Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals

We describe a decomposition algorithm for elliptic multiple zeta values, which amounts to the construction of an injective map $\psi$ from the algebra of elliptic multiple zeta values to a space of iterated Eisenstein integrals. We give many examples of this decomposition, and conclude with a short discussion about the image of $\psi$. It turns out that the failure of surjectivity of $\psi$ is in some sense governed by period polynomials of modular forms.Comment: v2, minor change

The meta-abelian elliptic KZB associator and periods of Eisenstein series

We compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve.Our main result is an explicit formula for this image in terms of Eichler integrals of Eisenstein series, and is analogous to Deligne’s computation of the depth one quotient of the Drinfeld associator.We also show how to retrieve Zagier’s extended period polynomials of Eisenstein series, as well as the values at zero of Beilinson–Levin’s elliptic polylogarithms from the meta-abelian elliptic KZB associator

Elliptic Double Zeta Values

We study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the elliptic KZB associator. Originally defined by iterated integrals on a once-punctured complex elliptic curve, it turns out that they can also be expressed as certain linear combinations of indefinite iterated integrals of Eisenstein series and multiple zeta values. In this paper, we prove that the $\mathbb{Q}$-span of these elliptic multiple zeta values forms a $\mathbb{Q}$-algebra, which is naturally filtered by the length and is conjecturally graded by the weight. Our main result is a proof of a formula for the number of $\mathbb{Q}$-linearly independent elliptic multiple zeta values of lengths one and two for arbitrary weight.Comment: 22 page

On the algebraic structure of iterated integrals of quasimodular forms

We study the algebra $\mathcal{I}^{QM}$ of iterated integrals of quasimodular forms for $\operatorname{SL}_2(\mathbb{Z})$, which is the smallest extension of the algebra $QM_{\ast}$ of quasimodular forms, which is closed under integration. We prove that $\mathcal{I}^{QM}$ is a polynomial algebra in infinitely many variables, given by Lyndon words on certain monomials in Eisenstein series. We also prove an analogous result for the $M_{\ast}$-subalgebra $\mathcal{I}^{M}$ of $\mathcal{I}^{QM}$ of iterated integrals of modular forms.Comment: v2, minor changes, to appear in Algebra and Number Theor

Environmental Heritage and the Ruins of the Future

We now have good reason to worry that many coastal cities will be flooded by the end of the century. How should we confront this possibility (or inevitability)? What attitudes should we adopt to impending inundation of such magnitude? In the case of place-loss due to anthropogenic climate change, I argue that there may ultimately be something fitting about letting go, both thinking prospectively, when the likelihood of preservation is bleak, and retrospectively, when we reflect on our inability to prevent destruction. I then explore some of the ethical complications of this response

Repatriation and the Radical Redistribution of Art

Museums are home to millions of artworks and cultural artifacts, some of which have made their way to these institutions through unjust means. Some argue that these objects should be repatriated (i.e. returned to their country or culture of origin). However, these arguments face a series of philosophical challenges. In particular, repatriation, even if justified, is often portrayed as contrary to the aims and values of museums. However, in this paper, I argue that some of the very considerations museums appeal to in order to oppose repatriation claims can be turned on their heads and marshaled in favor of the practice. In addition to defending against objections to repatriation, this argument yields the surprising conclusion that the redistribution of cultural goods should be much more radical than is typically supposed

Authenticity and the Aesthetic Experience of History

In this paper, I argue that norms of artistic and aesthetic authenticity that prioritize material origins foreclose on broader opportunities for aesthetic experience: particularly, for the aesthetic experience of history. I focus on Carolyn Korsmeyer’s recent articles in defense of the aesthetic value of genuineness and argue that her rejection of the aesthetic significance of historical value is mistaken. Rather, I argue that recognizing the aesthetic significance of historical value points the way towards rethinking the dominance of the very norms of authenticity that Korsmeyer endeavors to defend and explain

Portraits of the Landscape

Portraits are defined in part by their aim to reveal and represent the inner ‘character’ of a person. Because landscapes are typically viewed as lacking such an ‘inner life,’ one might assume that landscapes cannot be the subject of portraiture. However, the notion of landscape character plays an important role in landscape aesthetics and preservation. In this essay, I argue that landscape artworks can thus share in portraiture’s goal of capturing character, and in doing so present us with essential tools for revealing the often ineffable character of place. I explain the implications of this view for debates about scientific cognitivism in environmental aesthetics, representing the narrative dimension of landscape character and integrity, and appeals to the character of place in historic and environmental preservation