arXiv research

Study bubbling Kahler metrics using algebraic geometry.

Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.

We prove that, for every closed (not necessarily convex) hypersurface $Σ$ in $\mathbb{R}^{n+1}$ and every $p>n$, the $L^p$-norm of the trace-free part of the anisotropic second fundamental form controls from above the $W^{2,p}$-closeness of $Σ$ to the Wulff shape. In the isotropic setting, we provide a simpler proof. T…

The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of traders' strategies. Furthermore, we show that the distributions of returns gene…

Wave maps can have multiple bubbling solutions at blow-up points.

We consider a simple stochastic differential equation for modeling bubbles in social context. A prime example is bubbles in asset pricing, but similar mechanisms may control a range of social phenomena driven by psychological factors (for example, popularity of rock groups, or a number of students pursuing a given majo…

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that obser…

The present paper is a follow up of our paper \cite{nS}. We investigate here the maximization of higher order eigenvalues in a conformal class on a smooth compact boundaryless Riemannian surface. Contrary to the case of the first nontrivial eigenvalue as shown in \cite{nS}, bubbling phenomena appear.

What is the role of social interactions in the creation of price bubbles? Answering this question requires obtaining collective behavioural traces generated by the activity of a large number of actors. Digital currencies offer a unique possibility to measure socio-economic signals from such digital traces. Here, we foc…

We study a simple model of an asset market with informed and non-informed agents. In the absence of non-informed agents, the market becomes information efficient when the number of traders with different private information is large enough. Upon introducing non-informed agents, we find that the latter contribute signif…

We survey the known existence and non-existence results for $G_2$-instantons on non-compact cohomogeneity-1 $G_2$-manifolds and their consequences, including an explicit example of a family of $G_2$-instantons where bubbling, removable singularities and conservation of energy phenomena occur. We also describe several o…

We develop a strong diagnostic for bubbles and crashes in bitcoin, by analyzing the coincidence (and its absence) of fundamental and technical indicators. Using a generalized Metcalfe's law based on network properties, a fundamental value is quantified and shown to be heavily exceeded, on at least four occasions, by bu…

In the aftermath of the burst of the ``new economy'' bubble in 2000, the Federal Reserve aggressively reduced short-term rates yields in less than two years from 6.5% to 1.25% in an attempt to coax forth a stronger recovery of the US economy. But, there is growing apprehension that this is creating a new bubble in real…

In this paper we consider the functional whose critical points are solutions of the fractional CR Yamabe type equation on the sphere. We firstly study the behavior of the Palais-Smale sequences characterizing the bubbling phenomena and therefore we prove a multiplicity type result by showing the existence of infinitely…

In this paper we study the Palais-Smale sequences of the conformal Dirac-Einstein problem. After we characterize the bubbling phenomena, we prove an Aubin type result leading to the existence of a positive solution. Then we show the existence of infinitely many solutions to the problem provided that the underlying mani…

We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschitz curves) may be non-open, and may differ from the corresponding sets defined via piecewise $C^1$-curves. By refining the notion of a causal…

The substantial turmoil created by both 2000 dot-com crash and 2008 subprime crisis has fueled the belief that the two classical paradigms of economics, which are the invisible hand and the rational agent, are not appropriate to describe market dynamics and should be abandoned at the benefit of alternative new theoreti…

LLMs mimic human traders in finance, but not as much as expected.

The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal co…

The existence of the pricing kernel is shown to imply the existence of an ambient information process that generates market filtration. This information process consists of a signal component concerning the value of the random variable X that can be interpreted as the timing of future cash demand, and an independent no…

Given a smooth bounded domain $Ø\subseteq \R^2$, we consider the equation $\D v = 2 v_x \wedge v_y$ in $Ø$, where $v: Ø\to \R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple…

We initiate the systematic study of $G_2$-instantons with $SU(2)^2$-symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on $\mathbb{R}^4\times S^3$ with its two explicitly known distinct holonomy $G_2$ metrics, whic…

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a gen…

The paper finds multiple ways a special curvature can blow up in high dimensions.

Basic peculiarities of market price fluctuations are known to be well described by a recently developed random walk model in a temporally deforming quadric potential force whose center is given by a moving average of past price traces [Physica A 370, pp91-97, 2006]. By analyzing high-frequency financial time series of …

Let $E$ be a hermitian complex vector bundle over a compact Kähler surface $X$ with Kähler form $ω$, and let $D$ be an integrable unitary connection on $E$ defining a holomorphic structure $D^{\prime\prime}$ on $E$. We prove that the Yang-Mills flow on $(X,ω)$ with initial condition $D$ converges, in an appropriate sen…

Characterizes critical points in convex double and triple bubbles.

Survey on soap bubble partitions and their stability.

Bubbles are essential in certain economic models with high growth and low interest rates.

Solves complex Hessian equations in unstable cases, proving unique canonical solutions with singularities.

Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.

Rational bubbles form in nonstationary models of real assets.

Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.

Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.

Degenerate solutions found in 2D H-system bubbles with higher degrees.

This is the third installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 27 bubbles in 27 different global assets; for 25 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that docum…

On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experime…

Continuous time analysis of bubble formation in harmonic maps.

Trading bubbles form when traders adapt to price mismatches.

This is the second installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 7 bubbles in 7 different global assets; for 4 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that documen…

Solves the quintuple bubble problem on spheres and Euclidean spaces.

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The …

Paper evaluates whether AI is a bubble or a productivity revolution.

Study on metric bubbles in complex dimensions 1 and 2.

We reformulate the Cont-Bouchaud model of financial markets in terms of classical "super-spins" where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to mod…

Modeling stochastic arbitrage bubbles in Black-Scholes framework.

We present an advance bubble detection methodology based on the Log Periodic Power Law Singularity (LPPLS) confidence indicator for the early causal identification of positive and negative bubbles in the Chinese stock market using the daily data on the Shanghai Shenzhen CSI 300 stock market index from January 2002 thro…

Study predicts NFT bubbles using LPPL model.