司靈得 (Daniel Spector)

Upcoming Events 
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Date:  Tuesday, 10 Mar. 2026, 15:00-16:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Gabriele Cassese, Oxford University
Title: Martingales, laminates and Korn-type inequalities   
Abstract:
Korn-type inequalities quantify a fundamental rigidity principle in linear elasticity: the size of the full gradient of a displacement can be controlled by a reduced set of “strain-like” quantities. Motivated by a question of Chipot, one can ask for a minimal version of this principle: how many scalar linear measurements of the gradient does one need to control the whole gradient? I will present a reformulation of this problem in terms of rank-one convexity and quasiconvexity, leading to sharp bounds. A central new ingredient is a systematic connection between laminates and martingales, which produces explicit families realising the extremal behaviour. The same construction gives a streamlined, quantitative route to Ornstein-type non-inequalities for broad classes of first-order homogeneous operators. If time permits, I will discuss additional applications of this method to calculus of variations.

Date:  Tuesday, 17 Mar. 2026, 09:00-10:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Yohei Tsutsui, Kyoto University
Title: Another proof of Alvino's embedding via medians    
Abstract:
The median of a function on Euclidean space was introduced by F. John in 1965, and can be regarded as a type of average. Unlike the integral average, even for non-integrable functions, a median always exists. However, the median is not unique, in general. In fact, it is well-known that the set of all medians for a function is a closed interval. With the aid of a result due to Poelhuis and Torchinsky (2012), we can see that the endpoints of the closed interval are two distinct rearrangements. We introduce a fractional version of medians and give a similar expression for the set of all fractional medians. We introduce the maximal operator defined via medians instead of integral averages, and establish smoothing properties for the fractional maximal operator. Finally, we give a short proof of Alvino's embedding, \( L^{n/(n-1),1} \to BV \) by using properties of medians and the coarea formula. Our estimate is covered by a result by Spector (2020).

Date:  Tuesday, 17 Mar. 2026, 10:00-11:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Hiroki Ohyama, Kyoto University
Title: Long-time solvability and asymptotics for the 3D rotating MHD equations
Abstract:
We consider the initial value problem for the 3D incompressible rotating MHD equations around a constant magnetic field. We prove the long-time existence and uniqueness of solutions for small viscosity coefficient and high rotating speed. Moreover, we investigate the asymptotic behavior of solutions in the limit of vanishing viscosity and fast rotation, and show that the velocity and magnetic field converge to the zero vector and the solution to the linear heat equation, respectively. We also derive the rates of these convergences in some space-time norm.

Date:  Tuesday, 24 Mar. 2026, 15:00-16:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Marco Caroccia, University of Firenze
Title: TBA     
Abstract: TBA

Date:  Tuesday, 28 Apr. 2026, 15:00-16:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Paolo Bonicatto, University of Trento
Title: Geometric Transport Equation for currents: recent developments   
Abstract:
I will report on recent results concerning the Geometric Transport Equation for \(k\)-dimensional currents in \(\mathbb{R}^n\). This equation generalises the classical continuity and transport equations to model the motion of geometric objects such as lines and surfaces. I will discuss well-posedness results for Lipschitz velocity fields, highlighting a deep connection with the notion of decomposability bundle of a measure (introduced by Alberti and Marchese). This theory further extends to the time-dependent setting with minimal regularity in time of the vector field, thus offering a unified framework for the evolution of geometric data under non-smooth flows. If time allows, I will also outline a recent approach to the classical Frobenius’ theorem via the transport of currents. The vanishing bracket condition is recast into transport identities that remain meaningful even when one of the vector fields is a normal \(1\)-current and this perspective sheds light on some Alfvén-type statements in magnetohydrodynamics.