This book consists of a collection of articles dedicated to Valentin Poénaru, on topology and geometry in a broad sense. Poénaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this volume include hyperbolic geometry, 3-manifolds, complex and symplectic geometry, differential topology, combinatorial group theory, piecewise-linear topology, algebraic geometry, knots and links, homotopy theory, braid groups, phylogenetics, the history of geometry, and the philosophy of mathematics. This collection of articles, written by well-known researchers, provides a lively insight into a number of current research topics in geometry and topology.
1 Introduction, by Louis Funar and Athanase Papadopoulos.- 2 Primes,
Knots and Po, by Barry Mazur.- 3 A short history of open manifolds related to
complex analytic coordinates, by Dennis Sullivan.- 4 Universal
Spin Teichmüller Theory, I: The action of P(SL(2,Z)) on T ess+, by Robert C.
Penner.- 5 Universal Spin Teichmüller Theory, II: Finite presentation of
P(SL(2,Z)), by Robert C. Penner.- 6 Geometry of Fermats sum of squares, by
Greg McShane and Vlad Sergiescu.- 7 Ends and compactifications in geometric
topology, by Kenichi Ohshika.- 8 Axiomatic phylogenetics, by Vladimir
Turaev.- 9 About the diffeomorphisms of the 3-sphere and a famous theorem of
Cerf (4 = 0), by Franēois Laudenbach.- 10 Holomorphic tensors on Vaisman
manifolds, by Liviu Ornea and Misha Verbitsky.- 11 On the topology of
monotone Lagrangians of high dimension, by Mihai Damian.- 12 Kervaire
Problems in Stable Homotopy Theory, by Petr M. Akhmetev.- 13 Lifting generic
maps to embeddings, The double point obstruction, by Sergey A. Melikhov.- 14
Barcodes for continuous maps and a brief introduction to Alternative Morse
Theory, by Dan Burghelea.- 15 A note on the quasi simple filtration of finite
groups, by Francesco Russo.- 16 Lifting maps between graphs to embeddings, by
Alexey Gorelov.- 17 A note on the discriminant loci of a hypersurface of
bi-degree (m, n), by Susumu Tanabé.- 18 Welded graphs, Wirtinger groups and
punctured spheres, by Benjamin Audoux, Jean-Baptiste Meilhan and Akira
Yasuhara.- 19 On geometric representation of L-homology classes, by Friedrich
Hegenbarth and Duan D. Repov.- 20 On elementary invariants of genus one
knots and Seifert surfaces, by Christine Lescop.- 21 On a family of
hyperbolic Brunnian links and their volumes, by Duan D. Repov and Andrei
Yu. Vesnin.- 22 SL(2, Z), les tresses ą trois brins, le tore modulaire et
Aut+(F2), (daprčs Emil Artin et Jacob Nielsen), by Alexis Marin.- 23 All
the resources of pure mathematics: Mathematical physics and mathematics as
physics, by Arkady Plotnitsky.- 24 The case for absolute geometry, by Victor
Pambuccian.- 25 The Reconstruction of Theaetetus Theory of Ratios of
Magnitudes, by Stelios Negrepontis and Dimitrios Protopapas.- 26 Notice de
travaux, by Valentin Poénaru.- 27 Mathematical Adventures: A letter to Barry
Mazur, by Valentin Poénaru.- 28 Adventures in physics, by Valentin Poénaru.-
29 Dimitru Poénaru, my father, by Valentin Poénaru.- 30 Father Andrei, by
Valentin Poénaru.- 31 The magic summer of 1964, by Valentin Poénaru.- 32 Po,
a mathematician between humanism and science, Corrado Tanasi and Franco
Marchese.
Louis Funar (born 1967) is Directeur de Recherches at the French Centre National de la Recherche Scientifique and currently Director of the Institut Fourier, University Grenoble Alpes. His main fields of interest are geometry, topology and mathematical quantum field theory. He visited University of Pisa (1995), University of Palermo (1996-2006), Columbia University (1996-1997), Tokyo Institute of Technology (1999-2000), IMAR Bucharest (2001, 2007), University of Ljubljana (2005, 2006), Schrodinger Institute Vienna (2013, 2014). University Babes-Bolyai (2014, 2018, 2021). He is the author of more than 80 published articles.
Athanase Papadopoulos (born 1957) is Directeur de Recherche at the Centre National de la Recherche Scientifique. His main fields of interest are geometry and topology, the history and philosophy of mathematics, and mathematics and music. He has held visiting positions at the Institute for Advanced Study, Princeton (198485 and 199394), USC (19981999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), Lamé Chair of the State University of Saint Petersburg (2019), and has had several month visits to the Max-Plank Institute for mathematics (Bonn), the Erwin Schrödinger Institute (Vienna), the Graduate Center of CUNY (New York), the Tata Institute (Bombay), Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo), Presidency University (Calcutta) and Banaras Hindu University (Adjunct professor for the year 2024). He is the author of more than 200 published articles and 45 monographs and edited books on mathematics, history of mathematics, and music theory. At the University of Strasbourg, he is also member of the CREAA (Centre de Recherche et d'Expérimentation sur l'Acte Artistique).
