相关论文: $p$-adic Periods and Selmer Scheme Images

The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution which limits at a hyperbolic stable equilibrium of the past…

Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…

We study the unipotent Albanese map appearing in the non-abelian Chabauty method of Minhyong Kim. In particular we explore the explicit computation of the $p$-adic de Rham period map $j^{dr}_n$ on elliptic and hyperelliptic curves over…

In the quests to uncovering the fundamental structures that underlie some of the asymptotic Swampland conjectures we initiate the general study of asymptotic period vectors of Calabi- Yau manifolds. Our strategy is to exploit the…

We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into mixed Tate…

We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such…

We give new instances where Chabauty--Kim sets can be proved to be finite, by developing a notion of "generalised height functions" on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals…

This is an announcement of some of the results obtained as a part of the second author's Ph.D. thesis. In the first part, we prove that the fundamental group of an acylindrical complex of hyperbolic groups with finite edge groups is…

We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.

We develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in certain conditions the pinching path converges uniformly and…

Let f be a dominant rational map of P^k such that there exists s <k, with lambda_s(f)>lambda_l(f) for all l. Under mild hypotheses, we show that, for A outside a pluripolar set of the group of automorphisms of P^k, the map f o A admits a…

In this paper, we prove a combination theorem for a relatively acylindrical graph of relatively hyperbolic groups (Theorem 1.1). Here, we are extending the technique of [Tom21] and constructing Bowditch boundary of the fundamental group of…

We construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers. For the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period…

We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…

Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic…

In this paper, we develop an algorithm for computing Coleman--Gross (and hence Nekov\'a\v{r}) $p$-adic heights on hyperelliptic curves over number fields with arbitrary reduction type above $p$. This height is defined as a sum of local…

We describe an algorithm for distinguishing hyperbolic components in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperbolic components of the parameter spaces V1 -…

This work is motivated by the long-standing open problem of designing asymptotically order-optimal aperiodic polyphase sequence sets with respect to the celebrated Welch bound. Attempts were made by Mow over 30 years ago, but a…

In a context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding…

In the present paper, by conducting research on the dynamics of the $p$-adic generalized Ising mapping corresponding to renormalization group associated with the $p$-adic Ising-Vannemenus model on a Cayley tree, we have determined the…