Teichmuller dynamics and Hodge theory /
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Author / Creator: | Filip, Simion, author. |
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Imprint: | 2016. Ann Arbor : ProQuest Dissertations & Theses, 2016 |
Description: | 1 electronic resource (126 pages) |
Language: | English |
Format: | E-Resource Dissertations |
Local Note: | School code: 0330 |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11674565 |
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035 | |a AAI10129449 | ||
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100 | 1 | |a Filip, Simion, |e author. | |
245 | 1 | 0 | |a Teichmuller dynamics and Hodge theory / |c Filip, Simion. |
260 | |c 2016. | ||
264 | 1 | |a Ann Arbor : |b ProQuest Dissertations & Theses, |c 2016 | |
300 | |a 1 electronic resource (126 pages) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
500 | |a Advisors: Alex Eskin Committee members: Madhav Vithal Nori. | ||
502 | |b Ph.D. |c University of Chicago, Division of the Physical Sciences, Department of Mathematics |d 2016. | ||
510 | 4 | |a Dissertation Abstracts International, |c Volume: 77-12(E), Section: B. | |
520 | |a This thesis is concerned with applications of Hodge theory in Teichmuller dynamics. Recall that the moduli space pairs (X, o) of Riemann surfaces with a holomorphic 1-form carries a natural action of the group SL(2,R). The diagonal subgroup gives the Teichmuller geodesic flow, while full SL(2,R)-orbits give Teichmuller disks. The work of Eskin, Mirzakhani, and Mohammadi shows that the closure of a Teichmuller disk is always an immersed submanifold, usually called an "affine invariant submanifold" since it carries an affine structure. | ||
520 | |a The first part of the thesis studies the Variation of Hodge Structures (VHS) over an affine manifold, and more generally over a Teichmuller disk. The affine manifold carries a finite measure and this allows one to extend many of the results in the ordinary theory of VHS to this setting. | ||
520 | |a The second part of the thesis studies the Variation of Mixed Hodge Structures that arises in this setting. It shows that a certain part of it is particularly simple --- it is split. This, in turn, allows for an algebraic characterization of affine manifolds. | ||
546 | |a English | ||
590 | |a School code: 0330 | ||
690 | |a Mathematics. | ||
710 | 2 | |a University of Chicago. |e degree granting institution. | |
720 | 1 | |a Alex Eskin |e degree supervisor. | |
856 | 4 | 0 | |u http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:10129449 |y ProQuest |
856 | 4 | 0 | |u https://dx.doi.org/10.6082/M1QN64NB |y Knowledge@UChicago |
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928 | |t Library of Congress classification |l Online |c UC-FullText |u https://dx.doi.org/10.6082/M1QN64NB |z Knowledge@UChicago |g ebooks |i 11097500 |