Research
Research
Research
Research
3,132+ open-access research outputs.
We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of t…
As an alternative to PINNs, a Deep Ritz framework is proposed to solve fully nonlinear PDEs. A least-squares algorithm is advocated to decouple the nonlinearities from the variational features of seve…
Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an act…
In this article, we find finitely many numerical invariants to classify the diffeomorphism types of three dimensional simply connected Mori fibre spaces with torsion free homology groups.…
We introduce multiplicative Ehresmann connections on surjective submersions of Lie groupoids, extending both the classical notion of Ehresmann connections on fibre bundles and the more recent notion o…
We study the random-cluster model on trees and treelike graphs at low temperatures. This is a model of dependent percolation parametrized by an edge probability $p\in (0,1)$ and a clustering weight $q…
We study the complexity of the Thouless-Anderson-Palmer (TAP) free energy for Ising spin glasses with a general mixed p-spin covariance, working with the generalized TAP functional of Chen, Panchenko,…
We study the Ising model on a two-community stochastic block model, where $n$ spins are split into two equal groups with inter-community interaction parameter $\alpha_n\in[0,1]$. We provide a complete…
For an integer $n\geq 1$, consider the $n$-th metallic number $\phi_n=\frac{n+\sqrt{n^2+4}}{2}$ (e.g. $\phi_1$ is the golden number) and denote by $[\phi_n]_q$ its $q$-deformation in the sense of S. M…
We prove that, in the FK-percolation model, the probabilities of local events are uniformly analytic in the percolation parameter $p$ under suitable mixing assumptions on the measure, and satisfy a un…
We introduce an operator-algebraic framework for Morita equivalence of quantum graphs based on $\Delta$-equivalence of operator systems introduced by Eleftherakis, Kakariadis and Todorov. Adopting the…
The Cahn--Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, of…
We consider nested CLE$_4$ in a simply-connected domain and compute the following renormalised probabilities: the probability that two points belong to the same CLE$_4$ gasket and the probability that…
In this paper, we extend the study of graded equivalences to the case of general idempotent graded rings. We prove that the existence of a graded equivalence between two categories of graded torsion-f…
A finite pre-tensor category is a finite abelian category equipped with a right exact tensor product for which every projective object has duals. Finite tensor categories, for which every object has d…
By extending the Johnson--Barron projection method from one dimension to high dimensions and utilizing a Wang type dimension-free Harnack inequality, we obtain a new quantitative bound for the entropi…
In this paper, we study estimation of parameters in a two-parameter Potts model with $q$ colors and coupling matrix $A_N$. We characterize concrete sufficient conditions for existence of the pseudo-li…
We show that the $p$-part of the conductor of a generalised character of a finite group is equal to the conductor of its generalised decomposition numbers. We use this to show that $p$-parts of conduc…
Extracting approximate eigenpairs from a prescribed subspace is of fundamental importance in eigenvalue computation. While projecting the target eigenvector onto the subspace yields satisfactory accur…
We compute the homotopy groups at each unital abelian C*-algebra $C(T)$ in the Morita $3$-category of abelian C*-algebras, C*-algebras with central maps, C*-correspondences, and adjointable bimodule m…
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