This text summarizes and expands the content of a general audience talk given
in 2018 at the University of Mainz. Motivated by recent developments in
dependent type theory and infinity category theory, it presents a history of
ideas around ...
Unbiased and Consistent Nested Sampling via Sequential Monte Carlo
May 10, 2018
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Statistics
Computation
Computation
We introduce a new class of sequential Monte Carlo methods called nested
sampling via sequential Monte Carlo (NS-SMC), which reformulates the essence of
the nested sampling method of Skilling (2006) in terms of sequential Monte
Carlo techni...
PBH abundance from random Gaussian curvature perturbations and a local
density threshold
May 10, 2018
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Physics
Cosmology and Nongalactic Astrophysics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
The production rate of primordial black holes is often calculated by
considering a nearly Gaussian distribution of cosmological perturbations, and
assuming that black holes will form in regions where the amplitude of such
perturbations exce...
A massive class of N=2 AdS4 IIA solutions
May 9, 2018
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Physics
High Energy Physics - Theory
We initiate a classification of N=2 supersymmetric AdS4
solutions of (massive) type IIA supergravity. The internal space is locally
equipped with either an SU(2) or an identity structure. We focus on the SU(2)
structure and ...
On the Generalized Class of PR-warped product
submanifolds in para-K\"{a}hler Manifolds
May 9, 2018
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Mathematics
Differential Geometry
Differential Geometry
In this paper, we study a new generalized class of
PR-warped product submanifolds under the name
PR-pseudo-slant warped product submanifolds in
para-K\"{a}hler manifolds Mˉ. The results of ...
Topological finiteness properties of monoids. Part 2: special monoids,
one-relator monoids, amalgamated free products, and HNN extensions
May 9, 2018
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Mathematics
Group Theory
Algebraic Topology
Rings and Algebras
We show how topological methods developed in a previous article can be
applied to prove new results about topological and homological finiteness
properties of monoids. A monoid presentation is called special if the
right-hand side of each r...
Graded multiplicity in harmonic polynomials from the Vinberg setting
May 8, 2018
Mathematics
Representation Theory
We consider Vinberg θ-groups associated to a cyclic quiver on r
nodes. Let K be the product of general linear groups associated to the nodes,
acting naturally on V=⊕Hom(Vi,Vi+1). We study the
harmonic polyno...
Loop structure on equivariant K-theory of semi-infinite flag manifolds
May 4, 2018
Mathematics
Algebraic Geometry
Quantum Algebra
Representation Theory
We explain that the Pontryagin product structure on the equivariant K-group
of an affine Grassmannian considered in [Lam-Schilling-Shimozono, Compos. Math.
{\bf 146} (2010)] coincides with the tensor structure on the equivariant
K-group...
A Time-Dependent Model of Dark Energy Based on Four-Dimensional
Continuous Deformation Theory
May 1, 2018
Physics
General Physics
In this article, we investigate the mechanism of cosmological expansion and
inflation by modeling dark energy as a four-dimensional continuous medium, with
its elastic deformation described by a four-dimensional vector field. We
demonstrate...
Parity sequences of the 3x+1 map on the 2-adic integers and Euclidean
embedding
April 30, 2018
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Mathematics
Dynamical Systems
Number Theory
Dynamical Systems
Number Theory
In this paper, we consider the one-to-one correspondence between a 2-adic
integer and its parity sequence under iteration of the so-called "3x+1" map.
First, we prove a new formula for the inverse transform. Next, we briefly
review what is ...