Systolic Geometry and Topology

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SURV Mathematical Surveys and Monographs 137 Volume 137 The systole of a compact metric space X is a metric invariant of X, defined as the least length of a noncontractible loop in X. When X is a graph, the invariant is usually referred to as the girth, ever since the 1947 article by W. Tutte. The first nontrivial results for systoles of surfaces are the two classical inequalities of C. Loewner and P. Pu, relying on integral-geometric identities, in the case of the two-dimensional torus and real projective plane, Systolic Geometry respectively. Currently, systolic geometry is a rapidly developing Topology Systolic Geometry and field, which studies systolic invariants in their relation to other geometric invariants of a manifold. and Topology This book presents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities, and then proceeding to recent results, including a proof of M. Gromov’s filling area conjecture in a hyperelliptic setting. It then presents Gromov’s inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing a link both to ergodic theory and to properties of Mikhail G. Katz congruence subgroups of arithmetic groups. The author includes results on the systolic manifestations of Massey products, as well as of the classical Lusternik-Schnirelmann category. With an Appendix by Jake P. Solomon For additional information and updates on this book, visit AMS on the Web www.ams.org/bookpages/surv-137 www.ams.org Katz AMS American Mathematical Society SURV/137 Three color cover: PMS 297-Light Blue, PMS 723-Orange, and PMS 634 and ntone 634 (Blue) 240? pages on 50lb stock • Hardcover • Backspace 1 3/16'' .

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February 19, 2016
February 19, 2016 Professor HELGE HOLDEN SECRETARY OF THE INTERNATIONAL MATHEMATICAL UNION Dear Professor Holden, The Turkish Mathematical Society (TMD) as the Adhering Organization, applies to promote Turkey from Group I to Group II as a member of IMU. We attach an overview of the developments of Mathematics in Turkey during the last 10 years (2005- 2015) preceded by a historical account. With best regards, Betül Tanbay President of the Turkish Mathematical Society Report on the state of mathematics in Turkey (2005-2015) This is an overview of the status of Mathematics in Turkey, prepared for the IMU for promotion from Group I to Group II by the adhering organization, the Turkish Mathematical Society (TMD). 1-HISTORICAL BACKGROUND 2-SOCIETIES AND CENTERS RELATED TO MATHEMATICAL SCIENCES 3-NUMBER OF PUBLICATIONS BY SUBJECT CATEGORIES 4-NATIONAL CONFERENCES AND WORKSHOPS HELD IN TURKEY BETWEEN 2013-2015 5-INTERNATIONAL CONFERENCES AND WORKSHOPS HELD IN TURKEY BETWEEN 2013-2015 6-NUMBERS OF STUDENTS AND TEACHING STAFF IN MATHEMATICAL SCIENCES IN TURKEY FOR THE 2013-2014 ACADEMIC YEAR AND THE 2014-2015 ACADEMIC YEAR 7- RANKING AND DOCUMENTS OF TURKEY IN MATHEMATICAL SCIENCES 8- PERIODICALS AND PUBLICATIONS 1-HISTORICAL BACKGROUND Two universities, the Istanbul University and the Istanbul Technical University have been influential in creating a mathematical community in Turkey. The Royal School of Naval Engineering, "Muhendishane-i Bahr-i Humayun", was established in 1773 with the responsibility to educate chart masters and ship builders. Gaining university status in 1928, the Engineering Academy continued to provide education in the fields of engineering and architecture and, in 1946, Istanbul Technical University became an autonomous university which included the Faculties of Architecture, Civil Engineering, Mechanical Engineering, and Electrical and Electronic Engineering.
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