Relative plus constructions

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In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem—upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the beh ...

Let G be a finite subgroup of SU(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4/G, and conjecture a closed formula for their ge ...

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable p ...

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in Q-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to orders O in Q-division rings a ...

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localizatio ...

Maximally localized Wannier functions (MLWFs) are widely used in electronic-structure calculations. We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-like orbitals; these describe accurate ...

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we intr ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Chemical gas dispersion can represent a severe threat to human and animal lives, as well as to the environment. Constructing a map of the distribution of gas in a fast and reliable manner is critical to ensure accurate monitoring of at-risk facilities and ...

The immobilization of molecular catalysts imposes spatial constraints on their active site. We reveal that in bifunctional catalysis such constraints can also be utilized as an appealing handle to boost intrinsic activity through judicious control of the a ...

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

We present a lightweight goal-based model for multimodal, probabilistic trajectory prediction for urban driving. Previous conditioned-on-goal methods have used map information in order to establish a set of potential goals and then complete the correspondi ...

The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of E-infinity-ring spectra in various ways. In this work we first establish, in the context o ...

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the struc ...

In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...

The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of g ...

Relative plus constructions

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Cochains are all you need

Isogeny Problems with Level Structure

A DONALDSON-THOMAS CREPANT RESOLUTION CONJECTURE ON CALABI-YAU 4-FOLDS

Correspondence functors and duality

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Dense Packings via Lifts of Codes to Division Rings

Conditional Flatness, Fiberwise Localizations, And Admissible Reflections

Automated mixing of maximally localized Wannier functions into target manifolds

Collapse-invariant properties of spaces equipped with signals or directions

A Shadow Perspective on Equivariant Hochschild Homologies

Computational tools for twisted topological Hochschild homology of equivariant spectra

A Functional Perspective on Information Measures

Clustering and Informative Path Planning for 3D Gas Distribution Mapping: Algorithms and Performance Evaluation

Mapping Active Site Geometry to Activity in Immobilized Frustrated Lewis Pair Catalysts

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

A Lightweight Goal-Based model for Trajectory Prediction

The cotangent complex and Thom spectra

Subgroups of elliptic elements of the Cremona group

Homotopical relations between 2-dimensional categories and their infinity-analogues

Voss surfaces: A design space for geodesic gridshells