Meetings

Click on the theme item for the meeting plan for that theme.Click on the meeting item for references, exercises, and additional reading related to it.

**Theme 1 : Counting Complexity**- 14 meetings- Meeting 01 : Tue, Jan 15, 12:00 pm-12:50 pm
- Meeting 02 : Thu, Jan 17, 11:00 am-11:50 am
- Meeting 03 : Fri, Jan 18, 10:00 am-10:50 am
- Meeting 04 : Mon, Jan 21, 08:00 am-08:50 am
- Meeting 05 : Tue, Jan 22, 12:00 pm-12:50 pm
- Meeting 06 : Thu, Jan 24, 11:00 am-11:50 am
- Meeting 07 : Fri, Jan 25, 10:00 am-10:50 am
- Meeting 08 : Tue, Jan 29, 12:00 pm-12:50 pm
- Meeting 09 : Thu, Jan 31, 11:00 am-11:50 am
- Meeting 10 : Sun, Feb 03, 02:00 pm-03:00 pm
- Meeting 11 : Sun, Feb 03, 03:00 pm-04:00 pm
- Meeting 12 : Mon, Feb 04, 08:00 am-08:50 am
- Meeting 13 : Tue, Feb 05, 12:00 pm-12:50 pm
- Meeting 14 : Thu, Feb 07, 11:00 am-11:50 am

Administrative Announcements, Course Plan. References Exercises Reading Administrative Announcements, Course Plan.References : None Counting vs Decision. #CYCLE is in P implies P = NP. Counting classess : FRP, #P, FPSPACE and inclusions and implications to decision world. References Exercises Reading Counting vs Decision. #CYCLE is in P implies P = NP. Counting classess : FRP, #P, FPSPACE and inclusions and implications to decision world.References : None The bits and value of the #P function. Counting as a generalization of NP, BPP, RP, PP and Parity P. NP is contained in PP. inclusions. References Exercises Reading The bits and value of the #P function. Counting as a generalization of NP, BPP, RP, PP and Parity P. NP is contained in PP. inclusions.References : None #P = FP if and only if PP = P. Harness among counting problems. The notion of hardness. Attempt 1 : parsimonious reductions. References Exercises Reading #P = FP if and only if PP = P. Harness among counting problems. The notion of hardness. Attempt 1 : parsimonious reductions.References : None #P-hardness definition. #SAT is #P-complete. #IND-SET is #P-complete. Shortcomings of the theory. General oracle query model of #P-completeness. References Exercises Reading #P-hardness definition. #SAT is #P-complete. #IND-SET is #P-complete. Shortcomings of the theory. General oracle query model of #P-completeness.References : None The permanent and the determinant functions. Combinatorial interpretation of permanent of matrix with 0-1 entries. Counting perfect matchings. References Exercises Reading The permanent and the determinant functions. Combinatorial interpretation of permanent of matrix with 0-1 entries. Counting perfect matchings.References : None Permanent if integer matrices. Combinatorial interpretation in terms of cycle covers. The upper bound of FP^#P. Permanent over {-1,0,1} matrices is #P-complete. Proof idea, Gadget construction. References Exercises Reading Permanent if integer matrices. Combinatorial interpretation in terms of cycle covers. The upper bound of FP^#P. Permanent over {-1,0,1} matrices is #P-complete. Proof idea, Gadget construction.References : None Details of #P-completeness reduction. Reduction from PERM(-1,0,1) to PERM(0,1,...,n), and then to PERM(0,1). References <a href="http://pages.cs.wisc.edu/~holger/papers/DHMTW12final.pdf">Page 10-11 of this paper</a>. Exercises Reading Counting complexity chapter in the Arora-Barak Textbook. The gadget is slightly more complicated than what we did in class - but that was the first one discovered by Valiant in 1979. Details of #P-completeness reduction. Reduction from PERM(-1,0,1) to PERM(0,1,...,n), and then to PERM(0,1).References : Page 10-11 of this paper. Reading : Counting complexity chapter in the Arora-Barak Textbook. The gadget is slightly more complicated than what we did in class - but that was the first one discovered by Valiant in 1979. Toda's Theorem. The basic steps. U-SAT : Valiant Vazirani Reduction. References Exercises Reading Toda's Theorem. The basic steps. U-SAT : Valiant Vazirani Reduction.References : None Hash families, Pairwise independent hashing. Proof of the uniqueness lemma. Reduction to Parity SAT. Amplification of success probability. Generalizations to show that PH BP-reduces to Parity-SAT. References Exercises Reading Hash families, Pairwise independent hashing. Proof of the uniqueness lemma. Reduction to Parity SAT. Amplification of success probability. Generalizations to show that PH BP-reduces to Parity-SAT.References : None Any language that BP-reduces to Parity-SAT can be decided with a counting oracle. Proof idea. Toda's polynomials. Details of the proof. References Exercises Reading Any language that BP-reduces to Parity-SAT can be decided with a counting oracle. Proof idea. Toda's polynomials. Details of the proof.References : None Success Probability Amplification. Derandomization Problem. NP vs BPP. References Exercises Reading Success Probability Amplification. Derandomization Problem. NP vs BPP.References : None Two consequences of amplification lemma BPP is in Sigma^2. BPP is in P/poly. References Exercises Reading Two consequences of amplification lemma BPP is in Sigma^2. BPP is in P/poly.References : None The class P/poly. Meyer's theorem (statement). Karp-Lipton Collapse theorem : If NP is contained in P/poly then PH Collapses. References Exercises Reading The class P/poly. Meyer's theorem (statement). Karp-Lipton Collapse theorem : If NP is contained in P/poly then PH Collapses.References : None **Theme 2 : Probablistic Proof Systems**- 19 meetings- Meeting 15 : Fri, Feb 08, 10:00 am-10:50 am
- Meeting 16 : Mon, Feb 11, 08:00 am-08:50 am
- Meeting 17 : Tue, Feb 12, 12:00 pm-12:50 pm
- Meeting 18 : Thu, Feb 14, 11:00 am-11:50 am
- Meeting 19 : Fri, Feb 15, 10:00 am-10:50 am
- Meeting 20 : Sat, Feb 16, 02:00 pm-03:00 pm
- Meeting 21 : Sat, Feb 16, 03:00 pm-04:00 pm
- Meeting 22 : Mon, Feb 18, 08:00 am-08:50 am
- Meeting 23 : Wed, Feb 20, 04:15 pm-05:30 pm
- Meeting 24 : Thu, Feb 21, 11:00 am-11:50 am
- Meeting 25 : Fri, Feb 22, 10:00 am-10:50 am
- Meeting 26 : Sat, Feb 23, 10:00 am-11:00 am
- Meeting 27 : Mon, Mar 11, 08:00 am-08:50 am
- Meeting 28 : Tue, Mar 12, 12:00 pm-12:50 pm
- Meeting 29 : Thu, Mar 14, 11:00 am-11:50 am
- Meeting 30 : Fri, Mar 15, 10:00 am-10:50 am
- Meeting 31 : Sat, Mar 16, 11:00 am-11:50 am
- Meeting 32 : Sat, Mar 16, 12:00 pm-12:50 pm
- Meeting 33 : Mon, Mar 18, 08:00 am-08:50 am

