Related papers: Stability conditions in the mathematical Gauged Li…
We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and…
This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…
The path to the solution of Feder-Vardi dichotomy conjecture by Bulatov and Zhuk led through showing that more and more general algebraic conditions imply polynomial-time algorithms for the finite-domain Constraint Satisfaction Problems…
The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of K\"ahler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting'…
I present a brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory. It is emphasized how the application of…
We propose a conjectural stronger version of Bogomolov-Gieseker inequality for stable sheaves on quintic 3-folds. Our conjecture is derived from an attempt to construct a Bridgeland stability condition on graded matrix factorizations, which…
Let $(X,E)$ be a smooth log Calabi-Yau pair consisting of a smooth Fano surface $X$ and a smooth anticanonical divisor $E$. We obtain certain higher genus local Gromov-Witten invariants from the projectivization of the canonical bundle $Z…
We give a new numerical criterion in the spirit of GIT for existence of solutions to inverse Hessian equations, including in particular the J-equation. Our criterion is formulated in terms of stability of pairs in the sense of Paul. To that…
We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projective 3-folds. We give an equivalent conjecture which needs…
In this paper, we describe Mixed-Spin-P(MSP) fields for a smooth CY 3-fold $X_{3,3} \subset \mathbb{P}^2 \times \mathbb{P}^2$. Then we describe $\mathbb{C}^* -$fixed loci of the moduli space of these MSP fields. We prove that any virtual…
Taking into account the recently proposed poly-instanton corrections to the superpotential and combining the race-track with a KKLT respectively LARGE Volume Scenario in an intricate manner, we show that we gain exponential control over the…
At present, there exists no physically plausible example of a quantum field theory for which the existence of solutions has been proven mathematically. The Clay Mathematics Institute has offered a prize for proving existence for a class of…
In this paper, we see several basic properties of graded linear series. We firstly see that, if a graded linear series contains an ample series, then so are the pullbacks of the system under birational morphisms. Using this proposition, we…
In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…
We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a simple criterion, we prove the nonlinear stability of steady states which are decreasing functions…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
We study semilinear rough stochastic partial differential equations as introduced in [Gerasimovi{\v{c}}s, Hairer; EJP 2019]. We provide $\mathcal{L}^p(\Omega)$-integrable a priori bounds for the solution and its linearization in case the…
We study the stability of topological structures in generalized models with a single real scalar field. We show that it is driven by a Sturm-Liouville equation and investigate the conditions that lead to the existence of explicit…
The multisymplectic formalism of field theories developed by many mathematicians over the last fifty years is extended in this work to deal with manifolds that have boundaries. In particular, we develop a multisymplectic framework for first…
We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian…