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1.
Reschke, Paul.
Cohomological Insights for *Complex* Surface Automorphisms with Positive Entropy.

Degree: 2013, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/10162

I equate dynamical properties (e.g., positive entropy, existence of a periodic curve) of complex surface automorphisms with properties of the pull-back actions of such automorphisms on line bundles. I use these results to describe the measures of maximal entropy for positive-entropy surface automorphisms and to completely characterize the possible values of entropy for two-dimensional complex torus automorphisms.
*Advisors/Committee Members: DeMarco, Laura (advisor), Coskun, Izzet (committee member), Hadian-Jazi, Majid (committee member), Koch, Sarah (committee member), Takloo-Bighash, Ramin (committee member).*

Subjects/Keywords: Complex Dynamics; Entropy; Kahler Surfaces; Cohomological Actions; Complex Tori

…dimensional *complex* *tori* can be projective or non-projective, while
Enriques surfaces and rational… …*tori*: let X be
a two-dimensional *complex* torus, and let i be the involution on X coming from… …x29; describe the set of two-dimensional *complex* *tori* with infinite
automorphism groups in… …many different two-dimensional *complex* *tori*:
Theorem 1.9 Let λ be a Salem number such that… …The set of two-dimensional *complex* *tori* that admit automorphisms whose entropies are
log…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Reschke, P. (2013). Cohomological Insights for Complex Surface Automorphisms with Positive Entropy. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/10162

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Reschke, Paul. “Cohomological Insights for Complex Surface Automorphisms with Positive Entropy.” 2013. Thesis, University of Illinois – Chicago. Accessed July 10, 2020. http://hdl.handle.net/10027/10162.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Reschke, Paul. “Cohomological Insights for Complex Surface Automorphisms with Positive Entropy.” 2013. Web. 10 Jul 2020.

Vancouver:

Reschke P. Cohomological Insights for Complex Surface Automorphisms with Positive Entropy. [Internet] [Thesis]. University of Illinois – Chicago; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/10027/10162.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Reschke P. Cohomological Insights for Complex Surface Automorphisms with Positive Entropy. [Thesis]. University of Illinois – Chicago; 2013. Available from: http://hdl.handle.net/10027/10162

Not specified: Masters Thesis or Doctoral Dissertation

University of Lethbridge

2.
University of Lethbridge. Faculty of Arts and Science.
Strings on *complex* multiplication *tori* and rational conformal field theory with matrix level
.

Degree: 2013, University of Lethbridge

URL: http://hdl.handle.net/10133/3578

Conformal invariance in two dimensions is a powerful symmetry. Two-dimensional
quantum field theories which enjoy conformal invariance, i.e., conformal field theories
(CFTs) are of great interest in both physics and mathematics. CFTs describe the
dynamics of the world sheet in string theory where conformal symmetry arises as a
remnant of reparametrization invariance of the world-sheet coordinates. In statistical
mechanics, CFTs describe the critical points of second order phase transitions. On
the mathematics side, conformal symmetry gives rise to infinite dimensional chiral
algebras like the Virasoro algebra or extensions thereof. This gave rise to the study
of vertex operator algebras (VOAs) which is an interesting branch of mathematics.
Rational conformal theories are a simple class of CFTs characterized by a finite
number of representations of an underlying chiral algebra. The chiral algebra leads
to a set of Ward identities which gives a complete non-perturbative solution of the
RCFT. Identifying the chiral algebra of an RCFT is a very important step in solving
it. Particularly interesting RCFTs are the ones which arise from the compactificatin
of string theory as -models on a target manifold M. At generic values of the geo-
metric moduli of M, the corresponding CFT is not rational. Rationality can arise at
particular values of the modui of M. At these special values of the moduli, the chiral
algebra is extended. This interplay between the geometric picture and the algebraic
description encoded in the chiral algebra makes CFTs/RCFTs a perfect link between
physics and mathematics. It is always useful to find a geometric interpretation of a
chiral algebra in terms of a -model on some target manifold M. Then the next step
is to figure out the conditions on the geometric moduli of M which gives a RCFT.
In this thesis, we limit ourselves to the simplest class of string compactifications,
i.e., strings on tori. As Gukov and Vafa proved, rationality selects the complex-
multiplication tori. On the other hand, the study of the matrix-level affine algebra Um;K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of Um;K modular-invariant partition functions. Here we connect the
algebra U2;K to strings on 2-tori describable by rational conformal field theories. We
point out that the rational conformal field theories describing strings on complex-
multiplication tori have characters and partition functions identical to those of the
matrix-level algebra Um;K. This connection makes obvious that the rational theories
are dense in the moduli space of strings on Tm, and may prove useful in other ways.

