BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Olivier Le Gal (Université Savoie Mont-Blanc) DTSTART:20210524T120000Z DTEND:20210524T130000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/1 DESCRIPTION:Title: Topics in O-minimal Geometry\, Lecture 1\nby Olivier Le Gal (Univers ité Savoie Mont-Blanc) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nLecture 1. Semi-algebraic sets: definition and ba sic properties\, Tarski\, cell decomposition\, dimension.\n\n--\n\nWe invi ted Olivier le Gal to present the fundamental notions of o-Minimal Geometr y\, starting with the foundational example of the semi-algebraic structure . As a specialist in o-minimal geometry he will hint at how the four other s courses are related.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Goulwen Fichou (Université de Rennes I) DTSTART:20210524T131500Z DTEND:20210524T141500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/2 DESCRIPTION:Title: Regulous Functions\, Lecture 1\nby Goulwen Fichou (Université de Re nnes I) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nA bstract\nLecture 1. What is a regulous function? Typical example on the re al plane\, history\, strange behavior on singular sets.\n\n--\n\nRegulous function (continuous extensions of rational functions) have appeared almos t twenty years ago in the works of ​Kollár and Nowak. In the last six y ears they have been the focus of some serious interest. Goulwen Fichou wil l present us this category of functions and their specs as well as many cu rrent problems of Real Geometry where they naturally appear.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Sanz (Universidad de Valladolid) DTSTART:20210524T144500Z DTEND:20210524T154500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/3 DESCRIPTION:Title: Non-Oscillating Trajectories of Vector Fields\, Lecture 1\nby Fernan do Sanz (Universidad de Valladolid) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nA very interesting setting where Real Analytic Geometry interacts with Model Theory concerns the asymptotic beh aviour of trajectories of real analytic vector fields at singular points\, either as a single object or as pencils of such objects. Little is known is general and\, yet\, there are many partial results and examples about t his appealing topic. Fernando Sanz will tell us more about this\, and if t imes allows will be able to speak of some of his latest results and share a few hopes for still open problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Armin Rainer (Universität Wien) DTSTART:20210524T160000Z DTEND:20210524T170000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/4 DESCRIPTION:Title: From Ultra-differentiable to Quasi-Analytic Analysis\, Lecture 1\nby Armin Rainer (Universität Wien) as part of School of Real Geometry in Fo rtaleza - ScReGeFor\n\n\nAbstract\nThe mini-course is intended as an intro duction to ultradifferential analysis with special emphasis on ultra-diffe rentiable extension theorems. The development of differential analysis in the last century was decisively influenced by Whitney’s work on the exte nsion of differentiable functions from closed sets. We shall be interested in quantitative versions of Whitney’s extension theorem. The quantitati ve aspect is implemented by uniform growth properties of the multisequence of partial derivatives which measure the deviation from the Cauchy estima tes and hence from analyticity. These growth conditions determine ultradif ferentiable function classes which form a scale of regularity classes betw een the real analytic and the smooth class.\n\nLecture 1. We will recall W hitney’s classical extension theorem and formulate the quantitative prob lem. This will lead us to Denjoy–Carleman classes which are the ultradif ferentiable classes of main interest in this series of lectures. After dis cussing inclusion and stability properties we shall begin with the study o f the Borel map (i.e. infinite Taylor expansion) on Denjoy–Carleman clas ses. We will investigate when the Borel map is injective and\, in the cour se of this\, prove the Denjoy–Carleman theorem which discriminates betwe en quasianalytic and non-quasianalytic classes.\n\n--\n\nUltra-differentia ble Analysis concerns sub-algebras of smooth functions with constrained gr owth of the Taylor series coefficients. Besides its importance in the anal ysis of partial differential equations the development of this theory was influenced by the classical Whitney extension problem and the composition problem. Both problems followed a path that often meets sub-analytic geome try\, and later o-minimal geometry. Of special interest among the ultra-di fferentiable classes are the quasi-analytic classes which possess a (quasi -)analytic continuation property similar to the real analytic class. This property make these classes interesting from an analytic viewpoint and als o suitable for questions of tame geometry. In relation with asymptotic exp ansions of solutions of analytic ODEs they also naturally appear when deal ing with non-oscillation problems of the solutions. Armin Rainer will intr oduce us to ultra-differentiable classes\, in particular to quasi-analytic ones.