In this paper we identify the cotangent to the derived stack of
representations of a quiver Q with the derived moduli stack of modules over
the Ginzburg dg-algebra associated with Q. More generally, we extend this
result to finite type ...
Exact results on generalized Erd\H{o}s-Gallai problems
June 1, 2020
|
Mathematics
Combinatorics
Generalized Tur\'an problems have been a central topic of study in extremal
combinatorics throughout the last few decades. One such problem is maximizing
the number of cliques of size t in a graph of a fixed order that does not
contain an...
On the consistency of ZF with an elementary embedding from
Vλ+2 into Vλ+2
June 1, 2020
Mathematics
Logic
According to a theorem due to Kenneth Kunen, under ZFC, there is no ordinal
λ and non-trivial elementary embedding j:Vλ+2→Vλ+2. His proof relied on the Axiom of Choice (AC), and no proof from
ZF alone has been...
Twisted Quasi-elliptic cohomology and twisted equivariant elliptic
cohomology
May 31, 2020
Mathematics
Algebraic Topology
In this paper we construct a twisted version of quasi-elliptic cohomology.
This theory can be constructed as a K-theory of a loop space. After
establishing basic properties of the theory, including restriction,
change-of-group and induction...
Ridge Regularization: an Essential Concept in Data Science
May 30, 2020
Statistics
Computer Science
Methodology
Machine Learning
Machine Learning
Ridge or more formally ℓ2 regularization shows up in many areas of
statistics and machine learning. It is one of those essential devices that any
good data scientist needs to master for their craft. In this brief ridge fest I
have col...
Robertson's conjecture I. Well-quasi-ordering bounded tree-width graphs
by the topological minor relation
May 30, 2020
|
Mathematics
Combinatorics
Robertson and Seymour's celebrated Graph Minor Theorem states that graphs are
well-quasi-ordered by the minor relation. Unlike the minor relation, the
topological minor relation does not well-quasi-order graphs in general. Among
all known i...
Scattering theory for subcritical wave equation with inverse square
potential
May 29, 2020
| |
Mathematics
Analysis of PDEs
We consider the scattering theory for the defocusing energy subcritical wave
equations with an inverse square potential. By employing the energy flux method
we establish energy flux estimates on the light cone. Then by the
characteristic li...
Higher Complex Structures and Flat Connections
May 29, 2020
Mathematics
Physics
Differential Geometry
Mathematical Physics
Mathematical Physics
In 2018, Vladimir Fock and the author introduced a geometric structure on
surfaces, called higher complex structure, whose moduli space shares several
properties with Hitchin's component. In this paper, we establish various links
between fl...
Provably Good Solutions to the Knapsack Problem via Neural Networks of
Bounded Size
May 28, 2020
|
Computer Science
Statistics
Machine Learning
Computational Complexity
Discrete Mathematics
Neural and Evolutionary Computing
Machine Learning
The development of a satisfying and rigorous mathematical understanding of
the performance of neural networks is a major challenge in artificial
intelligence. Against this background, we study the expressive power of neural
networks through...
Higher R\'edei reciprocity and integral points on conics
May 28, 2020
|
Mathematics
Number Theory
Fix an integer l such that ∣l∣ is a prime 3 modulo 4. Let d>0 be
a squarefree integer and let Nd(x,y) be the principal binary quadratic form
of Q(d). Building on a breakthrough of Alexander Smith, we
give a...