Unified transform lab

Yale-NUS College



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


Title: Spectral methods for long time asymptotics of boundary value problems.

This grant can support projects related to D to N maps and their long time asymptotics.

Projects supported through this grant:

D to N maps for the Stokes equation as 1/3 fractional differential operators

Initial nonlocal value problems for evolution equations of high spatial order


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

This grant supported 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 supported through this grant:

Transform method for variable coefficient PDE

Long time asymptotics for periodic boundary data

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

Argument principle for root counting

Roots of holomorphic functions and the argument principle

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

Julia library for exponential polynomials

Relative growth of terms in exponential polynomials


Title: Dispersive quantisation via the unified transform method

This grant can support a project 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.

SRP22-FAC: Faculty led projects summer 2022

D to N maps for the wave equation

D to N maps for the heat equation in cylindrical coordinates

Nonlocal D to N maps for the heat equation

SRP21-FAC: Faculty led projects summer 2021

Comparison of derivations of the Q equation

Initial nonlocal value problems for evolution equations of high spatial order

Interface linearization of NLS solitons

Approximate diagonalizations in Fokas transform method for systems

SRP20-FAC: Faculty led projects summer 2020

Complex analytic arguments in the unified transform method

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