Related papers: Specialization Method in Krull Dimension two and E…
For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
In the setting of several commuting operators on a Hilbert space one defines the notions of invertibility and Fredholmness in terms of the associated Koszul complex. The index problem then consists of computing the Euler characteristic of…
Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…
In a recent paper by Kamrani et al. (2024), exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise was discussed, and the convergence order close to the Hurst parameter H was proved.…
A new class of compact K\"ahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong…
Let R be a commutative noetherian local ring. As an analogue of the notion of the dimension of a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of finitely generated R-modules is introduced in this…
Let $\mathcal{B}$ be a homogeneous differential operator of order $l=1$ or $l=2$. We show that a sequence of functions of the form $(\mathcal{B}u_j)_j$ converging in the $L^1$-sense to a compact, convex set $K$ can be modified into a…
In this paper, we bring together the worlds of model order reduction for stochastic linear systems and $\mathcal H_2$-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error…
Let p be a prime number which is split in an imaginary quadratic field k. Let \mathfrak{p} be a place of k above p. Let k_\infty be the unique Z_p-extension of k which unramified outside of \mathfrak{p}, and let K_\intfy be a finite…
In this article, we present the first half of our project on the Iwasawa theory of higher rank Galois deformations over deformations rings of arbitrary dimension. We develop a theory of Coleman maps for a very general class of coefficient…
The goal of this note is to explain a derivation of the formulas for the local Euler obstructions of determinantal varieties of general, symmetric and skew-symmetric matrices, by studying the invariant de Rham complex and using character…
In this paper we study extension problems for torsors in positive characteristic. Let $F$ be a field of characteristic $p>0$ and $U/F$ be a unipotent algebraic group. As our first main result, we prove that every $U$-torsor defined over the…
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…