Preface 1. Conference overview “There seem to be at least three layers of understanding: the first is acquain- tance with syntax, words, and symbols the second is meaning and the third can be called the meaning of meaning. The means of entering the deeper layers are to cogitate, research, reflect what we know at the first layer.” (M. Ram Murty, “The Art of Research”, Colloquium Lecture, Queen’s University at Kingston, Canada, 2001.) This is how M. Ram Murty, Professor and Head of the Department of Math- ematics and Statistics at Queen’s University in Kingston, Canada, might sound when talking to a friend, a colleague, or a student. A refined scholar, an intellectual with an unquenchable thirst for all facets of truth, scientific and philosophic, M. Ram Murty has had a profound impact on the development of number theory throughout the world. To honour his mathe- matical legacy, a conference focused on new research directions in number theory inspired by Murty’s most significant achievements was organized by Alina Car- men Cojocaru (University of Illinois at Chicago, USA), Chantal David (Concordia University, Montr´ eal, Canada), Hershy Kisilevsky (Concordia University, Montr´eal, Canada) and Francesco Pappalardi (Universit` a degli Studi Roma Tre, Rome, Italy) at the Centre de Recherches Math´ ematiques in Montr´ eal. The conference was ti- tled SCHOLAR—a Scientific Celebration Highlighting Open Lines of Arithmetic Research and took place during October 15–17 of 2013. The conference hosted about 100 participants representing several generations of research mathematicians, from beginning graduate students to emeritus profes- sors. The speakers included some of the most prominent researchers in number the- ory from around the world: Henri Darmon (McGill University, Montr´ eal, Canada) ´ Etienne Fouvry (Universit´ e Paris-Sud, Orsay, France) John Friedlander (Univer- sity of Toronto, Canada) Dorian Goldfeld (Columbia University, New York City, USA) Henryk Iwaniec (Rutgers University, New Brunswick, USA) Ernst Kani (Queen’s University, Kingston, Canada) Wen-Ching Winnie Li (Pennsylvania State University, State College, USA) Kumar Murty (University of Toronto, Canada) Yiannis Petridis (University College London, UK) Carl Pomerance (Dartmouth College, Hanover, USA) Dinakar Ramakrishnan (California Institute of Technol- ogy, Pasadena, USA) Michael I. Rosen (Brown University, Providence, USA) N. Saradha (Tata Institute of Fundamental Research, Mumbai, India) Joseph Silver- man (Brown University, Providence, USA) Cam Stewart (University of Waterloo, Canada) Dinesh S. Thakur (University of Rochester, USA) Yitang Zhang (Univer- sity of New Hampshire, Durham, USA). Their presentations illustrated research of highest caliber on a broad spectrum of arithmetic topics: abelian varieties function ix
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