相关论文: The Manin conjecture in dimension 2

Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.

We provide new sufficient conditions under which Ryser's conjecture holds.

We study the arithmetic of certain del Pezzo surfaces of degree 2. We produce examples of Brauer-Manin obstruction to the Hasse principle, coming from 2- and 4-torsion elements in the Brauer group.

These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate…

We present some new results on the cohomology of a large scope of SL\_2-groups in degrees above the virtual cohomological dimension; yielding some partial positive results for the Quillen conjecture in rank one. We combine these results…

This is a survey on Kawaguchi-Silverman conjecture.

This manuscript summarizes a series of three lectures on interactions of neutrinos . The lectures begin with a pedagogical foundation and then explore topics of interest to current and future neutrino oscillation and cross-section…

These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.

This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…

This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.

These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.

In the first part of these lectures the neutrino mixing hypothesis will be considered in detail. We will discuss the possible schemes of neutrino mixing and present the data of the recent experiments searching for effects due to…

We conjecture that the exceptional set in Manin's Conjecture has an explicit geometric description. Our proposal includes the rational point contributions from any generically finite map with larger geometric invariants. We prove that this…

We establish Manin's conjecture for a cubic surface split over Q and whose singularity type is 2A_2+A_1. For this, we make use of a deep result about the equidistribution of the values of a certain restricted divisor function in three…

Recently there was proposeda hypothesis about existence of the two large extradimensions. This hypothesis demands, e.g., modification of Newton law at submilimeter scale. In this brief report we show that this hypothesis cannot be correct…

This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.

This manuscript contains a detailed proof of the Poincare Conjecture. The arguments we present here are expanded versions of the ones given by Perelman in his three preprints posted in 2002 and 2003. This is a revised version taking in…

We classify codimension two analytic submanifolds X of projective space having the property that any line through a general point p having contact to order two with X at p automatically has contact to order three. We give applications to…

This is an introduction to Taubes's proof of the Weinstein conjecture, written for the AMS Current Events Bulletin. It is intended to be accessible to nonspecialists, so much of the article is devoted to background and context.