arXiv research

New bounds on manifold Betti numbers derived from semigroup norms.

The aim of this paper is to show that the dynamics of $L^p$ heat semigroups ($p>2$) on a symmetric space of non-compact type is very different from the dynamics of the $L^p$ heat semigroups if $p\leq 2$. To see this, it is shown that certain shifts of the $L^p$ heat semigroups have a chaotic behavior if $p>2$ and that …

Flat semigroups can represent normal weighted homogeneous surface singularities.

New infinite family of hyperbolic L-space knots with specific semigroups.

We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. As applications, constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds are identified, respectively, with different integral-differential formulas and semigroup inequaliti…

Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.

Proves representability of complex semigroup systems.

The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…

This monograph develops the theory of covariant Schrödinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. Basis differential operators in Riemannian manifolds IV. Some specif…

The paper studies a semigroup generated by finite intervals and characterizes its properties.

We introduce imprecise Markov semigroups to handle uncertainty in Markov processes.

The paper studies dynamical properties in semigroups modulo ideals.

The study connects complex surface singularities to numerical semigroups and their properties.

Intertwining curvature bounds for graphs and quantum Markov semigroups verified.

The paper associates knots to numerical semigroups and shows their Alexander polynomials coincide with semigroups' Poincaré series.

We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the context of iteration of a rational map of degree two or more, extends to finitely gene…

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. The Julia set of such a semigroup may not be connected in general. We show that for such a polynomial semigroup, if $A$ and $B$ are two connected compo…

The paper studies Lévy processes on compact manifolds, proving properties of their semigroups.

The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein distance contraction properties at different times.…

We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-Möbius element) to a class of Möbius semigroups which includes certain settings not yet been dealt with in the literature, namely, when the Julia set is not a thick…

New high-order approximations for CIR process using random grids.

Graphs approximate semigroups for diffusion on Riemannian manifolds.

DM uses semigroup property to tune diffusion time for better data analysis.

Constructs free semigroups with critical exponents close to but less than ambient groups.

We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized $Γ$-calculus techniques. The advantages and drawbacks of each of these methods are discussed.

Paper proposes deep learning for operators in semigroups, improving dynamical system modeling.

Paper analyzes a new Hopf-Lax semigroup in metric spaces.

We look at the semigroup generated by a system of heat equations. Applications to testing normality and option pricing are addressed.

Establishes geometric properties of elements in the positive semigroup of a general real semisimple Lie group.

Study dynamic risk measures with distributional uncertainty using optimal transport.

New heat semigroup characterizes Sobolev and BV spaces in Carnot groups.

The paper establishes new inequalities for Finsler measure spaces.

Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rect…

Study estimates gaps in semigroup products, proving embedding properties.

In this paper we first derive several results concerning the $L^p$ spectrum of arithmetic locally symmetric spaces whose $\Q$-rank equals one. In particular, we show that there is an open subset of $\C$ consisting of eigenvalues of the $L^p$ Laplacian if $p <2$ and that corresponding eigenfunctions are given by certain…

We investigate the dynamics of $2$-generator semigroups of polynomials with bounded planar postcritical set and associated random dynamics on the Riemann sphere. Also, we investigate the space ${\cal B}$ of such semigroups. We show that for a parameter $h$ in the intersection of ${\cal B}$, the hyperbolicity locus ${\c…

We define a Hamilton-Jacobi semigroup acting on continuous functions on a compact length space. Following a strategy of Bobkov, Gentil and Ledoux, we use some basic properties of the semigroup to study geometric inequalities related to concentration of measure. Our main results are that (1) a Talagrand inequality on a …

We investigate the Banach Lie groupoids and inverse semigroups naturally associated to W*-algebras. We also present statements describing relationship between these groupoids and the Banach Poisson geometry which follows in the canonical way from the W*-algebra structure.

Generates semigroups for differential expressions on Riemannian manifolds.

Study reveals different drivers of electricity price volatility across Europe.

In those lecture notes, we review some applications of heat semigroups methods in Riemannian and sub-Riemannian geometry. The notes contain parts of courses taught at Purdue University, Institut Henri Poincaré, Levico Summer School and Tata Institute.

Study quantum diffusion on spectral triples and spinor bundles.

New stability theory for Sinkhorn semigroups with explicit decay rates.

Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincaré or logarithmic Sobolev inequalities. Moreover an alternative method using the optimal mass transportation, is also given to obtain the logarithmic Sobolev inequa…

Construction of a semigroup with 15 generators and 84 relations is given. The center of this semigroup is in one-to-one correspondence with the set of all isotopy classes of non-oriented singular knots (links with finitely many double intersections in general position) in three-dimensional space.

Unified treatment of two extension problems using heat equation in Heisenberg group.

We show that all non-trivial continuous endomorphisms of the circle group are topologically mixing. We also show that there exists a large infinite class of continuous endomorphisms of any n-dimensional torus group which are topologically mixing. Lastly, we prove that any continuous endomorphism on an abelian polish se…