The precision synthesis of helical bilayer nanographenes (NGs) with new topology is of substantial interest because of their exotic physicochemical properties. However, helical bilayer NGs bearing non-hexagonal rings remain synthetically challenging. Here we present the efficient synthesis of the first helical bilayer nonbenzenoid nanographene (HBNG1) from a tailor-made azulene-embedded precursor, which contains a novel [10]helicene backbone with two embedded heptagons. Single-crystal X-ray analysis reveals its highly twisted bilayer geometry with a record small interlayer distance of 3.2 Å among the reported helical bilayer NGs. Notably, the close interlayer distance between the two layers offers intramolecular through-space conjugation as revealed by in situ spectroelectrochemistry studies together with DFT simulations. Furthermore, the chiroptical properties of the P/M enantiomers of HBNG1 are also evaluated by circular dichroism and circularly polarized luminescence.

Zugl.: Bonn, Universiẗat, Diss., 2006.

We compute the Hilbert-Kunz functions of two-dimensional rings of type ADE by using representations of their indecomposable, maximal Cohen-Macaulay modules in terms of matrix factorizations, and as first syzygy modules of homogeneous ideals.

My thesis is mostly concerned with algebraic and combinatorial aspects of the theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid. The Orlik-Terao algebra is a useful tool for studying hyperplane arrangements, especially for characterizing some non-combinatorial properties. The broken circuit complex, on the one hand, is closely related to the Orlik-Terao algebra, and on the other hand, plays a crucial role in the study of many combinatorial problem: the coefficients of the characteristic polynomial of a matroid are encoded in the f-vector of the broken circuit complex of the matroid. Among main results of the thesis are characterizations of the complete intersection and Gorenstein properties of the broken circuit complex and the Orlik-Terao algebra. I also study the h-vector of the broken circuit complex of a series-parallel network and relate certain entries of that vector to ear decompositions of the network. An application of the Orlik-Terao algebra in studying the relation space of a hyperplane arrangement is also included in the thesis.

My PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder.

The thesis deals with stochastic and algebraic aspects of the integer convex hull. In the first part, the intrinsic volumes of the randomized integer convex hull are investigated. In particular, we obtained an exact asymptotic order of the expected intrinsic volumes difference in a smooth convex body and a tight inequality for the expected mean width difference. In the algebraic part, an exact formula for the Bhattacharya function of complete primary monomial ideas in two variables is given. As a consequence, we derive an effective characterization for complete monomial ideals in two variables.

This thesis concerns two topics. The first topic, that is related to the Dedekind-Mertens Lemma, the notion of the so-called content algebra, is discussed in chapter 2. Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = \cap \lbrace I \colon I \text{~is an ideal of~} R \text{~and~} x \in IM \rbrace $. $M$ is said to be a \textit{content} $R$-module if $x \in c(x)M $, for all $x \in M$. The $R$-algebra $B$ is called a \textit{content} $R$-algebra, if it is a faithfully flat and content $R$-module and it satisfies the Dedekind-Mertens content formula. In chapter 2, it is proved that in content extensions, minimal primes extend to minimal primes, and zero-divisors of a content algebra over a ring which has Property (A) or whose set of zero-divisors is a finite union of prime ideals are discussed. The preservation of diameter of zero-divisor graph under content extensions is also examined. Gaussian and Armendariz algebras and localization of content algebras at the multiplicatively closed set $S^ \prime = \lbrace f \in B \colon c(f) = R \rbrace$ are considered as well. In chapter 3, the second topic of the thesis, that is about the grade of the zero-divisor modules, is discussed. Let $R$ be a commutative ring, $I$ a finitely generated ideal of $R$, and $M$ a zero-divisor $R$-module. It is shown that the $M$-grade of $I$ defined by the Koszul complex is consistent with the definition of $M$-grade of $I$ defined by the length of maximal $M$-sequences in I$. Chapter 1 is a preliminarily chapter and dedicated to the introduction of content modules and also locally Nakayama modules.

