Related papers: Motivic splitting principle
We propose an analogy of splitting principle in genus $0$ Gromov--Witten theory. More precisely, we show how the Gromov--Witten theory of a variety $X$ can be embedded into the theory of the projectivization of a vector bundle over $X$. An…
We show that an earlier conjecture of the author, on diophantine approximation of rational points on varieties, implies the ``abc conjecture'' of Masser and Oesterl'e. In fact, a weak form of the former conjecture is sufficient, involving…
Motivated reasoning posits that people distort how they process information in the direction of beliefs they find attractive. This paper creates a novel experimental design to identify motivated reasoning from Bayesian updating when people…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in…
We apply a paraconsistent logic to reason about fractions.
The goal of this paper is to prove: if certain 'standard' conjectures on motives over algebraically closed fields hold, then over any 'reasonable' $S$ there exists a motivic $t$-structure for the category of Voevodsky's $S$-motives (as…
Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneous varieties has begun to emerge. In particular,…
This study establishes the variational principle for local pressure in the sofic context.
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the rationality of motivic zeta-function.
We have developed an alternative formulation based on ${\bf F} = M {\bf a}$ rather than ${\bf F} = d{\bf P}/dt$ for studying variable mass systems. It is shown that ${\bf F} = M {\bf a}$ can be particularly useful in this context, as…
We prove a central limit theorem with aassumptions which are many weak than classical conditions
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
We consider Steinhaus cake dividing game.
This is a survey and research note on the modified Orlik conjecture derived from the division theorem introduced in [2]. The division theorem is a generalization of classical addition-deletion theorems for free arrangements. The division…
This is an attempt at an elementary exposition, with examples, of the theory of motivic integration developed by R. Cluckers and F. Loeser, with the view towards applications in representation theory of p-adic groups.
A simple application of the semipositivity.