“Draft:Federico Rodríguez Hertz”的意思、由来-开放百科全书

Premio Roberto Caldeyro Barcia Award (2005)}}Federico Juan Rodríguez Hertz (born 14 December 1974) is an Argentinian mathematician working primarily on dynamical systems and smoothergodic theory. He is a professor at the Pennsylvania State University^[1] and a member of the Anatole Katok Center for Dynamical Systems and Geometry^[2].

Early Life and Education

Rodríguez Hertz made his doctoral studies at IMPA between 1997 and 2001 under the supervision of Jacob Palis^[3]. Before joinining Penn State's Eberly College of Science Department of Mathematics in 2011 as a full professor he served as a professor of mathematics in the engineering school of the Universidad de la República in Uruguay.

Work and Research

Rodríguez Hertz has published numerous research papers in peer-reviewed journals such as Annals of Mathematics, Acta Mathematica, Journal of the American Mathematical Society, Inventiones Mathematicae, Contemporary Mathematics, and Journal of Modern Dynamics.

The first important contribution of Rodríguez Hertz is his PhD thesis dealing with stable ergodicity of linear toral automorphisms with two dimensional center^[4]. Before this work there were no tools for proving stable ergodicity of non-accessible system^[5].

Jointly with Jana Rodríguez Hertz, Ali Tahzibi and Raul Ures, Rodríguez Hertz has obtained deep results about geometry of Hopf brushes, especially in the low dimensional setting^[6]^[7].

Rodríguez Hertz obtained significant geometric information on the structure of ergodic decomposition in both partially hyperbolic and nonuniformly hyperbolic settings, which constitutes a significant advance in this classical subject. Perhaps equally important is that his work provides a new point of view on ergodicity of hyperbolic systems. Namely, he treated ergodicity as a rigidity problem. Indeed, if the majority of systems are believed to be ergodic, then it makes sense to classify the nonergodic examples and to see if the system at hand belongs to a small list of exceptions. This new point of view allows one to bring to the spotlight new powerful tools of rigidity theory, in particular topological and geometric methods.

Rodríguez Hertz also has further produced research in rigidity theory, which describes the flexibility and motion of groups of rigid bodies. His work in nonuniform measure rigidity has provided new insights into ergodic theory^[8]. A recent work of Aaron Brown and Federico Rodríguez Hertz provides a significant generalization of nonuniform-measure rigidity theory, at least in the two dimensional case^[9].

Federico Rodríguez Hertz is an editor of the Journal of Modern Dynamics. He has served as a referee for many scholarly journals, including Annals of Mathematics and Inventiones Mathematicae, and as an evaluator for the Fondo Nacional de Desarrollo Cientifico y Tecnologico, a Chilean research foundation promoting basic scientific and technological development in the country. He has given invited talks and workshops in conferences and at academic institutions in the United States, Canada, Argentina, Brazil, Uruguay, Chile, Poland, Mexico, Germany, Italy, France, Portugal and India.

Prizes

an invitation to give an address at the International Congress of Mathematicians in 2010 in Hyderabad, India

\\bibitem{Dolgo} D. Dolgopyat, {\\it The work of Federico Rodríguez Hertz on ergodicity of dynamical systems} (English summary), J. Mod. Dyn. 10 (2016), 175--189.

\\bibitem{Spat} R. Spatzier, {\\it On the work of Rodríguez Hertz on rigidity in dynamics} (English summary), J. Mod. Dyn. 10 (2016), 191--207.

References

1. ^{{Cite web|url=https://www.math.psu.edu/people/|title=Full Department Directory {{!}} Department of Mathematics|last=|first=|date=|website=www.math.psu.edu|archive-url=|archive-date=|dead-url=|access-date=2019-01-04}}
2. ^{{Cite web|url=https://www.math.psu.edu/dynsys/people|title=People {{!}} Anatole Katok Center for Dynamical Systems and Geometry|last=|first=|date=|website=www.math.psu.edu|archive-url=|archive-date=|dead-url=|access-date=2019-01-04}}
3. ^{{Cite web|url=https://www.genealogy.math.ndsu.nodak.edu/id.php?id=53788|title=Federico Rodriguez-Hertz - The Mathematics Genealogy Project|website=www.genealogy.math.ndsu.nodak.edu|access-date=2019-01-04}}
4. ^{{Cite web|url=http://annals.math.princeton.edu/2005/162-1/p02|title=Stable ergodicity of certain linear automorphisms of the torus {{!}} Annals of Mathematics|language=en-US|doi=10.4007/annals.2005.162.65|access-date=2019-01-04}}
5. ^{{Cite web|url=http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12625|title=The work of Federico Rodriguez Hertz on ergodicity of dynamical systems|last=Dolgopyat|first=Dmitry|date=2016-06-01|website=Journal of Modern Dynamics 2016, Volume 10, Pages 175-189|language=en|doi=10.3934/jmd.2016.10.175|access-date=2019-01-04}}
6. ^{{Cite journal|last=Ures|first=R.|last2=Tahzibi|first2=A.|last3=Hertz|first3=M. A. Rodriguez|last4=Hertz|first4=F. Rodriguez|date=2011-08-01|title=Uniqueness of SRB Measures for Transitive Diffeomorphisms on Surfaces|url=https://link.springer.com/article/10.1007/s00220-011-1275-0|journal=Communications in Mathematical Physics|language=en|volume=306|issue=1|pages=35–49|doi=10.1007/s00220-011-1275-0|issn=1432-0916}}
7. ^{{Cite journal|last=Ures|first=R.|last2=Tahzibi|first2=A.|last3=Hertz|first3=M. A. Rodriguez|last4=Hertz|first4=F. Rodriguez|date=2011-12-01|title=New criteria for ergodicity and nonuniform hyperbolicity|url=https://projecteuclid.org/euclid.dmj/1320674938|journal=Duke Mathematical Journal|language=EN|volume=160|issue=3|pages=599–629|doi=10.1215/00127094-1444314|issn=1547-7398}}
8. ^{{Cite web|url=http://annals.math.princeton.edu/2011/174-1/p10|title=Nonuniform measure rigidity {{!}} Annals of Mathematics|language=en-US|doi=10.4007/annals.2011.174.1.10|access-date=2019-01-04}}
9. ^{{Cite journal|last=Hertz|first=Federico|last2=Brown|first2=Aaron|date=2017|title=Measure rigidity for random dynamics on surfaces and related skew products|url=https://www.ams.org/home/page/|journal=Journal of the American Mathematical Society|language=en|volume=30|issue=4|pages=1055–1132|doi=10.1090/jams/877|issn=1088-6834}}