I'm broadly interested in the intersection of mathematics, computer science, physics, and engineering. More specifically, I'm passionate about computational geometric mechanics, structure-preserving simulations, discrete differential geometry, optimization, and stochastic mechanics. I also avidly follow research in the real-time computer graphics field.

We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. Using a discrete Hamiltonian formulation we achieve energy and Casimir preservation; formally, the flow evolves on infinite-dimensional coadjoint orbits. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions.

We derive the dynamics of harmonic components for incompressible inviscid fluids, which has previously been overlooked in the vorticity-streamfunction formulation for Euler equations. We elucidate the physical laws associated with the new equations and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.

This is a comprehensive course for graphics researchers to fill the gap between their undergraduate curriculum of multivariable calculus and cutting-edge graphics research. We use relevant examples from computer graphics to illustrate the theory of exterior calculus leading to advanced topics including continuum mechanics, fluid dynamics, and geometric optimizations.

We present a method for solving the wave equation on the entire infinite domain using only finite computation time and memory. We perform wave simulations in infinite spacetime using a finite discretization of the bounded spacetime with no additional loss of accuracy introduced by the Kelvin transformation.

We simulate Euler equations for inviscid fluids by using a novel formulation based on covectors. This new formulation is an entirely velocity-based method in the vein of advection-projection methods while emulating vortex methods. This allows for capturing more intricate vortex dynamics and reducing dissipation of energy with low computational overhead.

We solve infinite-domain simulation problems by applying the Kelvin transform. The transformation turns infinite-domain PDEs into bounded-domain ones via a domain inversion and a singularity factorization.

• June 2nd 2023: Talk on Covector Fluids paper at Pixel Cafe at UCSD CSE department. (In-person)
• April 22nd 2023: Talk on Covector Fluids paper at Southern California Fluids Conference. (In-person)
• February 28th 2023: Talk on Covector Fluids paper at Geometric Mechanics at UCSD Math department. (In-person)
• November 3rd 2022: Talk on Covector Fluids paper at joint oceanography seminar at UCSD Scripps Institution of Oceanography. (In-person)
• August 10th 2022: Talk on Covector Fluids paper at SIGGRAPH 2022. (In-person with recording here)
• August 4th 2022: Talk on Covector Fluids paper at Stanford University. (In-person)
• June 9th 2022: Talk on Covector Fluids paper at Visual Computing Center's retreat. (In-person)
• June 7th 2022: Discussion on Covector Fluids paper at McGill Univeristy. (Remote)
• June 2nd 2022: Talk on Covector Fluids paper at University of Waterloo Computer Graphics Lab (CGL). (Remote)
• May 10th 2022: Talk on Covector Fluids paper at SideFX Software. (Remote)
• September 24th 2021: Talk on Kelvin Transform paper at Toronto Geometry Colloquium (TGC). (Remote with recording here)
• August 11th 2021: Talk on Kelvin Transform paper at SIGGRAPH 2021. (Remote with recording here)

Throughout my studies, I've been very fortunate to intern at various places, and be mentored by all the wonderful folks listed below, so that I could pursue my childhood passion towards movies, animation, and gaming. These internships have allowed to me witness how much beautiful math, physics, and engineering goes into creating these forms of art, and contribute my share to them.

Mentors: Alexey Stomakhin, Steve Lesser

Mentors: Fernando de Goes, Andrew Butts, Mark Meyer
Worked on cloth deformation and simulation.

Mentor: Jose Doran
Worked on Call of Duty: Warzone 2.

Mentor: Michael Vance, Akimitsu Hogge
Worked on Call of Duty Black Ops: Cold War.

Mentor: Prof. Christopher Batty
Worked on adaptive quad/octree viscous fluid simulation.

Mentor: Ruben Penalva, Randy Tjandra
Worked on Watch Dogs Legion.

Mentor: Jeff Lait
Worked on Houdini 17 release.

Mentor: Neil Dickson, Derrick Moser
Worked on Houdini 16.5 release.

Mentor: Rob Bairos, Malcolm Bechard
Worked on Touch Designer engine.

Mentor: Jamie de Domenico
Worked on auto focus systems.

Volunteered to help instruct and lead the Canadian olympiad team.

This website was forked from Jon Barron.