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IITM
CS6845 - Pseudorandomness
Jan-May : 2020
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Today : Sat, Apr 20, 2024
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Jan 13 : First Lecture on Jan 13 at 8am.
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Meetings
Click on the theme item for the meeting plan for that theme.
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Theme 1 : Introduction and Overview
- 4 meetings
Meeting 01 : Mon, Jan 13, 08:00 am-08:50 am
Power of randomized algorithms. Examples. Derandomization task. Algorithm independent formulation. Trivial derandomization. Idea of a pseudorandom generator. Pseudoradomness. Definition and overview.
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Power of randomized algorithms. Examples. Derandomization task. Algorithm independent formulation. Trivial derandomization. Idea of a pseudorandom generator. Pseudoradomness. Definition and overview.
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Meeting 02 : Tue, Jan 14, 12:00 pm-12:50 pm
Randomness Extractors. Linear codes. Expander graphs. Pseudorandom objects. Introduction of the context, explicit construction questions and connections.
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Randomness Extractors. Linear codes. Expander graphs. Pseudorandom objects. Introduction of the context, explicit construction questions and connections.
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Meeting 03 : Thu, Jan 16, 11:00 am-11:50 am
Amplification of success probability. Randomness efficient amplification challenge. Sipser's matrix argument. Explicit construction question. Hitting sets. Updated list of pseudorandom objects.
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Amplification of success probability. Randomness efficient amplification challenge. Sipser's matrix argument. Explicit construction question. Hitting sets. Updated list of pseudorandom objects.
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Meeting 04 : Fri, Jan 17, 10:00 am-10:50 am
Success probability amplification for one-sided error algorithms. Definition of Dispersers. Amplification algorithm. Explicitness requirement.
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Success probability amplification for one-sided error algorithms. Definition of Dispersers. Amplification algorithm. Explicitness requirement.
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Theme 2 : Probabilistic Method
- 6 meetings
Meeting 05 : Mon, Jan 20, 08:00 am-08:50 am
Details of the analysis using dispersers. <br> Review of basic probability. Probabilistic method argument. The first example, 2-colorability of uniform hypergraphs.
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Details of the analysis using dispersers.
Review of basic probability. Probabilistic method argument. The first example, 2-colorability of uniform hypergraphs.
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Meeting 06 : Tue, Jan 21, 12:00 pm-12:50 pm
Expectation method. Sum-free sets. Existence of a sumfree subset of size at least n/3 in any set of n integers. Review of Ramsey theory. Ramsey numbers, and the known bounds for the diagonal Ramsey number.
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Expectation method. Sum-free sets. Existence of a sumfree subset of size at least n/3 in any set of n integers. Review of Ramsey theory. Ramsey numbers, and the known bounds for the diagonal Ramsey number.
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Meeting 07 : Thu, Jan 23, 11:00 am-11:50 am
Lower bounding the Ramsey number R(s,s). Using the expectation based variant to lower bound chromatic number of a graph.
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Lower bounding the Ramsey number R(s,s). Using the expectation based variant to lower bound chromatic number of a graph.
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Meeting 08 : Fri, Jan 24, 10:00 am-10:50 am
Lovasz Local Lemma. Symmetric and Asymmetric versions. Deriving Asymmetric version from the symmetric version. Applying the symmetric version for 2-coloring intersection bounded uniform hypergraphs. Proof idea for asymetric version.
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Lovasz Local Lemma. Symmetric and Asymmetric versions. Deriving Asymmetric version from the symmetric version. Applying the symmetric version for 2-coloring intersection bounded uniform hypergraphs. Proof idea for asymetric version.
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Meeting 09 : Mon, Jan 27, 08:00 am-08:50 am
Proof of the asymmetric version of the lemma. Applying it to get newer Ramsey number bounds.
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Proof of the asymmetric version of the lemma. Applying it to get newer Ramsey number bounds.
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Meeting 10 : Tue, Jan 28, 12:00 pm-12:50 pm
Applying the basic method to Expander Graphs to show existence of expander graphs. Explicit construction of exapnder graphs. Algebraic constructions.
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Applying the basic method to Expander Graphs to show existence of expander graphs. Explicit construction of exapnder graphs. Algebraic constructions.
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Theme 3 : Expander Graphs
- 10 meetings
Meeting 11 : Fri, Jan 31, 10:00 am-10:50 am
Variants of expansion. Boundary expansion, Vertex expansion, Edge expansion. Spectral expansion. Spectral expansion implies edge expansion.
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Variants of expansion. Boundary expansion, Vertex expansion, Edge expansion. Spectral expansion. Spectral expansion implies edge expansion.
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Meeting 12 : Sat, Feb 01, 10:00 am-11:30 am
Cheeger's Inequality. Proof.
