Curriculum Vitae Ana Rechtman

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1 Curriculum Vitae Ana Rechtman Personal Information date and place of birth : March 5, 1981, Mexico City, Mexico. citinzenships: Mexican and Italian. Positions Maître de Conférences à l Université de Strasbourg September 2011 Boas Assistant Professor at Northwestern University September August 2011 Postdoctoral scholarship from Consejo Nacional de Ciencia y Tecnología (Mexico) for a research visit at University of Illinois at Chicago Address IRMA, Université de Strasbourg 7 rue René Descartes Strasbourg Cedex, France telephone: (+33) (0) fax: (+33) (0) rechtman@math.unistra.fr web page: www-irma.u-strasbg.fr/ rechtman 1

2 Education Ph. D. in Mathematics École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées, Lyon, France. Graduated with High Honor in Febraury title: Pièges dans la théorie des feuilletages : exemples et contre-exemples. advisor: Étienne Ghys, ENS-Lyon, France. jury: Patrice Le Calvez (Université Paris 6, France), Fernando Alcalde Cuesta (Universidad de Santiago de Compostela, Spain). Sorin Dumitrescu (Université d Orsay, France), Damien Gaboriau (ENS-Lyon, France). rechtman/documents/these.pdf Master (Recherche) Mathematics and Applications Université Claude Bernard Lyon 1, Lyon, France. master thesis: La conjecture de Seifert pour les flots qui préservent un volume. advisor: Étienne Ghys, ENS-Lyon BA in Mathematics Universidad Nacional Autónoma de México (UNAM), Facultad de Ciencias, Mexico city, Mexico. undergraduate thesis: Sistemas dinámicos holomorfos: flujos de Anosov y acciones del grupo afín complejo. advisor: Alberto Verjovsky, UNAM. Sotero Prieto prize Languages 1. Spanish, fluent. My native language. 2. English, fluent. Speaking, reading and writing. 3. French, fluent. Speaking, reading and writing. 4. Italian, fluent. Speaking, reading and writing. 2

3 Publications rechtman/publications.html Articles Existence of periodic orbits for geodesible vector fields on closed 3-manifolds Ergodic Theory and Dynamical Systems 30, no. 6, , Abstract In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In particular, Reeb vector fields and vector fields that admit a global section are geodesible. We will classify the closed 3-manifolds that admit aperiodic volume preserving C ω geodesible vector fields, and prove the existence of periodic orbits for C ω geodesible vector fields (not volume preserving), when the 3-manifold is not a torus bundle over the circle. We will also prove the existence of periodic orbits of C 2 geodesible vector fields on some closed 3-manifolds. Minimal Følner foliations are amenable With Fernando Alcalde Cuesta. Discrete and Continuous Dynamical Systems - Series A, Vol. 31, no. 3, Abstract For finitely generated groups, amenability and Følner properties are equivalent. However, contrary to a widespread idea, Kaimanovich showed that the Følner condition does not imply amenability for discrete measured equivalence relations. In this paper, we exhibit two examples of C foliations of closed manifolds that are Følner and non amenable with respect to a finite transverse invariant measure and a transverse invariant volume, respectively. We also prove the equivalence between the two notions when the foliation is minimal, that is all the leaves are dense, giving a positive answer to a question of Kaimanovich. The equivalence is stated with respect to transverse invariant measures or some tangentially smooth measures. The latter include harmonic measures, and in this case the Følner condition has to be replaced by η-følner (where the usual volume is modified by the modular form η of the measure). 3

4 Periodic orbits of Euler vector fields on 3-manifolds Preprint Abstract In this paper we study periodic orbit in the flow of non-singular steady Eluer fields X on closed 3-manifolds, that is X is a solution of time independent Euler equations. We show, that when X is C 2 the flow always posses a periodic orbit unless the manifold is a torus bundle over the circle. Moreover, we show that if the ambient manifold is S 3, the flow possesses an unknotted periodic orbit. These results generalize preavious results of J. Etnyre and R. Ghrist [?] by weakening the real analytic hypothesis to C 2. Averaging sequences With Fernando Alcalde Cuesta. To appear at Pacific Journal of Mathematics. Abstract In the spirit of Goodman-Plante average condition for the existence of a transverse invariant measure for foliations, we give an averaging condition to find tangentially smooth measures with prescribed Radon-Nikodym cocycle. Harmonic measures are examples of tangentially smooth measures for foliations; we also present sufficient hypothesis on the averaging condition in order to obtain a harmonic measure. The Weinstein conjecture for real projective spaces via holomorphic curves techniques With Klaus Niederkrüger. Journal of Topology and Analysis, Volume 3, Issue 4, , Abstract Helmut Hofer introduced in 93 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3-manifolds (M, ξ) with π 2(M) 0. We modify Hofer s argument to prove the Weinstein conjecture for some examples of higher dimensional contact manifolds. In particular, we are able to show that the connected sum with a real projective space always has closed Reeb orbits. As a by-product we generalize the notion of a P S-overtwisted contact manifold. 4

5 Other Publications 1. Coathor and member of the editorial committee of the Mathematical Calendars (in spanish). Since 2002 we publish the Mathematical Calendars, a challenge a day, for high school students and teachers. The aim is to promote the Mathematical Olympiads in Mexico Member of the editorial committee of Tzaloa (in spanish). Mathematical publication for high school students and teachers, the first number appeared in January Published by the Mexican Mathematical Society and Mexican Mathematical Olympiad. 5

