Related papers: Compactness and convexity results for closed relat…

We use type I string models with supersymmetry broken by compactification (\`a la Scherk-Schwarz) in order to test the weak gravity conjecture in the presence of runaway potentials in a perturbative string theory setting. For a finite value…

For a given closed convex planar curve $\gamma$ with smooth boundary and a given $p>0$, the string construction yields a family of nested billiards $\Gamma_p$ for which $\gamma$ is a caustic. The action of the corresponding reflections…

Let $\Omega\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^2$-smooth boundary. We study the compactness of composition operators on the Bergman spaces of smoothly bounded convex domains. We give a partial…

We derive a constraint (string equation) which together with the Toda Lattice hierarchy determines completely the integrable structure of the compactified 2D string theory. The form of the constraint depends on a continuous parameter, the…

We show that bounded families of global classical relativistic strings that can be written as graphs are relatively compact in C0 topology, but their accumulation points include many non relativistic strings. We also provide an alternative…

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…

We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target…

This thesis investigates correspondences between open and closed strings. This is done on the level of coupled open-closed moduli spaces and from a string field theoretic point of view. The construction of boundary string field theory on…

Motivated by closed string perturbation theory arguments by S. Shenker, we consider non-perturbative effects of characteristic strength $\mathcal{O}(e^{-1/g_{s}})$, with $g_{s}$ the closed string coupling constant, in supersymmetric…

We reconsider the issue of large-volume compactifications of the heterotic string in light of the recent discoveries about strongly-coupled string theories. Our conclusion remains firmly negative with respect to classical compactifications…

The optimal transport map between the standard Gaussian measure and an $\alpha$-strongly log-concave probability measure is $\alpha^{-1/2}$-Lipschitz, as first observed in a celebrated theorem of Caffarelli. In this paper, we apply two…

An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of…

We study closed string evolution in the pp-wave spacetime assuming different pulse shapes (square and sech-squared) in the exact gravitational wave metric. It is shown that the shape of a circular closed string deforms permanently, after…

For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…

We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative answer to a conjecture proposed by the…

We study a relative trace formula for a compact Riemann surface with respect to a closed geodesic $C$. This can be expressed as a relation between the period spectrum and the ortholength spectrum of $C$. This provides a new proof of…

For the relativistic string with massive ends arbitrary small disturbances of the uniform rotation of the rectilinear string are investigated. There are two classes of these oscillations with different spectra of frequencies. They are…

We review the current knowledge about the theoretical foundations of the effective string theory for confining flux tubes and the comparison of the predictions to pure gauge lattice data. A concise presentation of the effective string…

We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multi-loop diagrams describes the 't Hooft…

We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…