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Dutertre (Université d'Angers) DTSTART:20210525T120000Z DTEND:20210525T130000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/5 DESCRIPTION:Title: Real Equisingularity and Curvature Measures\, Lecture 1\nby Nicolas Dutertre (Université d'Angers) as part of School of Real Geometry in Fort aleza - ScReGeFor\n\n\nAbstract\nLecture 1. On the topology of semi-algebr aic sets: stratified critical points and an index theorem.\n\n--\n\nUnlike their complex counterparts\, equisingularity results for tame families of subsets are harder to come by in Real Tame Geometry. Nevertheless a promi sing\, though not unexpected\, approach is to walk in the world of integra l geometry and get sufficient conditions in terms of continuity of certain functions built from curvature measures associated with the members of th e family. Nicolas Dutertre will introduce us to his tools from Geometric m easure theory (Lipschitz-Killing Measures) and how they naturally appear w ith good properties in equisingularity problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Goulwen Fichou (Université de Rennes I) DTSTART:20210525T131500Z DTEND:20210525T141500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/6 DESCRIPTION:Title: Regulous Functions\, Lecture 2\nby Goulwen Fichou (Université de Re nnes I) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nA bstract\nLecture 2. Regulous functions: first properties\, regularity on a stratification and regularity after blowings-up.\n\n--\n\nRegulous functi on (continuous extensions of rational functions) have appeared almost twen ty years ago in the works of ​Kollár and Nowak. In the last six years t hey have been the focus of some serious interest. Goulwen Fichou will pres ent us this category of functions and their specs as well as many current problems of Real Geometry where they naturally appear.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Olivier Le Gal (Université Savoie Mont-Blanc) DTSTART:20210525T144500Z DTEND:20210525T154500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/7 DESCRIPTION:Title: Topics in O-minimal Geometry\, Lecture 2\nby Olivier Le Gal (Univers ité Savoie Mont-Blanc) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nLecture 2. O-minimality : Definition of an o-mini mal expansion of the field of real\, finiteness properties\, selection lem ma\, $C^k$.\n\n--\n\nWe invited Olivier le Gal to present the fundamental notions of o-Minimal Geometry\, starting with the foundational example of the semi-algebraic structure. As a specialist in o-minimal geometry he wil l hint at how the four others courses are related.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Armin Rainer (Universität Wien) DTSTART:20210525T160000Z DTEND:20210525T170000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/8 DESCRIPTION:Title: From Ultra-differentiable to Quasi-Analytic Analysis\, Lecture 2\nby Armin Rainer (Universität Wien) as part of School of Real Geometry in Fo rtaleza - ScReGeFor\n\n\nAbstract\nThe mini-course is intended as an intro duction to ultradifferential analysis with special emphasis on ultra-diffe rentiable extension theorems. The development of differential analysis in the last century was decisively influenced by Whitney’s work on the exte nsion of differentiable functions from closed sets. We shall be interested in quantitative versions of Whitney’s extension theorem. The quantitati ve aspect is implemented by uniform growth properties of the multisequence of partial derivatives which measure the deviation from the Cauchy estima tes and hence from analyticity. These growth conditions determine ultradif ferentiable function classes which form a scale of regularity classes betw een the real analytic and the smooth class.\n\nLecture 2 (Tue\, May 25\, 1 3:00). Next we will study the image of the Borel map on Denjoy–Carleman classes which naturally sits in the sequence space defined by the characte ristic bounds. The quasianalytic and the non-quasianalytic case are fundam entally different. While in the non-quasianalytic case we will give necess ary and sufficient conditions for the Borel map being onto the sequence sp ace\, we shall see that on quasianalytic classes\, strictly containing the real analytic class\, the Borel map is never onto. This will be complemen ted by some results on the description of the Borel image and a discussion of further intricacies of the quasianalytic setting.\n\n--\n\nUltra-diffe rentiable Analysis concerns sub-algebras of smooth functions with constrai ned growth of the Taylor series coefficients. Besides its importance in th e analysis of partial differential equations the development of this theor y was influenced by the classical Whitney extension problem and the compos ition problem. Both problems followed a path that often meets sub-analytic geometry\, and later o-minimal geometry. Of special interest among the ul tra-differentiable classes are the quasi-analytic classes which possess a (quasi-)analytic continuation property similar to the real analytic class. This property make these classes interesting from an analytic viewpoint a nd also suitable for questions of tame geometry. In relation with asymptot ic expansions of solutions of analytic ODEs they also naturally appear whe n dealing with non-oscillation problems of the solutions. Armin Rainer wil l introduce us to ultra-differentiable classes\, in particular to quasi-an alytic ones.