This book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others.
Recently, a deeper structure of...
This book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual...
This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. The main mathematical objects are infinite-dimensional Dirac operators on the abstract Boson–Fermion Fock space. The target audience consists of graduate students and researchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional analysis. The major topics are the clarification of general mathematical structures that some models in the SQFT have in common, and the...
This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensiona...
This book is based on the author's mini course delivered at Tokyo University of Marine Science and Technology in March 2019.
The shuffle approach to Drinfeld–Jimbo quantum groups of finite type (embedding their "positive" subalgebras into q-deformed shuffle algebras) was first developed independently in the 1990s by J. Green, M. Rosso, and P. Schauenburg. Motivated by similar ideas, B. Feigin and A. Odesskii proposed a shuffle approach to elliptic quantum groups around the same time. The shuffle algebras in the present book can be viewed as trigonometric...
This book is based on the author's mini course delivered at Tokyo University of Marine Science and Technology in March 2019.
This book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021.
Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall–Littlewood polynomials and play important roles in various fields of mathematics and mathematical...
This book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polyn...