Interactive Proof Systems. Deterministic, Randomized. Protocol for GI-bar. Public vs Private randomness. References Exercises Reading Interactive Proof Systems. Deterministic, Randomized. Protocol for GI-bar. Public vs Private randomness.References : None Interactive Proofs for the permanent, LFKN protocol. References Exercises Reading Interactive Proofs for the permanent, LFKN protocol.References : None Arithmetization, LFKN protocol on the sum-expression. References Exercises Reading Arithmetization, LFKN protocol on the sum-expression.References : None Lecture cancelled. Compensatory lecture TBA. References Exercises Reading Lecture cancelled. Compensatory lecture TBA.References : None Shamir's degree reduction method. IP=PSPACE. PSPACE algorithm for IP. References Exercises Reading Shamir's degree reduction method. IP=PSPACE. PSPACE algorithm for IP.References : None Public Coin Protocols. The class AM. Protocol for GI-bar. Goldwaser-Sipser Set Lower Bound Protocol. References Exercises Reading Public Coin Protocols. The class AM. Protocol for GI-bar. Goldwaser-Sipser Set Lower Bound Protocol.References : None Perfect completeness for protocols. If GI is NP-complete then PH is in Sigma^2. References Exercises Reading Perfect completeness for protocols. If GI is NP-complete then PH is in Sigma^2.References : None Achieving perfect completeness for Arthur-Merlin Games. References Exercises Reading Achieving perfect completeness for Arthur-Merlin Games.References : None MA is contained in AM. <br> Set-Lower Bound is very general : From private coin protocol to public coin protocols. <br> Probabilistically Checkable Proofs, Basic definitions. GAP3SAT problem. References Exercises Reading MA is contained in AM.

