# 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.

You can hear me talk at
SIAM UQ2020,
SIAM MS2020,
SIAM MPE2020,
or ENOC2020,
which will take place (sometime) in 2021.