Study of pseudo-Riemannian manifolds with M{ö}bius group actions.
problem Characterizing pseudo-Riemannian manifolds with specific group actions.
method Analyzing the action of the conformal group on compact manifolds.
result If the non-compact semi-simple part of the conformal group is M{ö}bius, the manifold is conformally flat.
Flat semigroups can represent normal weighted homogeneous surface singularities.
problem Representability of flat semigroups in normal weighted homogeneous surface singularities.
method Study of numerical semigroups associated with surface singularities and prove representability conditions.
result A numerical semigroup is representable if and only if it can be written as a quotient of a flat semigroup.
New infinite family of hyperbolic L-space knots with specific semigroups.
problem Characterizing semigroups of L-space knots.
method Defined formal semigroups from Alexander polynomials and analyzed hyperbolic knots.
result Found an infinite family of hyperbolic L-space knots with semigroups generated by five elements.
Theory of covariant Schrödinger semigroups on Riemannian manifolds developed.
problem Developing theory for Schrödinger semigroups on Riemannian manifolds.
method Sobolev spaces, heat kernels, differential operators, Wiener measure, Dynkin and Kato potentials.
result Properties and continuity of covariant Schrödinger semigroups established.
Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.
problem Understanding intrinsic Hopf-Lax semigroup and its relation to intrinsic slope.
method Introduces and proves the link between intrinsic Hopf-Lax semigroup and intrinsic slope.
result Intrinsic Hopf-Lax semigroup is a subsolution of Hamilton-Jacobi type equality.
Proves representability of complex semigroup systems.
problem Representability of systems of proportionally modular numerical semigroups.
method Canonical equivariant resolution of weighted homogeneous surface singularities.
result Every system of proportionally modular numerical semigroups is representable.
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…
New algorithm draws Julia sets for Möbius semigroups not previously possible.
problem Drawing Julia sets for Möbius semigroups with non-thick attractors.
method Backward Iteration algorithm extension to Möbius semigroups.
result Julia sets of Möbius semigroups can be drawn, including those not thick attractors.
The paper studies a semigroup generated by finite intervals and characterizes its properties.
problem Characterizing the semigroup generated by finite intervals.
method Analyzing the semigroup BωFn, showing Green relations coincide, isomorphic to partial convex order isomorphisms, and studying shift-continuous topologies. result The semigroup BωFn is isomorphic to the semigroup of partial convex order isomorphisms and admits only Rees congruences. The paper studies dynamical properties in semigroups modulo ideals.
problem Analyzing shadowing, expansivity, and stability in semigroups with ideals.
method Investigates shadowing, expansivity, and stability properties in uniform transformation semigroups modulo an ideal.
result Establishes that if a semigroup exhibits shadowing and expansivity modulo an ideal, it is also topologically stable modulo that ideal.
The study connects complex surface singularities to numerical semigroups and their properties.
problem Understanding the geometry and properties of strongly flat semigroups and their generalizations.
method Analyzing complex surface singularities and their associated semigroups, proving properties of Frobenius numbers.
result Strongly flat semigroups associated with negative definite Seifert homology spheres are numerical semigroups.
Heat semigroups used to solve geometric inequalities on manifolds.
problem Finding geometric inequalities on Riemannian and sub-Riemannian manifolds.
method Heat semigroups techniques applied to Riemannian and sub-Riemannian geometry.
result Applications of heat semigroups in geometric inequalities.
Flexible knot construction for low genus surfaces.
problem Finding knots with unexpectedly low genus surfaces.
method Flexible construction of knots in 3-sphere that bound surfaces of low genus in punctured open books.
result First examples of knots with differing genus in different homology balls.
Intertwining curvature bounds for graphs and quantum Markov semigroups verified.
problem Intertwining curvature bounds for graphs and quantum Markov semigroups.
method Introducing and verifying curvature bounds in various examples.
result Improved entropic curvature bounds for depolarizing semigroups and qubits.
The paper associates knots to numerical semigroups and shows their Alexander polynomials coincide with semigroups' Poincaré series.
problem Understanding the algebraic structure of numerical semigroups through topological representations.
method Associaing iterated torus knots to free numerical semigroups and analyzing their knot complements and Alexander polynomials.
result Alexander polynomials of knots associated with free numerical semigroups coincide with the semigroup's 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.
problem Gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.
method Establishes Bismut-type formulas and gradient estimates for Feynman--Kac semigroups on Riemannian manifolds with boundary, under geometric conditions formulated in terms of Ricci curvature and second fundamental form.
result Derives pointwise gradient estimates for the Neumann semigroup under variable, possibly unbounded, lower curvature bounds.
Derive derivatives of Feynman-Kac semigroups on Riemannian manifolds.
problem Analyze the derivatives of Feynman-Kac semigroups on Riemannian manifolds.
method Use local martingales and geometric assumptions to derive Bismut-type formulae and local estimates.
result Prove Bismut-type formulae for first and second derivatives of Feynman-Kac semigroups.
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.
problem Analyzing Lévy processes on compact Riemannian manifolds.
method Proving properties of Feller semigroups and generators on Lp spaces. result The generator has a discrete spectrum of eigenvalues and the semigroup is trace-class when the process has a non-trivial Brownian part.
Graphs approximate semigroups for diffusion on Riemannian manifolds.
problem Approximating semigroups for diffusion on Riemannian manifolds.
method Discretized approximation using random walks on proximity graphs.
result Quantitative error estimates for convergence of discrete semigroups to continuous semigroups.
