相关论文: Characterization of SDP Designs That Yield Certain…

The characterization of bipartite distance-regularized graphs, where some vertices have eccentricity less than four, in terms of the incidence structures of which they are incidence graphs, is known. In this paper we prove that there is a…

We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N=2 superconformal field theories. We also determine the mini-versal deformation of these…

We classify all the supersymmetric configurations of ungauged N=2,d=4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric…

We define three combinatorial models for \hat{sl(n)} crystals, parametrized by partitions, configurations of beads on an `abacus', and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible…

In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional…

The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides the split cases, one for each complex simple Lie algebra, there are two kinds of non-split…

We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly…

Let M be a closed oriented smooth 4-manifold admitting symplectic structures. If M is minimal and has b^+=1, we prove that there is a unique symplectic canonical class up to sign, and any real second cohomology class of positive square is…

We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…

The interplay between coding theory and $t$-designs has attracted a lot of attention for both directions. It is well known that the supports of all codewords with a fixed weight in a code may hold a $t$-design. In this paper, by determining…

A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of…

Symplectic (respectively orthogonal) triple systems provide constructions of Lie algebras (resp. superalgebras). However, in characteristic 3, it is shown that this role can be interchanged and that Lie superalgebras (resp. algebras) can be…

The M-theory fieldstrength and its dual, given by the integral lift of the left hand side of the equation of motion, both satisfy certain cohomological properties. We study the combined fields and observe that the multiplicative structure…

The fact that every compact oriented 4-manifold admits spin$^c$ structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct nor transparent. This article gives a new proof using twistor spaces that is…

We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure \fb{that guarantee the unique solvability of double saddle-point systems}. We consider…

We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and…

We study $\mathbb{Z}_N$ one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its…

While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as…

We introduce and discuss Jones pairs. These provide a generalization and a new approach to the four-weight spin models of Bannai and Bannai. We show that each four-weight spin model determines a ``dual'' pair of association schemes.

Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where circuits with non-negative weights (monotone circuits) can…