Waldhausen’s K-theory of the sphere spectrum (closely related to the algebraic K-theory of the integers) is naturally augmented as an S^{0}-algebra, and so has a Koszul dual. Classic work of Deligne...
Authors: Jack Morava
Citation:Research in the Mathematical Sciences
2015
2:8
Let K be an algebraically closed, complete non-Archimedean field. The purpose of this paper is to carefully study the extent to which finite morphisms of algebraic K-curves are controlled by certain combinatorial...
Authors: Omid Amini, Matthew Baker, Erwan Brugallé and Joseph Rabinoff
Citation:Research in the Mathematical Sciences
2015
2:7
In this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out our study, we use p-adic...
Authors: Nathan Kaplan, Jake Marcinek and Ramin Takloo-Bighash
Citation:Research in the Mathematical Sciences
2015
2:6
We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which approximates the dynamics of the Euler equations on the solid boundary of a cylindrical domain. We prove...
Authors: Thomas Y Hou and Pengfei Liu
Citation:Research in the Mathematical Sciences
2015
2:5
We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves. For fixed genus g, our moduli space is a stacky f...
Authors: Sarah Brodsky, Michael Joswig, Ralph Morrison and Bernd Sturmfels
Citation:Research in the Mathematical Sciences
2015
2:4
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of facets of a polytope with the vertices of the dual polytope to g...
Authors: Rainer Sinn
Citation:Research in the Mathematical Sciences
2015
2:3
In this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2,2t+1). We use this to define a family of q-series, the simples...
Authors: Kazuhiro Hikami and Jeremy Lovejoy
Citation:Research in the Mathematical Sciences
2015
2:2
Nahm sums are q-series of a special hypergeometric type that appear in character formulas in the conformal field theory, and give rise to elements of the Bloch group, and have interesting modularity properties. I...
Authors: Stavros Garoufalidis and Thang TQ Lê
Citation:Research in the Mathematical Sciences
2015
2:1
Recently, a beautiful paper of Andrews and Sellers has established linear congruences for the Fishburn numbers modulo an infinite set of primes. Since then, a number of authors have proven refined results, for...
Authors: Pavel Guerzhoy, Zachary A Kent and Larry Rolen
Citation:Research in the Mathematical Sciences
2014
1:17
Cryo-electron microscopy is a technique in structural biology for determining the 3D structure of macromolecules. A key step in this process is detecting common lines of intersection between unknown embedded i...
Authors: David Dynerman
Citation:Research in the Mathematical Sciences
2014
1:14
In this paper, we consider the Fourier coefficients of a special class of meromorphic Jacobi forms of negative index considered by Kac and Wakimoto. Much recent work has been done on such coefficients in the c...
Authors: Kathrin Bringmann, Thomas Creutzig and Larry Rolen
Citation:Research in the Mathematical Sciences
2014
1:11
In recent work, Bhargava and Shankar have shown that the average size of the 2-Selmer group of an elliptic curve over is exactly 3, and Bhargava and Ho have shown that the average size of the 2-Selmer group in...
Authors: Zev Klagsbrun and Robert J Lemke Oliver
Citation:Research in the Mathematical Sciences
2014
1:15
We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin’s Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dime...
Authors: David H Yang
Citation:Research in the Mathematical Sciences
2014
1:10
We prove new bounds on the average sensitivity of the indicator function of an intersection of k halfspaces. In particular, we prove the optimal bound of
...
Authors: Daniel Kane
Citation:Research in the Mathematical Sciences
2014
1:13
Don Zagier suggested a natural construction, which associates a real number and p-adic numbers for all primes p to the cusp form g=Δ of weight 12. He claimed that these quantities constitute a rational adele. In ...
Authors: Pavel Guerzhoy
Citation:Research in the Mathematical Sciences
2014
1:7
Almost 40 years ago, H. Cohen formulated a conjecture about the modularity of a certain infinite family of functions involving the generating function of the Hurwitz class numbers of binary quadratic forms.
Authors: Michael H Mertens
Citation:Research in the Mathematical Sciences
2014
1:6
A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes p_{1}, p_{2} with |p_{1}-p_{2}| ≤ 600 as a consequence of the Bombieri-Vinogradov Theorem. In this paper, w...
Authors: Jesse Thorner
Citation:Research in the Mathematical Sciences
2014
1:4
In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field, we found that the moments (mean, variance, and higher moments) of novel statistics on set p...
Authors: Bobbie Chern, Persi Diaconis, Daniel M Kane and Robert C Rhoades
Citation:Research in the Mathematical Sciences
2014
1:2
In this paper, we relate umbral moonshine to the Niemeier lattices - the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice, we attach a finite gro...
Authors: Miranda CN Cheng, John FR Duncan and Jeffrey A Harvey
Citation:Research in the Mathematical Sciences
2014
1:3