175 citations · 459 across the 17 of their papers we have counts for
18 papers
The geometric cobordism hypothesis
Daniel Grady, Dmitri Pavlov
We prove a generalization of the cobordism hypothesis of Baez--Dolan and Hopkins--Lurie for bordisms with arbitrary geometric structures, such as Riemannian metrics, complex and sy…
Extended field theories are local and have classifying spaces
Daniel Grady, Dmitri Pavlov
We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (infinity,d)-category of bordisms with geometric data, suc…
Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
Daniel Grady, Hisham Sati
We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. The conditions for lifting the latter to the former are identified using…
Twisted differential KO-theory
Daniel Grady, Hisham Sati
We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS).…
Ramond-Ramond fields and twisted differential K-theory
Daniel Grady, Hisham Sati
We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors o…
Cobordisms of global quotient orbifolds and an equivariant Pontrjagin-Thom construction
Daniel Grady
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometri…
Differential KO-theory: constructions, computations, and applications
Daniel Grady, Hisham Sati
We provide several constructions in differential KO-theory. First, we construct a differential refinement of the -genus and a pushforward leading to a Riemann-Roch theorem…
Higher-twisted periodic smooth Deligne cohomology
Daniel Grady, Hisham Sati
Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham co…
Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
Daniel Grady, Hisham Sati
We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' correspon…
Parametrized geometric cobordism and smooth Thom stacks
Daniel Grady, Hisham Sati
We develop a theory of parametrized geometric cobordism by introducing smooth Thom stacks. This requires identifying and constructing a smooth representative of the Thom functor ac…
Twisted smooth Deligne cohomology
Daniel Grady, Hisham Sati
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed…
Biologically Inspired Radio Signal Feature Extraction with Sparse Denoising Autoencoders
Benjamin Migliori, Riley Zeller-Townson, Daniel Grady +1
Automatic modulation classification (AMC) is an important task for modern communication systems; however, it is a challenging problem when signal features and precise models for ge…
Spectral sequences in smooth generalized cohomology
Daniel Grady, Hisham Sati
We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be o…
Primary operations in differential cohomology
Daniel Grady, Hisham Sati
We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a…
Massey products in differential cohomology via stacks
Daniel Grady, Hisham Sati
We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties a…
Robust classification of salient links in complex networks
Daniel Grady, Christian Thiemann, Dirk Brockmann
Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of t…
Modularity maximization and tree clustering: Novel ways to determine effective geographic borders
Daniel Grady, Rafael Brune, Christian Thiemann +2
Territorial subdivisions and geographic borders are essential for understanding phenomena in sociology, political science, history, and economics. They influence the interregional…
The structure of borders in a small world
C. Thiemann, F. Theis, D. Grady +2
Geographic borders are not only essential for the effective functioning of government, the distribution of administrative responsibilities and the allocation of public resources, t…