EXPOSITIONS

  • Local-Search Techniques for Geometric Algorithms.
    Invited talk I gave at the Culminating Workshop of Bernoulli Semester on Discrete and Computational Geometry, Lausanne, November 2010.

  • The Centerpoint Theorem and its Relatives.
    Invited talk I gave at the Bernoulli conference on Discrete and Computational Geometry, Lausanne, August 2010.

  • Centerpoint theorem, Radon's theorem, Tverberg's theorem, Using Brouwer's fixed point theorem, Partitioning problems.
    This series of five lectures were given to undergraduate students at the LUMS math summer camp, Summer 2010.

  • An Invitation to Discrete Geometry.
    This talk was given to undergraduate/high school students to give them a flavor of problems in discrete geometry. Same as lecture 1 of the above link, March 2010.

  • Slides on the point-line incidences problem.
    Slides on constructing optimal cuttings using the Chazelle-Friedman sample-and-repair technique, Crossing Lemma proofs, and their use for point-line incidences problem. I tried to make the cutting construction as simple, clean and intuitive as possible, so that the later work of Clarkson-Varadarajan, Ezra et al. etc. is much simpler to understand. Given on January 2008.

  • Slides on Entropy.
    Slides on entropy, from a combinatorial point of view. How the entropy definition etc. falls out from the binomial bounds, and the use of entropy in Shannon's error-correcting theorem. Prepared Fall 2007.

  • Slides for the course "Complexity Theory".
    My complete set of slides, around 20 lectures worth, of the graduate course "Complexity Theory" are here. You are free to use these slides, but please refer to the source (this page, or the complexity course page). Email me if you would like the TeX source of these slides. Prepared in Spring 2007.