In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order
808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
= 246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
≈ 8×1053.
In the area of modern algebra known as group theory, the baby monster groupB (or, more simply, the baby monster) is a sporadic simple group of order
In mathematics, the bimonster is a group that is the wreath product of the monster group M with Z2:
In algebraic geometry, a Kummer quartic surface, first studied by Ernst Kummer, is an irreducible nodal surface of degree 4 in with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of the Jacobian by the Kummer involution x ↦ −x. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a torus by the Kummer involution gives a K3 surface with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces.
Shigefumi Mori is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds.
Robert Arnott Wilson is a retired mathematician in London, England, who is best known for his work on classifying the maximal subgroups of finite simple groups and for the work in the Monster group. He is also an accomplished violin, viola and piano player, having played as the principal viola in the Sinfonia of Birmingham. Due to a damaged finger, he now principally plays the kora.
Wolf Paul Barth was a German mathematician who discovered Barth surfaces and whose work on vector bundles has been important for the ADHM construction. Until 2011 Barth was working in the Department of Mathematics at the University of Erlangen-Nuremberg in Germany.
In the area of modern algebra known as group theory, the Janko groupJ4 is a sporadic simple group of order
In mathematics, the Freudenthal magic square is a construction relating several Lie algebras. It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at the right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though Vinberg's symmetric method gives a symmetric construction.
In algebraic geometry, a Togliatti surface is a nodal surface of degree five with 31 nodes. The first examples were constructed by Eugenio G. Togliatti. Arnaud Beauville proved that 31 is the maximum possible number of nodes for a surface of this degree, showing this example to be optimal.
In algebraic geometry, a Barth surface is one of the complex nodal surfaces in 3 dimensions with large numbers of double points found by Wolf Barth. Two examples are the Barth sextic of degree 6 with 65 double points, and the Barth decic of degree 10 with 345 double points.
In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality
Yoichi Miyaoka is a mathematician who works in algebraic geometry and who proved the Bogomolov–Miyaoka–Yau inequality in an Inventiones Mathematicae paper.
In algebraic geometry, an Endrass surface is a nodal surface of degree 8 with 168 real nodes, found by Stephan Endrass. As of 2007, it remained the record-holder for the most number of real nodes for its degree; however, the best proven upper bound, 174, does not match the lower bound given by this surface.
In mathematics, Wiman's sextic is a degree 6 plane curve with four nodes studied by Anders Wiman . It is given by the equation
In mathematics, a Manin triple (g, p, q) consists of a Lie algebra g with a non-degenerate invariant symmetric bilinear form, together with two isotropic subalgebras p and q such that g is the direct sum of p and q as a vector space. A closely related concept is the (classical) Drinfeld double, which is an even dimensional Lie algebra which admits a Manin decomposition.
In algebraic geometry, a nodal surface is a surface in projective space whose only singularities are nodes. A major problem about them is to find the maximum number of nodes of a nodal surface of given degree.
Charles Herschel Sisam was an American mathematician.
Allesandra Sarti is an Italian mathematician specializing in algebraic geometry. She is the namesake of the Sarti surface, and has also published research on K3 surfaces. She works in France as a professor at the University of Poitiers and deputy director of the Institut national des sciences mathématiques et de leurs interactions (Insmi) of the French National Centre for Scientific Research in Paris.
Sextic with 48 node
Sextic with 48 node
Octic with 72 nodes
Octic with 144 nodes
Dodectic surface with 360 nodes
3D model of Sarti surface
