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πŸ”— Contact Information

tel: +1-516-912-3162
address: 570 Park Ave, Apt 8D, New York, NY 10065

πŸ”— Research Interests

Theory. Universal algebra, logic, complexity theory, type theory, category theory, machine learning.
Practice. Proof mechanization in Agda, functional programming for Big Data in Scala/Spark.

πŸ”— Education

πŸ”— Academic Appointments

  • Postdoctoral Fellow, Charles University, Dept. of Algebra, Prague (2019--2021).
  • Burnett Meyer Instructor, University of Colorado, Dept. of Mathematics, Boulder (2017--2019).
  • Visiting Assistant Professor, University of Hawaii, Dept. of Mathematics, Honolulu (2016--2017).
  • Postdoctoral Associate, Iowa State University, Dept. of Mathematics, Ames (2014--2016).
  • Visiting Assistant Professor, Univ South Carolina, Dept. of Mathematics, Columbia (2012--2014).

πŸ”— Industry Appointments

  • Senior Research Scientist, Textron Systems Corp., Digital Imaging Research, Maui (2001--2006) Worked full-time on AFOSR contracts developing new algorithms and parallel (smp and mpi) programs for processing images acquired by Haleakala Observatories, including Multi-frame Blind Deconvolution for removing distorting effects of Earth's atmosphere from images of satellites and other NEOs; executed our programs on the MHPCC supercomputer.

πŸ”— Publications

  1. Constraint Satisfaction Problems over Finite Structures, with Libor Barto and Antoine Mottet.
    36th Annual ACM/IEEE Symp. on Logic in Comp. Sci. (LICS 2021), pp. 1--13 (preprint link)

  2. Bounded homomorphisms and finitely generated fiber products of lattices, with Peter Mayr and Nik RuΕ‘kuc.
    Intl. J. of Algebra and Computation (30):693--710, 2020 (preprint link)

  3. Polynomial-time tests for difference terms in idempotent varieties, with Ralph Freese and Matthew Valeriote.
    International Journal of Algebra and Computation (29):927--949, 2019 (preprint link)

  4. Isotopic algebras with nonisomorphic congruence lattices, Algebra Universalis (72):295--298, 2014 (preprint link)

  5. Expansions of finite algebras & their congruence lattices, Algebra Universalis (69):257--278, 2013 (preprint link)

  6. Proceedings of Algebras and Lattices in Hawaii 2018, editor, with K. Adaricheva, J. Hyndman (Lulu Press).

  7. Topics in nonabelian harmonic analysis and DSP applications (best paper award)
    Proceedings of the International Symposium on Musical Acoustics, Nara, Japan, 2004 (preprint link)

  8. Characterizing musical signals with Wigner-Ville interferences
    Proceedings of the International Computer Music Conference (ICMC 2002), Gothenburg, Sweden, 2002 (preprint link)

  9. Approximating eigenvalues of large stochastic matrices
    Proceedings of the 8th Copper Mt. Conference on Iterative Methods, Colorado, 1998 (preprint link)

Publications in Process.

Books (these are works in progress)

πŸ”— Courses Taught

Charles University in Prague

  1. Universal Algebra (NMAG 405) Winter 2020 (link)

University of Colorado, Boulder

  1. Discrete Mathematics with Lean prover component (Math 2001) Spring 2019
  2. Discrete Mathematics with Lean prover component (Math 2001) Fall 2018
  3. Abstract Algebra (Math 3140) Fall 2018
  4. Model Theory graduate course (Math 6000) Spring 2018
  5. Linear Algebra (Math 2130) Spring 2018
  6. Linear Algebra (Math 2130), Fall 2017.

