Peter Horak, Ph.D.

Professor ; Graduate Faculty

Specialty: Discrete Mathematics, Theoretical Computer Science, Cryptography, Coding Theory

Horak, Peter

Contact information

Dept: Interdisciplinary Arts and Sciences
Room: GWP 413
Phone: 253-692-4558
Email: horak@u.washington.edu
Web: http://faculty.washington.edu/horak/
Schedule: Autumn 2013 office hours: Tuesdays & Thursdays, 12:30-1:30 p.m. - All office hours are held in the TLC.

Degrees

  • Ph.D., Mathematics, Comenius University, Slovakia, 1980.
  • M.S., Mathematics, Comenius University, Slovakia, 1975.
  • B.S., Comenius University, Slovakia, 1974.

Biography

My main research interests are discrete mathematics and computer science. So far I have published more than 80 scientific papers that belong to the areas of Combinatorics, Computer science, Convex and Discrete geometry, Group theory, Information and communication circuits, Number theory, and Operation research. Some of these papers have been published in the top journals as European J. of Combinatorics, J. of Combinatorial Theory A and B, Discrete & Computational Geometry, and IEEE Transactions of IT. These papers have been cited more than 600 times, including several monographs, and, following Google Scholar, my h-index equals 14.

In Combinatorics I have focused on graph theory, design theory and codes, in computer science on cryptography, algorithms and complexity, a security of databases. I solved 4 problem posed by Paul Erdos, and a problem posed by Donald Knuth. My Erdos number equals to 1. At the moment my scientific interest are centered on the research related to the NATO grant SfP Project 984520 Secure Implementation of Post-Quantum Cryptography, see http://147.175.106.232/nato/ for more details. I am an international expert on this grant.

As to teaching, I have taught a wide variety of courses in Mathematics and Computer Science ranging from the introductory level to the graduate one. I was supervising several undergraduate research projects but I am mainly interested in working with graduate students. I was a co-supervisor of the PhD thesis for Ms. Leticia B. Rodriguez from the Federal University of Rio de Janeiro. Her thesis has been awarded the 2nd prize in the contest held by the Brazilian Math. Society. At the moment I have 2 PhD graduate students, one from the College of EE and IT, Slovak University of Technology, and one from Department of Mathematics, University of Aveiro, Portugal.

Research

  • At the moment I am focused on scientific problems of the NATO grant mentioned above. 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.
  • I have a research seminar for two UWT students related to the NATO grant.
  • With P.Valtr, from Charles University, Prague, we work on a problem in Discrete Geometry related to Minkowski's conjecture.
  • With I. Semaev from University of Bergen, and with Zsot Tuza from University of Panonoa, Hungary, we work on solving sparse systems of equation that are related to Algebraic Cryptoanalysis.
  • With T. Etzion from Technion, Haifa we work on a problem related to perfect codes.
  • With V. Hromada from Slovak Technical University on the enumeration of perfect Lee codes.

Teaching

I am co-supervisor of Ms. Catarina Cruz, a Ph.D. student, Universidade de Aveiro, Portugal, of Ing. Viliam Hromada, a PhD student at Slovak University of Technology, and a co-supervisor of Tomas Fabsic, another PhD student from Slovak University of Technology.

I have developed the course TMATH 214 that has been offered many times during the last 7 years.

I have submitted a course proposal for courses Cryptography I and II, 400/graduate courses.

