司靈得 (Daniel Spector)

Upcoming Events 
*Anyone interested in the topics is welcome to attend the seminar in person. (Note: Seminars are held in person only; livestreams and recordings are not provided.)

Date:  Tuesday, 6 Oct. 2026, 15:00-16:00 TST (GMT+8) , in Room 509 in NCTS in NTU
Speaker: Joydwip Singh, Indian Institute of Science Education and Research Mohali
Title: Linear and bilinear Bochner-Riesz means on Métivier groups    
Abstract:
In this talk, we discuss about the boundedness of linear and bilinear Bochner-Riesz means associated with the sub-Laplacian on Métivier groups. Métivier groups are two-step stratified Lie groups, which are generalisation of Heisenberg groups. For such groups there are two notion of dimensions, one is topological dimension and the other is homogeneous dimension and in general, topological dimension is strictly smaller than the homogeneous dimension. It is also known that many sharp spectral multiplier results are given in terms of the topological dimension. Here we also show that, in case of Métivier groups, the smoothness parameter of the linear maximal and bilinear Bochner-Riesz means can be expressed in terms of the topological dimension of the underlying space.

Date:  Tuesday, 13 Oct. 2026, 09:00-10:00 TST (GMT+8) , in Room 509 in NCTS in NTU
Speaker: Lorenzo De Gaspari, University of Western Australia
Title: From gullies to curves: dimension reduction in a wildfire model 
Abstract:
Bushfires pose significant environmental and societal challenges, and understanding how they propagate is important for improving prediction and mitigation strategies. We study a model for wildfire propagation, analyzing a nonlocal parabolic partial differential equation posed in thin tubular domains modeling narrow gullies. In this talk, we discuss the effective behaviour of the system as the width of the gully becomes very small. In this asymptotic regime, the model undergoes a dimensional reduction, turning the original problem into a geometric evolution equation posed on the axis of the gully.

Date:  Tuesday, 3 Nov. 2026, 09:00-10:00 TST (GMT+8) , in Room 509 in NCTS in NTU
Speaker: Ramiro Lafuente, University of Queensland
Title: TBA
Abstract: TBA

Date:  Tuesday, 17 Nov. 2026, 15:00-16:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Prashant Athavale, Clarkson University
Title: Star-Norm Bounds and Total Variation Flow, with Applications to Crystallographic Imaging    
Abstract:
The dual of the total-variation seminorm, sometimes called the star-norm in image processing, arises naturally in variational and multiscale image decomposition. One way to understand this norm is through the equation $f = \mathrm{div}\, p$. A bounded vector field $p$ satisfying this equation immediately provides an upper bound for the star-norm of $f$. Hierarchical constructions developed by Eitan Tadmor in connection with the Bourgain-Brezis problem give a constructive way of producing such bounded solutions. However, obtaining sharp and computationally useful estimates of the star-norm of a general image remains an interesting open problem.

I will use this question as a starting point for a related line of work based on multiscale total-variation methods. Hierarchical $(BV, L^2)$ decompositions lead, in a continuous-scale limit, to total-variation flow. For weighted TV flow, the accumulated flow parameter gives an explicit upper bound on the weighted star-norm of the residual and, after finite-time extinction, on the star-norm of the image itself. Introducing spatially varying weights also makes it possible to suppress noise while reducing diffusion across significant edges.

I will then discuss how these ideas arise in electron backscatter diffraction (EBSD), where images encode crystallographic orientations of polycrystalline materials. In this setting, denoising and restoration must account for crystallographic symmetry while preserving grain boundaries, whose geometry carries important physical information. I will describe our use of total-variation and weighted total-variation methods for restoring EBSD orientation maps and extracting their geometric structure.

I will conclude with several open questions, including sharper and more computable estimates of the star-norm, connections between hierarchical bounded solutions and TV-based multiscale representations, and variational methods that better preserve the geometry of crystallographic images. These problems suggest several directions in which techniques from nonlinear analysis, geometric analysis, and image processing may interact.  

Date:  Tuesday, 24 Nov. 2026, 15:00-16:00 TST (GMT+8) , in 509 in NCTS in NTU
Speaker: Suman Mukherjee, Indian Institute of Technology Bombay
Title: TBA    
Abstract: TBA   

Date:  Tuesday, 1 Dec. 2026, 09:00-10:00 TST (GMT+8) , in 509 in NCTS in NTU
Speaker: Jesse Gell-Redman, University of Melbourne
Title: TBA    
Abstract: TBA