Research

I have three main research interests: quantum computation, evolutionary game theory, and philosophy of mathematics. For quantum computation I study under Prof. Andrew Childs at the Institute for Quantum Computing. My research concentrates on the negative adversary method for proving lower bounds on quantum query complexity. Previously, I worked with Prof. Prakash Panangaden in the Cryptography and Quantum Information Laboratory trying to understand the structure of unitary t-designs. These combinatorial designs provide a method to simplify integrating polynomials of degree less than t over U(d). From Deceomber 2010 to January 2011, I was a visitor at the Centre for Quantum Technologies in Singapore.

My involvement in evolutionary game theory stems from my research alongside Prof. Thomas R. Shultz in the Laboratory for Natural and Simulated Cognition. Of particular interest to me is the evolution of cooperation in viscous environments. Most recently I have become interested in games on networks and evolutionary graph theory in general. My interest lead me to found the Evolutionary Game Theory Reading Group. During my time at the LNSC I also worked on neural networks both from a modeling and theoretical perspective. I hope to converge my interests by applying methods from quantum computing to the analysis of neural nets. My interest in the philosophy of mathematics is mostly for personal growth and understanding.

Papers

[i] M. Hartshorn, T.R. Shultz, AK, and R.A. Hammond. The evolutionary dominance of ethnocentrism. (in progress)
[ii] AK. Structure of Unitary t-designs (in progress) [pdf 1, pdf 2, MO Q]
[iii] J.Z. Xue, AK, F. Guichard, and A. Costopoulos. Fidelity selection: a mechanism for the reduction of novelty in evolutionary systems. (in progress)
[iv] AK, and K. Brown. Coevolution of development rate and social investment in offspring. (in progress)

[6] AK, and T.R. Shultz. Ethnocentrism maintains cooperation, but keeping one's children close fuels it. Proceedings of the 33rd annual conference of the cognitive science society, 2011. [pdf]
[5] AK. Robustness of ethnocentrism to changes in inter-personal interactions. Complex Adaptive Systems - AAAI Fall Symposium, 2010. [pdf, slides]
[4] AK. A connectionist study on the interplay of nouns and pronouns in personal pronoun acquisition. Cognitive Computation, 2010.
[3] AK. The cognitive cost of ethnocentrism. Proceedings of the 32nd annual conference of the cognitive science society, 2010. [pdf1, slides]
[2] AK, K. Brown, and T.R. Shultz. Self-esteem and the matching effect in mate selection. Proceedings of the 32nd annual conference of the cognitive science society, 2010. [pdf]
[1] T.R. Shultz, M. Hartshorn, and AK. Why is ethnocentrism more common than humanitarianism? Proceedings of the 31st annual conference of the cognitive science society, 2009. [pdf]

Posters and presentations

2011
July 19 Evolution of ethnocentrism with minimal cognition in a spatially structured population
SCSCS 2nd Meeting, Boston
with Thomas R. Shultz 		slides
June 1 Evolution of ethnocentrism with minimal cognition in a spatially structured population.
McGill University 		slides
March 22 Properties of unitary t-designs.
IQC Theory Lunch
February 3 Replicator dynamics on random graphs.
C&O Graduate Student Seminar
2010
December 9 Lower bounds in the quantum query model.
AQuA Student Congress, CQT, Singapore 		1, 2, 3, 4
November 11 Robustness of ethnocentrism to changes in inter-personal interactions
Complex Adaptive Systems - AAAI Fall Symposium 		slides
November 9 Lower bounds on quantum query complexity.
SUMS Talk
November 9 Evolutionary game theory and cognition.
Guest Lecture for PSYC532: Cognitive Science 		slides
August 13 The cognitive cost of ethnocentrism.
32nd Annual Conference of the Cognitive Science Society 		slides
August 9 Evolution and cognitive cost of ethnocentrism.
43rd Annual Meeting of the Society for Mathematical Psychology 		slides
July 14 Structure of unitary t-designs.
CQISC, University of Calgary
July 9 Combinatorial designs in quantum computation.
CUMC, University of Waterloo
March 26 Introduction to unitary t-designs.
Institute for Quantum Computing, University of Waterloo 		slides
February 13 Unitary t-designs.
SUMM student conference, Montreal 		slides
January 7 Introduction to unitary t-designs.
INTRIQ student conference 		slides
2009
November 12 Evolutionary game theory and cognition.
Guest Lecture for PSYC532: Cognitive Science 		slides
November 5 Evolving Cooperation.
TEDx McGill 		video
1, 2, 3
October 26 Calculus and combinatorics in quantum information theory.
SUMS Talk
October 7 Properties of unitary t-designs
Cryptography and Quantum Information Seminar 		slides
August 31 Calculus, Combinators and (quantum) computation
SOCS undergraduate summer research symposium 		slides
June 4 The evolution of cooperation in a competitive world.
Cognitio 		poster
2008
October 17 The evolution of cooperation in a competitive world.
Undergraduate research conference 		poster
August 29 Evolutionary game theory
SOCS undergraduate summer research symposium 		slides