<?xml version="1.0" encoding="UTF-8"?>
<rss version="2.0"
	xmlns:content="http://purl.org/rss/1.0/modules/content/"
	xmlns:wfw="http://wellformedweb.org/CommentAPI/"
	xmlns:dc="http://purl.org/dc/elements/1.1/"
	xmlns:atom="http://www.w3.org/2005/Atom"
	xmlns:sy="http://purl.org/rss/1.0/modules/syndication/"
	xmlns:slash="http://purl.org/rss/1.0/modules/slash/"
	>

<channel>
	<title>Aleph Zero Categorical</title>
	<atom:link href="http://blog.jpolak.org/?feed=rss2" rel="self" type="application/rss+xml" />
	<link>http://blog.jpolak.org</link>
	<description>There Can Be Only One</description>
	<lastBuildDate>Thu, 13 Jun 2013 21:48:25 +0000</lastBuildDate>
	<language>en-US</language>
	<sy:updatePeriod>hourly</sy:updatePeriod>
	<sy:updateFrequency>1</sy:updateFrequency>
	<generator>http://wordpress.org/?v=3.5.1</generator>
		<item>
		<title>Graphing the Mandelbrot Set</title>
		<link>http://blog.jpolak.org/?p=1078</link>
		<comments>http://blog.jpolak.org/?p=1078#comments</comments>
		<pubDate>Thu, 13 Jun 2013 21:44:57 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[analysis]]></category>
		<category><![CDATA[elementary]]></category>
		<category><![CDATA[computation]]></category>
		<category><![CDATA[fractal]]></category>
		<category><![CDATA[mandelbrot set]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=1078</guid>
		<description><![CDATA[A class of fractals known as Mandelbrot sets, named after Benoit Mandelbrot, have pervaded popular culture and are now controlling us. Well, perhaps not quite, but have you ever wondered how they are drawn? Here is an approximation of one: From now on, Mandelbrot set will refer to the following set: for any complex number [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=1078</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Visualising the Real Orthogonal Group</title>
		<link>http://blog.jpolak.org/?p=1057</link>
		<comments>http://blog.jpolak.org/?p=1057#comments</comments>
		<pubDate>Sun, 09 Jun 2013 22:16:45 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[group-theory]]></category>
		<category><![CDATA[orthogonal group]]></category>
		<category><![CDATA[visualisation]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=1057</guid>
		<description><![CDATA[In the post Can You See in Four Dimensions?, we saw some ways of visualising functions plotted in four-dimensional &#8216;space&#8217; in various ways. Of course, we used colour and time for two dimensions because it is a bit difficult to plot in four actual spatial dimensions! Here is another example: the orthogonal group over the [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=1057</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Can You See in Four Dimensions?</title>
		<link>http://blog.jpolak.org/?p=998</link>
		<comments>http://blog.jpolak.org/?p=998#comments</comments>
		<pubDate>Sat, 08 Jun 2013 16:38:32 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[number-theory]]></category>
		<category><![CDATA[complex functions]]></category>
		<category><![CDATA[four dimensions]]></category>
		<category><![CDATA[visualisation]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=998</guid>
		<description><![CDATA[Have you ever tried to visualise the graph of a complex function ? The problem with complex functions is that usually we graph a complex number as an ordered pair on a Euclidean plane, which corresponds to . Unfortunately, this means that if we want to graph complex functions as we do real functions, we [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=998</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Preprints and Classics 2: Langlands, traces, derived</title>
		<link>http://blog.jpolak.org/?p=994</link>
		<comments>http://blog.jpolak.org/?p=994#comments</comments>
		<pubDate>Fri, 07 Jun 2013 19:01:45 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[math]]></category>
		<category><![CDATA[derived categories]]></category>
		<category><![CDATA[hyperbolic groups]]></category>
		<category><![CDATA[langlands]]></category>
		<category><![CDATA[preprints]]></category>
		<category><![CDATA[quivers]]></category>
		<category><![CDATA[traces]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=994</guid>
		<description><![CDATA[Here are some papers I&#8217;ve seen on the arXiv today that sound interesting: Schapira and Schneiders, Derived category of filtered objects Frenkel and Teleman, Geometric Langlands Correspondence Near Opers Chen and Zhu, Non-abelian Hodge theory for algebraic curves over characteristic p Nadler, Cyclic symmetries of A_n-quiver representations Furber and Jacobs, Towards a Categorical Account of [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=994</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Highlights in Linear Algebraic Groups 14: Singular Tori</title>
		<link>http://blog.jpolak.org/?p=984</link>
		<comments>http://blog.jpolak.org/?p=984#comments</comments>
		<pubDate>Fri, 07 Jun 2013 16:53:03 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[algebraic-geometry]]></category>
		<category><![CDATA[group-theory]]></category>
		<category><![CDATA[regular tori]]></category>
		<category><![CDATA[roots]]></category>
		<category><![CDATA[singular tori]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=984</guid>
