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We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula i...
We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if n...
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
The arctic curve, i.e. the spatial curve separating ordered (or ‘frozen’) and disordered (or ‘temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root...
We consider an asymmetric variant of disordered Gla-uber dynamics of Ising spins on a one-dimensional lattice, where each spin flips according to the relative state of the spin to its left.
Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rati...
Let $K$ be a complete discrete valued field of characteristic zero with residue field $k_K$ of characteristic $p > 0$. Let $L/K$ be a finite Galois extension with the Galois group $G$ and suppose tha...
Let $G$ be a complex simple Lie group and let $\g = \hbox{\rm Lie}\,G$. Let $S(\g)$ be the $G$-module of polynomial functions on $\g$ and let $\hbox{\rm Sing}\,\g$ be the closed algebraic cone of sin...
Our first theorem is a version of the five lemma in a certain situation of pointed sets arising from non-abelian 1-cohomology. For our second, we show that a connected, unipotent algebraic group Q ac...
We solve the loop equations of the β-ensemble model analogously to the solution found for the Hermitian matrices β = 1. For β = 1, the solution was expressed using the algebraic spectral curve of equa...

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