University of Hawaii

  1. Applied Calculus (Math 215) Spring 2017
  2. Senior Seminar (Math 480) Spring 2017
  3. Calculus IV (Math 244) Fall 2016
  4. Introduction to Advanced Math (Math 321) Fall 2016

Iowa State University

  1. Linear Algebra (Math 317) Spring 2016
  2. Linear Algebra (Math 317) Fall 2015
  3. Survey of Calculus (Math 160) Fall 2015
  4. Elementary Linear Algebra (Math 207) Spring 2015
  5. Calculus I (Math 165) Spring 2015
  6. Abstract Algebra (Math 301) Fall 2014
  7. Calculus I (Math 165) Fall 2014

University of South Carolina

  1. Linear Algebra graduate course (Math 700) Spring 2014
  2. Calculus I (Math 141) Spring 2014
  3. Discrete Structures (Math 374) Fall 2013
  4. Calculus for Business and Social Sciences (Math 122) Fall 2013
  5. Discrete Structures (Math 374) Spring 2013
  6. Calculus for Business and Social Sciences (Math 122) Spring 2013
  7. Vector Calculus (Math 241) Fall 2012
  8. Calculus for Business and Social Sciences (Math 122) Fall 2012

University of Hawaii

  1. Probability Theory (Math 371) Summer 2011
  2. Applied Calculus I (Math 215) Summer 2009
  3. Mathematical Reasoning (Math 100) Summer 2010

πŸ”— Certificates in Data Science

  • Blockchain Basics (SUNY at Buffalo) 4-week Coursera course; grade: 100% (verified certificate)
  • Big Data Analysis with Scala and Spark (Ecole Polytechnique Federale de Lausanne), 4-week Coursera course; grade: 93.4% (verified certificate)
  • Functional Programming Principles in Scala (Ecole Polytechnique Federale de Lausanne), 6-week Coursera course; grade: 100% (verified certificate)
  • Functional Programming Design in Scala (Ecole Polytechnique Federale de Lausanne), 4-week Coursera course; grade: 100% (verified certificate)
  • Parallel Programming in Scala (Ecole Polytechnique Federale de Lausanne), 4-week Coursera course; grade: 100%, (verified certificate)
  • Startup Engineering (Stanford University), 12-week Coursera course; grade: 99.3 (verified certificate)

πŸ”— Honors and Awards

  • NSF Research Grant (no. 1500218 (2015--2018)
    Project Title: Algebras and algorithms, structure and complexity theory
    Description: 3-yr collaborative research on algebraic approaches to constraint satisfaction problems
    Role: Postdoctoral research fellow on a team with 6 senior scientists and 3 postdocs

  • Magellan Scholar Grant (2013--2014)
    Project Title: What does a nonabelian group sound like?
    Description: See
    Role: Faculty mentor for undergraduate research

  • ARCS Sarah Ann Martin Award for Outstanding Research in Mathematics, Honolulu 2011.

  • Best Paper Award, International Symposium on Musical Acoustics, Nara, Japan, 2004.

πŸ”— Synergistic Activities

  • Organizer

  • Editor for Journal: "Algebra Universalis" 2018--present.

  • Referee for Journals: "Algebra Universalis," "Order" and "Journal of Logic & Analysis," 2012--present.

  • Working Group on Graduate Education, University of Hawaii.
    Graduate Student Representative on committee of deans and department heads;
    helped draft resolution for Committee on Research and Graduate Education.

  • Graduate Student Organization: Faculty Senate Student Rep., Academic Committee Chair, Math Department Rep.
    Mentor for Undergraduate Research: Mathematical Biology Program (mentored students in math and dsp for classifying marine life audio signals)

  • Student Advising
    • University of Colorado, Boulder: Served on doctoral candidacy exam committee for the following ph.d. students: Jordan DuBeau, Ali Latfi, Athena Sparks, Michael Wheeler, and Jeffrey Shriner.
    • Iowa State University: REU mentor for Charlotte Aten; Honors thesis advisor for Joshua Thompson; Putnam Exam mentor at weekly exam practice meetings; Undergraduate Tea cohost of weekly undergraduate student gatherings; Iowa 4-H Youth Conference volunteer mentor.
    • University of South Carolina: Honors thesis mentor for Matthew Corley; South Carolina High School Math Contest exam design committee; Faculty mentor for Pi Mu Epsilon (math honors society).