Set-Lower Bound is very general : From private coin protocol to public coin protocols.

Probabilistically Checkable Proofs, Basic definitions. GAP3SAT problem.References : None qCSP, L is in PCP(O(log n), q) if and only if L reduces to qCSP. Reduction from qCSP to GAPSAT. References Exercises Reading qCSP, L is in PCP(O(log n), q) if and only if L reduces to qCSP. Reduction from qCSP to GAPSAT.References : None Inapproximability of Independent set Problem. GAPCSP to GAPIS. PCP for LIN, Attempts References Exercises Reading Inapproximability of Independent set Problem. GAPCSP to GAPIS. PCP for LIN, AttemptsReferences : None Proof in the long-code form. Need of linearity testing. Linearity testing. Local decoding. The proof of PCP for LIN. References Exercises Reading Proof in the long-code form. Need of linearity testing. Linearity testing. Local decoding. The proof of PCP for LIN.References : None Proof of Linearity testing. References Exercises Reading Proof of Linearity testing.References : None Generalization to Quadratic Programs. References Exercises Reading Generalization to Quadratic Programs.References : None Dinur's Proof of PCP theorem. The proof outline. Query reduction step. References Exercises Reading Dinur's Proof of PCP theorem. The proof outline. Query reduction step.References : None Degree reduction. References Exercises Reading Degree reduction.References : None Expanderization. References Exercises Reading Expanderization.References : None Gap Amplification (construction) References Exercises Reading Gap Amplification (construction)References : None Gap Amplification (argument). Alphabet reduction. References Exercises Reading Gap Amplification (argument). Alphabet reduction.References : None **Theme 3 : Circuit Complexity and Lower Bounds**- 24 meetings- Meeting 34 : Tue, Mar 19, 12:00 pm-12:50 pm
- Meeting 35 : Thu, Mar 21, 11:00 am-11:50 am
- Meeting 36 : Fri, Mar 22, 10:00 am-10:50 am
- Meeting 37 : Sat, Mar 23, 04:30 pm-05:30 pm
- Meeting 38 : Sat, Mar 23, 05:30 pm-06:30 pm
- Meeting 39 : Mon, Mar 25, 08:00 am-08:50 am
- Meeting 40 : Tue, Mar 26, 10:00 am-10:50 am
- Meeting 41 : Thu, Mar 28, 11:00 am-11:50 am
- Meeting 42 : Mon, Apr 01, 08:15 am-08:50 am
- Meeting 43 : Tue, Apr 02, 12:00 pm-12:50 pm
- Meeting 44 : Thu, Apr 04, 11:00 am-11:50 am
- Meeting 45 : Fri, Apr 05, 10:00 am-10:50 am
- Meeting 46 : Sat, Apr 06, 08:15 am-09:15 am
- Meeting 47 : Sat, Apr 06, 09:15 am-10:15 am
- Meeting 48 : Mon, Apr 08, 12:00 pm-12:50 pm
- Meeting 49 : Tue, Apr 09, 12:00 pm-12:50 pm
- Meeting 50 : Fri, Apr 12, 10:00 am-10:50 am
- Meeting 51 : Mon, Apr 15, 08:00 am-08:50 am
- Meeting 52 : Tue, Apr 16, 12:00 pm-12:50 pm
- Meeting 53 : Thu, Apr 18, 11:00 am-11:50 am
- Meeting 54 : Fri, Apr 19, 10:00 am-10:50 am
- Meeting 55 : Mon, Apr 22, 08:00 am-08:50 am
- Meeting 56 : Tue, Apr 23, 12:00 pm-12:50 pm
- Meeting 57 : Wed, Apr 24, 05:30 pm-06:30 pm

Boolean Circuit Model of Computation. The first few questions. Why circuits? Connections to parallel algorithm design. The relevant parameters of the circuit model - Size, depth, fanin. <br> What is allowed as a gate? Basis and completeness. Post's characterization of a complete basis (statement). References Class notes. Exercises Reading Boolean Circuit Model of Computation. The first few questions. Why circuits? Connections to parallel algorithm design. The relevant parameters of the circuit model - Size, depth, fanin.

