Unified transform lab

Yale-NUS College

Funding

Grants

The unified transform lab enjoys healthy funding from two grants to support undergraduate research.

IG18-PRB102

Title: Numerical & spectral unified transform method: complicated boundary conditions.

This grant can support projects relating to the reimplementation of the unified transform method as a fully algorithmic mathematical construction and as a computer program, particularly for multipoint problems. Necessary first steps include spectral analysis of differential operators with multipoint boundary conditions, and building a julia package for efficient handling of exponential polynomials.

Projects already supported through this grant:

Wave equation with nonlocal conditions

UTM as diagonalization of multipoint differential operators

UTM stage 1 for interface linearization of KdV solitons

Adjoints of general interface differential operators

Julia library for exponential sums and survey of Langer's work

Argument principle for root counting

Numerical locus of zeros of exponential polynomials

Asymptotic locus of zeros of exponential polynomials

Analytic-geometric asymptotic analysis of exponential polynomials

IG18-CW003

Title: Dispersive quantisation via the unified transform method

This grant can support a small number of projects related to dispersive quantisation, particularly the development and implementation of numerical algorithms to detect these effects.

Projects already supported through this grant:

Generalized Fourier series methods using ApproxFun

Yale-NUS College Summer Research Programme

The unified transform lab has been fortunate to receive significant support for undergraduate research from the Yale-NUS College summer research programme (SRP) for faculty led and student initiated projects. Most projects in the unified transform lab are faculty led, but occasionally a student initiated project is possible. Several students have been enrolled in SRP but funded through another grant. Students enrolled in SRP are also invited to attend seminars in general research practice run by CIPE and participate in the Summer Research Symposium in September. Because of the added value offered by SRP, students who have no prior research experience are strongly encouraged to consider enrollment in SRP, regardless of funding source. If you are interested in SRP funding, please look out for opportunities and deadlines.

SRP20-FAC: Faculty led projects summer 2020

Interface linearization of NLS solitons

SRP19-STU: Student initiated projects summer 2019

Adjoints of general multipoint differential operators

SRP19-FAC: Faculty led projects summer 2019

Adjoints of interface differential operators

SRP18-FAC: Faculty led projects summer 2018

Linear evolution equations on the half line with dynamic boundary conditions

Efficient representation of functions and numerical integration: julia & ApproxFun