Statistics of Cohomological Automorphic Representations on Unitary
Groups via the Endoscopic Classification
December 22, 2022
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Mathematics
Number Theory
Representation Theory
Consider the family of automorphic representations on a unitary group with
cohomological factor π0​ at infinity and given split level. We compute
statistics of this family as the level goes to infinity. For unramified unitary
groups and...
A version of Hilbert's 16th Problem for 3D polynomial vector fields:
Counting isolated invariant tori
December 22, 2022
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Mathematics
Dynamical Systems
Hilbert's 16th Problem, about the maximum number of limit cycles of planar
polynomial vector fields of a given degree m, has been one of the most
important driving forces for new developments in the qualitative theory of
vector fields. In...
Transitioning from perturbative to non-perturbative splittings within
QCD jets
December 22, 2022
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Physics
High Energy Physics - Phenomenology
The study of Quantum Chromodynamics (QCD) at ultra-relativistic energies can
be performed in a controlled environment through lepton-hadron deep inelastic
scatterings. In such collisions, the high-energy partonic emissions that follow
from ...
Random walks and contracting elements III: Outer space and outer
automorphism group
December 22, 2022
Mathematics
Group Theory
Geometric Topology
Probability
Continuing from the author's previous article 'Random walks and contracting
elements I', we study random walks on (possibly asymmetric) metric spaces using
the bounded geodesic image property (BGIP) of certain isometries. As an
application,...
Random walks and contracting elements II: Translation length and
Quasi-isometric embedding
December 22, 2022
Mathematics
Probability
Group Theory
Geometric Topology
Continuing from a companion article: 'Random walks and contracting elements
I: Deviation inequality and limit laws', we study random walks on metric spaces
with contracting elements. We prove that random subgroups of the isometry group
of a...
The Selberg trace formula for spin Dirac operators on degenerating
hyperbolic surfaces
December 22, 2022
Mathematics
Differential Geometry
Analysis of PDEs
We investigate the spectrum of the spin Dirac operator on families of
hyperbolic surfaces where a set of disjoint simple geodesics shrink to 0,
under the hypothesis that the spin structure is non-trivial along each pinched
geodesic. The m...
Estimating network-mediated causal effects via principal components
network regression
December 22, 2022
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Statistics
Methodology
We develop a method to decompose causal effects on a social network into an
indirect effect mediated by the network, and a direct effect independent of the
social network. To handle the complexity of network structures, we assume that
laten...
Scalable Multi-Agent Reinforcement Learning for Warehouse Logistics with
Robotic and Human Co-Workers
December 22, 2022
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Computer Science
Machine Learning
Artificial Intelligence
Multiagent Systems
Robotics
We consider a warehouse in which dozens of mobile robots and human pickers
work together to collect and deliver items within the warehouse. The
fundamental problem we tackle, called the order-picking problem, is how these
worker agents must...
Learning to Detect and Segment for Open Vocabulary Object Detection
December 22, 2022
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Computer Science
Computer Vision and Pattern Recognition
Open vocabulary object detection has been greatly advanced by the recent
development of vision-language pretrained model, which helps recognize novel
objects with only semantic categories. The prior works mainly focus on
knowledge transferr...
Locally Constant Fibrations and Positivity of Curvature
December 22, 2022
Mathematics
Algebraic Geometry
Up to finite \'etale cover, any smooth complex projective variety X with
nef anti-canonical bundle is a holomorphic fibre bundle over a K-trivial
variety with locally constant transition functions. We show that this result is
optimal by...