Title	Refined tropical curve counting and motivic integration
Creator	Nicaise, Johannes
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-05-05T16:31
Description	Motivated by mathematical physics, Göttsche and Shende have defined "quantized" versions of certain enumerative invariants for linear systems on surfaces. Block and Göttsche have proposed formulas for the corresponding multiplicities for tropical curves, refining the classical tropical multiplicities. In certain cases, they were able to prove a correspondence theorem for these refined invariants. In joint work with Sam Payne and Franziska Schroeter, we suggest a geometric interpretation of the Block-Göttsche multiplicities as \(\chi_y\) genera of semi-algebraic analytic domains over the field of Puiseux series. In order to define and compute these \(\chi_y\) genera, we use the theory of motivic integration developed by Hrushovski and Kazhdan and we explore its connections with tropical geometry.
Extent	63 minutes
Subject	Mathematics; Algebraic geometry; Combinatorics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Imperial College
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2016-11-04
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0320903
URI	http://hdl.handle.net/2429/59650
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

Open Collections

BIRS Workshop Lecture Videos

Refined tropical curve counting and motivic integration Nicaise, Johannes

Description

Item Metadata

Item Media

Item Citations and Data

Rights