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the title of each lecture.
Date:
Tuesday, 3 Mar. 2026, 09:00-10:00 TST (GMT+8) , in Room M212 in NTNU
Gongguan Campus Mathematics Building Speaker:Long Huang,
Guangzhou University
Title: Capacitary Muckenhoupt weights
Abstract:
In this talk, we mainly introduce a new class of capacitary Muckenhoupt weights denoted by \( A_{p,\delta} \).
It is proved to be a proper subset of standard Muckenhoupt's \( A_p \) weight.
By proposing a new approach, we then show Muckenhoupt's theorem, reverse Hölder's inequality,
self-improving property, and Jones' factorization theorem within this capacitary Muckenhoupt weight framework.
Finally, we will reveal the deep connections between \( A_{p,\delta} \) with \( \text{BMO} \) and
\( \text{BLO} \) spaces with respect to Hausdorff contents.
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: On the contact surface of Cheeger sets
Abstract: Geometrical properties of Cheeger
sets have been deeply studied by many authors since their
introduction, as a way of bounding from below the first Dirichlet
p-Laplacian eigenvalue. They represent, in some sense, the first
eigenfunction of the Dirichlet 1-Laplacian of a domain. In this talk
we will introduce a property, studied in collaboration with Simone
Ciani, concerning their contact surface with the ambient space. In
particular, we will show that the contact surface cannot be too
small, with a lower bound on the (Hausdorff) dimension strictly
related to the regularity of the ambient space. The talk will focus
on the introduction of the problem and on the proof of the
dimensional bounds. Functional to the whole argument is the notion
of removable singularity, as a tool for extending solutions of PDEs
under some regularity constraint. Finally, examples providing the
sharpness of the bounds in the planar case are briefly treated.