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Intersections on moduli spaces of curves
Stockholm University, Faculty of Science, Department of Mathematics.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen , 2004. , 3 p.
Keyword [en]
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-238ISBN: 91-7265-933-5 (print)OAI: oai:DiVA.org:su-238DiVA: diva2:191347
Public defence
2004-10-01, sal 14, hus 5, Kräftriket, Stockholm, 10:15
Opponent
Supervisors
Available from: 2004-09-10 Created: 2004-09-10Bibliographically approved
List of papers
1. Polynomial Hurwitz Numbers and Intersections on \overline{\mathcal{M}}_{0,k}
Open this publication in new window or tab >>Polynomial Hurwitz Numbers and Intersections on \overline{\mathcal{M}}_{0,k}
2003 In: Functional analysis and its applications, ISSN 0016-2663, Vol. 37, no 1, 78-80 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23313 (URN)
Note
Part of urn:nbn:se:su:diva-238Available from: 2004-09-10 Created: 2004-09-10Bibliographically approved
2. Hurwitz numbers for generalised polynomials and two-pointed ramification cycles
Open this publication in new window or tab >>Hurwitz numbers for generalised polynomials and two-pointed ramification cycles
2003 In: Russian Mathematical Surveys, ISSN 1468-4829, Vol. 58, no 1, 195-196 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23314 (URN)
Note
Part of urn:nbn:se:su:diva-238Available from: 2004-09-10 Created: 2004-09-10Bibliographically approved
3. Geometry of meromorphic functions and intersections on moduli spaces of curves
Open this publication in new window or tab >>Geometry of meromorphic functions and intersections on moduli spaces of curves
2003 In: International mathematics research notices, ISSN 1073-7928, no 38, 2051-2094 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23315 (URN)
Note
Part of urn:nbn:se:su:diva-238Available from: 2004-09-10 Created: 2004-09-10Bibliographically approved
4. Intersections in Genus 3 and the Boussinesq Hierarchy
Open this publication in new window or tab >>Intersections in Genus 3 and the Boussinesq Hierarchy
2003 In: Letters in mathematical physics, ISSN 0377-9017, Vol. 65, no 2, 125-131 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-23316 (URN)
Note
Part of urn:nbn:se:su:diva-238Available from: 2004-09-10 Created: 2004-09-10Bibliographically approved
5. Some relations for Hurwitz numbers
Open this publication in new window or tab >>Some relations for Hurwitz numbers
2005 (English)In: Functional analysis and its applications, ISSN 0016-2663, E-ISSN 1573-8485, Vol. 39, no 02, 160-162 p.Article in journal (Refereed) Published
Abstract [en]

We obtain new relations for Hurwitz numbers of functions with one polynomial and one arbitrary critical value. (All other critical values are supposed to be simple.) This is a straightforward generalization of our earlier results on Hurwitz numbers of functions with one polynomial critical value.

Keyword
Hurwitz number - intersection
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-23317 (URN)10.1007/s10688-005-0032-6 (DOI)
Note
Part of urn:nbn:se:su:diva-238Available from: 2004-09-10 Created: 2004-09-10 Last updated: 2017-12-13Bibliographically approved
6. Combinatorics of binomial decomposition of the simplest Hodge integrals
Open this publication in new window or tab >>Combinatorics of binomial decomposition of the simplest Hodge integrals
In: Proceeding of the conference on Gromov-Witten invariants of spin curves and orbifoldsChapter in book (Other academic) Accepted
Identifiers
urn:nbn:se:su:diva-23318 (URN)
Note
Part of urn:nbn:se:su:diva-238Available from: 2004-09-10 Created: 2004-09-10Bibliographically approved

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