Igor Carboni Oliveira

  | Royal Society University Research Fellow & Assistant Professor
  | Department of Computer Science, University of Warwick, UK
  | Division of Theory and Foundations (FoCS)
  | Centre for Discrete Mathematics and its Applications (DIMAP)





| Contact Details.
Email:  igor.oliveira@warwick.ac.uk  |  igorcarb@gmail.com    Room:  CS2.02    Office hours:  Please contact me to schedule an appointment.    Address:  Info   

| News.
- Slides of my talk at the LMS Computer Science Colloquium are now available (PDF and PPT).
- If you want to learn about exciting new ideas in complexity theory, check out the Oxford-Warwick Complexity Meetings.
- STOC 2020 Workshop on "MCSP and Hardness Magnification". Videos of all talks are now available.
- An expository article discusses computational complexity and my recent work on hardness magnification. See my notes and slides for a technical perspective.
- I'm interesed in advising phd students with a strong theoretical background. See below for more information.
| About Me.
I'm a member of the Division of Theory and Foundations (FoCS) and of the Centre for Discrete Mathematics and its Applications (DIMAP) at the University of Warwick. Previously, I was a postdoctoral researcher at the Algorithms and Complexity Theory Group at the University of Oxford, a research fellow at UC Berkeley's Simons Institute, and a postdoctoral fellow at the School of Mathematics at Charles University in Prague. I completed my phd in the Theory of Computation Group at Columbia University. In a more distant past, I was a student at University of Campinas in Brazil.

| Research Interests.
Computational complexity theory and its connections to algorithms, combinatorics, and mathematical logic. In particular, over the last few years I have been involved with the following research directions:

Unconditional complexity lower bounds
Connecting the design of algorithms to complexity lower bounds
Probabilistic Kolmogorov complexity and its applications
Hardness magnification: understanding the difficulty of proving weak lower bounds

Unprovability results in mathematical logic 
Meta-complexity and NP-hardness of circuit minimisation and related problems

My work is currently supported by a Royal Society University Research Fellowship (PI) and an EPSRC New Horizons Grant (co-I).

| Seminars.
[Oxford-Warwick Complexity Meetings]  [DIMAP Seminar]  [Combinatorics Seminar]  [CS Colloqium] [Probability Seminar]  [Math Postgraduate Seminar]  [Mathematics Colloqium]  

| Teaching Activities.
CS418: "Advanced Topics in Algorithms and Complexity" (Warwick, Term 1 - 2021/2022). 
Logic and Complexity Student Seminar: "Infinitary Methods in Complexity Theory" (Prague, Winter Term, 2016).
Logic and Complexity Student Seminar: "Bounded Arithmetic and Feasible Complexity Theory" (Prague, Summer Term, 2016).
Logic and Complexity Student Seminar: "Reading Group" (Prague, Winter Term, 2015).

| Publications and Preprints.

A few representative results and highlights include:

- Showing that the design of provably correct learning algorithms (even with quantum computing) requires progress in computational complexity theory.
- Discovery of a hardness magnification phenomenon showing that extremely minor extensions of known complexity lower bounds lead to breakthroughs.  
- A proof that infinitely many prime numbers have succinct and effective representations (and much more).
- Optimality of divide-and-conquer for solving small distance graph connectivity with very fast parallel computations.
- Some well-known logical theories cannot prove the easiness of computational problems.
- A proof that the circuit minimisation of total functions is NP-hard.

List of Publications:  