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Cheeger's Inequality. Proof.
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Meeting 13 : Tue, Feb 04, 12:00 pm-12:50 pm
Expander Mixing Lemma.
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Expander Mixing Lemma.
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Meeting 14 : Thu, Feb 06, 11:00 am-11:50 am
Every connected graph has a noticeable spectral gap.
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Every connected graph has a noticeable spectral gap.
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Meeting 15 : Fri, Feb 07, 10:00 am-10:50 am
Graph Products - Powering, Tensoring, Replacement Product.
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Graph Products - Powering, Tensoring, Replacement Product.
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Meeting 16 : Sat, Feb 08, 10:00 am-11:30 am
Spectral Analysis of Replacement Product. Combinatorial Analysis of Replacement Product.
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Spectral Analysis of Replacement Product. Combinatorial Analysis of Replacement Product.
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Meeting 17 : Mon, Feb 10, 08:00 am-08:50 am
Random Walks on Expanders.
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Random Walks on Expanders.
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Meeting 18 : Tue, Feb 11, 12:00 pm-12:50 pm
Amplifying success probability using Expanders. One-sided and Two-sided error version.
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Amplifying success probability using Expanders. One-sided and Two-sided error version.
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Meeting 19 : Thu, Feb 13, 11:00 am-11:50 am
Dispersers from Expanders
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Dispersers from Expanders
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Meeting 20 : Fri, Feb 14, 10:00 am-10:50 am
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Theme 4 : Unplanned
- 40 meetings
Meeting 21 : Mon, Feb 17, 08:00 am-08:50 am
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Meeting 22 : Tue, Feb 18, 12:00 pm-12:50 pm
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Meeting 23 : Thu, Feb 20, 11:00 am-11:50 am
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Meeting 24 : Fri, Feb 21, 10:00 am-10:50 am
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Meeting 25 : Mon, Feb 24, 08:00 am-08:50 am
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Meeting 26 : Tue, Feb 25, 12:00 pm-12:50 pm
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Meeting 27 : Thu, Feb 27, 11:00 am-11:50 am
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Meeting 28 : Fri, Feb 28, 10:00 am-10:50 am
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Meeting 29 : Mon, Mar 02, 08:00 am-08:50 am
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Meeting 30 : Tue, Mar 03, 12:00 pm-12:50 pm
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Meeting 31 : Thu, Mar 05, 11:00 am-11:50 am
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Meeting 32 : Fri, Mar 06, 10:00 am-10:50 am
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Meeting 33 : Mon, Mar 09, 08:00 am-08:50 am
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Meeting 34 : Tue, Mar 10, 12:00 pm-12:50 pm
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Meeting 35 : Thu, Mar 12, 11:00 am-11:50 am
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Meeting 36 : Fri, Mar 13, 10:00 am-10:50 am
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Meeting 37 : Mon, Mar 16, 08:00 am-08:50 am
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Meeting 38 : Tue, Mar 17, 12:00 pm-12:50 pm
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Meeting 39 : Thu, Mar 19, 11:00 am-11:50 am
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Meeting 40 : Fri, Mar 20, 10:00 am-10:50 am
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Meeting 41 : Mon, Mar 23, 08:00 am-08:50 am
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Meeting 42 : Tue, Mar 24, 12:00 pm-12:50 pm
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Meeting 43 : Thu, Mar 26, 11:00 am-11:50 am
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Meeting 44 : Fri, Mar 27, 10:00 am-10:50 am
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Meeting 45 : Mon, Mar 30, 08:00 am-08:50 am
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Meeting 46 : Tue, Mar 31, 12:00 pm-12:50 pm
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Meeting 47 : Thu, Apr 02, 11:00 am-11:50 am
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Meeting 48 : Fri, Apr 03, 10:00 am-10:50 am
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Meeting 49 : Mon, Apr 06, 08:00 am-08:50 am
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Meeting 50 : Tue, Apr 07, 12:00 pm-12:50 pm
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Meeting 51 : Thu, Apr 09, 11:00 am-11:50 am
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Meeting 52 : Fri, Apr 10, 10:00 am-10:50 am
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Meeting 53 : Mon, Apr 13, 08:00 am-08:50 am
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Meeting 54 : Tue, Apr 14, 12:00 pm-12:50 pm
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Meeting 55 : Thu, Apr 16, 11:00 am-11:50 am
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Meeting 56 : Fri, Apr 17, 10:00 am-10:50 am
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Meeting 57 : Mon, Apr 20, 08:00 am-08:50 am
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Meeting 58 : Tue, Apr 21, 12:00 pm-12:50 pm
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Meeting 59 : Thu, Apr 23, 11:00 am-11:50 am
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Meeting 60 : Fri, Apr 24, 10:00 am-10:50 am
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