Below is a list of topics and papers. You need to read one paper from this list (or any related paper of your choice).

Here is a short-list that could be more useful. I think papers 1, 3, 4, 5, 10 are probably the most self-contained ones and possibly 2, 8, 9 as well.

- Decoding
Reed-Solomon code beyond the Error-correction diameter. by Madhu Sudan
- Trevisan's extractor. Extractors
and Pseudorandom Generators L Trevisan
- Hardness versus Randomness. Nisan-Wigderson.
- Lower bounds for AC_0 using Håstad's
Switching Lemma. J. Håstad, Almost Optimal
Lower Bounds for Small Depth Circuits.
- Lower bounds for monotone circuits. Lower bounds for the
monotone complexity of some Boolean function .
A. Razborov.
- New simpler proof of PCP Theorem by Irit
Dinur
- Lattice problems
in NP intersect coNP, Oded
Regev and Dorit Aharonov
- J. Kahn, M. Saks, and D. Sturtevant. A topological
approach to evasiveness. Combinatorica,
4:297--306, 1984.
- Pseudorandom Generator
for Space Bounded Computation by N. Nisan
- Klim Efremenko: 3-Query
Locally Decodable Codes of Subexponential Length
- Reingold's proof showing that UNDIRECTED-ST-CONNECTIVITY is in L .

List Decoding of Reed Solomon Codes:

- Decoding
Reed-Solomon code beyond the Error-correction diameter. by Madhu Sudan
- Improved
decoding of Reed-Solomon and algebraic-geometry codes (Madhu Sudan and Venkatesan Guruswami)
- Survey by Madhu Sudan List decoding:
Algorithms and applications. and Course Notes
- Limits to list decoding assuming hardness of Discrete
Log. On the list and
bounded distance decodibility of Reed-Solomon
codes.

Qi Cheng and Daqing Wan.

Applications of Coding Theory in Complexity:

- Some
Applications of Coding Theory in Computational Complexity Survey by Luca
Trevisan.
- Trevisan's extractor. Extractors
and Pseudorandom Generators L Trevisan
- Pseudorandom
generators without the XOR lemma (M. Sudan, L. Trevisan
and S. Vadhan)

Random self-reducibility:

- Random self reducibility for permanent, discrete log. On the
Hardness of the PermanentD.
Sivakumar, J. Cai and A. Pavan.
- On the
random-self-reducibility of complete sets. L. Fortnow
and J. Feigenbaum.
- On
Worst-Case to Average-Case Reductions for NP Problems (L. Trevisan and A. Bogdanov)

Derandomization of BPP under Hardness Assumptions:

- Hardness
versus Randomness Nisan-Wigderson.
- P=BPP
unless E has subexponential circuits: Derandomizing the XOR Lemma Impagliazzo-Wigderson
- Pseudorandom
generators without the XOR lemma (M. Sudan, L. Trevisan
and S. Vadhan)
- Derandomizing BPP - A survey ( Lecture notes ) by Avi Wigderson.

Derandomizing small space algorithms:

- Pseudorandom Generator
for Space Bounded Computation by N. Nisan
- RL is
contained in SC by N. Nisan.
- Algorithmic
Derandomization via Complexity Theory by D. Sivakumar

Limited Independence and Derandomization :

- Pairwise
Independence and Derandomization Survey by Luby and Wigderson.
- Simple
constructions of almost k-wise independent random variables N. Alon, O. Goldreich, J. Hastad and R. Peralta.
- Small-Bias Probability
Spaces: Efficient Constructions and Applications. Joseph Naor, Moni Naor.
- Algorithmic
Derandomization via Complexity Theory by D. Sivakumar

Extractor/Expander Constructions:

- Trevisan's extractor. Extractors
and Pseudorandom Generators L Trevisan
- Zig-zag expander construction
O. Reingold, S. Vadhan,
A. Wigderson. Entropy
Waves, The Zig-Zag
Graph Product, and New Constant-Degree Expanders and Extractors.
- Nati Linal
and Avi Wigderson's
course on Expander Graphs and Their Applications.
- Tutorial given by Salil Vadhan at FOCS `02: Randomness
Extractors and their Many Guises
- Reingold's proof showing that UNDIRECTED-ST-CONNECTIVITY is in L .

