Perspectives in Lie Theory, Softcover reprint of the original 1st ed. 2017 Springer INdAM Series, Vol. 19

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Part I Lecture notes. - 1 Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE.- 2 An introduction to algebras of chiral differential operators.- 3 Representations of Lie Superalgebras.- 4 Introduction toW-algebras and their representation theory. Part II Contributed papers.- 5 Representations of the framisation of the Temperley–Lieb algebra.- 6 Some semi-direct products with free algebras of symmetric invariants.- 7 On extensions of affine vertex algebras at half-integer levels.- 8 Dirac cohomology in representation theory.- 9 Superconformal Vertex Algebras and Jacobi Forms.- 10 Centralizers of nilpotent elements and related problems.- 11 Pluri-Canonical Models of Supersymmetric Curves.- 12 Report on the Broué-Malle-Rouquier conjectures.- 13 A generalization of the Davis-Januszkiewicz construction.- 14 Restrictions of free arrangements and the division theorem.- 15 The pure braid groups and their relatives.- 16 Homological representations of braid groups and the space of conformal blocks.- 17 Totally nonnegative matrices, quantum matrices and back, via Poisson geometry.

Giovanna Carnovale received her PhD from the University of Utrecht in 1999 under the direction of Tom Koornwinder. She has held post-doc positions in Cergy-Pontoise, Paris VI, Antwerp, and Rome Tor Vergata. In 2001 she took on a position in Padua, where she has been an associate professor since 2015. Her research interests are in algebra, especially Lie theory, Hopf algebra theory, and representation theory, as well as their the interplay with geometry.

Fabrizio Caselli received his PhD from the Università di Roma La Sapienza in 2003 under the direction of Francesco Brenti. He has held post-doc positions in Lyon and Rome. In 2006 he took on a position in Bologna, where he has been an associate professor since 2014. His main research interests are in algebra and combinatorics, in particular Kazhdan-Luszig theory, Coxeter groups, complex reflection groups and their representations.

Corrado De Concini received his PhD in Mathematics from the University of Warwick in 1975 under the direction of George Lusztig. He has been a professor of mathematics since 1983. Since 1996 he has been a professor at the University of Roma, La Sapienza. He has been a visiting researcher at numerous institutes, including Brandeis University, Mittag Leffler Institute, Tata Institute of Fundamental Research, Harvard University, and MIT. He serves on the editorial boards of Rendiconti Accademia Nazionale dei Lincei, Journal of Transformation Groups, IMRN, Rendiconti di Matematica, Rendiconti del Seminario Matematico-Padova, and Communications in Contempo