A5071115614- Mathematical Dynamics and Fractals
- Quantum chaos and dynamical systems
- Geometry and complex manifolds
- Stochastic processes and statistical mechanics
- Geometric Analysis and Curvature Flows
- Algebraic Geometry and Number Theory
- Geometric and Algebraic Topology
- Cardiovascular Function and Risk Factors
- Heart Failure Treatment and Management
- Bladder and Urothelial Cancer Treatments
- Classical Antiquity Studies
- Ancient Mediterranean Archaeology and History
- Advanced Differential Equations and Dynamical Systems
- advanced mathematical theories
- Analytic Number Theory Research
- Cardiac pacing and defibrillation studies
- Archaeological and Historical Studies
- Cardiac Health and Mental Health
- Pediatric Urology and Nephrology Studies
- Cardiac Valve Diseases and Treatments
- Markov Chains and Monte Carlo Methods
- Cardiovascular and exercise physiology
- Workplace Health and Well-being
- Venous Thromboembolism Diagnosis and Management
- Urinary and Genital Oncology Studies
University of Maryland, College Park
2015-2024
Istituti Clinici Scientifici Maugeri
2021-2024
George Mason University
2022
University of Milan
2020-2021
University of Toronto
2004-2020
Université Paris-Sud
2006-2020
Park University
2014-2019
Humanitas University
2018
IRCCS Humanitas Research Hospital
2018
Giorgio Cini Foundation
2017
for their interest during the slow progress of this work and discussing with me ideas on subject.I am grateful to R. Gunning his encouragement enthusiasm several discussions content Section 4, which improved very much my understanding moduli
We prove that a typical interval exchange transformation is either weakly mixing or it an irrational rotation.We also conclude translation flow on surface of genus g ≥ 2 (with prescribed singularity types) mixing.*A.Avila would like to thank Jean-Christophe Yoccoz for several very productive discussions and Jean-Paul Thouvenot proposing the problem his continuous
There are infinitely many obstructions to the existence of smooth solutions cohomological equation Uu=f, where U is vector field generating horocycle flow on unit tangent bundle SM a Riemann surface M finite area and f given function SM. We study Sobolev regularity these obstructions, construct equation, derive asymptotics for ergodic averages flows.
We investigated predictive factors of failure and performed a resource consumption analysis in patients who underwent active surveillance for nonmuscle invasive bladder cancer.This prospective observational study monitored with history pathologically confirmed stage pTa (grade 1-2) or pT1a 2) cancer, recurrent small size number tumors without hematuria positive urine cytology. The primary end point was the rate surveillance. Assessment variables per year direct hospital were secondary...
In patients with heart failure the risk of systemic thromboembolism and benefit anticoagulation are uncertain. To assess incidence factors associated an increased risk, 406 consecutive chronic were prospectively investigated. Their left ventricular ejection fraction was 23±8%, pulmonary wedge pressure 19±10 mmHg cardiac index 2.3±1.41. min−1 . m−2 body surface area. Two hundred in NYHA functional class III-IV. thirty-two receiving oral anticoagulants. Over a follow-up period 16±11 months,...
This text is an expanded version of the lecture notes a minicourse (with same title this text) delivered by authors in Będlewo school ``Modern Dynamics and its Interaction with Analysis, Geometry Number Theory'' (from 4 to 16 July, 2011).  In first part text, i.e., from Sections 1 5, we discuss Teichmüller moduli space translation surfaces, flow $SL(2,\mathbb{R})$-action on these spacesand Kontsevich--Zorich cocycle over geodesic flow. We sketch two applications ergodic properties...
Abstract Natriuretic peptides (NP) are recognized as the most powerful predictors of adverse outcomes in heart failure (HF). We hypothesized that a measure functional limitation, assessed by 6-min walking test (6MWT), would improve accuracy prognostic model incorporating NP. This was multicenter observational retrospective study. studied value severe impairment (SFI), defined inability to perform 6MWT or distance walked during < 300 m, 1696 patients with HF admitted cardiac...
Following recent work of T.~Alazard and C.~Shao on applications para-differential calculus to smooth conjugacy stability problems for Hamiltonian systems, we prove finite codimension invariant surfaces (in differentiability classes) flat geodesic flows translation surfaces. The result is also based the author cohomological equation flows.
A cyclic cover of the complex projective line branched at four appropriate points has a natural structure square-tiled surface. We describe combinatorics such surface, geometry corresponding Teichmüller curve, and compute Lyapunov exponents determinant bundle over curve with respect to geodesic flow. This paper includes new example (announced by G. Forni C. Matheus in \cite{Forni:Matheus}) stratum Abelian differentials genus maximally degenerate Kontsevich--Zorich spectrum (the only known...
We introduce a twisted cohomology cocycle over the Teichmüller flow and prove “spectral gap” for its Lyapunov spectrum with respect to Masur–Veech measures. then derive Hölder estimates on spectral measures bounds speed of weak mixing almost all translation flows in every stratum Abelian differentials Riemann surfaces, as well deviation ergodic averages product surface circle.
We establish a geometric criterion on $SL(2, R)$-invariant ergodic probability measureon the moduli space of holomorphic abelian differentials Riemann surfacesfor nonuniform hyperbolicity Kontsevich--Zorich cocycle realHodge bundle. Applications include measures supported R)$-orbits ofall algebraically primitive Veech surfaces (see also [7]) andof all Prym eigenforms discovered in [34], as well canonicalabsolutely continuous connected components strata modulispace [4, 17]). The...
We consider smooth time-changes of the classical horocycle flows onthe unit tangent bundle a compact hyperbolic surface and provesharp bounds on rate equidistribution ofmixing. then derive results spectrum time-changesand show that is absolutely continuous with respect tothe Lebesgue measure real line maximal spectraltype equivalent to Lebesgue.
We refine the theory of cohomological equation for translation flows on higher genus surfaces with goal proving optimal results Sobolev regularity solutions and distributional obstructions. For typical our are sharp we find expected relation between obstructions Lyapunov exponents Kontsevich-Zorich renormalization cocycle. As a consequence exactly determine dimension space in each class terms exponents. fixed arbitrary surface direction, probably not but best which can be achieved available...
We study the Lyapunov spectrum of Kontsevich--Zorich cocycle on $SL(2,\mathbb{R})$-invariant subbundles Hodge bundle over support a probability measure moduli space Abelian differentials. In particular, we prove formulas for partial sums exponents in terms second fundamental form (or Kodaira--Spencer map) with respect to Gauss--Manin connection and investigate relations between central {Oseldets} subbundle kernel form. illustrate our conclusions two special cases.
We construct an orientable holomorphic quadratic differential on a Riemann surface of genus 4 whose SL(2,R)-orbit is closed and has highly degenerate Kontsevich - Zorich spectrum. This example related to previous similar construction in 3 by the first author.