What is allowed as a gate? Basis and completeness. Post's characterization of a complete basis (statement).References : Class notes. P/poly = functions computed by polynomial sized circuits. The circuit lower-bound problem. Uniformity, Log-space Uniformity. P is computed by uniform polysize circuits. Review of parameters and questions. References Exercises Reading P/poly = functions computed by polynomial sized circuits. The circuit lower-bound problem. Uniformity, Log-space Uniformity. P is computed by uniform polysize circuits. Review of parameters and questions.References : None Shannon's counting argument. Lupanov's construction. References Exercises Reading Shannon's counting argument. Lupanov's construction.References : None Gate Elimination Argument for Circuit Lower Bounds. Lower bounds for Parity and Threshold. References Exercises Reading Gate Elimination Argument for Circuit Lower Bounds. Lower bounds for Parity and Threshold.References : None Simple functions and their circuits, PARITY, ADD. References Exercises Reading Simple functions and their circuits, PARITY, ADD.References : None The class NC.The class AC-hierarchy. Interleaving with NC hierarchy. Uniform NC^1 is contained in L. References Exercises Reading The class NC.The class AC-hierarchy. Interleaving with NC hierarchy. Uniform NC^1 is contained in L.References : None NL is contained in uniform-AC^1. Back to NC^1, Adding n, n-bit numbers. Trivial AC^1 upper bound. Offman's technique and the NC^1 upper bound. Majority in NC^1. Constant depth reductions. References Exercises Reading NL is contained in uniform-AC^1. Back to NC^1, Adding n, n-bit numbers. Trivial AC^1 upper bound. Offman's technique and the NC^1 upper bound. Majority in NC^1. Constant depth reductions.References : None Zooming in to NC^1. Review of constant depth reductions. <br>Six Problems : ADD(n,n). MULT(2,n), Th(n,k), BCOUNT, MAJ. <br>NC^1 upper bounds. Constant depth reductions among these problems. Motivation and definition of the class TC^0. References Exercises Reading Zooming in to NC^1. Review of constant depth reductions.

Six Problems : ADD(n,n). MULT(2,n), Th(n,k), BCOUNT, MAJ.

