In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by Candelas et al. (1985), after Eugenio Calabi who first conjectured that such surfaces might exist, and Shing-Tung Yau who proved the Calabi conjecture.
Shing-Tung Yau is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and Professor Emeritus at Harvard University. Until 2022 he was the William Caspar Graustein Professor of Mathematics at Harvard, at which point he moved to Tsinghua.
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
Nigel James Hitchin FRS is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
The mathematical term perverse sheaves refers to the objects of certain abelian categories associated to topological spaces, which may be a real or complex manifold, or more general topologically stratified spaces, possibly singular.
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.
Victor Ginzburg is a Russian American mathematician who works in representation theory and in noncommutative geometry. He is known for his contributions to geometric representation theory, especially, for his works on representations of quantum groups and Hecke algebras, and on the geometric Langlands program. He is currently a Professor of Mathematics at the University of Chicago.
Idun Reiten is a Norwegian professor of mathematics. She is considered to be one of Norway's greatest mathematicians today. With national and international honors and recognition, she has supervised 11 students and has 28 academic descendants as of March 2024. She is an expert in representation theory, and is known for work in tilting theory and Artin algebras.
Thomas Andrew Bridgeland is a Professor of Mathematics at the University of Sheffield. He was a senior research fellow in 2011–2013 at All Souls College, Oxford and, since 2013, remains as a Quondam Fellow. He is most well-known for defining Bridgeland stability conditions on triangulated categories.
Maurice Auslander was an American mathematician who worked on commutative algebra, homological algebra and the representation theory of Artin algebras. He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras.
In algebra, Auslander–Reiten theory studies the representation theory of Artinian rings using techniques such as Auslander–Reiten sequences and Auslander–Reiten quivers. Auslander–Reiten theory was introduced by Maurice Auslander and Idun Reiten and developed by them in several subsequent papers.
In mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and associated tilting functors. Here, the second algebra is the endomorphism algebra of a tilting module over the first algebra.
In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants. Given a compact moduli space of sheaves on a Calabi–Yau threefold, its Donaldson–Thomas invariant is the virtual number of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class. The Donaldson–Thomas invariant is a holomorphic analogue of the Casson invariant. The invariants were introduced by Simon Donaldson and Richard Thomas. Donaldson–Thomas invariants have close connections to Gromov–Witten invariants of algebraic three-folds and the theory of stable pairs due to Rahul Pandharipande and Thomas.
Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.
Mark William Gross is an American mathematician, specializing in differential geometry, algebraic geometry, and mirror symmetry.
Paul Stephen Aspinwall is a British theoretical physicist and mathematician, who works on string theory and also algebraic geometry.
Yongbin Ruan is a Chinese mathematician, specializing in algebraic geometry, differential geometry, and symplectic geometry with applications to string theory.
Christof Geiß, also called Geiss Hahn or Geiß Hahn, is a German mathematician.
Dmitri Olegovich Orlov, is a Russian mathematician, specializing in algebraic geometry. He is known for the Bondal-Orlov reconstruction theorem (2001).
Andrei Vladimirovich Roiter was a Ukrainian mathematician, specializing in algebra.