		<description><![CDATA[From Highlights 12 and Highlights 13, we have gained quite a bit of information on connected reductive groups of semisimple rank 1. Recall, this means that has rank 1 where is the radical of , which is in turn the connected component of the unique maximal normal solvable subgroup of . But wait, why have [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=984</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Highlights in Linear Algebraic Groups 13: Centralisers of Tori</title>
		<link>http://blog.jpolak.org/?p=977</link>
		<comments>http://blog.jpolak.org/?p=977#comments</comments>
		<pubDate>Fri, 07 Jun 2013 16:40:29 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[algebraic-geometry]]></category>
		<category><![CDATA[group-theory]]></category>
		<category><![CDATA[centraliser]]></category>
		<category><![CDATA[reductive group]]></category>
		<category><![CDATA[semisimple rank 1]]></category>
		<category><![CDATA[torus]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=977</guid>
		<description><![CDATA[In Highlights 12, we used some of the equivalent conditions for a connected algebraic group over a field to have semisimple rank 1 in the study of reductive groups (these are the groups whose unipotent radical is trivial). Precisely, we showed that such a must have a semisimple commutator subgroup whose dimension is three, and [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=977</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Highlights in Linear Algebraic Groups 12: Radical, Reductive</title>
		<link>http://blog.jpolak.org/?p=965</link>
		<comments>http://blog.jpolak.org/?p=965#comments</comments>
		<pubDate>Fri, 07 Jun 2013 16:29:04 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[algebraic-geometry]]></category>
		<category><![CDATA[group-theory]]></category>
		<category><![CDATA[algebraic groups]]></category>
		<category><![CDATA[radical]]></category>
		<category><![CDATA[reductive]]></category>
		<category><![CDATA[semisimple]]></category>
		<category><![CDATA[solvable]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=965</guid>
		<description><![CDATA[To analyse the structure of a group G you will need the radical and a torus T. The group of Weyl may also may also suit to prevent the scattering of many a root. Functors are nice including the one of Lie Parabolics bring in the ge-o-metry! The theory of weights may seem oh so [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=965</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Homotopy on Chain Complexes</title>
		<link>http://blog.jpolak.org/?p=957</link>
		<comments>http://blog.jpolak.org/?p=957#comments</comments>
		<pubDate>Wed, 29 May 2013 01:13:54 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[homological-algebra]]></category>
		<category><![CDATA[homotopy]]></category>
		<category><![CDATA[model categories]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=957</guid>
		<description><![CDATA[Let be any associative ring with unit and an -module. If is a projective module and , is necessarily projective? The answer is yes, as the reader probably surmised. The argument is short: suppose is a surjective homomorphism and is any homomorphism. Then lifts to and is the appropriate lift of . A retraction of [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=957</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Wild Spectral Sequences Ep. 3: Cohomological Dimension</title>
		<link>http://blog.jpolak.org/?p=949</link>
		<comments>http://blog.jpolak.org/?p=949#comments</comments>
		<pubDate>Wed, 29 May 2013 01:05:00 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[group-theory]]></category>
		<category><![CDATA[homological-algebra]]></category>
		<category><![CDATA[cohomological dimension]]></category>
		<category><![CDATA[spectral sequence]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=949</guid>
		<description><![CDATA[Last time in Wild Spectral Squences 2, we saw how to prove the five lemma using a spectral sequence. Today, we&#8217;ll see a very simple application of spectral sequences to the concept of cohomological dimension in group cohomology. We will define the well-known concept of cohomological dimension of a group , and then show how [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=949</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Preprints and Classics 1: Higher cats, squarefree, max modulus</title>
		<link>http://blog.jpolak.org/?p=942</link>
		<comments>http://blog.jpolak.org/?p=942#comments</comments>
		<pubDate>Mon, 29 Apr 2013 01:59:42 +0000</pubDate>
		<dc:creator>Jason Polak</dc:creator>
				<category><![CDATA[category-theory]]></category>
		<category><![CDATA[measure-theory]]></category>
		<category><![CDATA[number-theory]]></category>
		<category><![CDATA[haar measure]]></category>
		<category><![CDATA[higher categories]]></category>
		<category><![CDATA[k theory]]></category>
		<category><![CDATA[links]]></category>
		<category><![CDATA[maximum modulus principle]]></category>
		<category><![CDATA[squarefree integers]]></category>

		<guid isPermaLink="false">http://blog.jpolak.org/?p=942</guid>
		<description><![CDATA[Mostly to take a break from marking exams, I thought I&#8217;d start a new recurring series here about mathematics papers and books that I find, both new and old. The &#8220;new&#8221; will consist mainly of preprints that look interesting (to encourage me to browse the arXiv) and the &#8220;old&#8221; will consists of papers I will [...]]]></description>
		<wfw:commentRss>http://blog.jpolak.org/?feed=rss2&#038;p=942</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
	</channel>
</rss>