NC^1 upper bounds. Constant depth reductions among these problems. Motivation and definition of the class TC^0.References : None Symmetric Functions are in TC^0. Motivation and definition of the class ACC^0. The hierarchy interleaving with NC and AC hierarchies. References Exercises Reading Symmetric Functions are in TC^0. Motivation and definition of the class ACC^0. The hierarchy interleaving with NC and AC hierarchies.References : None Formulas, BF = NC^1. Formula size lower bounds, References Exercises Reading Formulas, BF = NC^1. Formula size lower bounds,References : None Sabbotavskaya's Lower bound using Restrictions. Lower Bounds for Parity. References Exercises Reading Sabbotavskaya's Lower bound using Restrictions. Lower Bounds for Parity.References : None Nechiporuk's Method. Lower bound for Indirect Access function. References Exercises Reading Nechiporuk's Method. Lower bound for Indirect Access function.References : None Proof of Nechiporuk's Theorem. References Exercises Reading Proof of Nechiporuk's Theorem.References : None Nechiporuk's "hardness embedding" technique. Extensions of Sabotavskaya's argument to random restrictions. Andreev's Lower Bound. Shrinkage Exponent. References Exercises Reading Nechiporuk's "hardness embedding" technique. Extensions of Sabotavskaya's argument to random restrictions. Andreev's Lower Bound. Shrinkage Exponent.References : None Constant depth circuits cannot compute parity in polysize. Overview of the proof. Trivial cases like AND, OR. First nontrivial case - DNF. The switching Lemma. Proof of Switching Lemma. References <a href="homes.cs.washington.edu/~beame/papers/primer.ps">Switching Lemma Primer</a>. Exercises Reading Constant depth circuits cannot compute parity in polysize. Overview of the proof. Trivial cases like AND, OR. First nontrivial case - DNF. The switching Lemma. Proof of Switching Lemma.References : Switching Lemma Primer. Inductive Argument. Exponential size lower bounds for constant depth circuits computing parity. References <a href="homes.cs.washington.edu/~beame/papers/primer.ps">Switching Lemma Primer</a>. Exercises Reading Inductive Argument. Exponential size lower bounds for constant depth circuits computing parity.References : Switching Lemma Primer. Representation of Boolean functions by polynomials. Upper bound on the degree required to agree with a size s depth d ckt on most of the inputs. References <a href="http://users-cs.au.dk/arnsfelt/CT08/scribenotes/lecture10.pdf">Notes - Kristoffer Hansen</a> Exercises Reading Representation of Boolean functions by polynomials. Upper bound on the degree required to agree with a size s depth d ckt on most of the inputs.References : Notes - Kristoffer Hansen If we can represent PARITY using a polynomial of degree t, then we can represent all functions with polynomials of degree (n+t)/2. But there are not that many polynomials whose degree is that small but there are too many Boolean functions. Razborov-Smolensky lower bound for PARITY. References <a href="http://users-cs.au.dk/arnsfelt/CT08/scribenotes/lecture10.pdf">Notes - Kristoffer Hansen</a> Exercises Reading If we can represent PARITY using a polynomial of degree t, then we can represent all functions with polynomials of degree (n+t)/2. But there are not that many polynomials whose degree is that small but there are too many Boolean functions. Razborov-Smolensky lower bound for PARITY.References : Notes - Kristoffer Hansen Monotone Circuits, Lower Bounds known. Negation Limited circuits - the story so far. Razoborov's lower bound for monotone circuits. Proof strategy. References <a href="www.cmi.ac.in/~ramprasad/lecturenotes/raz_clique.pdf">Ramprasad's lecture notes based on Arvind's lecture</a>. Exercises Reading Monotone Circuits, Lower Bounds known. Negation Limited circuits - the story so far. Razoborov's lower bound for monotone circuits. Proof strategy.References : Ramprasad's lecture notes based on Arvind's lecture. Clique Approximators. Construction of the approximate circuit. Sunflower Lemma. References <a href="www.cmi.ac.in/~ramprasad/lecturenotes/raz_clique.pdf">Ramprasad's lecture notes based on Arvind's lecture</a>. Exercises Reading Clique Approximators. Construction of the approximate circuit. Sunflower Lemma.References : Ramprasad's lecture notes based on Arvind's lecture. Lower bound on the error estimate for the approximate circuit. Upper bound on the error by counting that for each gate. The lower bound argument. References <a href="www.cmi.ac.in/~ramprasad/lecturenotes/raz_clique.pdf">Ramprasad's lecture notes based on Arvind's lecture</a>. Exercises Reading Lower bound on the error estimate for the approximate circuit. Upper bound on the error by counting that for each gate. The lower bound argument.References : Ramprasad's lecture notes based on Arvind's lecture. Branching Programs and Skew circuits. From space bounded algorithms to Branching Programs. Width of the Branching Programs. References <a href="http://www.ccs.neu.edu/home/viola/classes/gems-08/lectures/le11.pdf"></a> Exercises Reading Branching Programs and Skew circuits. From space bounded algorithms to Branching Programs. Width of the Branching Programs.Programs over groups. Permutations. Conjugates, Cycle conjugacy lemma. References <a href="http://www.ccs.neu.edu/home/viola/classes/gems-08/lectures/le11.pdf"></a> Exercises Reading Programs over groups. Permutations. Conjugates, Cycle conjugacy lemma.Barrington's theorem for width-5. Role of Non-solvability of the group. References <a href="http://www.ccs.neu.edu/home/viola/classes/gems-08/lectures/le11.pdf"></a> Exercises Reading Barrington's theorem for width-5. Role of Non-solvability of the group.**Theme 4 : Hardness vs Randomness**- 4 meetings- Meeting 58 : Fri, Apr 26, 10:00 am-10:50 am
- Meeting 59 : Fri, Apr 26, 05:00 pm-06:30 am
- Meeting 60 : Mon, Apr 29, 08:00 am-08:50 am
- Meeting 61 : Mon, Apr 29, 05:00 pm-06:30 pm
- Derandomization and Circuit Lower Bounds Notes by Markus Blaeser
- [AB] Textbook section 20.4, assumed Lemma 20.20.

