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Mutually algebraic structures and `automatic' quantifier elimination
Mutually algebraic structures `automatic' quantifier elimination
2015/9/28
Mutually algebraic structures and `automatic' quantifier elimination.
Characterizing model completeness among mutually algebraic structures
algebraic structures model completeness
2015/9/28
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...
Mutually algebraic structures and expansions by predicates
algebraic structures predicates
2015/9/28
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...
ALGEBRAIC STRUCTURES ON THE TOPOLOGY OF MODULI SPACES OF CURVES AND MAPS
MODULI SPACES CURVES AND MAPS
2015/7/14
We discuss selected topics on the topology of moduli spaces
of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
Algebraic arctic curves in the domain-wall six-vertex model
Algebraic arctic domain-wall six-vertex model
2011/1/20
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...
Algebraic Properties of a Disordered Asymmetric Glauber Model
Algebraic Properties Disordered Asymmetric Glauber Model
2011/1/18
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.
Birkhoff strata of the Grassmannian Gr$\mathrm{^{(2)}}$: Algebraic curves
Birkhoff strata the Grassmannian
2010/11/23
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...
On cohomology of Witt vectors of algebraic integers and a conjecture of Hesselholt
Witt vectors algebraic integers conjecture of Hesselholt
2010/11/19
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...
On the algebraic set of singular elements in a complex simple Lie algebra
algebraic singular elements
2010/11/19
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...
Restriction maps on 1-cohomology of (algebraic) groups
Restriction maps on 1-cohomology of groups
2010/11/11
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...
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
Topological expansion of beta-ensemble model quantum algebraic geometry sectorwise approach
2010/12/14
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...