Sergey Nikolenko

Sergey Nikolenko

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   Research
CS and crypto
Bioinformatics
Machine learning
Algebraic geometry
Algebra
Bayesian networks
Earth sciences

   Teaching
 2014
ML, KFU
Game Theory, HSE
Mech. Design, HSE
ML, CSClub Kazan
Game theory, HSE
Math. logic, AU
Machine learning, STC
Machine learning, AU
 2013
Discrete math, HSE
Machine learning, STC
Math. logic, AU
Cryptography, AU
 2012
Machine learning, STC
Math. logic, AU
Machine learning II, AU
Machine learning, AU
Machine learning, EMC
 2011
Cryptography, AU
Math. logic, AU
Machine learning, AU
 2010
Math. logic, AU
Machine learning, AU
Cryptography, AU
 2009
Crypto in CS Club
Statistics
Machine learning, AU
Cryptography
 2008
Speech recognition
MD for CS Club
ML for CS Club
Mechanism design
 2007
Machine Learning
Probabilistic learning

  External links
Google Scholar profile
DBLP profile
LiveJournal account
userinfonikolenko (in Russian)

Algebraic geometry and ChowMaple

Bio excerpt

In 2004, I was visiting Bielefeld University for two months and met Kirill Zainoulline and Nikita Semenov, who were working on motive theory there. They introduced me to the problems, and we were able to program a Maple package which could multiply elements of the Chow ring. The results were quite interesting: we were able to decompose the motives of projective homogeneous varieties F4/P1 and F4/P4, providing an explicit decomposition. We also proved their motivic isomorphism (while the varieties themselves are not isomorphic).

In 2005, we redesigned some of the algorithms, and the program was able to handle E6/P1, E6/P6, and E8/P8.

ChowMaple package

The package requires John Stembridge's coxeter and weyl packages which are available here. Here you can download the ChowMaple package itself and a brief manual on how to use it. It may still change, as I do not think it is very user-friendly right now. Please note that the package saves its results on your HDD, so do not be alarmed if a large file entitled polys.txt or multiply.txt suddenly appears. It has been so designed to avoid unnecessary (and very lengthy) computations.

Publications

  1. S.I. Nikolenko, N. Semenov, K. Zainoulline. Motivic decomposition of anisotropic varieties of type F4 into generalized Rost motives. Journal of K-Theory, vol. 3, 2009, pp. 85-102 (.pdf, 181kb)
  2. S.I. Nikolenko, N. Semenov, K. Zainoulline. Motivic decomposition of anisotropic varieties of type F4 and generalized Rost motives. ArXiv preprint. (.pdf, 215kb)
  3. S.I. Nikolenko, N. Semenov. Chow ring structure made simple. ArXiv preprint. (.pdf, 783kb)