Communication complexity :

See the book by Nisan and Kushilevitz for background material.

- Information
theory methods in communication complexity D. Sivakumar,
Ziv Bar-Yossef, T.S. Jayram and S. Ravi Kumar.
- An
information statistics approach to data stream and communication
complexity D. Sivakumar, Ziv
Bar-Yossef, T.S. Jayram,
and Ravi Kumar
- Multiparty
Protocols, Pseudorandom Generators for Logspace,
and Time-Space Tradeoffs Laszlo Babai, Noam
Nisan, Mario Szegedy.

Circuit Lower Bounds using Communication Complexity:

- Chapters 10 and 11 of Kushilevitz
Nisan.
- Approach to ACC^0 via number-on-forehead model (See
Princeton notes lecture
20)
- Circuit
Complexity and Communication Complexity lecture notes by Ran Raz
- Monotone
Circuits for Matching Require Linear DepthR.Raz, A.Wigderson

Circuit Lower bounds I:

- Lower bounds for AC_0 using Håstad's
Switching Lemma. J. Håstad, Almost Optimal
Lower Bounds for Small Depth Circuits.
- Lower bounds for monotone circuits. Lower bounds for the
monotone complexity of some Boolean function .
A. Razborov.
- Limits to current techniques. Natural Proofs A. Razborov and S. Rudich

Circuit Lower Bounds II (Algebraic Methods):

- Algebraic methods in the theory of lower bounds for
Boolean circuit complexity, by Roman Smolensky.
- Lower bounds for Montone Span
Programs. Superpolynomial lower bounds for monotone span
programs, by Laszlo Babai, Anna Gal and Avi Wigderson.
- Algebraic lower bounds for AC_0. The
Expressive Power of Voting Polynomials by J. Aspnes,
R. Beigel, M. Furst,
and S. Rudich.

Decision tree complexity and evasiveness:

- H. Buhrman and R. de Wolf. Complexity
Measures and Decision Tree Complexity: A Survey.
- Lecture
notes on Evasivenss of Graph Properties L. Lovasz and N. Young.
- J. Kahn, M. Saks, and D. Sturtevant. A topological
approach to evasiveness. Combinatorica,
4:297--306, 1984.
- Andrew Yao: Monotone Bipartite Graph Properties are
Evasive. SIAM J. Comput. 17(3): 517-520 (1988

Combinatorial Property Testing:

- O. Goldreich Combinatorial
Property Testing -- A Survey
- O. Goldreich Short Locally
Testable Codes and Proofs (survey)

Complexity of Lattice Problems:

- Lattice problems
in NP intersect coNP, Oded
Regev and Dorit Aharonov
- On the Limits of
Non-Approximability of Lattice Problems O. Goldreich and S. Goldwasser
- Hardness
of Approximating the Shortest Vector in a Lattice. Subhash
Khot.
- Complexity
of SVP---A reader's digest Ravi Kumar and D. Sivakumar

Quantum Computing:

- Shor's algorithm, Grover's
algorithm, Hidden subgroup problem. Umesh Vazirani's course on
Quantum Computing,
- Ronald de Wolf. Quantum
Communication and Complexity. Survey paper.
- Quantum
Computation and Lattice Problems, Oded Regev.

Foundations of Cryptography:

See the book of the same name by Oded Goldreich. Any single chapter could be a reasonable project

- One-way functions
- Pseudorandom generators for cryptography
- Zero-knowledge Proofs. (advanced)

PCPs and Hardness of Approximation:

- Proof of PCP Theorem. See Sanjeev Arora's
thesis.
- New simpler proof of PCP Theorem by Irit
Dinur.
- Hardness results for various problems. Notes from the
course on PCPs
and Hardness of Approximation . (Mail Subhash for the complete set of notes).
- Inapproximability of Combinatorial Optimization
Problems. Survey Paper by Luca Trevisan