This AY I will teach:

  • TMATH 110 - Introductory Statistics
  • TMATH 214 - Analytical Thinking
  • TMATH 308 - Linear Algebra
  • CSS 322 - Discrete Mathematics II A graduate course for the Institute: Approximation algorithms
  • 400/graduate course: Cryptography I

Selected Publications

  • P. Horak, Tilings in Lee metric, European J. of Combinatorics, 30 (2009), 480-489.
  • P. Horak, A. Rosa, On a problem of Marco Buratti, Electronic J. Combinatorics, R20, 2009.
  • B. AlBdaiwi, P. Horak, M. Milazzo, Enumerating and decoding perfect Lee codes, Designs, Codes, and Cryptography 52 (2009), 155-162.
  • O. Grosek, P. Horak, P. Zajac, On Complexity of Round Transformations, Discrete Math. 309 (2009), 5527-5534.
  • P. Horak, On Perfect Lee Codes, Discrete Math. 309 (2009), 5551-5561.
  • L. R. Bueno, P. Horak, On hamiltonian cycles in the prism over the odd graphs, J. Graph Th. 68 (2011), 177-188.
  • P. Horak, B. AlBdaiwi, Non-periodic tilings of R by crosses, Discrete & Computational Geometry 47 (2012), 1-16.
  • O. Grosek, P.Horak, On quasigroups with few associative triples, Designs, Codes, and Cryptography 64 (2012), 221-227.
  • P. Horak, B. AlBdaiwi, Diameter perfect Lee codes, IEEE Trans. on Information Theory 58 (2012), 5490-5499. 83.
  • C. Araujo-Martinez, I. J. Dejter and P. Horak, A generalization of Lee codes, to appear in Designs, Codes, and Cryptography.

Affiliations

YMCA Tacoma. I designed a program to assist high school students in their pursuit of a college education within YMCA mission to build Strong Kids, Strong Families and Strong Communities. A great majority of the population that participate in these programs are African-American students.

Professional Service

Member of the editorial board of journals:

  • Journal of Combinatorial Designs, (Willey & Sons) since 2008
  • Mathematica Slovaca, (Springer) since 2007
  • Journal of Combinatorial Mathematics and Combinatorial Computing, (Charles Babbage Research Center, Canada) since 1994
  • Journal of Combinatorics, Information and System Sciences,(MD publications, India) since 1993
  • Guest editor of the volume 308, Issue 18, 2009 of Discrete Mathematics (Elsevier)
  • Reviewer of 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.
  • Reviewer of NSERC (Canada) and National Security Agency (USA) grant applications.

Honors and Awards

  • A key note speaker at:
    • Combinatorics 2012, Sep 9-15, 2012, Perugia, Italy.
  • Invited lectures at Universities:
    • Australia: University of Newcastle, NSW
    • Brazil: Federal University, Rio de Janeiro; Federal University, Goiania
    • Canada: University of Calgary; Simon Fraser University, Vancouver; University of Toronto; Universite de Montreal; University of Regina; McMaster University, Hamilton; University of Victoria
    • Czech Republic: Charles University, Prague
    • Germany: University of Augsburg
    • Hungary: Mathematical Institute of the Hungarian Academy of Sciences
    • Italy: University of Catania; University of Messina
    • Japan: Science University, Tokyo; Keio University, Yokohama
    • Kuwait: Kuwait University
    • Netherlands: University of Groningen; Technishe Universiteit Eindhoven
    • New Zealand: University of Otago, Dunedin
    • Norway: University of Bergen Oman: Sultan Qabus University
    • Poland: Mathematical Institute of AGH Krakow
    • Portugal: University of Aveiro
    • Puerto Rico: University of Puerto Rico
    • Russia: Economic University, Nizny Novgorod
    • Israel: Ben Gurion University, Beer'sheva
    • Slovakia: Comenius University; Slovak University of Technology
    • Slovenia: University of Ljubljana
    • South Africa, University of Cape Town
    • Taiwan: National Sun Yat-sen University, Kaohsiung; National Chiao Tung University, Hsinchu;, Academica Sinica, Taipei; National Dong Hwa University, Haulienz
    • USA: Emory University, Atlanta; Georgia Institute of Technology, Atlanta; University of Hawaii; University of Illinois at Champaign/Urbana; University of Illinois at Chicago; University of Nebraska, Lincoln; Auburn University, Alabama; Southern Illinois University, Carbondale; University of West Georgia, Carrollton, Illinois State University, Normal
    • Zimbabwe: University of Zimbabwe, Harare