Please email me if you are interested in any of the papers I haven't yet uploaded.

PCPs and Hardness of Approximation
· SDP gaps and UGC-hardness for MaxCutGain.   With Ryan O'Donnell (FOCS 2006).
· New results for learning noisy parities and halfspaces.   With Vitaly Feldman, Parikshit Gopalan and Ashok Kumar Ponnuswami (FOCS 2006).
· Hardness of approximating the closest vector problem with pre-processing.   With Misha Alekhnovich, Guy Kindler, Nisheeth Vishnoi (FOCS 2005).
· Hardness of approximating the shortest vector problem in lattices.   (FOCS 2004, shared the Best Paper Award, invited to JACM)
· Ruling out PTAS for graph min-bisection, densest subgraph and bipartite clique.   (FOCS 2004, invited to SICOMP).
· Optimal inapproximability results for MAX-CUT and other two-variable CSPs ?   With Guy Kindler, Ryan Odonnell, Elchanan Mossel (FOCS 2004, invited to SICOMP)
· A new PCP outer verifier with applications to homogeneous linear equations and max-bisection.   With Jonas Holmerin (STOC 2004)
· Hardness of approximating the shortest vector problem in high \ell_p norms.   (FOCS 2003, Best Student Paper Award, invited to JCSS)
· A 3-query non-adaptive PCP with perfect completeness.   With Rishi Saket. (Complexity 2006)
· Vertex cover might be hard to approximate within 2-\epsilon.   With Oded Regev. (Complexity 2003, invited to JCSS)
· A strong inapproximability gap for a generalization of minimum bisection.   With Jonas Holmerin. (Complexity 2003)
· A new multilayered PCP and the hardness of hypergraph vertex cover.   With Irit Dinur, Venkatesan Guruswami, Oded Regev (STOC 2003, invited to JCSS, to appear in SICOMP)
· Hardness of coloring 3-colorable 3-uniform hypergraphs.   (FOCS 2002)
· Vertex Cover on k-Uniform Hypergraphs is Hard to Approximate within Factor (k-3-\epsilon).   With Irit Dinur, Venkatesan Guruswami (ECCC Report TR02-027)
· Hardness results for approximate hypergraph coloring.   (STOC 2002)
· On the power of unique 2-prover 1-round games.   (STOC/Complexity joint session, 2002)
· Improved inapproximability results for maxclique, chromatic number and approximate graph coloring.   (FOCS 2001, invited to JCSS)
· Query efficient PCPs with perfect completeness.   With Johan Hastad (FOCS 2001)

Metric Embeddings
· The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into L1.   With Nisheeth Vishnoi (FOCS 2005, shared the Best Paper Award, invited to JACM).
· Non-embeddability theorems via Fourier analysis.   With Assaf Naor (FOCS 2005).
· On earthmover distance, metric labeling, and 0-extension.   With Howard Karloff, Aranyak Mehta and Yuval Rabani (STOC 2006).
· Integrality gaps for sparsest cut and minimum linear arrangement problems.   With Nikhil Devanur, Rishi Saket and Nisheeth Vishnoi (STOC 2006).

Lower Bounds
· Cell-probe lower bounds for partial match problem.   With T.S. Jayram, S. Ravi Kumar, Yuval Rabani   (STOC 2003, invited to JCSS)
· Near-optimal lower bounds on the multi-party communication complexity of set-disjointness.   With Amit Chakrabarti, Xiaodong Sun (Complexity 2003)
· Evasiveness of subgraph containment and related properties.   With Amit Chakrabarti, Yaoyun Shi (In SICOMP, preliminary version in STACS 2001)
· Improved lower bounds on the randomized complexity of graph properties.   With Amit Chakrabarti (ICALP 2001)

Miscellaneous
· Fitting algebraic curves to noisy data.   With Sanjeev Arora (STOC 2002, invited to JCSS)
· Parameterized complexity of finding hereditary properties.   With Venkatesh Raman (COCOON 2000, invited to TCS)

Other Technical Writings
· Monotone span programs. Junior Thesis, IIT Bombay, 1998. Advisor :   Sundar Vishwanathan .
· Set systems with restricted intersections. Senior Thesis, IIT Bombay, 1999. Advisor : Sundar Vishwanathan.