6 Teaching experience Differential equations. Université de Strasbourg, France Topics in dynamics. Master class in collaboration with Charles Pugh and Amie Wilkinson. Northwestern University, USA Introduction to probability theory and Markov processes. Northwestern University, USA Differential Calculus. Northwestern University, USA Teaching Assistant at Universidad Nacional Autónoma de México, Facultad de Ciencias, Mexico city, Mexico. Calculus courses for first and second year students (Calculus IV, Fall 2002, Calculus I, Spring 2003, Calculus I I, Fall 2003) Trainer of the Mexican Mathematical Olympiads team, and member of the organizing committee. 6

7 Research Talks at Conferences 1. The minimal set of Kuperberg s plug. Todai Forum, Lyon, France. October The minimal set of Kuperberg s plug. 26th Summer Conference on Topology and its Applications, New York, USA. July Existence of periodic orbits for Euler vector fields on 3-manifolds. Midwest Dynamics, Northwestern University, USA. November Minimal Følner foliations are amenable. Atlantic Seminar of Ergodic Geometry at the International Centre of Mathematical Meetings, Castro Urdiales, Spain. May A non-amenable Følner foliation. Short communication at the Advanced Course on Foliations: Dynamics-Geometry-Topology, Centre de Recerca Matemtica, Barcelona, Spain. May Talks at seminars 1. The minimal set of Kuperberg s plug. Universität München, Munich, Allemagne. Janvier L ensemble minimal du pige de Kuperberg. Seminar at Université Paris 6, France. December Existence d orbites périodiques pour les champs d Euler. Seminar at Université Aix-Marseille 1, France. January Existence d orbites périodiques pour les champs d Euler. Seminar at Université Paris 6, France. January Existence d orbites périodiques pour les champs d Euler. Seminar at Université de Rennes, France. January

8 6. Existence d orbites périodiques pour les champs d Euler. Seminar at Université de Strasbourg, France. January Existence of periodic orbits for Euler vector fields on 3-manifolds. Seminar at Hebrew University, Jerusalem, Israel. June Existence d orbites périodiques pour les champs de vecteurs géodésibles. Seminar at Université Paul Sabatier, Toulouse, France. June Existence of periodic orbits for geodesible vector fields on 3-manifolds. Seminar at University of Chicago, USA. March Existence of periodic orbits for geodesible vector fields on 3-manifolds. Seminar at CALTECH, Pasadena, Californie, USA. March Una foliación minimal y Følner es promediable. Seminar at the Mathematics Institute UNAM, Cuernavaca, Mexico. October Existencia de órbitas periódicas para los flujos geodesibles en dimensión 3. Seminar at the Mathematics Institute UNAM, Mexico city, Mexico. September Existencia de órbitas periódicas para los flujos geodesibles en dimensión 3. Seminar at the Mathematics Institute UNAM, Oaxaca, Mexico. September Existencia de órbitas periódicas para los flujos geodesibles en dimensión 3. Seminar at the Centro de Investigaciones en Matemáticas (CIMAT), Guanajuato, Mexico. September Una foliación minimal y Følner es promediable. Seminar at Universidad de Santiago de Compostela, Spain. January Existence d orbites périodiques pour les flots géodésibles en dimension 3. Seminar at Université Paris 13, France. January Periodic orbits of geodesible vector fields on 3-manifolds. Seminar at Northwestern à Evanston, USA. January A non-amenable Følner foliation. Seminar at University of Illinois at Chicago, USA. November Existence d orbites périodiques pour les flots géodésibles en dimension 3. Seminar at Université Claude Bernard Lyon 1, France. March Existence d orbites périodiques pour les flots géodésibles en dimension 3. Special day ANR-Symplexe, Université de Rennes, France. February International Congress of Mathematical Education 11(ICME 11), Talk: Rising the national education level should be an objective of mathematical competitions. Monterrey, Mexico. Julio

9 Minicourses 1. Kuperberg s example and the dynamics of the minimal set. Universidade de Sao Paulo, Sao Carlos, Brazil. February Kuperberg s plug. Colima Workshop on Geometry, Facultad de Ciencias de la Universidad de Colima, México. October Kuperberg s example and existence of periodic orbits on 3-dimensional manifolds. Instituto de Matemáticas (UNAM), Cuernavaca, México. January Other Conferences I attended 1. ANR-Symplexe meeting. Le théorème d uniformisation. École Normale Supérieure de Lyon, France. Julio International Conference, Thompson s Groups: New Developments and Interfaces. CIRM, Marseille, France. June ANR-Symplexe meeting. Dynamique topologique sur les surfaces. Université de Rennes, France. March ANR-Symplexe meeting. L homologie de Floer. École Normale Supérieure de Lyon, France. September ANR-Symplexe meeting. Autour de la topologie de contact. Université Paris 13, Villetaneuse, France. February School and workshop in geometry and topology of singularities, 60th birthday celebration for Lê Dũng Tráng. Mathematics Institute UNAM, Cuernavaca, Mexico. January XXXVI Congreso Nacional de la Sociedad Matemática Mexicana. Durango, Mexico. October International Congress Alberto Fest. Complex geometry and dynamics. Alberto Verjovsky s Birthday, Mathematics Institute UNAM, Cuernavaca, Mexico. January XXXV Congreso Nacional de la Sociedad Matemática Mexicana. Pachuca, Mexico. October

10 Collaborators Fernando Alcalde Cuesta, from the Universidad de Santiago de Compostela, Spain. Steven Hurder, from the University of Illinois at Chicago, USA. Victor Kleptsyn, from the Université de Rennes, France. Klaus Niederkrüger, from the Université Paul Sabatier à Toulouse, France. Alberto Verjovsky, from the Mathematics Institute UNAM, Cuernavaca, Mexico. 10