@article{BaumgaertelLledo1997,
  author    = {Baumg{\"a}rtel, Hellmut and Lled{\´o}, Fernando},
  title     = {Some results on superselection structures for C*-algebras with nontrivial center},
  isbn      = {981-02-3984-X},
  year      = {1997},
  language  = {en}
}
@article{BaumgaertelLledo1997,
  author    = {Baumg{\"a}rtel, Hellmut and Lled{\´o}, Fernando},
  title     = {Superselection structures for C*-algebras with nontrivial center},
  year      = {1997},
  language  = {en}
}
@book{BaumgaertelLledo2000,
  author    = {Baumg{\"a}rtel, Hellmut and Lled{\´o}, Fernando},
  title     = {Dual group actions on C*-algebras and their description by Hilbert extensions},
  series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  volume    = {445},
  journal   = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  publisher = {Techn. Univ.},
  address   = {Berlin},
  pages     = {14 S.},
  year      = {2000},
  language  = {en}
}
@phdthesis{Becker2005,
  author    = {Becker, Christian},
  title     = {On the Riemannian geometry of Seiberg-Witten moduli spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-5425},
  school      = {Universit{\"a}t Potsdam},
  year      = {2005},
  abstract  = {In this thesis, we give two constructions for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an L2-metric on Yang-Mills moduli spaces as given by Groisser and Parker. To construct a Riemannian metric on the total space of the Seiberg-Witten bundle in a similar way, we define the reduced gauge group as a subgroup of the gauge group. We show, that the quotient of the premoduli space by the reduced gauge group is isomorphic as a U(1)-bundle to the quotient of the premoduli space by the based gauge group. The total space of this new representation of the Seiberg-Witten bundle carries a natural quotient L2-metric, and the bundle projection is a Riemannian submersion with respect to these metrics. We compute explicit formulae for the sectional curvature of the moduli space in terms of Green operators of the elliptic complex associated with a monopole. Further, we construct a Riemannian metric on the cobordism between moduli spaces for different perturbations. The second construction of a Riemannian metric on the moduli space uses a canonical global gauge fixing, which represents the total space of the Seiberg-Witten bundle as a finite dimensional submanifold of the configuration space. We consider the Seiberg-Witten moduli space on a simply connected K\äuhler surface. We show that the moduli space (when nonempty) is a complex projective space, if the perturbation does not admit reducible monpoles, and that the moduli space consists of a single point otherwise. The Seiberg-Witten bundle can then be identified with the Hopf fibration. On the complex projective plane with a special Spin-C structure, our Riemannian metrics on the moduli space are Fubini-Study metrics. Correspondingly, the metrics on the total space of the Seiberg-Witten bundle are Berger metrics. We show that the diameter of the moduli space shrinks to 0 when the perturbation approaches the wall of reducible perturbations. Finally we show, that the quotient L2-metric on the Seiberg-Witten moduli space on a K\ähler surface is a K\ähler metric.},
  subject      = {Eichtheorie},
  language  = {en}
}
@article{Becker2014,
  author    = {Becker, Christian},
  title     = {Relative differential cohomology},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2112},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-07034-6; 978-3-319-07033-9},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-07034-6_2},
  pages     = {91 -- 180},
  year      = {2014},
  abstract  = {We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.},
  language  = {en}
}
@article{Becker2016,
  author    = {Becker, Christian},
  title     = {Cheeger-Chern-Simons Theory and Differential String Classes},
  series = {Annales de l'Institut Henri Poincar{\~A}©},
  volume    = {17},
  journal   = {Annales de l'Institut Henri Poincar{\~A}©},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-016-0485-6},
  pages     = {1529 -- 1594},
  year      = {2016},
  abstract  = {We construct new concrete examples of relative differential characters, which we call Cheeger-Chern-Simons characters. They combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. We study the differential cohomology of compact Lie groups G and their classifying spaces BG. We show that the even degree differential cohomology of BG canonically splits into Cheeger-Simons characters and topologically trivial characters. We discuss the transgression in principal G-bundles and in the universal bundle. We introduce two methods to lift the universal transgression to a differential cohomology valued map. They generalize the Dijkgraaf-Witten correspondence between 3-dimensional Chern-Simons theories and Wess-Zumino-Witten terms to fully extended higher-order Chern-Simons theories. Using these lifts, we also prove two versions of a differential Hopf theorem. Using Cheeger-Chern-Simons characters and transgression, we introduce the notion of differential trivializations of universal characteristic classes. It generalizes