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Dutertre (Université d'Angers) DTSTART:20210526T120000Z DTEND:20210526T130000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/9 DESCRIPTION:Title: Real Equisingularity and Curvature Measures\, Lecture 2\nby Nicolas Dutertre (Université d'Angers) as part of School of Real Geometry in Fort aleza - ScReGeFor\n\n\nAbstract\nLecture 2. Lipschitz-Killing measures and Gauss-Bonnet theorems\n\n--\n\nUnlike their complex counterparts\, equisi ngularity results for tame families of subsets are harder to come by in Re al Tame Geometry. Nevertheless a promising\, though not unexpected\, appro ach is to walk in the world of integral geometry and get sufficient condit ions in terms of continuity of certain functions built from curvature meas ures associated with the members of the family. Nicolas Dutertre will intr oduce us to his tools from Geometric measure theory (Lipschitz-Killing Mea sures) and how they naturally appear with good properties in equisingulari ty problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Goulwen Fichou (Université de Rennes I) DTSTART:20210526T131500Z DTEND:20210526T141500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/10 DESCRIPTION:Title: Regulous Functions\, Lecture 3\nby Goulwen Fichou (Université de R ennes I) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\n Abstract\nLecture 3. Łojasiewicz property and real algebra: expansion of continuous function\, Nullstellensatz\, real algebraic versus regulous set s.\n\n--\n\nRegulous function (continuous extensions of rational functions ) have appeared almost twenty years ago in the works of ​Kollár and Now ak. In the last six years they have been the focus of some serious interes t. Goulwen Fichou will present us this category of functions and their spe cs as well as many current problems of Real Geometry where they naturally appear.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Olivier Le Gal (Université Savoie Mont-Blanc) DTSTART:20210526T144500Z DTEND:20210526T154500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/11 DESCRIPTION:Title: Topics in O-minimal Geometry\, Lecture 3\nby Olivier Le Gal (Univer sité Savoie Mont-Blanc) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nLecture 3. Polynomial boundedness versus exponen tial: Chris Miller's dichotomy growth theorem\, Hardy field of an o-minima l structure\, asymptotic of definable functions\, Łojasiewicz inequality in polynomially bounded structures.\n\n--\n\nWe invited Olivier le Gal to present the fundamental notions of o-Minimal Geometry\, starting with the foundational example of the semi-algebraic structure. As a specialist in o -minimal geometry he will hint at how the four others courses are related. \n LOCATION:https://researchseminars.org/talk/ScReGeFor/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Sanz (Universidad de Valladolid) DTSTART:20210526T160000Z DTEND:20210526T170000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/12 DESCRIPTION:Title: Non-Oscillating Trajectories of Vector Fields\, Lecture 2\nby Ferna ndo Sanz (Universidad de Valladolid) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nA very interesting setting where Rea l Analytic Geometry interacts with Model Theory concerns the asymptotic be haviour of trajectories of real analytic vector fields at singular points\ , either as a single object or as pencils of such objects. Little is known is general and\, yet\, there are many partial results and examples about this appealing topic. Fernando Sanz will tell us more about this\, and if times allows will be able to speak of some of his latest results and share a few hopes for still open problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Olivier Le Gal (Université Savoie Mont-Blanc) DTSTART:20210527T120000Z DTEND:20210527T130000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/13 DESCRIPTION:Title: Topics in O-minimal Geometry\, Lecture 4\nby Olivier Le Gal (Univer sité Savoie Mont-Blanc) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nLecture 4. Quasi-analytic classes and o-minimali ty: In this session we deal with the link between quasi-analytic classes a nd o-minimality. We review some examples of o-minimal structures generated by quasi-analytic classes.\n\n--\n\nWe invited Olivier le Gal to present the fundamental notions of o-Minimal Geometry\, starting with the foundati onal example of the semi-algebraic structure. As a specialist in o-minimal geometry he will hint at how the four others courses are related.