arXiv research

Study negative definite spin fillings of knot covers.

Proves Gromov's conjecture on total mean curvature using surgery and positive mass theorems.

Study shows certain spin manifolds can't meet DEC condition.

Researchers prove an inequality linking spin manifold fill-ins to hyperspherical radius.

The paper calculates involutive Heegaard Floer homology for specific 3-manifolds.

New rigidity theorems for spin fill-ins with non-negative scalar curvature.

Proves upper bound on filling radius for manifolds with positive scalar curvature.

Upper bound for total mean curvature of spin fill-ins is proven.

This note fills a hole in the author's previous paper ``Ricci-Flat Holonomy: a Classification'', by dealing with irreducible holonomy algebras that are subalgebras or real forms of $\mbb{C} \oplus \mf{spin}(10,\mbb{C})$. These all turn out to be of Ricci-type.

In this paper we study ${\rm Spin}(7)$-instantons on asymptotically conical ${\rm Spin}(7)$-orbifolds (and manifolds) obtained by filling in certain squashed $3$-Sasakian $7$-manifolds. We construct a $1$-parameter family of explicit ${\rm Spin}(7)$-instantons. Taking the parameter to infinity, the family (a) bubbles o…

Given a spin$^c$ rational homology sphere $(Y,\mathfrak{s})$ with $\mathfrak{s}$ self-conjugate and for which the reduced monopole Floer homology $\mathit{HM}_{\bullet}(Y,\mathfrak{s})$ has rank one, we provide obstructions to the intersection forms of its Stein fillings which are not negative definite. The proof of th…

Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.

Study shows only two topological configurations for Spin(7)-manifold fibrations, ruling out smooth Cayley fibrations.

We determine the contributions of isolated singularities of spin V 4-manifolds to the index of the Dirac operator over them. From these data we derive certain constraints on the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds, and also on the embeddings of the real projective planes into 4-manif…

Study cyclic group actions on spin 4-manifolds with boundary using Seiberg-Witten theory.

We define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be the conformal infinity of a conformally compact Einstein metric on $X$.

New invariant connects symplectic fillings and contact structures.

The study sets constraints on 4-manifold forms linked to specific invariants.

Assume that we are given a closed chord-generic Legendrian submanifold $Λ\subset P \times \mathbb R$ of the contactisation of a Liouville manifold, where $Λ$ moreover admits an exact Lagrangian filling $L_Λ \subset \mathbb R \times P \times \mathbb R$ inside the symplectisation. Under the further assumptions that this …

New links in 3-manifolds have large systole.

The paper proves positive energy-momentum theorems for charged AdS initial data sets.

Study PL bordism theories with quantitative bounds on filling simplices.

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of ``optimal'' solutions is generically exponentially large: rationality is thus de fact…

Upper estimate of Dirac eigenvalue linked to hyperspherical radius.

This paper explores 4-planes in Spin(7) manifolds with symplectic structures.

Study symplectic fillings of lens spaces, focusing on virtually overtwisted contact structures.

Proves positive mass theorems for specific ALF and ALG manifolds.

We study the supersymmetric Wilson loop as introduced by Caron-Huot, which attaches to lightlike polygons certain edge and vertex operators, whose shape is determined by supersymmetry constraints. We state explicit formulas for the vertex operators to all orders in the Graßmann expansion, thus filling a gap in the lite…

New bounds set for stable 2-systole in specific geometric spaces.

Study shows constraints on slopes for knot manifolds with specific tori.

Study local topological constraints on Berry curvature in spin-orbit coupled Bose-Einstein condensates.

Study bounds total mean curvature of fill-ins with scalar curvature constraints.

New spinorial functional connects Perelman's W- and F-functionals.

Study fermionic theories, their anomalies, and modular transformations.

Developed Gompf connected sum for orbifolds, constructing symplectic and K-contact manifolds.

This article provides a novel framework to evaluate limit order tactics that highlights expected fill price, adverse price selection cost, and opportunity cost. We formulate the problem of optimal execution of market orders with nonlinear market impact, power law decay kernel, and stochastic and deterministic liquidity…

We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings with semisimple symplectic cohomologies. Manifolds with these properties can be constructed by generalizing the boundary connected sum operation to our setting, and are related to certain birational surgeries like blow-d…

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold $M^n$ admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics $\barη$ on $M^n \times {\mathbb R}$ such that $(M^n \ti…

We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes…

In this article we give a sharp upper bound on the possible values of the Euler characteristic for a minimal symplectic filling of a tight contact structure on a lens space. This estimate is obtained by looking at the topology of the spaces involved, extending this way what we already knew from the universally tight ca…

Study of conformally compact metrics and Lovelock tensors in even dimensions.

According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle moves on such diagrams that do not change the corresponding contact manifold. As an …

Study on harmonic spinors on specific Lie groups.

We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3-sphere, and hats in blow-ups of the (punctured) com…

We introduce a refinement of the Ozsvath-Szabo complex associated to a balanced sutured manifold $(X,τ)$ by Juhasz. An algebra $A_τ$ is associated to the boundary of a sutured manifold and a filtration of its generators by $H^2(X,\partial X;\Z)$ is defined. For a fixed Spin^c structure $s$ over the manifold $X'$, which…

We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces. Our met…

This study examines non-retail trading on Polymarket, revealing unique behavior patterns and structural limitations.

This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing p…