Related papers: Rank 2 fusion rings are complete intersections

We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries…

Complete intersections may be unexpectedly simple over fields of positive characteristic: for instance, they may be unirational despite being of general type. One explanation is given by profiles, structure that tracks the special shape of…

We classify all fusion categories for a given set of fusion rules with three simple object types. If a conjecture of Ostrik is true, our classification completes the classification of fusion categories with three simple object types. To…

A fusion category of rank $4$ has either four self-dual objects or exactly two self-dual objects. We study fusion categories of rank $4$ with exactly two self-dual objects, giving nearly a complete classification of those based ring that…

We prove in most cases that a general smooth complete intersection in the projective space has no non-trivial automorphisms.

This paper proves finite generation of the log canonical ring without Mori theory.

In this article, we find the equations defining the Rees algebra for certain Monomial Curves explicitly and use them to prove that the blowup scheme is not smooth. This proves a conjecture of Francia in affirmative, which says that a…

Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer groups that commutes with restriction. We additionally…

We prove that every smooth complete intersection X defined by s hypersurfaces of degree d_1, ... , d_s in a projective space of dimension d_1 + ... + d_s is birationally superrigid if 5s +1 is at most 2(d_1 + ... + d_s + 1)/sqrt{d_1...d_s}.…

We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.

We classify all fusion categories of rank 3 that admit a pivotal structure over an algebraically closed field of characteristic zero. Also in the Appendix (joint with D.Nikshych) we give some restrictions on Grothendieck rings of near-group…

We answer a question due to A. Myasnikov by proving that all expected ranks occur as the ranks of intersections of finitely generated subgroups of free groups.

We compute the automorphism group of the affine surfaces with the coordinate ring isomorphic to a cluster algebra of rank 2.

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect…

We show that every (not necessarily saturated) fusion system can be realized as a full subcategory of the fusion system of a finite group. This result extends our previous work \cite{Park2010} and complements the related result…

An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary…

We calculate intersection forms of all 4-dimensional almost-flat manifolds

We describe Lagrangian algebras in twisted Drinfeld centres for finite groups. Using the full centre construction, we establish a 1-1 correspondence between Lagrangian algebras and module categories over pointed fusion categories.

We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…