Date/Time : 11 Nov 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Hu Yukuan, National University of Singapore

This talk presents a geometric and optimization-based perspective on computing electronic excited states. Starting from the many-body Schrödinger equation, we discuss variational wavefunction approximations and the nonlinearity introduced by restricting the electronic energy to parameter manifolds. We review linear-response, state-averaged, and state-specific approaches, emphasizing their distinct formulations of approximate excited states.

Focusing on state-specific calculations, we introduce a constrained saddle dynamic for locating saddle points of prescribed Morse index on Riemannian manifolds. The Grassmann bundle geometry provides a framework for analyzing the dynamic and constructing discretizations using retractions and vector transport, with linear stability and local linear convergence guarantees at nondegenerate saddle points. Numerical experiments with Hartree–Fock and complete active space self-consistent field models illustrate the approach. We conclude with challenges in developing faster saddle-search methods and navigating excited-state potential energy surfaces.

Add to calendar :

Date/Time : 04 Nov 2026 16:30
Venue : S16 #04-35
Speaker : Zujun Hou, FISCA Healthcare Co, Singapore/Nanjing

The diagnostic value of perfusion imaging is widely acknowledged, and the technology has been successfully incorporated into clinical practice guidelines. However, its clinical utility remains largely confined to the diagnosis of central nervous system disorders, seeing infrequent application in organs outside the brain. This presentation will examine the technical challenges associated with current perfusion imaging methods and elucidate the reasons for its restricted application beyond the brain. Subsequently, recent advancements in dynamic contrast-enhanced imaging will be introduced, which enable the simultaneous and reliable estimation of blood flow and vascular wall permeability, thereby extending the feasibility of perfusion imaging to extra-cerebral body organs.

Add to calendar :

Date/Time : 21 Oct 2026 16:30
Venue : S16 #04-35
Speaker : Sun Lukang, National University of Singapore

In this talk, I will report on a nonlocal continuity equation on $\mathbb{R}^d$ in which a probability density is driven by attraction toward a background measure $\omega$ and by self-repulsion, with power-law kernels $|x|^{1+a}$ and $|x|^{1+r}$, $a,r\in[0,1)$. I will show global Lagrangian well-posedness, and uniform-in-time bounds on the support when attraction dominates ($a>r$, or $a=r$ with $\omega(\mathbb{R}^d)>1$). For $0\le r\le a<1$, I will characterize zero-flux stationary states through a fractional free-boundary problem, give explicit examples in dimensions one to three that agree with particle simulations, and show that solutions with bounded energy and moments converge along a sequence of times to such a state, and converge narrowly when their $\Omega$-limit set contains a single stationary state. This is joint work with Massimo Fornasier and Hui Huang.

Add to calendar :

Date/Time : 14 Oct 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Bertram Düring, University of Warwick

Many nonlinear diffusion equations can be interpreted as gradient flows whose dynamics are driven by internal energies and given external potentials, examples include the heat equation and the porous medium equation. When solving these equations numerically, schemes that respect the equations’ special structure are of particular interest. In this talk we present a Lagrangian scheme for nonlinear diffusion equations. For discretisation of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. We present numerical experiments for the porous medium equation in two space dimensions.

Add to calendar :

Date/Time : 30 Sep 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Melvin Leok, University of California San Diego

Adjoint systems are widely used to inform control, optimization, and design in systems described by ODEs or DAEs. At the level of PDEs, advection equations and mean field games also have the structure of adjoint systems, and all adjoint systems have a Hamiltonian structure.

We utilize symplectic and presymplectic geometry to investigate the properties of adjoint systems associated with ODEs and DAEs, respectively. We show that the adjoint-variational quadratic conservation laws, which are critical to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems.

We develop structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators which admit discrete analogues of these quadratic conservation laws. This can be used to train neural networks arising from time-discretizations of neural ODEs, even ones based on implicit-in-time discretization.

Finally, we investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary PDE has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels.

Add to calendar :

Date/Time : 24 Sep 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : David Lee, Australian Bureau of Meteorology

Energy conserving variational discretisations that preserve the skew symmetric structure of the non-canonical Hamiltonian form of the moist compressible Euler equations are extended to conserve the quadratic variance of thermodynamic tracers. This is important for the simulation of thermal processes since tracer variance represents a convex invariant of the equations of motion, so its conservation is strongly related to the stable simulation of those processes.

Moist processes are incorporated into the energy and tracer variance stable formulation such that the intrinsic thermodynamic variables (pressure, temperature and chemical potentials of the different moisture species) are derived via the derivatives of a thermodynamic potential (the internal energy) with respect to the prognostic model variables (density, entropy and mass fractions of the moisture species). This ensures thermodynamic consistency for the representation of non-equilibrium moist phase exchanges.

A neural network is then trained to learn the phase exchanges within the thermodynamically consistent framework, via kilometer scale output of a regional weather model. The resulting energy and tracer variance conserving, thermodynamically consistent model of the moist compressible Euler equations is then used to simulate three phase convection at sub-kilometer scale.

Add to calendar :

Date/Time : 16 Sep 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Jackie Lok, National University of Singapore

Recently, a class of algorithms based on combining classical fixed-point iterations with repeated random sparsification has been successfully applied to very large-scale linear algebra problems, where storing the full solution vector itself may be prohibitive. However, a general mathematical understanding of when this approach can achieve dimension-independent computational and storage requirements remains limited.

In this talk, we study a randomly sparsified power method for computing the leading eigenvector of a column-stochastic matrix. We prove a dimension-independent error bound that depends on the approximate sparsity of the solution vector and the mixing time of the Markov chain associated with the matrix, establishing the possibility for high-quality approximation in very high dimensions. On the other hand, we show that a deterministically sparsified counterpart can fail, demonstrating a provable separation between deterministic and random sparsification.

Add to calendar :

Date/Time : 19 Aug 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Liu Lei, Chongqing University

Nonlinear waves on nonzero asymptotic backgrounds, such as breathers and rogue waves, have been hot research topics in recent years. Starting with the three-wave resonant interactions system, we identify a specific rogue waves-building mechanism based on modulational instability (MI) which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. We also report the emergence of a previously unexplored species of solitary waves-time-localized solitons, which coincides with the condition for the occurrence of the zero-wavenumber-gain MI. These results can be extended to the Massive Thirring model

Add to calendar :

Date/Time : 04 Aug 2026 11:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Timo Sprekeler, Texas A&M University

In this talk, we discuss a computational multiscale method for the mixed formulation of Darcy’s problem, based on a stable localized orthogonal decomposition in Raviart-Thomas finite element spaces. In the spirit of numerical homogenization, the construction provides low-dimensional coarse approximation spaces that incorporate fine-scale information from the heterogeneous coefficients by solving local patch problems on a fine mesh. The resulting numerical scheme is applicable beyond periodicity and scale-separation. This is joint work with Patrick Henning (Bochum) and Hao Li (Hong Kong).

Add to calendar :