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In this paper, we propose a modified Kudla-Rapoport conjecture for the Kr\"amer model of unitary Rapoport-Zink space at a ramified prime, which is a precise identity relating intersection numbers of special cycles to derivatives of…
We give a detailed description of the model construction procedures about our new approach to the family structure of the standard model. SM-like chiral fermion spectra, largely "derivable" from the gauge anomaly constraints, are formulated…
Mayr and Meyer found ideals with the doubly exponential ideal membership property. In the analysis of the associated primes of these ideals (in math.AC/0209344), a new family of ideals arose. This new family is presented and analyzed in…
Based on the structure theory of pairs of skew-symmetric matrices, we give a conjecture for the Hilbert series of the exterior algebra modulo the ideal generated by two generic quadratic forms. We show that the conjectured series is an…
The parameters of many classes of birth-death processes cannot be inferred uniquely from phylogenetic trees: infinitely many parameter combinations yield the same distribution of phylogenetic trees. Here, we show that parameter…
For an odd prime p, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G,X) of abelian type, such that G splits over a tamely ramified extension of Q_p. The local structure of…
In this paper we define an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebra. This family is likely to play a key role in classifying…
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…
In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
We propose a conjecture extending the classical construction of elliptic units to complex cubic number fields $K$. The conjecture concerns special values of the elliptic gamma function, a holomorphic function of three complex variables…
In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the…
Angular parts of certain solvable models are studied. We find that an extension of this class may be based on suitable trigonometric identities. The new exactly solvable Hamiltonians are shown to describe interesting two- and three-particle…
One of the most important and unanswered problems in particle physics is the origin of the three generations of quarks and leptons. The standard Model does not provide any hint regarding its sequential charge assignments, which remain a…
This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability…
We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
We point out a somewhat mysterious appearance of $SU_c(3)$ representations, which exhibit the behaviour of three full generations of standard model particles. These representations are found in the Clifford algebra $\mathbb{C}l(6)$, arising…
An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the…
We use a combination of analytic models and computer simulations to gain insight into the dynamics of evolution. Our results suggest that certain interesting phenomena should eventually emerge from the fossil record. For example, there…