well-established notions of differential String classes to arbitrary degree. Specializing to the class , we recover isomorphism classes of geometric string structures on Spin (n) -bundles with connection and the corresponding spin structures on the free loop space. The Cheeger-Chern-Simons character associated with the class together with its transgressions to loop space and higher mapping spaces defines a Chern-Simons theory, extended down to points. Differential String classes provide trivializations of this extended Chern-Simons theory. This setting immediately generalizes to arbitrary degree: for any universal characteristic class of principal G-bundles, we have an associated Cheeger-Chern-Simons character and extended Chern-Simons theory. Differential trivialization classes yield trivializations of this extended Chern-Simons theory.},
  language  = {en}
}
@article{BeckerBeniniSchenkeletal.2019,
  author    = {Becker, Christian and Benini, Marco and Schenkel, Alexander and Szabo, Richard J.},
  title     = {Cheeger-Simons differential characters with compact support and Pontryagin duality},
  series = {Communications in analysis and geometry},
  volume    = {27},
  journal   = {Communications in analysis and geometry},
  number    = {7},
  publisher = {International Press of Boston},
  address   = {Somerville},
  issn      = {1019-8385},
  doi       = {10.4310/CAG.2019.v27.n7.a2},
  pages     = {1473 -- 1522},
  year      = {2019},
  abstract  = {By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125 (2003), 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.},
  language  = {en}
}
@misc{BeckerSchenkelSzabo2017,
  author    = {Becker, Christian and Schenkel, Alexander and Szabo, Richard J.},
  title     = {Differential cohomology and locally covariant quantum field theory},
  series = {Reviews in Mathematical Physics},
  volume    = {29},
  journal   = {Reviews in Mathematical Physics},
  number    = {1},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0129-055X},
  doi       = {10.1142/S0129055X17500039},
  pages     = {42},
  year      = {2017},
  abstract  = {We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr{\´e}chet-Lie group structure on differential cohomology groups.},
  language  = {en}
}
@article{BeckusBellissardCornean2019,
  author    = {Beckus, Siegfried and Bellissard, Jean and Cornean, Horia},
  title     = {Holder Continuity of the Spectra for Aperiodic Hamiltonians},
  series = {Annales de l'Institut Henri Poincar{\´e}},
  volume    = {20},
  journal   = {Annales de l'Institut Henri Poincar{\´e}},
  number    = {11},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-019-00848-6},
  pages     = {3603 -- 3631},
  year      = {2019},
  abstract  = {We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Holder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.},
  language  = {en}
}
@misc{BeckusBellissardDeNittis2019,
  author    = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe},
  title     = {Corrigendum to: Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 - 2977]},
  series = {Journal of functional analysis},
  volume    = {277},
  journal   = {Journal of functional analysis},
  number    = {9},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2019.06.001},
  pages     = {3351 -- 3353},
  year      = {2019},
  abstract  = {A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.},
  language  = {en}
}
@article{BeckusBellissardDeNittis2020,
  author    = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe},
  title     = {Spectral continuity for aperiodic quantum systems},
  series = {Journal of mathematical physics},
  volume    = {61},
  journal   = {Journal of mathematical physics},
  number    = {12},
  publisher = {American Institute of Physics},
  address   = {Melville, NY},
  issn      = {0022-2488},
  doi       = {10.1063/5.0011488},
  pages     = {19},
  year      = {2020},
  abstract  = {This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson-Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay-Rudin-Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution.},
  language  = {en}
}
@article{BeckusEliaz2021,
  author    = {Beckus, Siegfried and Eliaz, Latif},
  title     = {Eigenfunctions growth of R-limits on graphs},
  series = {Journal of spectral theory / European Mathematical Society},
  volume    = {11},
  journal   = {Journal of spectral theory / European Mathematical Society},
  number    = {4},
  publisher = {EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut f{\"u}r Mathematik, Technische Universit{\"a}t},
  address   = {Berlin},
  issn      = {1664-039X},
  doi       = {10.4171/JST/389},
  pages     = {1895 -- 1933},
  year      = {2021},
  abstract  = {A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.},
  language  = {en}
}
@article{BeckusPinchover2020,
  author    = {Beckus, Siegfried and Pinchover, Yehuda},
  title     = {Shnol-type theorem for the Agmon ground state},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {2},
  publisher = {EMS Publishing House},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/296},
  pages     = {355 -- 377},
  year      = {2020},
  abstract  = {LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.},
