相关论文: A survey of Gersten's conjecture

In this paper we investigate three unsolved conjectures in geometric combinatorics, namely Falconer's distance set conjecture, the dimension of Furstenburg sets, and Erdos's ring conjecture. We formulate natural $\delta$-discretized…

The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.

In this paper we are interested in the stability of the $2$-rank of the class group in the cyclotomic $\mathbb{Z}_2$-extension of real biquadratic fields. In fact, we give several families of real biquadratic fields $K$ such that $…

This paper is based on four lectures given at the Trieste Summer School 1994 on theories of fermion masses. The first two lectures introduce three mechanisms which have been used to construct models of fermion masses. We then discuss some…

In this paper we prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight, using congruences between Klingen Eisenstein series and…

In the lectures given at '96 Kashikojima Summer Institute, Amagi-Highland Seminars, and Yukawa Institute Workshop, the old-fashioned dualities and the theory of extended objects are reviewed, starting from 't Hooft-Mandelstam duality and…

In this Ph.D. thesis, we study tachyon condensation in string field theories. In chapter 2, we review Witten's bosonic string field theory and calculate the tachyon potential. In chapter 3, we calculate the tachyon potential in Berkovits'…

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological…

Bootstrapping and other resampling methods are increasingly appearing in the textbooks and curricula of courses that introduce undergraduate students to statistical methods. In order to teach the bootstrap well, students and instructors…

These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…

You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free…

A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to…

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.

Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…

In these proceedings, we review recent progress in analyzing the behavior of lower-dimensional supergravity theories when combined with swampland conjectures. We show that within supergravity the effectiveness and usefulness of swampland…

We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the Combinatorial Invariance Conjecture of the Kazhdan--Lusztig polynomials for the…