Related papers: Flops connect minimal models
Given a quasi-projective 3-fold X with only Gorenstein terminal singularities, we prove that the flop functors beginning at X satisfy higher degree braid relations, with the combinatorics controlled by a real hyperplane arrangement H. This…
We study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus…
This is a PhD Thesis on the connection between subfactors (more precisely, their corresponding fusion categories) and Conformal Field Theory (CFT). Besides being a mathematically interesting topic on its own, subfactors have also attracted…
This article focuses on the problem of predicting a response variable based on a network-valued predictor. Our motivation is the development of interpretable and accurate predictive models for cognitive traits and neuro-psychiatric…
We show in this work that homology in degree d of a congruence group, in a very general framework, defines a weakly polynomial functor of degree at most 2d and we describe this functor modulo polynomial functors of smaller degree. Our main…
In this paper, by introducing some kind of small loop transfer spaces at a point, we study the behavior of topologized fundamental groups with the compact-open topology and the whisker topology, $\pi_{1}^{qtop}(X,x_{0})$ and…
In this paper, we want to study the link between the presence of compact objects with some analytic structure and the global geometry of a weakly complete surface. We begin with a brief survey of some now classic results on the local…
For Hermitian connections on a Hermitian complex line bundle over a Riemannian manifold $(X,g)$, we can define the ``volume", which can be considered to be the ``mirror" of the standard volume for submanifolds. We call the critical points…
Weak feature representation problem has influenced the performance of few-shot classification task for a long time. To alleviate this problem, recent researchers build connections between support and query instances through embedding patch…
We describe a new class of minimal link diagrams. This class includes certain alternating diagrams, the standard diagrams of all torus links, and numerous homogeneous diagrams whose minimality has not been proven before. Besides, we…
Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer science. They also provide a natural framework for the…
Recent work on permutation-based model merging has shown impressive low- or zero-barrier mode connectivity between models from completely different initializations. However, this line of work has not yet extended to the Transformer…
This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely…
Minimal log discrepancies (mld's) are related not only to termination of log flips, and thus to the existence of log flips but also to the ascending chain condition (acc) of some global invariants and invariants of singularities in the Log…
Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard…
We first improve an old result of McMahon and show that a metric minimal flow whose enveloping semigroup contains less than $2^{\mathfrak{c}}$ (where ${\mathfrak{c}} ={2^{\aleph_0}}$) minimal left ideals is PI. Then we show the existence of…
We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of…
The latest ACT data release disfavors the attractor $n_s=1-2/N$. In inflationary models with nonminimal coupling, such attractors typically arise in the strong coupling limit. To align with observational constraints, we focus on nonminimal…
Model merging combines task experts into one model and avoids joint training, retraining, or deploying many expert models, but the merged model often still underperforms task experts. We study this performance gap through feature drift, the…
A phenomenological model is proposed which describes the effect of both dc and rf magnetic fields, $H$, on the microwave surface impedance, Z_s=R_s+jX_s, of a superconductor containing weak link. Two cases are considered; a weak link…