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2013 Erwin Schrödinger International Institute for Mathematical Physics CONTENTS Erwin Schrödinger International Institute Preface—Turning Over the Page .................................................................................................................................................................... 2 for Mathematical Physics Boltzmanngasse 9 Erwin Schrödinger International Institute 1090 Vienna / Austria for Mathematical Physics—Structure and Activities .......................................................................................... 5 T +43-1-4277-28301 F +43-1-4277-9283 [email protected] At the Interface of Mathematics and Physics www.esi.ac.at Some Thoughts on the Fruitful and Ongoing Interaction Between Mathematics and Physics by Wendelin Werner ................................................................................................................................................................................................................ 10 Algebras, Groups and Strings by Peter Goddard ........................................................................................................................................................................................................................... 12 A Deeper Union? Poincaré on Mathematics and Mathematical Physics by Jeremy Gray .................................................................................................................................................................................................................................... 16 A Physicist Involved in Purely Algebraic Research: The Case of H. B. G. Casimir by Martina R. Schneider ................................................................................................................................................................................................ 21 Changing Views—Images and Figures of Thought in the Mathematical Sciences by Joachim Schwermer ....................................................................................................................................................................................................... 25 Scientific Activities Thematic Programmes ..................................................................................................................................................................................................... 32 Research in Teams Programme .................................................................................................................................................................... 33 Junior Research Fellowship Programme .................................................................................................................................. 34 Summer Schools ............................................................................................................................................................................................................................ 35 Impressions ............................................................................................................................................................................................................................................... 36 Senior Research Fellowship Programme ................................................................................................................................. 38 Gathering Evidence: My Time as a Senior Research Fellow by James W. Cogdell ................................................................................................................................................................................................................. 39 Data and Statistics ........................................................................................................................................................................................................................... 44 1 / esi 2013 PREFACE PREFACE Preface―Turning Over the Page of these activities add an important personal funding for the Erwin Schrödinger International by Joachim Schwermer perspective to this catalogue of possible scholarly Institute for Mathematical Physics to support the experiences. five-year appointment of a Simons Junior Professor In view of the strategic exchanges between in Mathematics or Mathematical Physics. mathematics and mathematical physics that have It is the Institute’s foremost objective to ad- occurred over the course of the last decades and vance scientific knowledge ranging over a broad even beyond, one finds personal reflections of band of fields and themes in mathematics and scientists on their experiences as scholars whose theoretical physics. Creating a space where fruitful work is rooted in mathematics and physics. They collaborations and the exchange of ideas between Restart. In October 2010, when the Erwin the new governing board of the esi, called the found a creative way to capture their thoughts re- scientists can unfold is decisive. With the esi now Schrödinger International Institute for Math- “Kollegium”, to carry on the mission of the esi garding the interaction between mathematics and being a research centre within the University of ematical Physics (esi) had been in existence as an and to retain its international reputation. These mathematical physics and specific advances in their Vienna, the best way of achieving this is to ensure independent research institute since 1993, the aims include, in particular, to support research at work. In the same vein, historical case studies deal- that the esi continues to interweave leading inter- scientific directorate and the international commu- the University of Vienna, to contribute to its inter- ing with fundamental facets or specific develop- national scholars and the local scientific community. nity of scholars had to learn with great distress of national visibility and appeal, and to stimulate ments in which the interrelations of mathematics The research and the interactions that take place at the intention of the government of Austria to cease the scientific environment in Austria. Setting aside and physics have unfolded extend the discussion. the Institute will have a lasting impact on those funding for the esi. Due to budgetary measures all the technical issues the transition process of Another note follows the interplay between thought who get their scientific education in Vienna. affecting a large number of independent research the esi involved, and which had to be taken care and images in the mathematical sciences and how institutions in Austria, funding of the esi would be of, the esi could begin restoring its fundamental visual thinking may function in the creative process Joachim Schwermer terminated as of January 1st, 2011. Since its start it scientific activities. This was and still is the prevalent in mathematics, physics and their crossroads. Director was the mission of the esi to advance research in task: striving to be excellent and thereby keeping its Finally, a concluding section in this booklet Erwin Schrödinger International Institute mathematics, physics and mathematical physics at position within the international scientific commu- documents to some extent the scientific activities of for Mathematical Physics the highest international level through fruitful nity of scholars as a research institute with a specific the esi, starting from its beginnings. The Institute interaction between scientists from these disciplines. unique character. The esi is a place that is very con- has always remained true to its commitment: pro- An abrupt end for the scientific activities of the ducive to research and, at the same time, integrates moting and supporting original scholarship in the Institute and the closure of the esi appeared on the scientific education and research in mathematics mathematical sciences. horizon. Weeks of trembling uncertainty followed, and mathematical physics. mixed with signs of a solution in which the Univer- In retrospect, though the planning horizon Securing the future. The Erwin Schrödinger Inter- sity of Vienna would be involved. In the wake of was very short, the Thematic Programmes, scheduled national Institute for Mathematical Physics fills a a protest action by renowned scholars and academic already far ahead for 2011 and 2012, turned out in unique role in (post-) graduate education and sci- institutions worldwide, an agreement was achieved the end to be successful scientific events. Addition- entific research in mathematics and mathematical in January 2011 that the esi could continue to exist ally, various workshops and other activities could be physics, and in Austria, in particular. However, one but now as a research centre (“Forschungsplatt- solicited for the year 2012 on short notice, involving, has to give careful consideration to ways in which form”) at the University of Vienna. As a partner in in particular, young researchers who came to the the esi arrangements might be made more stable this agreement the Ministry of Science and Research Institute for the first time as organizers. In addition, as it goes into a period of various challenges re- (bmwf) guaranteed to fund the “new” esi through by January 1, 2012, the Erwin Schrödinger Institute garding its financial resources. As mentioned, the University yearly with a reduced budget until had established the Research in Teams Programme the Ministry has only guaranteed to fund the esi 2015. At a time when pure research and scholarly
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