Grants
The unified transform lab enjoys healthy funding from grants to support undergraduate research.
IG22-SDG101
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
IG18-PRB102
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
IG18-CW003
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:
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
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
SRP19-STU: Student initiated projects summer 2019
SRP19-FAC: Faculty led projects summer 2019
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