Related papers: Solution of W-Constraints for R-Spin Intersection …
Computing the crossing number of a graph is one of the most classical problems in computational geometry. Both it and numerous variations of the problem have been studied, and overcoming their frequent computational difficulty is an active…
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
We study a generalization of the weighted Fermat-Torricelli problem in the plane, which is derived by replacing vertices of a convex polygon by 'small' closed convex curves with weights being positive real numbers on the curves, we also…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
We address the problem of computing bounds for the self-intersection number (the minimum number of self-intersection points) of members of a free homotopy class of curves in the doubly-punctured plane as a function of their combinatorial…
We present a method for proving the existence of solutions to a class of one dimensional variational problems. The method is demonstrated by two examples of optimal interpolation problems which are motivated by engineering applications. In…
We study threshold properties of random constraint satisfaction problems under a probabilistic model due to Molloy. We give a sufficient condition for the existence of a sharp threshold that leads (for boolean constraints) to a necessary…
In this article we give a survey of homology computations for moduli spaces $\mathfrak{M}_{g,1}^m$ of Riemann surfaces with genus $g\geqslant 0$, one boundary curve, and $m\geqslant 0$ punctures. While rationally and stably this question…
We give a recipe to compute the geometric intersection number of an integral lamination with a particular type of integral lamination on an n-times punctured disk. This provides a way to find the geometric intersection number of two…
In this article, we establish the logarithmic foundation for compactifying the moduli stacks of the gauged linear sigma model using stable log maps of Abramovich-Chen-Gross-Siebert. We then illustrate our method via the key example of…
We analyse the subring of the Chow ring with support generated by the irreducible components of the special fibre of the Gross-Schoen desingularization of a d-fold self product of a semi-stable curve over the spectrum of a discrete…
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof…
This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…
In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial…
Inspired by Eynard-Orantin topological recursions, we reformulate the Virasoro constraints for curves as residues of multilinear differentials. As applications they can be used to compute the $n$-point functions of Gromov-Witten invariants…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…