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Dutertre (Université d'Angers) DTSTART:20210527T131500Z DTEND:20210527T141500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/14 DESCRIPTION:Title: Real Equisingularity and Curvature Measures\, Lecture 3\nby Nicolas Dutertre (Université d'Angers) as part of School of Real Geometry in For taleza - ScReGeFor\n\n\nAbstract\nLecture 3. Lipschitz-Killing measures an d Gauss-Bonnet theorems\n\n--\n\nUnlike their complex counterparts\, equis ingularity results for tame families of subsets are harder to come by in R eal Tame Geometry. Nevertheless a promising\, though not unexpected\, appr oach is to walk in the world of integral geometry and get sufficient condi tions in terms of continuity of certain functions built from curvature mea sures associated with the members of the family. Nicolas Dutertre will int roduce us to his tools from Geometric measure theory (Lipschitz-Killing Me asures) and how they naturally appear with good properties in equisingular ity problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Armin Rainer (Universität Wien) DTSTART:20210527T144500Z DTEND:20210527T154500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/15 DESCRIPTION:Title: From Ultra-differentiable to Quasi-Analytic Analysis\, Lecture 3\nb y Armin Rainer (Universität Wien) as part of School of Real Geometry in F ortaleza - ScReGeFor\n\n\nAbstract\nThe mini-course is intended as an intr oduction to ultradifferential analysis with special emphasis on ultra-diff erentiable extension theorems. The development of differential analysis in the last century was decisively influenced by Whitney’s work on the ext ension of differentiable functions from closed sets. We shall be intereste d in quantitative versions of Whitney’s extension theorem. The quantitat ive aspect is implemented by uniform growth properties of the multisequenc e of partial derivatives which measure the deviation from the Cauchy estim ates and hence from analyticity. These growth conditions determine ultradi fferentiable function classes which form a scale of regularity classes bet ween the real analytic and the smooth class.\n\nLecture 3. The third lectu re is devoted to the Whitney extension problem for arbitrary closed sets. The key ingredient is the existence of optimal cut-off functions which yie ld\, in combination with a family of Whitney cubes\, a suitable partition of unity on the complement of the closed set. We shall see that this parti tion of unity allows us to glue the local extensions for the singleton (Bo rel map) to a global extension. We will also discuss the existence of cont inuous linear extension operators which is intimately related to interesti ng topological invariants of the involved function spaces.\n\n--\n\nUltra- differentiable Analysis concerns sub-algebras of smooth functions with con strained growth of the Taylor series coefficients. Besides its importance in the analysis of partial differential equations the development of this theory was influenced by the classical Whitney extension problem and the c omposition problem. Both problems followed a path that often meets sub-ana lytic geometry\, and later o-minimal geometry. Of special interest among t he ultra-differentiable classes are the quasi-analytic classes which posse ss a (quasi-)analytic continuation property similar to the real analytic c lass. This property make these classes interesting from an analytic viewpo int and also suitable for questions of tame geometry. In relation with asy mptotic expansions of solutions of analytic ODEs they also naturally appea r when dealing with non-oscillation problems of the solutions. Armin Raine r will introduce us to ultra-differentiable classes\, in particular to qua si-analytic ones.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Sanz (Universidad de Valladolid) DTSTART:20210527T160000Z DTEND:20210527T170000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/16 DESCRIPTION:Title: Non-Oscillating Trajectories of Vector Fields\, Lecture 3\nby Ferna ndo Sanz (Universidad de Valladolid) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nA very interesting setting where Rea l Analytic Geometry interacts with Model Theory concerns the asymptotic be haviour of trajectories of real analytic vector fields at singular points\ , either as a single object or as pencils of such objects. Little is known is general and\, yet\, there are many partial results and examples about this appealing topic. Fernando Sanz will tell us more about this\, and if times allows will be able to speak of some of his latest results and share a few hopes for still open problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Goulwen Fichou (Université de Rennes I) DTSTART:20210528T120000Z DTEND:20210528T130000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/17 DESCRIPTION:Title: Regulous Functions\, Lecture 4\nby Goulwen Fichou (Université de R ennes I) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\n Abstract\nLecture 4. Advanced results (if time allows): curve rationality\ , seminormalisation.