Subjects/Keywords: rational conformal field theory; symmetry principles; complex multiplication tori; string theory; Conformal invariants; String models; Quantum field theory; Torus (Geometry); Mathematical physics; Mathematical analysis; General relativity (Physics); Dissertations, Academic

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Science, U. o. L. F. o. A. a. (2013). Strings on complex multiplication tori and rational conformal field theory with matrix level . (Thesis). University of Lethbridge. Retrieved from http://hdl.handle.net/10133/3578

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Science, University of Lethbridge. Faculty of Arts and. “Strings on complex multiplication tori and rational conformal field theory with matrix level .” 2013. Thesis, University of Lethbridge. Accessed July 10, 2020. http://hdl.handle.net/10133/3578.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Science, University of Lethbridge. Faculty of Arts and. “Strings on complex multiplication tori and rational conformal field theory with matrix level .” 2013. Web. 10 Jul 2020.

Vancouver:

Science UoLFoAa. Strings on complex multiplication tori and rational conformal field theory with matrix level . [Internet] [Thesis]. University of Lethbridge; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/10133/3578.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Science UoLFoAa. Strings on complex multiplication tori and rational conformal field theory with matrix level . [Thesis]. University of Lethbridge; 2013. Available from: http://hdl.handle.net/10133/3578

Not specified: Masters Thesis or Doctoral Dissertation

ETH Zürich

3. Maier, Alex G. On Simultaneous Equidistributing and Nondense Points for Noncommuting Endomorphisms.

Degree: 2017, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/130831

Subjects/Keywords: TORI (GEOMETRY); KOMPLEXE LIESCHE TRANSFORMATIONSGRUPPEN, ORBITS UND QUOTIENTENRÄUME (TOPOLOGIE); COMPLEX LIE TRANSFORMATION GROUPS, ORBITS AND QUOTIENT SPACES (TOPOLOGY); TORI (GEOMETRIE); GEOMETRIE HOMOGENER RÄUME UND LIESCHER GRUPPEN (DIFFERENTIALGEOMETRIE); GEOMETRY OF HOMOGENEOUS SPACES AND LIE GROUPS (DIFFERENTIAL GEOMETRY); info:eu-repo/classification/ddc/510; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Maier, A. G. (2017). On Simultaneous Equidistributing and Nondense Points for Noncommuting Endomorphisms. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/130831

Chicago Manual of Style (16^{th} Edition):

Maier, Alex G. “On Simultaneous Equidistributing and Nondense Points for Noncommuting Endomorphisms.” 2017. Doctoral Dissertation, ETH Zürich. Accessed July 10, 2020. http://hdl.handle.net/20.500.11850/130831.

MLA Handbook (7^{th} Edition):

Maier, Alex G. “On Simultaneous Equidistributing and Nondense Points for Noncommuting Endomorphisms.” 2017. Web. 10 Jul 2020.

Vancouver:

Maier AG. On Simultaneous Equidistributing and Nondense Points for Noncommuting Endomorphisms. [Internet] [Doctoral dissertation]. ETH Zürich; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/20.500.11850/130831.

Council of Science Editors:

Maier AG. On Simultaneous Equidistributing and Nondense Points for Noncommuting Endomorphisms. [Doctoral Dissertation]. ETH Zürich; 2017. Available from: http://hdl.handle.net/20.500.11850/130831