- Pseudodeterministic algorithms and the structure of probabilistic time  (with Zhenjian Lu and Rahul Santhanam).
- An efficient coding theorem via probabilistic representations and its applications  (with Zhenjian Lu).  [ slides ]   video ] 
- Quantum learning algorithms imply circuit lower bounds  (with Srinivasan Arunachalam, Alex Grilo, Tom Gur, and Aarthi Sundaram).  arXiv ]
   Quantum Information Processing (QIP), 2021. 
- NP-hardness of circuit minimization for multi-output functions  (with Rahul Ilango and Bruno Loff).  ECCC ]   [ Ilango's TCS+ talk ]   [ Ilango's CCC talk ]   [ Loff's HSE talk ]   [ see also Allender's survey ]
   Computational Complexity Conference (CCC), 2020.
- Algorithms and lower bounds for de Morgan formulas of low-communication leaf gates  (with Valentine Kabanets, Sajin Koroth, Zhenjian Lu, and Dimitrios Myrisiotis).  ECCC ]   [ Myrisiotis' CCC talk ]
   Computational Complexity Conference (CCC), 2020.
- Consistency of circuit lower bounds with bounded theories  (with Jan Bydzovsky and Jan Krajicek).  arXiv ]   [ slides ]   [ short slides ]   video ]   [ see also Krajicek's Fields talk ]  
   Logical Methods in Computer Science, 2020.
- Beyond natural proofs: hardness magnification and locality  (with Lijie Chen, Shuichi Hirahara, Jan Pich, Ninad Rajgopal, and Rahul Santhanam).  arXiv ]   notes ]   [ video ]   [ slides ]
   Innovations in Theoretical Computer Science (ITCS), 2020.
- Randomness and intractability in Kolmogorov complexity.  ECCC ]   [ slides ]   video ]
   International Colloquium on Automata, Languages and Programming (ICALP), 2019.
- Parity helps to compute Majority  (with Rahul Santhanam and Srikanth Srinivasan).  ECCC ]   [ slides ]
   Computational Complexity Conference (CCC), 2019.
- Hardness magnification near state-of-the-art lower bounds  (with Jan Pich and Rahul Santhanam).  ECCC ]   notes ]   [ slides ]
   Computational Complexity Conference (CCC), 2019.
- Expander-based cryptography meets natural proofs  (with Rahul Santhanam and Roei Tell).  ECCC ]
   Innovations in Theoretical Computer Science (ITCS), 2019.
- Hardness magnification for natural problems  (with Rahul Santhanam).  ECCC ]   [ slides ]   [ video ]   notes ]   [ informal exposition ]    
   Symposium on Foundations of Computer Science (FOCS), 2018.
- On monotone circuits with local oracles and clique lower bounds  (with Jan Krajicek).  [ CJTCS ]   [ arXiv ]
   Chicago Journal of Theoretical Computer Science (CJTCS), 2018.
- Pseudo-derandomizing learning and approximation  (with Rahul Santhanam).  ECCC ]   [ slides ]  
   International Workshop on Randomization and Computation (RANDOM), 2018.
- NP-hardness of Minimum Circuit Size Problem for OR-AND-MOD circuits  (with Shuichi Hirahara and Rahul Santhanam).  ECCC ]
   Computational Complexity Conference (CCC), 2018.
- An average-case lower bound against ACC  (with Ruiwen Chen and Rahul Santhanam).   ECCC ]   [ slides ]   [ see also Chen-Ren for subsequent developments ]
   Latin American Theoretical Informatics (LATIN, co-winner of the Best Paper Award), 2018.
- Conspiracies between learning algorithms, circuit lower bounds, and pseudorandomness  (with Rahul Santhanam).   [ arXiv ]   [ slides ]   video ]
   Computational Complexity Conference (CCC), 2017.
- Addition is exponentially harder than counting for shallow monotone circuits  (with Xi Chen and Rocco Servedio).   arXiv  [ slides ]   video ]
   Symposium on Theory of Computing (STOC), 2017.
- Pseudodeterministic constructions in subexponential time  (with Rahul Santhanam).   ECCC ]   [ slides ]  [ see also Santhanam's IAS talk ]   
   Symposium on Theory of Computing (STOC), 2017.
- Unprovability of circuit upper bounds in Cook's theory PV  (with Jan Krajicek).   arXiv ]   [ slides ]
   Logical Methods in Computer Science, Volume 13, Issue 1, 2017.
- Erdos-Ko-Rado for random hypergraphs: asymptotics and stability  (with Marcelo Gauy and Hiep Han).   arXiv ]
   Combinatorics, Probability and Computing, 26(3), 406-422, 2017.
- Near-optimal small-depth lower bounds for small distance connecticity  (with Xi Chen, Rocco Servedio, and Li-Yang Tan).   arXiv ]   [ see also Srinivasan's exposition ]
   Symposium on Theory of Computing (STOC), 2016.
- An algebraic formulation of the graph reconstruction conjecture  (with Bhalchandra Thatte).   arXiv ]
   J. Graph Theory, 81: 351-363, 2016.
- On the monotone complexity of the satisfiability problem.   Chapter 3 - Phd Thesis ]
   Manuscript, 2015.
- Learning circuits with few negations.  (with Eric Blais, Clement Canonne, Rocco Servedio, and Li-Yang Tan).   ECCC ]
   International Workshop on Randomization and Computation (RANDOM), 2015.
- Majority is incompressible by AC[p] circuits  (with Rahul Santhanam).   ECCC ]   [ slides ]
   Conference on Computational Complexity (CCC), 2015.
- The power of negations in cryptography  (with Siyao Guo, Tal Malkin, and Alon Rosen).   ePrint ]   [ slides ]  [ Tal's MSR talk ] 
   Theory of Cryptography Conference (TCC), 2015.
- A simple algorithmic explanation for the concentration of measure phenomenon.   pdf ]
   A short note not intended for publication, 2014.
- Algorithms versus circuit lower bounds.   ECCC ]   [ slides
   Survey / ECCC Report, 2013.
- Constructing hard functions from learning algorithms  (with Adam Klivans and Pravesh Kothari).   ECCC ]   [ slides
   Conference on Computational Complexity (CCC), 2013.

