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Integrable systems involves the study of physically relevant nonlinear equations, which includes many families of well-known, highly important partial and ordinary differential equations. Building on ...
A conjecture of AutoGraphiX on the relation between the Randi´c index R and the algebraic connectivity a of a connected graph G is:R a  n − 3 + 2p2 2 ! /  2(1 − cos  n )  with ...
We consider a purely massive local relativistic quantum theory specified by a family of von Neumann algebras indexed by the space-time regions. We assume that, affiliated with the local algebras, ther...
We provide a characterization of infinite algebraic Galois extensions of the rationals with uniformly bounded local degrees, giving a detailed proof of all the results announced in Checcoli and Zannie...
Hochster's Theta Pairing and Algebraic Equivalence     Hochster's Theta Pairing  Algebraic Equivalence       font style='font-size:12px;'> 2010/11/24
We define a variant of Hochster's theta pairing and prove that it is constant in flat families of modules over hypersurfaces with isolated singularities. As a consequence, we show that the theta pair...
On algebraic cellular automata     On algebraic cellular automata  math       font style='font-size:12px;'> 2010/11/24
We investigate some general properties of algebraic cellular automata, i.e., cellular automata over groups whose alphabets are affine algebraic sets and which are locally defined by regular maps. When...
We construct lci nilpotent scheme structures $Y \subset P$ on a smooth variety $X$ embedded in a smooth variety $P$, which are, locally, (i.e. in $\widehat{\mathcal O}_{p,P}$ ) given by ideals of the ...
We construct a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutation, pairs of ...
Primitive algebraic algebras of polynomially bounded growth     algebras  polynomially bounded growth       font style='font-size:12px;'> 2010/11/23
We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In additio...
We prove irreducibility for the space of cyclic covers of fixed numerical type between smooth projective curves, and also for the space of cyclic covers of prime order and of fixed numerical-combinato...
L-cumulants, L-cumulant embeddings and algebraic statistics     L-cumulant embeddings  algebraic statistics       font style='font-size:12px;'> 2010/11/12
In this paper we generalize the combinatorial definition of cumulants. Obtained in this way L-cumulants keep all the desired properties of the classical cumulants like semi-invariance and vanishing f...
The worst situation in computing the minimal nonnegative solution $X_*$ of a nonsymmetric algebraic Riccati equation $\mathcal R(X)=0$ associated with an M-matrix occurs when the derivative of $\math...
Lectures on algebraic categorification     Lectures  algebraic categorification       font style='font-size:12px;'> 2010/11/8
This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.
Algebraic Theories and (Infinity,1)-Categories     Algebraic Theories  math       font style='font-size:12px;'> 2010/11/19
We adapt the classical framework of algebraic theories to work in the setting of (infinity,1)-categories developed by Joyal and Lurie. This gives a suitable approach for describing highly structured o...
On the algebraic cobordism spectra MSL and MSp     the algebraic cobordism spectra  MSL  MSp       font style='font-size:12px;'> 2010/11/9
We construct algebraic cobordism spectra MSL and MSp. They are commutative monoids in the category of symmetric T^{2}- spectra. The spectrum MSp comes with a natural symplectic orientation given eithe...

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