\n\n--\n\nRegulous function (continuous extensions of rational functions) have appeared almost twenty years ago in the works of ​Kollár and Nowak. In the last six years they have been the focus of so me serious interest. Goulwen Fichou will present us this category of funct ions and their specs as well as many current problems of Real Geometry whe re they naturally appear.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Dutertre (Université d'Angers) DTSTART:20210528T131500Z DTEND:20210528T141500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/18 DESCRIPTION:Title: Real Equisingularity and Curvature Measures\, Lecture 4\nby Nicolas Dutertre (Université d'Angers) as part of School of Real Geometry in For taleza - ScReGeFor\n\n\nAbstract\nLecture 4. Some results on real equising ularity.\n\n--\n\nUnlike their complex counterparts\, equisingularity resu lts for tame families of subsets are harder to come by in Real Tame Geomet ry. Nevertheless a promising\, though not unexpected\, approach is to walk in the world of integral geometry and get sufficient conditions in terms of continuity of certain functions built from curvature measures associate d with the members of the family. Nicolas Dutertre will introduce us to hi s tools from Geometric measure theory (Lipschitz-Killing Measures) and how they naturally appear with good properties in equisingularity problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Armin Rainer (Universität Wien) DTSTART:20210528T144500Z DTEND:20210528T154500Z DTSTAMP:20260418T094802Z UID:ScReGeFor/19 DESCRIPTION:Title: From Ultra-differentiable to Quasi-Analytic Analysis\, Lecture 4\nb y Armin Rainer (Universität Wien) as part of School of Real Geometry in F ortaleza - ScReGeFor\n\n\nAbstract\nThe mini-course is intended as an intr oduction to ultradifferential analysis with special emphasis on ultra-diff erentiable extension theorems. The development of differential analysis in the last century was decisively influenced by Whitney’s work on the ext ension of differentiable functions from closed sets. We shall be intereste d in quantitative versions of Whitney’s extension theorem. The quantitat ive aspect is implemented by uniform growth properties of the multisequenc e of partial derivatives which measure the deviation from the Cauchy estim ates and hence from analyticity. These growth conditions determine ultradi fferentiable function classes which form a scale of regularity classes bet ween the real analytic and the smooth class.\n\nLecture 4. An ultradiffere ntiable Whitney approximation theorem will enable us to conclude that the extension can always be chosen real analytic off the given closed set. Fur thermore\, we will discuss the extension problem with a controlled loss of regularity. This requires a different approach which is closely related t o the characterization of ultradifferentiable classes by almost analytic e xtensions. We will address several applications such as Lojasiewicz’s th eorem on regularly situated sets or Whitney’s spectral theorem in the ul tradifferentiable framework. Finally\, we shall take a glimpse on other ul tradifferentiable classes\, in particular\, Braun–Meise–Taylor classes .\n\n--\n\nUltra-differentiable Analysis concerns sub-algebras of smooth f unctions with constrained growth of the Taylor series coefficients. Beside s its importance in the analysis of partial differential equations the dev elopment of this theory was influenced by the classical Whitney extension problem and the composition problem. Both problems followed a path that of ten meets sub-analytic geometry\, and later o-minimal geometry. Of special interest among the ultra-differentiable classes are the quasi-analytic cl asses which possess a (quasi-)analytic continuation property similar to th e real analytic class. This property make these classes interesting from a n analytic viewpoint and also suitable for questions of tame geometry. In relation with asymptotic expansions of solutions of analytic ODEs they als o naturally appear when dealing with non-oscillation problems of the solut ions. Armin Rainer will introduce us to ultra-differentiable classes\, in particular to quasi-analytic ones.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Sanz (Universidad de Valladolid) DTSTART:20210528T160000Z DTEND:20210528T170000Z DTSTAMP:20260418T094802Z UID:ScReGeFor/20 DESCRIPTION:Title: Non-Oscillating Trajectories of Vector Fields\, Lecture 4\nby Ferna ndo Sanz (Universidad de Valladolid) as part of School of Real Geometry in Fortaleza - ScReGeFor\n\n\nAbstract\nA very interesting setting where Rea l Analytic Geometry interacts with Model Theory concerns the asymptotic be haviour of trajectories of real analytic vector fields at singular points\ , either as a single object or as pencils of such objects. Little is known is general and\, yet\, there are many partial results and examples about this appealing topic. Fernando Sanz will tell us more about this\, and if times allows will be able to speak of some of his latest results and share a few hopes for still open problems.\n LOCATION:https://researchseminars.org/talk/ScReGeFor/20/ END:VEVENT END:VCALENDAR