamiltonian Mechanics)
• PHYS 130A-B (Quantum Physics)
• PHYS 140A-B (Statistical and Thermal Physics)
• PHYS 133 (Material science laboratory-)
• PHYS 120 (Circuits and Electronics)
• PHYS 211A (Solid state physics I)

Volunteering at the SPS (Society of Physics students) club for physics demonstrations and outreach at elementary schools (2021-2023)