<p>The massive tome of <a href="http://dx.doi.org/10.1007/978-3-662-03338-8">Burgisser-Clausen-Shokrollahi</a> is the standard reference for algebraic complexity theory (and I'm not really sure there are others from the complexity point of view, though there are definitely others about algebraic algorithms), but doesn't do much of PIT. </p>

<p>The surveys of <a href="http://dx.doi.org/10.1561/0400000043">Chen-Kayal-Wigderson</a> (<a href="http://www.math.ias.edu/~avi/PUBLICATIONS/ChenKaWi2011.pdf">freely available from Wigderon's webpage</a>) and <a href="http://dx.doi.org/10.1561/0400000039">Shpilka-Yehudayoff</a> (<a href="http://www.cs.technion.ac.il/~shpilka/publications/SY10.pdf">freely available from Shpilka's webpage</a>) cover much more of the recent results on lower bounds and derandomizing PIT for small algebraic circuit classes.</p>

<p><a href="http://www.cse.iitk.ac.in/users/manindra/survey/Determinant.pdf">Agrawal's 2006 ICM address</a> gives a good overview of the permanent versus determinant problem, and despite being 8 years old is still fairly up to date. (I think the only more recent lower bound is <a href="http://arxiv.org/abs/1004.4802">Landsberg-Manivel-Ressayre</a>, which gets the same lower bound but for approximative determinantal complexity instead of just determinantal complexity.) </p>

CC BY-SA 3.0
2014-07-10T16:22:34.247Z
2014-07-10T16:22:34.247Z
Joshua Grochow
<p>I want to learn about algebraic algorithms and complexity thoery. In particular, I am interested in PIT.</p>

<p>Is there a set of lecture notes, books, papers and surveys for students who have read standard textbook about theory like Sipser's book or the Arora-Barak's complexity textbook. </p>

<p>The set of references will includes recent advanced results. </p>

<cc.complexity-theory><reference-request><algebraic-complexity><arithmetic-circuits>
A course for learning algebraic complexity
shen
# A course for learning algebraic complexity

(Asked by: username_0 on 2014-07-10)

I want to learn about algebraic algorithms and complexity thoery. In particular, I am interested in PIT.

Is there a set of lecture notes, books, papers and surveys for students who have read standard textbook about theory like Sipser's book or the Arora-Barak's complexity textbook.

The set of references will includes recent advanced results.

**Tags:** cc.complexity-theory, reference-request, algebraic-complexity, arithmetic-circuits

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## 1 answers

### Answer by username_1 on 2014-07-10. Score: 8

The massive tome of [Burgisser-Clausen-Shokrollahi](http://dx.doi.org/10.1007/978-3-662-03338-8) is the standard reference for algebraic complexity theory (and I'm not really sure there are others from the complexity point of view, though there are definitely others about algebraic algorithms), but doesn't do much of PIT.

The surveys of [Chen-Kayal-Wigderson](http://dx.doi.org/10.1561/0400000043) ([freely available from Wigderon's webpage](http://www.math.ias.edu/~avi/PUBLICATIONS/ChenKaWi2011.pdf)) and [Shpilka-Yehudayoff](http://dx.doi.org/10.1561/0400000039) ([freely available from Shpilka's webpage](http://www.cs.technion.ac.il/~shpilka/publications/SY10.pdf)) cover much more of the recent results on lower bounds and derandomizing PIT for small algebraic circuit classes.

[Agrawal's 2006 ICM address](http://www.cse.iitk.ac.in/users/manindra/survey/Determinant.pdf) gives a good overview of the permanent versus determinant problem, and despite being 8 years old is still fairly up to date. (I think the only more recent lower bound is [Landsberg-Manivel-Ressayre](http://arxiv.org/abs/1004.4802), which gets the same lower bound but for approximative determinantal complexity instead of just determinantal complexity.)


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