Research works

Connectivity for square percolation and coarse cubical rigidity in random right-angled Coxeter groups

Abstract We consider a random right-angled Coxeter group (RACG), upper W Subscript normal upper Gamma W Γ $W_{\Gamma}$ , whose presentation graph normal upper Gamma Γ $\Gamma$ is taken to be an Erdős–Rényi random graph, i.e. normal upper Gamma tilde script upper G Subscript n com...

Forward and Inverse Problems of a Semilinear Transport Equation

Abstract. We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport model with general boundary data,...

Convergence Analysis of a High-Order Multiscale Finite Element Method (MsFEM) for Stokes Flows in Heterogeneous Media

Abstract. An enriched nonconforming Multiscale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media was proposed in [Q. Feng, G. Allaire, and P. Omnes, Multiscale Model. Simul., 20 (2022), pp. 462–492]. The main feat...

Pair correlation conjecture for the zeros of the Riemann zeta‐function I: Simple and critical zeros

Abstract Montgomery in 1973 introduced the pair correlation conjecture (PCC) for zeros of the Riemann zeta‐function. He also conjectured that asymptotically 100% of the zeros are simple. His reasoning to support these two conjectures used the Riemann hypothesis (RH). Building on...

Complex interpolation of power-weighted Sobolev spaces with boundary conditions

We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the distance to the boundary and do not necessari...

On the Geographic Spread of Chikungunya Between Brazil and Florida: A Multipatch Model with Time Delay

Abstract. Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of Aedes mosquitoes infected with the chikungunya virus (CHIKV). CHIKV has been imported annually to Florida in the last decade due to Miami’s crucial location as a hub for international trave...

Not all accuracy is equal: Prioritizing independence in infectious disease forecasting

Ensemble forecasts have become a cornerstone of large-scale disease response, underpinning decision making at agencies such as the US Centers for Disease Control and Prevention (CDC). Their growing use reflects the goal of combining multiple models to improve accuracy and stabili...

Weak-Strong Uniqueness for the Landau Equation by a Relative Entropy Method

Abstract. We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in sta...

A Deep BSDE Approach for the Simultaneous Pricing and Delta-Gamma Hedging of Large Portfolios Consisting of High-Dimensional Multi-asset Bermudan Options

Abstract. A deep BSDE approach is presented for the pricing and delta-gamma hedging of high-dimensional Bermudan options with applications in portfolio risk management. Large portfolios of a mixture of multi-asset European and Bermudan derivatives are cast into the framework of d...

On the Heat Content of Compact Quantum Graphs

Abstract We study the heat content for Laplacians on compact, finite metric graphs with Dirichlet conditions imposed at the “boundary” (i.e., a given set of vertices) and standard conditions imposed elsewhere. We prove a closed formula of combinatorial flavor, as it is expressed...

On the intersection of pairs of trees

We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson distribution with expected value $2$. This is appl...

Minimal Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$

We study the Riesz and logarithmic energies on the Grassmannian \operatorname{Gr}_{2,4} of 2 -dimensional subspaces of \mathbb{R}^{4} . We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform measure, and we obtain asymptotic upper and lo...

On Operator Estimates in the Homogenization of Lévy-Type Operators with Periodic Coefficients

Abstract. The paper deals with homogenization of self-adjoint operators in [Formula: see text] of the form [Formula: see text], where [Formula: see text], and [Formula: see text] is a small parameter. It is assumed that the function [Formula: see text] is [Formula: see text]-peri...

Enhanced detectability of axion’s electromagnetic response with a RF-excited magnetic field in cavity

A bstract Haloscope is one of the typical installations to detect the electromagnetic responses (EMRs) of axion field in radio-frequency (RF) and microwave bands. Given that the detectable signals of the usual Haloscope-type detectors (HTDs), biased only by high stationary magnet...

TMA-Grid: an open-source, zero-footprint web application for FAIR tissue microarray de-arraying

Tissue microarrays (TMAs) significantly increase analytical efficiency in histopathology and large-scale epidemiologic studies by allowing multiple tissue cores to be scanned on a single slide. The individual cores can be digitally extracted and then linked to metadata for analys...

Forest-skein groups III: simplicity

An Ore forest-skein category provides three forest-skein groups equipped with a powerful diagrammatic calculus analogous to Richard Thompson’s groups F\subset T\subset V . We investigate when forest-skein groups have simple derived subgroups and establish two characterisations: a...

Decay of excess for the abelian Higgs model

We prove that entire critical points (u,\nabla) of the self-dual U(1) -Yang–Mills–Higgs functional E_{1} , with energy E_{1}(u,\nabla;B_{R})\leq(1+\tau(n))\cdot2\pi\omega_{n-2}R^{n-2} for all R>0 , have unique blow-down. Moreover, we show that they are two-dimensional in ambient...

Existence and Uniqueness Results for a Mean-Field Game of Optimal Investment

Abstract We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indi...

Quasi-rigid operators and hyperrecurrence

We study recurrent operators from a new perspective by introducing the notion of hyperrecurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach space is quasi-rigid if and only if it is a...

Mean-Field Limit for Stochastic Control Problems under State Constraint

Abstract. We study the convergence problem of mean-field control theory in the presence of state constraints and nondegenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems for many interacting particles s...