  language  = {en}
}
@phdthesis{Behm1995,
  author    = {Behm, Sebastian},
  title     = {Pseudo-differential operators with parameters on manifolds with edges},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {149 Bl.},
  year      = {1995},
  language  = {en}
}
@phdthesis{Beinrucker2015,
  author    = {Beinrucker, Andre},
  title     = {Variable selection in high dimensional data analysis with applications},
  school      = {Universit{\"a}t Potsdam},
  pages     = {VII, 107},
  year      = {2015},
  language  = {en}
}
@article{BeinruckerDoganBlanchard2016,
  author    = {Beinrucker, Andre and Dogan, Urun and Blanchard, Gilles},
  title     = {Extensions of stability selection using subsamples of observations and covariates},
  series = {Statistics and Computing},
  volume    = {26},
  journal   = {Statistics and Computing},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0960-3174},
  doi       = {10.1007/s11222-015-9589-y},
  pages     = {1059 -- 1077},
  year      = {2016},
  abstract  = {We introduce extensions of stability selection, a method to stabilise variable selection methods introduced by Meinshausen and Buhlmann (J R Stat Soc 72:417-473, 2010). We propose to apply a base selection method repeatedly to random subsamples of observations and subsets of covariates under scrutiny, and to select covariates based on their selection frequency. We analyse the effects and benefits of these extensions. Our analysis generalizes the theoretical results of Meinshausen and Buhlmann (J R Stat Soc 72:417-473, 2010) from the case of half-samples to subsamples of arbitrary size. We study, in a theoretical manner, the effect of taking random covariate subsets using a simplified score model. Finally we validate these extensions on numerical experiments on both synthetic and real datasets, and compare the obtained results in detail to the original stability selection method.},
  language  = {en}
}
@article{BellingeriFrizPaychaetal.2022,
  author    = {Bellingeri, Carlo and Friz, Peter and Paycha, Sylvie and Preiß, Rosa Lili Dora},
  title     = {Smooth rough paths, their geometry and algebraic renormalization},
  series = {Vietnam journal of mathematics},
  volume    = {50},
  journal   = {Vietnam journal of mathematics},
  number    = {3},
  publisher = {Springer},
  address   = {Singapore},
  issn      = {2305-221X},
  doi       = {10.1007/s10013-022-00570-7},
  pages     = {719 -- 761},
  year      = {2022},
  abstract  = {We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the key to a purely algebraic form of Lyons' extension theorem, the renormalization of rough paths following up on [Bruned et al.: A rough path perspective on renormalization, J. Funct. Anal. 277(11), 2019], as well as a related notion of "sum of rough paths". We first develop our ideas in a geometric rough path setting, as this best resonates with recent works on signature varieties, as well as with the renormalization of geometric rough paths. We then explore extensions to the quasi-geometric and the more general Hopf algebraic setting.},
  language  = {en}
}
@article{Benini2016,
  author    = {Benini, Marco},
  title     = {Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies},
  series = {Journal of mathematical physics},
  volume    = {57},
  journal   = {Journal of mathematical physics},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.4947563},
  pages     = {1249 -- 1279},
  year      = {2016},
  abstract  = {Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincare duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincare duality for the new cohomology groups. Published by AIP Publishing.},
  language  = {en}
}
@article{BeniniCapoferriDappiaggi2017,
  author    = {Benini, Marco and Capoferri, Matteo and Dappiaggi, Claudio},
  title     = {Hadamard States for Quantum Abelian Duality},
  series = {Annales de l'Institut Henri Poincar{\´e}},
  volume    = {18},
  journal   = {Annales de l'Institut Henri Poincar{\´e}},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-017-0593-y},
  pages     = {3325 -- 3370},
  year      = {2017},
  abstract  = {Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a -algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states on this algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three -algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor and in the case of ultra-static globally hyperbolic spacetimes with compact Cauchy surfaces, we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors, we obtain a state for the full theory, ultimately implementing Abelian duality transformations as Hilbert space isomorphisms.},
  language  = {en}
}
@article{BeniniSchenkel2017,
  author    = {Benini, Marco and Schenkel, Alexander},
  title     = {Quantum Field Theories on Categories Fibered in Groupoids},
  series = {Communications in mathematical physics},
  volume    = {356},
  journal   = {Communications in mathematical physics},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-017-2986-7},
  pages     = {19 -- 64},
  year      = {2017},
  abstract  = {We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.},
  language  = {en}
}