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        <h1>Simon Brain</h1>

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<a href="index.html">Home</a> &middot;

Research &middot;

<a href="talks.html">Talks</a> &middot;

<a href=“teaching.html”>Teaching</a> &middot;

<a href="cv.html">CV</a>


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<p>

<strong>Research Interests</strong>

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<p>

My research interests lie in noncommutative geometry and geometric analysis, in particular:

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            <div align="left">Yang-Mills theory in noncommutative geometry; moduli spaces of instantons on noncommutative four-manifolds;</div>

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          <li> <div align="left">noncommutative geometry of quantum groups and their homogeneous spaces;</div>

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            <div align="left”>complex structures on noncommutative homogeneous spaces; noncommutative twistor theory;</div>

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            <div align="left">unbounded (i.e. constructive) KK-theory and applications.</div>

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<strong>Publications</strong>

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In reverse chronological order of writing:


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<i>Operator Spaces and Noncommutative Geometry in Interaction</i> (with <a href="http://www.math.chalmers.se/~goffeng/index.xml" onclick="window.open(this.href);return false;">Magnus Goffeng</a>, <a href="http://findresearcher.sdu.dk:8080/portal/en/person/kaad" onclick="window.open(this.href);return false;">Jens Kaad</a> and <a href="https://www.analysis.uni-hannover.de/mesland.html" onclick="window.open(this.href);return false;">Bram Mesland</a>, Eds.)

Oberwolfach Reports 13 (2016, 267–295 (29pp)</div>


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<i>Gauge Theory for Spectral Triples and the Unbounded Kasparov Product</i> (with <a href="https://www.analysis.uni-hannover.de/mesland.html" onclick="window.open(this.href);return false;">Bram Mesland</a> and <a href="http://www.waltervansuijlekom.nl/" onclick="window.open(this.href);return false;">Walter D. van Suijlekom</a>). 

J. Noncommut. Geom. 10 (2016), 135–206 (72pp)</div>


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<i>The Gysin Sequence for Quantum Lens Spaces</i> (with <a href="http://www.math.ru.nl/~farici/" onclick="window.open(this.href);return false;">Francesca Arici</a> and <a href="http://www.dmi.units.it/~landi/" onclick="window.open(this.href);return false;">Giovanni Landi</a>). 

J. Noncommut. Geom. 9 (2015), 1077--1111 (35pp) </div>


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<i> The Noncommutative Topology of Anti-Self-Dual Gauge Fields</i>. 

J. Geom. Phys. 72 (2013), 34--53 (20pp) </div>


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<i>Moduli Spaces of Instantons on Toric Noncommutative Manifolds</i> (with <a href="http://www.dmi.units.it/~landi/" onclick="window.open(this.href);return false;">Giovanni Landi</a> and <a href="http://www.waltervansuijlekom.nl/" onclick="window.open(this.href);return false;">Walter D. van Suijlekom</a>),

Adv. Theor. Math. Phys. 17 (2013), 1129--1193 (65pp) </div>


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<i>Differential and Twistor Geometry of the Quantum Hopf Fibration</i> (with <a href="http://www.dmi.units.it/~landi/" onclick="window.open(this.href);return false;">Giovanni Landi</a>).

Commun. Math. Phys. 315 (2012), 489--530 (41pp) </div>


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<li><div align="left"> <i>The ADHM Construction of Instantons on Noncommutative Spaces</i> (with <a href="http://www.waltervansuijlekom.nl/" onclick="window.open(this.href);return false;">Walter D. van Suijlekom</a>).

Rev. Math. Phys. 23 (2011), 261--307 (47pp) </div>


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<i>The 3D Spin Geometry of the Quantum Two-Sphere</i> (with <a href="http://www.dmi.units.it/~landi/" onclick="window.open(this.href);return false;">Giovanni Landi</a>). 

Rev. Math. Phys. 22 (2010), 963--993 (31pp) </div>


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<i>Moduli Spaces of Noncommutative Instantons: Gauging Away Noncommutative Parameters</i> (with <a href="http://www.dmi.units.it/~landi/" onclick="window.open(this.href);return false;">Giovanni Landi</a>). 

Quart. J. Math. 63 (2012), 41--86 (46pp) </div>


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<i>Families of Monads and Instantons from a Noncommutative ADHM Construction</i> (with <a href="http://www.dmi.units.it/~landi/" onclick="window.open(this.href);return false;">Giovanni Landi</a>).

In "Quanta of Maths", a special volume of the Clay Mathematics Institute dedicated to Alain Connes. Clay Math. Proc. 11 (2010), 55--84 (30pp) </div>


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<i>Quantisation of Twistor Theory by Cocycle Twist</i> (with <a href="http://www.maths.qmul.ac.uk/~majid/Welcome.html/“ onclick="window.open(this.href);return false;">Shahn Majid</a>). 

Commun. Math. Phys. 284 (2008), 713--774 (62pp) </div>

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<p>
Preprints of some of these articles may be found here (courtesy of ArXiv) 

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