Peter Horak, Ph.D.
My main research interests are discrete mathematics and theoretical computer science; I have published some 90 scientific papers on these topics. In discrete mathematics my main focus is on combinatorics, graph theory, design theory, in computer science on coding theory, cryptography, complexity of algorithms, and security of databases. I travel and speak widely; I delivered invited lectures in more than twenty five countries on six continents. I am a member of the editorial boards of four international research journals.
I solved 4 problems posed by Paul Erdös, and a problem posed by Donald Knuth. My Erdös number is 1. At the moment my scientific interest are centered on the research related to the NATO grant “Secure Implementation of Post-Quantum Cryptography”, see http://re-search.info/.
I enjoy doing research with students both on undergraduate and graduate levels. I was a co-supervisor of the Ph.D. thesis for Ms. Leticia B. Rodriguez from the Federal University of Rio de Janeiro. Her thesis has been awarded the 2nd prize by the Brazilian Math. Society. Currently I advise two Ph.D students, one from Slovak University of Technology, Slovakia, and one from University of Aveiro, Portugal.
- At the moment I am focused on scientific problems of the NATO grant “Secure Implementation of Post-Quantum Cryptography”, see http://re-search.info/. With Prof. Grosek from Slovak University of Technology, who is the PI of the grant, we work on ciphers that will be secure even in the coming era of the quantum computers.
- With Dr. Semaev from University of Bergen, and with Dr. Tuza from the Mathematical Institute of the Hungarian Academy of Sciences, we work on solving sparse systems of equation that are related to Algebraic Cryptanalysis.
- With Dr. Etzion from Technion, Haifa we work on problems related to perfect codes, Sidon sets, and the Golomb-Welch conjecture.
- For a long time I keep working on problems inspired by Minkowski’s conjecture on tiling a space by clusters of unit cubes.
In recent years I have been focused on incorporating my research into teaching. As I part of this effort I have introduced new courses T12H 412 Cryptography and TMATH 413 Coding Theory. I supervise undergraduate/ graduate research in these areas both at UWT and abroad.
Member of the editorial board of journals:
Journal of Combinatorial Designs, Wiley &Sons, USA, since 2008.
Mathematica Slovaca, Springer Verlag / De Gruyter, Germany, since 2007.
Journal of Combinatorial Mathematics and Combinatorial Computing, Charles Babbage Research Center, Canada, since 1994.
International Journal of Mathematics & Statistics, CESER Publications, India, since 2014; since 2015 an Associate Chief Editor.
Journal of Combinatorics, Information and System Sciences, MD Publications PVT, India, 1993 - 2011.
Guest editor of the volume 308, Issue 18, 2009 of Discrete Mathematics (Elsevier)
Zentralblatt fur Mathematik, Mathematical Reviews, many journals, e.g., Combinatorica, Ars Combinatoria, Utilitas Mathematics, J.Graph Theory, Discrete Math., Designs, Codes and Cryptography, J. Combinatorial Designs, J.Combinatorial Th. Ser B, Graphs and Combinatorics, Theoretical Computer Science, Australasian J. Combinatorics, Linear Algebra and its Applications, Discussiones Mathematicae Graph Theory, Discrete Mathematics & Theoretical Computer Science, SIAM on Discrete Math, J. Combinatorial Optimization, and Mathematica Slovaca.
NSERC (Canada) and National Security Agency (USA) grant applications.
Honors and Awards
Australia: University of Newcastle, NSW 1996, 1998.
∙ Austria: Technische Universität Wien 2011.
∙ Brazil: Federal University, Rio de Janeiro 2000, 2007; Federal University, Goiania 2007.
∙ Canada: University of Calgary 1987, 1990; Simon Fraser University, Vancouver 1987, 1989, 2005, 2010; University of Toronto 1987; Universite de Montreal 1991; University of Regina 2000; McMaster University, Hamilton 2003, 2005, 2007, 2009, 2010, 2012; University of Victoria 2006, 2010.
∙ China: Zhejiang Normal University, Jinhua, 2013.
∙ Czech Republic: Charles University, Prague 1997, 2011, 2013.
∙ Germany: University of Augsburg 2013.
∙ Hungary: Mathematical Institute of the Hungarian Academy of Sciences 1994, 2011.
∙ Israel: Ben Gurion University, Beer'sheva 2011.
∙ Italy: University of Catania 2007; University of Messina 2008.
∙ Japan: Science University, Tokyo 2004; Keio University, Yokohama 2004.
∙ Kuwait: Kuwait University 2005, 2009, 2011, 2015.
∙ Netherlands: University of Groningen 2008; Technishe Universiteit Eindhoven 2008.
∙ New Zealand: University of Otago, Dunedin 2000.
∙ Norway: University of Bergen 2012, 2014.
∙ Oman: Sultan Qabus University 2001.
∙ Poland: Mathematical Institute of AGH Krakow 1995.
∙ Portugal: University of Aveiro 2008, 2011.
∙ Puerto Rico: University of Puerto Rico 2005, 2006, 2010.
∙ Russia: Economic University, Nizny Novgorod 2011.
∙ Slovakia: Comenius University 2009; Slovak University of Technology 2007, 2011.
∙ Slovenia: University of Ljubljana 2010.
∙ South Africa, University of Cape Town 2011.
∙ Taiwan: National Sun Yat-sen University, Kaohsiung 1996, 2007; National Chiao Tung University, Hsinchu 1996, 2007; Academica Sinica, Taipei 1996; National Dong Hwa University, Haulien 2007.
∙ USA: Emory University, Atlanta 2004, 2006, 2008, 2009; Georgia Institute of Technology, Atlanta 2004, 2009; University of Hawaii 2011, 2013; University of Illinois at Champaign/Urbana 2008; University of Illinois at Chicago 1994; University of Nebraska, Lincoln 1990, 1994; Auburn University, Alabama 2003, 2004, 2006, 2008, 2009, 2010, 2011, 2012; Southern Illinois University, Carbondale 1991, 2004; University of West Georgia, Carrollton 2004; Illinois State University, Normal 2004, 2008.
∙ Zimbabwe: University of Zimbabwe, Harare 2001.