Related papers: Motives, Periods, and Functoriality

This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$,…

In the previous author's paper the Macdonald norm conjecture (including the famous constant term conjecture) was proved. This paper contains the proof of the remaining two (the duality and evaluation conjectures). The evaluation theorem is…

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically…

Motivic local systems over a curve in finite characteristic form a countable set endowed with an action of the absolute Galois group of rational numbers commuting with the Frobenius map. I will discuss three series of conjectures about such…

We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f…

There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…

We study an extension of $\mtl$ in pointwise time with rational expression guarded modality $\reg_I(\re)$ where $\re$ is a rational expression over subformulae. We study the decidability and expressiveness of this extension ($\mtl$+$\varphi…

Let $F$ be a number field and $D$ a quaternion algebra over $F$. Take a cuspidal automorphic representation $\pi$ of $D_{\mathbb{A}}^\times$ with trivial central character and a cusp form $\phi$ in $\pi$. Using the prehomogeneous zeta…

Given a perfect field of exponential characteristic $e$ and a functor $f:\mathcal A\to\mathcal B$ between symmetric monoidal strict $V$-categories of correspondences satisfying the cancellation property such that the induced morphisms of…

We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring.They have various specific properties which do not hold for…

Let $G$ be a split connected semisimple group over a field. We give a conjectural formula for the motive of the stack of $G$-bundles over a curve $C$, in terms of special values of the motivic zeta function of $C$. The formula is true if…

We relate the recognition principle for infinite $\mathbf P^1$-loop spaces to the theory of motivic fundamental classes of D\'eglise, Jin, and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories…

Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings -- Noetherian semirings, natural numbers -- are proper. Properness matters as the equivalence problem for weighted automata…

For a finite dimensional real vector space V with inner product, let F(V) be the block structure space, in the sense of surgery theory, of the projective space of V. Continuing a program launched in part I, we investigate F as a functor on…

There has been a recent coming together of the Converse Theorem for $\gln$ and the Langlands-Shahidi method of controlling the analytic properties of automorphic $L$-functions which has allowed us to establish a number of new cases of…

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…

A simple criterion for a functor to be finitary is presented: we call $F$ finitely bounded if for all objects $X$ every finitely generated subobject of $FX$ factorizes through the $F$-image of a finitely generated subobject of $X$. This is…

We provide a universal characterization of the construction taking a scheme $X$ to its stable $\infty$-category $\text{Mot}(X)$ of noncommutative motives, patterned after the universal characterization of algebraic K-theory due to…

In this article we further the study of noncommutative numerical motives. By exploring the change-of-coefficients mechanism, we start by improving some of our previous main results. Then, making use of the notion of Schur-finiteness, we…

The functional composition principle is generalized by taking into account of history of context change. Analysis of Peres' example shows hysteresis of value assignments. It is shown that value assignments which depend on the history of…