Related papers: On Peixoto's Conjecture for Flows on Non-orientabl…
Most expressive variational families -- such as normalizing flows -- lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present a general recipe for…
A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors, we study the existence or non-existence of…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
We are concerned with the theory of existence and uniqueness of flows generated by divergence free vector fields with compact support. Hence, assuming that the velocity vector fields are measurable, bounded, and the flows in the Euclidean…
We circumvent one of the roadblocks in associating Floer homotopy types to monotone Lagrangians, namely the curvature phenomena occurring in high dimensions. Given $N \ge 3$ and $R$ a connective $\mathbb E_1$-ring spectrum, there is a…
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
Geometric modularity has recently been conjectured to be a characteristic feature for flux vacua with $W=0$. This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string…
It is well-known that the flows generated by two smooth vector fields commute, if the Lie bracket of these vector fields vanishes. This assertion is known to extend to Lipschitz continuous vector fields, up to interpreting the vanishing of…
For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse…
In this paper, we consider incompressible Euler flows in $ \mathbb{R}^{4} $ under bi-rotational symmetry, namely solutions that are invariant under rotations in $\mathbb{R}^{4}$ fixing either the first two or last two axes. With the…
In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with…
An orbifold is a Morita equivalence class of a proper {\' e}tale Lie groupoid. A unitary equivalence class of spectral triples over the algebra of smooth invariant functions are associated with any compact spin orbifold. In the case of an…
We prove that the classification of real-analytic vector fields on the two-torus up to orbital topological equivalence does not admit a complete numerical invariant that is a Borel function. Moreover, smooth vector fields that are difficult…
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial…
In order to utilize the full potential of tailored flows of electromagnetic energy at the nanoscale, we need to understand its general behaviour given by its generic representation of interfering random waves. For applications in on-chip…
We consider a $C^r$ semiflow $\{ \varphi_t \}_{t \geq 0}$ on a Banach space $X$ admitting a stable fixed point $x$. We show, along the lines of the parameterization method (Cabr\'e et al., 2003), the existence of a $C^r$ invariant foliation…
Certain families of manifolds which support Anosov flows do not support expanding, quasi-isometric foliations.
We develop a version of Seiberg--Witten Floer cohomology/homotopy type for a spin$^c$ 4-manifold with boundary and with an involution which reverses the spin$^c$ structure, as well as a version of Floer cohomology/homotopy type for oriented…
On each compact, connected, orientable surface of genus greater than one we construct a class of flows without self-similarities.
In this thesis we explore the vacua structure of type IIA orientifold (CY) compactifications with fluxes, from the 4d and the 10d point of view. We start by reviewing type IIA Calabi-Yau orientifold compactifications with fluxes. We…