This dissertation deploys theories of spatiotemporal experience and organization, most prominently Mikhail Bakhtin’s “chronotope,” to set contemporary literature, film, and music into dialogue with theories of post-Wende social and political experiences and possibility that speak, with Francis Fukuyama, as the contemporary as the “End of History.” Where these interlocutors of Fukuyama generally affirm or intensify his view of the contemporary as a time where historical progress slows to a halt, historical memory recedes from view, and the conditions of subjecthood are rephrased from participation in a struggle for progress to mindless consumption and technocratic tinkering, I engage contemporary artwork to flesh out and ultimately peer beyond the boundaries of the real and the possible these social theories articulate. Through a series of close readings of German films, music albums, and novels published between 1995 and 2021, I examine how German authors, filmmakers, and musicians pursue depictions of the malaises of the End of History while also resolutely pointing to the fissures in liberal capitalist hegemony where history—its past and its future—again becomes visible. Mikhail Bakhtin’s notion of the chronotope, a text’s unified expression of space and time, is central to my method of analysis. In tracing the chronotopic contours of contemporary works of music, film, and literature, I argue, we—as readers, viewers, and listeners—are engaged to think and act alongside the forms and figures that populate the worlds their authors create. In doing so, we ultimately uncover forceful accusations, resolute alternatives, and even hopeful antidotes to the deficiencies of our present that help us both to soberly contemplate the implications the pessimistic formulations of contemporary theory have on our lives, communities, and futures but also to formulate possibilities for them that lie beyond their analytical purview.In a series of close readings of my literary, filmic, and musical primary texts, I engage theorists of the post-Cold War, post-Wende contemporary who write about the political order and social conditions emerging out of the triumph of neoliberalism and market capitalism over socialist, communist, and fascist alternatives. The dissertation begins by establishing a wide view of the contemporary, tracing in its first chapter chronotopic resonances of Hartmut Rosa’s “social acceleration” thesis—which locates the aimlessness and alienation of contemporary society within the accelerationist logic of market capitalist modes of production—across the full temporal arc of the contemporary. Pairing Christian Kracht’s Faserland (1995) with Fatma Aydemir's Ellbogen (2017), I argue that the futilities and frustrations of the modern subject, as foretold in Fukuyama’s “End of History” essay and fleshed out in Rosa’s writings on social acceleration, find resonance not only in the wealthy, educated, white protagonist of Faserland’s 1990s, but also in the impoverished, undereducated, Turkish-Kurdish protagonist of Ellbogen some twenty years later. What connects these two accounts across decades and differences in identities, I demonstrate, is not merely a shared sense of alienation and despair, but a shared, underlying chronotopic characterization of the contemporary. These commonalities appear, I demonstrate, when we connect Rosa’s “social acceleration” thesis to diegetic chronotopes of perpetual motion that depict modern subjects’ inability to avail themselves of the ostensibly liberatory potential of liberal capitalism’s accelerated lifeworld. Chapter 2 then considers Byung-Chul Han’s theory of auto-exploitation and the dilemma of the music novel at a time where the rebellion of punk against social integration has been thoroughly incorporated into capitalism. Reading Marc Degens’ Fuckin Sushi (2015), I examine the novel’s concept of “Abrentnern” as a model for personal and communal fulfillment for those who turn to art as a means self-determination in the age of auto-exploitation. Unlike Kracht and Aydemir, however, Degens sees the closing off of historical possibilities for the good life enjoyed by his punk forbears—here, self-determination through transgressive artistic praxis—not as the contemporary subject’s damnation to cyclical patterns of despair but as a challenge to conceive of the good life anew. Working humorously through its hapless protagonist Niels’ repeated attempts to escape the seemingly inevitable for-profit co-option of his sincere artistic efforts, the novel serves to unveil the persistence of blind spots in this regime of totalizing exploitation. What results is an account of the double-edged logic of capitalist productivity’s ostensible totalization of labor-time. Capitalism, Niels unwittingly discovers, is a logic of production so overwhelming that it continuously drives subjects towards the discovery of new alterities that, for a brief time at least, allow subjects once again to slip between the cracks. The third chapter explores a similar phenomenon of halting resistance to the conditions of the capitalist present through the lens of futurity. Here, I push back against Mark Fisher’s theory of the dominance of “Capitalist Realism” in the contemporary aesthetic imagination, identifying and developing the notion of “subtle futurity”—the modest, yet resolute rephrasing of future possibility beyond the “way things are” of the present—in Leif Randt’s Schimmernder Dunst über CobyCounty (2011) In this light, I argue, Randt’s gestures towards a different future, however halting, mark a significant effort to imagine a benevolent form of future possibility within the context of an era often suspected to have been exhausted of its utopian sentiment. The final two chapters turn to past-minded works that more forcefully repudiate notions of the present as static or closed off from the movement of history. Chapter Four considers W.G. Sebald’s 1995 novel, Die Ringe des Saturn, and The Caretaker’s 2012 album, Patience (After Sebald), developing an account of the chronotopic means by which these works revisit materials of the past within the present. Chronotopic motifs of paraphrase—techniques of sampling in The Caretaker and narrative polyphony in Sebald—come together within macro-level chronotopic frameworks of peripatetic movement—looping repetition in The Caretaker and the retracing of bygone journeys in Sebald—to testify to the unanswered questions and unfinished work of history over and against notions of the present as a time where the past has been relegated to mere museum content or nostalgia for bygone ways of living. Where Chapter Four speaks primarily to the formal mechanisms by which the present rediscovers the past, Chapter Five examines two specific chronotopic innovations for thematically engaging constellations of past-present inter-temporality. Both Sharon Dodua Otoo’s 2021 novel, Adas Raum, and Christian Petzold’s 2018 film, Transit, develop chronotopes wherein past and present are intermingled in increasingly inseparable ways. Adas Raum, I demonstrate, is organized spatiotemporally as a nexus of coiled loops—pasts and presents intertwine, heaven and earth are tangled together, and the fates of human beings and even non-human objects follow spatial and temporal trajectories that weave in and out of conventional linear understandings of space and time. In similar fashion, past and present become inseparable in Petzold’s film, an adaptation of the Anna Seghers’ 1944 novel of the same name, through thematic and formal approaches of blurring that blend the plight of refugees of Seghers’ era with those of Petzold’s present day. History, then, appears remarkably robust in these texts, unfolding accounts of how human beings living through their present might take guidance from the generations that preceded them in the struggle for a better world.