Robert J. Webber

I am Ph.D. student advised by Jonathan Weare at the Courant Institute of Mathematical Sciences. You can reach me at rw2515 [AT] nyu [DOT] edu.

I research Monte Carlo methods with applications in geophysics and chemistry. As a mathematician, I work to identify sources of error, prove error bounds, and improve Monte Carlo accuracy. To find out more, check out my curriculum vitae or take a look at the projects below.

Mathematics: analysis of algorithms

• For two decades, the ``variational approach to conformational dynamics" (VAC) has been used to identify slowly-decorrelating functions in biochemical systems, yet very little is known about the causes and the extent of VAC's error. To provide new insight, I proved the convergence of VAC estimates and derived error bounds [arXiv] [PDF].
• Many Monte Carlo algorithms use resampling schemes. Some resampling schemes produce more error than others, and there is not a good understanding of why this occurs. In response to this problem, I developed new mathematics to identify minimal variance resampling schemes [arXiv] [PDF].
• Collaborators: Douglas Dow, Erik Thiede, Aaron Dinner, and Jonathan Weare.

Geophysics: tropical cyclones

• It is challenging to study statistics of intense tropical cyclones because simulations are expensive and intense tropical cyclones are rare. I developed an efficient new rare event sampling algorithm and applied the algorithm to study intense tropical cyclones [online publication] [PDF].
• The rapid intensification process in tropical cyclones is mysterious. I helped develop an algorithm that identifies the most likely pathway leading to rapid intensification in a high-resolution weather model [online publication] [PDF].
• Collaborators: David Plotkin, Morgan O'Neill, Jonathan Weare, and Dorian Abbot.

Chemistry: many-electron systems

• It can be expensive to compute the ground-state energy of the Schrödinger operator for many-electron systems, particularly when systems are strongly correlated. I helped design a Monte Carlo scheme for computing the ground-state energy that produced efficiency gains of up to a thousand [online publication].
• We recently wrote a second paper that further improved the efficiency of the computational approach [arXiv] [PDF].
• Collaborators: Samuel Greene, Jonathan Weare, and Timothy Berkelbach.