Date/Time : 03 Aug 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Lu Jian, South China Normal University

Minkowski type problems arise from modern convex geometry. In the smooth case, they are usually equivalent to solving a class of Monge-Ampere type equations defined on the unit hypersphere. These equations could be degenerate or singular in different conditions. We will talk about some new results on the existence, uniqueness, and regularity of solutions to several Minkowski type problems.

Add to calendar :

Date/Time : 01 Aug 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Chen Greif, The University of British Columbia

Double saddle-point systems are drawing increasing attention in the past few years, due to the importance of associated applications and the challenge in developing efficient numerical solvers. In this talk we describe some of their numerical properties and make some distinctions between this family and the more well-established class of classical 2-by-2 block-structured saddle-point systems. We derive eigenvalue bounds, expressed in terms of extremal eigenvalues and singular values of block sub-matrices. The analysis includes bounds for preconditioned matrices based on block diagonal preconditioners using Schur complements, and it is shown that in this case the eigenvalues are clustered within a few intervals bounded away from zero. Analysis for approximations of Schur complements is included. We illustrate some of the numerical challenges and our findings on a Marker-and-Cell discretization of the Stokes-Darcy equations.

Add to calendar :

Date/Time : 31 Jul 2023 15:00
Venue : S17 #04-05 (SR2)
Speaker : Gao Weiguo, Fudan University

In this talk, we first introduce the shiftedCholeskyQR3 algorithm which has been proposed as an optional choice of the orthogonalization algorithms recently. We extend the error analysis result for oblique inner product and show that the new error bound is optimal. We discuss the loss of orthogonality and validate our conclusions through numerical experiments.

Additionally, we present a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and then performs one-sided Jacobi rotations in the working precision as iterative refinement. By carefully transforming a lower precision solution to a higher precision one, our algorithm achieves about 2x speedup on the x86-64 architecture compared to the usual one-sided Jacobi SVD algorithm in LAPACK, without sacrificing the accuracy.

Add to calendar :

Date/Time : 27 Jul 2023 16:30
Venue : S17 #04-05 (SR2)
Speaker : Li Yingzhou, Fudan University

We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts a classical optimizer to minimize the objective function with respect to the parameters in ansatz circuits. The objective function has an orthogonality constraint implicitly embedded, which allows qOMM to apply a different ansatz circuit to each input reference state. We carry out numerical simulations that seek to find excited states of H2, LiH, and a toy model consisting of four hydrogen atoms arranged in a square lattice in the STO3G basis with UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.

Add to calendar :

Date/Time : 27 Jul 2023 15:00
Venue : S17-04-06 (SR 1)
Speaker : Weinan E, AISI and Peking University

For many years, the lack of good algorithms has severely limited our ability to conduct scientific research. At its heart, the difficulty comes from the notorious “curse of dimensionality” problem. Deep learning is exactly the kind of tool needed to address this problem. In the last few years, we have seen a tremendous amount of scientific progress made as a result of the AI revolution, both in our ability to make use of the fundamental principles of physics and in our ability to make use of experimental data.

In this talk, I will analyze the origin of the AI for Science revolution, review some of the major progresses made so far, and discuss how it will impact the way we do scientific research.

Add to calendar :

Date/Time : 30 Jun 2023 22:00
Venue : via Zoom
Speaker : Dawei Shen, Sorbonne University

Join Zoom Meeting
https://nus-sg.zoom.us/j/83328843795?pwd=bUEvRU5UaVJad054UFUzV2RaUTZsQT09

Meeting ID: 833 2884 3795
Passcode: 706950

I will start with an introduction of the Einstein-vacuum equations and the history of stability problems of black holes. Then, I will talk about the double null foliations of spacetimes, which induce the null structure equations and Bianchi equations. Next, I will introduce the linearization procedure and the linearized equations. Finally, I will present my main result, which provides a new proof of Kerr stability in external regions, which was first obtained by Caciotta-Nicolò in 2010 using vectorfield method.

Add to calendar :

Date/Time : 28 Jun 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Dai Shuyang, Wuhan University

In this talk, we present some modeling and simulations of heterogeneous structures in material sciences. The first part is the multiscale continuum model of defect structures in crystalline materials. The interface structure for twist, tilt and misfit grain boundaries are described by the dislocation network. The model incorporates both the anisotropy elasticity of each grain in crystalline materials and the molecular dynamics calculation informed interaction between two bulks, i.e., the nonlinear generalized stacking-fault energy. The second part is the simulations of dielectric inhomogeneous systems. We proposed several approaches to accelerate the calculation of static and dynamic properties of charged polymers in 3D dielectric inhomogeneity system.

Add to calendar :

Date/Time : 16 Jun 2023 15:00
Venue : S17 #04-04 (SR3)
Speaker : Zhu Feng, University of Wisconsin

Putting a hyperbolic metric on a complete finite-type surface gives us a linear representation (the holonomy representation) with many nice geometric and dynamical properties: for instance it is discrete and faithful, and in fact stably quasi-isometrically embedded. This picture can be generalised in (at least) two ways. First, the notion of geometric finiteness generalises this picture in the context of rank-one Lie groups such as PSL(2,R) or PSL(2,C). Second, Anosov representations generalise this picture to higher-rank Lie groups such as PSL(d,K) for d>2.

Add to calendar :

Date/Time : 17 May 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Susanne Brenner, Lousiana State University

Elliptic optimal control problems are infinite dimensional least-squares data fitting problems where the models are defined by second order elliptic boundary value problems. In the presence of pointwise constraints on the state variable, the traditional approach becomes more challenging due to the reduced regularity of the adjoint state. In this talk I will explain how to adopt finite element methods originally designed for fourth order elliptic boundary value problems to this class of optimal control problems and present a unified framework for their analysis.

Add to calendar :