Derandomization Problem, Hardness assumptions. Pseudo random generators. References <a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a> Exercises Reading Derandomization Problem, Hardness assumptions. Pseudo random generators.References : Derandomization and Circuit Lower Bounds Notes by Markus Blaeser Nisan-Wigderson generator, NW Design. Proof of pseudorandomness. Intuition for hybrid argument. References <a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a> Exercises Reading Nisan-Wigderson generator, NW Design. Proof of pseudorandomness. Intuition for hybrid argument.References : Derandomization and Circuit Lower Bounds Notes by Markus Blaeser Details of Hybrid Argument. References <a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a> Exercises Reading Details of Hybrid Argument.References : Derandomization and Circuit Lower Bounds Notes by Markus Blaeser Crash course on coding theory, Local Decoding, Local list decoding. Using codes to reduce from Worst case hard functions to Average Case hard function. <br> From Derandomization to Hard Functions - Impagliazzo-Kabanets Theorem. References <ul> <li><a href="http://www-cc.cs.uni-saarland.de/media/oldmaterial/derandcircuit.pdf">Derandomization and Circuit Lower Bounds</a> Notes by Markus Blaeser</a></li> <li>[AB] Textbook section 20.4, assumed Lemma 20.20.</li> </ul> Exercises Reading Crash course on coding theory, Local Decoding, Local list decoding. Using codes to reduce from Worst case hard functions to Average Case hard function.

From Derandomization to Hard Functions - Impagliazzo-Kabanets Theorem.References : **Evaluation Meetings**- 18 meetings- Meeting 62 : Mon, Apr 15, 04:30 pm-05:30 pm
- Meeting 63 : Wed, Apr 17, 04:00 pm-06:00 pm
- Meeting 64 : Thu, Apr 18, 04:30 pm-05:30 pm
- Meeting 65 : Fri, Apr 19, 11:00 am-12:00 pm
- Meeting 66 : Wed, Apr 24, 09:00 am-10:00 am
- Meeting 67 : Wed, Apr 24, 10:00 am-11:00 am
- Meeting 68 : Wed, Apr 24, 11:00 am-12:00 pm
- Meeting 69 : Wed, Apr 24, 12:00 pm-01:00 pm
- Meeting 70 : Thu, Apr 25, 12:00 pm-12:30 pm
- Meeting 71 : Sat, Apr 27, 09:00 am-10:00 am
- Meeting 72 : Sat, Apr 27, 10:00 am-11:00 am
- Meeting 73 : Sat, Apr 27, 11:00 am-12:00 pm
- Meeting 74 : Sat, Apr 27, 12:00 pm-01:00 pm
- Meeting 75 : Mon, Apr 29, 02:00 pm-03:00 pm
- Meeting 76 : Mon, Apr 29, 03:00 pm-04:00 pm
- Meeting 77 : Mon, Apr 29, 04:00 pm-05:00 pm
- Meeting 78 : Wed, May 01, 11:00 am-06:00 pm
- 11:00 - 11:30 : Akshay Degewekar
- 11:35 - 12:05 : Saikrishna Badarinarayanan
- 12:10 - 12:40 : Karthik Abhinav
- 12:45 - 13:15 : Sidhartha S.
- 14:00 - 14:30 : Niels Stroeher
- 14:35 - 15:05 : Alexandra Weber
- 15:10 - 15:40 : Gaurav Singh
- 15:45 - 16:15 : Saurabh Kumar Verma
- 16:20 - 16:50 : Vishal Pandya
- 16:55 - 17:25 : Ramnath Jayachandran
- 17:30 - 18:00 : Anant Dhayal
- Meeting 79 : Wed, May 01, 09:00 am-10:30 am

Interim Meeting <br> 16:30 - 17:00 : Sidhartha Sivakumar : <br> 17:00 - 17:30 : Karthik Abhinav References Exercises Reading Interim Meeting

16:30 - 17:00 : Sidhartha Sivakumar :

17:00 - 17:30 : Karthik AbhinavReferences : None Interim Meeting <br> 16:00 - 16:30 : Saikrishna Badrinarayanan <br> 16:30 - 17:00 : Gaurav Singh <br> References Exercises Reading Interim Meeting

16:00 - 16:30 : Saikrishna Badrinarayanan

16:30 - 17:00 : Gaurav SinghReferences : None Interim Meeting <br> 16:30 - 17:00 : Anant Dhayal <br> 17:00 - 17:30 : Ramnath Jayachandran<br> 17:30 - 18:00 : Vishal Pandya References Exercises Reading Interim Meeting

