We prove an analogue in Arakelov geometry of the Grothendieck-RiemannRoch theorem.

We survey connections of the Grothendieck inequality and its variants to combinatorial optimization and computational complexity.

The Schur polynomials s ? are essential in understanding the representation theory of general linear group. They also describe cohomology ring Grassmannians. For ?=(n,n-1,?,1) a staircase shape and ??? subpartition, Stembridge equality states that ?/? =s T . This provides information about symmetry ring. stable Grothendieck G , dual g developed by Buch, Lam, Pylyavskyy, variants K-theory Using ...

We introduce families of two-parameter multivariate polynomials indexed by pairs partitions v,w – biaxial double (β,q)-Grothendieck which specialize at q=0 and v=1 to β-Grothendieck from torus-equivariant connective K-theory. Initially defined recursively via divided difference operators, our main result is that these new arise as partition functions solvable lattice models. Moreover, the assoc...

The definition of the Grothendieck-Teichmüller group by Drinfeld was motivated by applications to quantum group theory and by Grothendieck’s program aiming to understand a geometric counterpart of absolute Galois groups. The purpose of the this outlook chapter is to give an overview of this program, and to survey the connections between the structures occurring in our study of the homotopy of o...