Yahoo! Research
111 W. 40th Street, 17th Floor
New York, NY 10018 (map)

goel AT yahoo-inc DOT com
Tel: 212-571-8149 (work)
Tel: 607-339-9903 (mobile)

EDUCATION
Research Fellow, Dept. of Mathematics, University of Southern California, 2006 - 2007
Research Fellow, Dept. of Mathematics, Stanford University, 2005 - 2006
PhD in Applied Mathematics, Cornell University, 2005
MS in Computer Science, Cornell University, 2003
BS in Mathematics, University of Chicago, 1999

Hello! I work in the social networks groups at Yahoo! Research. When I'm not doing math I like to relax by playing cello, and learning to play the sitar that I couldn't resist bringing back from India on a recent trip. If you're bored, check out two web projects I've worked on: Quirksome and Friendcast

2006-2007 (USC)

  • Math 407: Probability Theory (Spring Semester)
  • Math 218: Probability for Business
  • Math 407: Probability Theory (Fall Semester)
  • Math 506: Stochastic Processes

2005-2006 (Stanford University)

  • Summer Math Institute
  • Math 103: Matrix Theory and its Applications

2004-2005 (Cornell University)

  • Math 171: Statistical Theory and Application in the Real World
  • Math 112: Calculus II
  • Math Explorers Club
  • Expanding Your Horizons
  • Graduate Student School Outreach Program (GSSOP)

RESEARCH INTERESTS

  • Theoretical and applied probability
  • Quantitative analysis of finite Markov chains
  • Applied statistics

How many times do you need to shuffle a deck of cards before it is close to random? Intuitively, if you shuffle enough times, the order of the cards shouldn't depend on the initial order of the deck. This intuition was in fact confirmed already in the early twentieth century by Markov and Poincaré. But given 52 cards, exactly how many times do you need to shuffle the deck? 10? 100? 1000? More generally, while classical results show that under mild conditions finite Markov chains converge to equilibrium exponentially fast, those results help little in answering the type of non-asymptotic question posed above.

Much of my research deals with understanding the convergence behavior of finite Markov chains. Recently, I've also become interested in applications of Markov chain theory.

PUBLICATIONS/PREPRINTS

  • Pricing Combinatorial Markets for Tournaments
    With Yiling Chen and David Pennock (submitted).

  • Horseshoes in Multidimensional Scaling and Kernel Methods
    With Persi Diaconis and Susan Holmes (accepted).

  • Respondent-Driven Sampling as Markov Chain Monte Carlo
    With Matthew J. Salganik (submitted)

  • Analysis of Top to Bottom-k Shuffles
    Annals of Applied Probability, Vol 16, No. 1, February 2006, 30-55.

  • Mixing Time Bounds via the Spectral Profile
    With Ravi Montenegro and Prasad Tetali
    Electronic Journal of Probability, Vol 11, January 2006.

  • Modified Logarithmic Sobolev Inequalities for Some Models of Random Walk
    Stochastic Processes and Their Applications, Volume 114, November 2004, 51-79.

EXPOSITORY/MISCELLANEA

  • An Invisible Minority: Asian Americans in Mathematics
    Notices of the American Mathematical Society, Vol 53, No. 8, September 2006.

  • The Art of Anonymity: Exploring DC-Nets
    The UMAP Journal, Vol 26, No. 4, Winter 2005, 459-470.

  • Estimating Mixing Times: Techniques and Applications
    PhD Thesis, Cornell University, August 2005.

INVITED TALKS

  • Horseshoes in Multidimensional Scaling (slides)
    Probability Seminar, UC-Irvine Department of Mathematics, March 2007
    Probability Seminar, USC Department of Mathematics, March 2007
    Yahoo! Research Labs, February 2007
    Probability Seminar, UCLA Department of Mathematics, February 2007

  • Respondent-Driven Sampling as Markov Chain Monte Carlo (slides)
    Social Networks Symposium, John Jay College, August 2007
    USC Department of Mathematics, February 2007

  • Interpreting Eigenmaps
    Georgia Tech Department of Mathematics, April 2006

  • Shuffling Cards: Estimating Mixing Times for Finite Markov Chains
    Colloquium, Université de Montréal Département de Mathématiques, February 2006

  • Mixing Time Bounds Via the Spectral Profile
    Seymour Sherman Lecture and Conference, Indiana University, April 2006
    Probability Seminar, UC-Berkeley Department of Mathematics, April 2006
    Probability Seminar, Stanford University Department of Mathematics, October 2005
    Probability Seminar, UC-San Diego Department of Mathematics, October 2005

  • Mixing Times for Top to Bottom Shuffles
    Combinatorics Seminar, MIT Department of Mathematics, February 2005
    Probability Seminar, Cornell University Department of Mathematics, February 2005
    Workshop on Markov Chains, MSRI, January 2005
    Probability Seminar, UW-Madison Department of Mathematics, January 2005

  • Estimating Convergence Rates for Finite Markov Chains
    Probability Seminar, Univ of Toronto Dept. of Mathematics, December 2004