16:30 - 17:00 : Anant Dhayal

17:00 - 17:30 : Ramnath Jayachandran

17:30 - 18:00 : Vishal PandyaReferences : None Interim Meeting: <br> 11:00 - 11:30 : Akshay Degwekar<br> 11:30 - 12:00 : Alexandra Weber & Niels StrĂ¶her. References Exercises Reading Interim Meeting:

11:00 - 11:30 : Akshay Degwekar

11:30 - 12:00 : Alexandra Weber & Niels StrĂ¶her.References : None Karthik Abhinav: <a href="http://www.cs.sfu.ca/~kabanets/Research/isolation.html">Is Valiant-Vazirani Lemma Probability improvable?</a>. References Exercises Reading Karthik Abhinav: Is Valiant-Vazirani Lemma Probability improvable?.References : None Vishal Pandya: <a href="http://people.csail.mit.edu/dmoshkov/courses/adv-comp/accnexp.pdf">Lower Bounds from satisfiability testing algorithms</a>. References Exercises Reading Vishal Pandya: Lower Bounds from satisfiability testing algorithms.References : None Sidhartha Sivakumar: <a href="">Characterization of Complete Basis.</a> <br> (reference will be sent separately). References Exercises Reading References : None Saikrishna Badrinarayanan: <a href="http://www.cse.iitk.ac.in/users/abhik/files/ss.pdf">Two Applications of Inductive Counting</a>. References Exercises Reading Saikrishna Badrinarayanan: Two Applications of Inductive Counting.References : None Interim Meeting : <br> 12:30 - 13:00 : Saurabh Verma. References Exercises Reading Interim Meeting :

12:30 - 13:00 : Saurabh Verma.References : None Anant Dhayal: <a href="http://www.cs.utexas.edu/~klivans/r6.ps">Linear Advice for Randomized Logarithmic Space</a>. References Exercises Reading Anant Dhayal: Linear Advice for Randomized Logarithmic Space.References : None Ramnath Jayachandran: <a href="http://eccc.hpi-web.de/report/2012/059/download/">Uniform Circuits, Lower Bounds, and QBF Algorithms</a>. References Exercises Reading Ramnath Jayachandran: Uniform Circuits, Lower Bounds, and QBF Algorithms.References : None Saurabh Verma: <a href="http://people.csail.mit.edu/madhu/ST05/scribe/lect04.ps">BenOr-Cleve Construction of Constant-width Branching Programs.</a> References Exercises Reading References : None Gaurav Singh: <a href="">Polylogarithmic Threshold is in AC^0.</a><br> (reference will be sent). References Exercises Reading References : None Akshay Degwekar: <a href="www.wisdom.weizmann.ac.il/~ranraz/publications/Ptensor.pdf">Tensor Ranks and Arithmetic Formula Lower Bounds</a>. References Exercises Reading Akshay Degwekar: Tensor Ranks and Arithmetic Formula Lower Bounds.References : None Neils & Alexandra : <a href="http://ftp.cs.rutgers.edu/pub/allender/amplifying.pdf">Amplifying Lower Bounds by Means of Self-Reducibility.</a> References Exercises Reading Neils & Alexandra : Amplifying Lower Bounds by Means of Self-Reducibility.References : None Niels & Alexandra: <a href="http://ftp.cs.rutgers.edu/pub/allender/pathetic2.pdf">Uniform Derandomization from Pathetic Lower Bounds.</a> References Exercises Reading Niels & Alexandra: Uniform Derandomization from Pathetic Lower Bounds.References : None Viva : Schedule (30 minutes each)<br> <ul> <li>11:00 - 11:30 : Akshay Degewekar </li> <li>11:35 - 12:05 : Saikrishna Badarinarayanan</li> <li>12:10 - 12:40 : Karthik Abhinav</li> <li>12:45 - 13:15 : Sidhartha S.</li> <li>14:00 - 14:30 : Niels Stroeher</li> <li>14:35 - 15:05 : Alexandra Weber</li> <li>15:10 - 15:40 : Gaurav Singh</li> <li>15:45 - 16:15 : Saurabh Kumar Verma</li> <li>16:20 - 16:50 : Vishal Pandya</li> <li>16:55 - 17:25 : Ramnath Jayachandran</li> <li>17:30 - 18:00 : Anant Dhayal</li> </ul> References Exercises Reading Viva : Schedule (30 minutes each)

References : None Endsem Exam References Exercises Reading Endsem ExamReferences : None