There will be a broad conference on "Arithmetic geometry and dynamical systems," at the City University of New York during the period May 29- June 1, 2012. Information about the conference can be found at http://math.gc.cuny.edu/conferences/szpirofest.html
The conference will focus on the following three major themes and their interconnections: "unlikely intersections in algebraic groups," "non-abelian Chabouty method," and "arithmetic dynamics." Such a conference is particularly timely in view of the many recent breakthroughs in these subjects.
Solving Diophantine equations, i.e., finding solutions in rational integers of polynomial equations is one of the earliest branches of mathematics. The CUNY conference on Diophantine geometry and dynamical systems will survey the most recent advances in this ancient subject. All the conference topics are central to number theory and extremely active subjects of current research. By bringing together leaders in these areas, the hope is to further inspire cross-fertilization among these closely connected, fundamental areas of mathematics. A major goal would be to encourage younger researchers and graduate students to attend, so as to introduce them to a very active field and to prepare them for further research.
Our conference " Arithmetic geometry and arithmetic dynamics"has attracted about 70 participants, including 18 speakers and about 35 graduate students and post-docs. The conference was held from May 29--June 01, 2013 at the Graduate Center of CUNY with 18 lectures by top experts in the world. The talks explained recent breakthroughs in arithmetical geometry and arithmetical dynamics. All speakers have presented their new results in number theory and arithmetic geometry,including many of those topics not well studied in USA; and all participants have actively involved in the workshop by interacting with speakers and other experts during the lectures and the long breaks between lectures. The following new rerults were reported in the conference: 1. Unlikely intersections in dynamical system and Shimura varieties(Umbert,Masser,Tucker,Ullmo). 2.Arakelov theory(Moriwaki,Yuan,Bost,Chen,Chambert-Loir,Gubler,Burgos). 3. Algebraic geometry (Illusie,Moret-Bailly,Gillet,Peskine,Baker). 4. Number theory (Silverman, Poonen). Some new directions and future research programs for students and post-docs have been resulted from the new methods or theories introduced in the lectures. For example, a model theoretic method has been introduced by Masser and Zannier for solving questions in unlikely intersections, and a theory of differential forms and current on Berkovich spaces has been constructed by Chambert-Loir,and a new statistical model for Selmer group has been introduced by Poonen.