New bounds on manifold Betti numbers derived from semigroup norms.
problem Estimating the first Betti number of compact Riemannian manifolds.
method Birman-Schwinger principle and Schatten norm estimates for semigroup differences, without ultracontractivity assumptions.
result Explicit bounds on Betti numbers depend on Ricci tensor norms.
DM uses semigroup property to tune diffusion time for better data analysis.
problem Difficulty in tuning diffusion time for optimal data analysis.
method Proposes a semigroup criterion to select diffusion time.
result Effective and robust method for picking diffusion time.
Constructs free semigroups with critical exponents close to but less than ambient groups.
problem Creating free semigroups with critical exponents close to but less than ambient groups.
method Constructing finitely generated free subsemigroups with specific properties.
result Free semigroups with critical exponents arbitrarily close to but strictly less than ambient groups.
Paper proposes deep learning for operators in semigroups, improving dynamical system modeling.
problem Modeling unknown autonomous dynamical systems using time series data at varying time lags.
method Novel deep learning approach embedding semigroup property into data-driven learning process.
result Framework reduces data dependency, improves accuracy, robustness, and stability for long-time prediction.
Develops semigroup approach for Finsler geometry, proving isoperimetric inequality.
problem Proving isoperimetric inequality for Finsler manifolds.
method Semigroup approach, Bochner-Weitzenböck formula, gradient estimate, lower weighted Ricci curvature bound.
result Proves Bakry-Ledoux's Gaussian isoperimetric inequality for non-reversible metrics.
The aim of this paper is to show that the dynamics of Lp heat semigroups (p>2) on a symmetric space of non-compact type is very different from the dynamics of the Lp heat semigroups if p≤2. To see this, it is shown that certain shifts of the Lp heat semigroups have a chaotic behavior if p>2 and that …
Paper analyzes a new Hopf-Lax semigroup in metric spaces.
problem Analyzing a new Hopf-Lax semigroup in metric spaces.
method Using continuous sections of quotient maps and variational problems.
result The 'symmetrized' Hopf-Lax semigroup is a subsolution of Hamilton-Jacobi type equation.
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.
problem Generalizing Lusztig's total positivity to the setting of general real semisimple Lie groups.
method Classifying Lie groups admitting a positive structure and establishing key properties of unipotent positive semigroups.
result Establishes key geometric properties of elements in the positive semigroup.
New heat semigroup characterizes Sobolev and BV spaces in Carnot groups.
problem Lack of explicit representations and symmetry in heat kernels in sub-Riemannian geometry.
method Establishes a new heat semigroup characterisation using integral decoupling property.
result Characterizes Sobolev and BV spaces in Carnot groups.
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.
problem Estimating singular value gaps in semigroup products.
method Lower estimates for singular value gaps of free products of semigroups in ping-pong position.
result Groups generated by semigroups in ping-pong position are quasi-isometrically embedded.
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 B of such semigroups. We show that for a parameter h in the intersection of 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 …
Generates semigroups for differential expressions on Riemannian manifolds.
problem Analyzing differential expressions on Riemannian manifolds.
method Study of generalized Ornstein-Uhlenbeck differential expressions and their maximal realizations.
result Generates analytic quasi-contractive semigroups in weighted Lp-spaces. 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.
Study quantum diffusion on spectral triples and spinor bundles.
problem Characterize quantum diffusion on almost commutative spectral triples.
method Spin geometry, C *-Dirichlet forms, quantum stochastic flows.
result Existence of covariant quantum stochastic flows on spinor bundles.
The paper generalizes the Black-Scholes model and inequality.
problem Developing a new model for call price surfaces.
method Introducing a noncommutative semigroup structure and using convex order compatibility.
result Each one-parameter semigroup corresponds to a unique log-concave probability density.
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
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…
The Clifford torus is unique when its isoperimetric ratio is prescribed.
problem Proving the uniqueness of the Clifford torus with a prescribed isoperimetric ratio.
method Reduction to a positivity question of a polynomial recurrence.
result The conjecture can be reduced to a polynomial recurrence positivity question.
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.
Let M be a compact Riemannian manifold with boundary $\pp M$ and $L= \DD+Z$ for a C1-vector field Z on M. Several equivalent statements, including the gradient and Poincaré/log-Sobolev type inequalities of the Neumann semigroup generated by L, are presented for lower bound conditions on the curvature of L …
Characterizes convergence of orbits of holomorphic semigroups in the unit disc.
problem Understanding the convergence behavior of orbits of holomorphic semigroups.
method Analyzes the shape of the starlike domain image of the Koenigs function and uses properties of quasi-geodesics.
result Characterizes convergence types (non-tangential and tangential) in terms of the domain's shape and quasi-geodesic properties.
Abstract: Nonlinear random walk with distributionally robust transition probabilities.
problem Modeling nonlinear random walks with robust transition probabilities.
method Scaling limit and nonlinear semigroup approach.
result Explicit computation of the generator and corresponding PDE.
We introduce imprecise Markov semigroups to handle uncertainty in Markov processes.
problem Uncertainty in transition probabilities and invariant measures of Markov processes.
method Topology, geometry, and probability techniques to analyze ergodic limits under model uncertainty.
result Uniform long-term bounds collapse asymptotically in certain regimes.
New family of knots with L-space surgeries but not algebraic.
problem Characterizing knots with L-space surgeries.
method Infinite family construction and new semigroup invariant.
result No nontrivial linear combination of knots in the family is concordant to an algebraic knot.