Tuomas Orponen
Tuomas Orponen
These are lecture notes for a mini-course given in Banff in June 2024. They discuss the problem of bounding the number of δ -incidences I δ ( P , L ) : = { ( p , ℓ ) ∈ P × L : p ∈ [ ℓ ] δ } und...
Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal [0.03%]
热带模式理论中的投影超曲面（I）：Macaulay理想
Alex Fink,Jeffrey Giansiracusa,Noah Giansiracusa et al.
Alex Fink et al.
A "tropical ideal" is an ideal in the idempotent semiring of tropical polynomials that is also, degree by degree, a tropical linear space. We introduce a construction based on transversal matroids that canonically extends any principal idea...
Jonathan M Fraser
Jonathan M Fraser
Dimension interpolation is a novel programme of research which attempts to unify the study of fractal dimension by considering various spectra which live in between well-studied notions of dimension such as Hausdorff, box, Assouad and Fouri...
Period-like polynomials for L-series associated with half-integral weight cusp forms [0.03%]
与半整权重尖形式相关的L-级数的周期型多项式
James Branch,Nikolaos Diamantis,Wissam Raji et al.
James Branch et al.
Given the L-series of a half-integral weight cusp form, we construct polynomials behaving similarly to the classical period polynomial of an integral weight cusp form. We also define a lift of half-integral weight cusp forms to integral wei...
Domagoj Bradač,Jacob Fox,Benny Sudakov
Domagoj Bradač
The q-color Ramsey number of a k-uniform hypergraph G, denoted r(G; q), is the minimum integer N such that any coloring of the edges of the complete k-uniform hypergraph on N vertices contains a monochromatic copy of G. The study of these n...
Modular knots, automorphic forms, and the Rademacher symbols for triangle groups [0.03%]
模纽结、自守形式和三角群的Rademacher符号
Toshiki Matsusaka,Jun Ueki
Toshiki Matsusaka
É. Ghys proved that the linking numbers of modular knots and the "missing" trefoil K 2 , 3 in S 3 coincide with the values of a highly ubiquitous function called the Rademacher symbol for SL 2 Z . In this article, we replace SL 2 Z =...
Designing rotationally invariant neural networks from PDEs and variational methods [0.03%]
基于偏微分方程和变分方法设计旋转不变神经网络
Tobias Alt,Karl Schrader,Joachim Weickert et al.
Tobias Alt et al.
Partial differential equation models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desi...
Wonjun Lee,Siting Liu,Wuchen Li et al.
Wonjun Lee et al.
With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemics by the ...
The n-queens completion problem [0.03%]
n后问题
Stefan Glock,David Munhá Correia,Benny Sudakov
Stefan Glock
An n-queens configuration is a placement of n mutually non-attacking queens on an n × n chessboard. The n-queens completion problem, introduced by Nauck in 1850, is to decide whether a given partial configuration can be completed to a...
Jan Draisma,Felipe Rincón
Jan Draisma
Every tropical ideal in the sense of Maclagan-Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in trop...