[PhD Thesis]  Unconditional lower bounds in complexity theory
.   [ External Link ]  
Columbia University, June/2015 (Advisors: Tal Malkin and Rocco Servedio).
[Master's Thesis]  Computational complexity and the P vs. NP problem  (In Portuguese).   External Link ]   Related Note ]  
University of Campinas, August/2010 (Advisor: Arnaldo Vieira Moura).

Open Problems:
Simons Institute ("Lower Bounds in Computational Complexity" - Fall/2018)

Informal expositions | media coverage | online discussions:  
[ Simons Institute ]   [ Godel's Lost Letter ]   [ Shtetl Optimized I ]   
[ Shtetl Optimized II ]   [ Oxford Inspired Research ]   [ CS@Columbia ]   [ Oded's Choices ]   

| Professional Activities.
Organization of Workshops:
- Krajicek Fest  (Tabor, Czech Republic, 1 September, 2020).
 [The event has been postponed.]
Oxford Complexity Day  (University of Oxford, 27 July, 2018).

Program Committee Member:  
- Computational Complexity Conference (CCC), 2021.

| Students and Postdocs.
Bruno Pasqualotto Cavalar (PhD Student). Funded by a Chancellor's International Scholarship. 
Zhenjian Lu (Postdoc). Funded by a Royal Society URF.

| Recent and Upcoming Events.

A list with a few recent and upcoming conferences and workshops that could be of interest to students and researchers, including events that I might attend.

LMS Computer Science Colloquium  (Online, 19 November, 2020).
24th Annual Conference on Quantum Information Processing (QIP)  (Online, 30/January to 5/February, 2021).
37th British Colloquium for Theoretical Computer Science (BCTCS)  (Online, 29-31 March, 2021).
Dagstuhl Workshop: Computational Complexity of Discrete Problems  (Schloss Dagstuhl, 21-26 March, 2021).
Computational Complexity Conference (CCC)  (Toronto, 19-23 July, 2021).
DIMACS Workshop on Meta-Complexity, Barriers, and Derandomization  (DIMACS/Rutgers, 9-13 August, 2021)

Check DIMAP's website for local events.

| Information for Students, Postdocs, Visitors, etc.

Warwick Students.
  If you're a student at Warwick interested in working with me, don't hesitate to get in touch to discuss this possibility.
PhD. Warwick has one of the strongest theory groups in the UK, with close interactions between the CS and Math departments. If you would like to apply for a phd position, more information can be found here (check also these scholarships: link1, link2link3link4). I would be happy to support the application of strong candidates based in the UK or from abroad.
You can find some potential topics here.
Postdocs. There are many opportunities for postdocs to come to Warwick, and some of them offer quite generous conditions. A few options are discussed on these pages: link1link2, and link3. You can also check funding opportunities available through Warwick IAS. The best strategy is to contact me as early as possible if you would like to apply for a position or fellowship.
Finally, check also the department's vacancies.

Resources for Warwick visitors