πŸ”— Summer Schools Attended

πŸ”— Talks

  1. Complexity of the Homomorphism Problem for Boolean Models
    European virtual CSP seminar, Online, 2020.
  2. Computational Tools for Universal Algebra Research
    CSP World Congress 2020, Vols am Schlern, Italy 2020.
  3. Formalizing Universal Algebra with Dependent and Inductive Types
    AMS Joint Mathematics Meetings; Special Session: Algebras and Algorithms, Denver, CO 2020.
  4. Computing Difference Term Operations in Polynomial Time
    BLAST Conference, University of Denver, Denver, CO 2018.
  5. Why Universal Algebra Needs Inductive, Dependent Types, Oregon Programming Languages Summer School, Eugene, OR 2018.
  6. A Tutorial Introduction to the Lean Prover, University of Colorado Logic Seminar, Boulder, CO 2018.
  7. The Lambda Calculus and Dependent Type Theory, University of Colorado Logic Seminar, Boulder, CO 2018.
  8. Representing Finite Lattices as Congruence Lattices, Colorado State University Algebra Seminar, Fort Collins, CO 2017.
  9. A Polynomial-time Test for Difference Terms in Idempotent Varieties, BLAST Conference, Vanderbilt University, Nashville, TN 2017.
  10. Algebraic approach to complexity of constraint satisfaction, University of Hawaii Logic and Analysis Seminar, Honolulu, HI 2017 (slides).
  11. Universal Algebraic Methods for Constraint Satisfaction Problems, AMS Fall Western Sectional Meeting: Special Session in Algebraic Logic, Denver, CO 2016.
  12. The Rectangularity Theorem of Barto and Kozik, Conference on Algebras and Algorithms, Boulder, CO 2016.
  13. Constraint Satisfaction Problems and Universal Algebra, Midlands Graduate School in the Foundation of Computing Science, Birmingham, England 2016.
  14. Permutability in Diamonds, Iowa State Algebra and Combinatorics Seminar, Ames, IA 2016.
  15. Which Commutative Idempotent Binars are Tractable?, Vanderbilt Shanks workshop: Open Problems in Universal Algebra, Nashville, TN 2015.
  16. Some Small Finite Algebras Yielding Tractable CSP Templates, Iowa State Algebra and Combinatorics Seminar, Ames, IA 2015.
  17. Algebraic CSP and Tractability of Commutative Idempotent Binars, BLAST Conference, University of North Texas, Denton, TX 2015.
  18. Isotopic Algebras, Iowa State Algebra and Combinatorics Seminar, Ames, IA 2015.
  19. What Does a Nonabelian Group Sound Like?, MAA Special Session: At the Intersection of Mathematics and the Arts, Baltimore, MD 2014.
  20. Interval Enforceable Properties of Finite Groups, AMS Special Session on Finite Universal Algebra, Louisville, KY 2013.
  21. Tutorial: UACalc at the command line and in the cloud, Workshop on Computational Universal Algebra, Louisville, KY 2013.
  22. Approximating Eigenvalues of Large Stochastic Matrices, University of South Carolina Combinatorics Seminar, Columbia, SC 2013.
  23. Congruence Lattices of Finite Algebras (plenary lecture), BLAST Conference, Chapman University, Orange, CA 2013.
  24. Transposition Principles for Subgroups and Equivalence Relations, Zassenhaus Group Theory Conference, Asheville, NC 2013.
  25. Isotopic Algebras with Nonisomorphic Congruence Lattices, AMS Special Session on Algebras, Lattices, and Varieties, Boulder, CO 2013.
  26. Synchronizing Automata and the Černy Conjecture, Graduate Algebra Seminar, University of Colorado, Boulder, CO 2013.
  27. The Finite Lattice Representation Problem in Four Parts, University of South Carolina Algebra and Logic Seminar, Columbia, SC 2012.
  28. Interval Sublattice Enforceable Properties of Finite Groups, The 31st Ohio State-Denison Mathematics Conference, Columbus, OH 2012.
  29. Expansions of Finite Algebras and their Congruence Lattices, American Mathematical Society sectional meeting, Honolulu, HI 2012.
  30. Intervals in Subgroup Lattices and Permutation Representations, Western Carolina University Group Theory Seminar, Cullowhee, NC 2012.
  31. Recent Progress on the Finite Lattice Representation Problem, Achievement Rewards for College Scientists: Scholar Presentations, Honolulu, HI 2011.
  32. The Finite Lattice Representation Problem, First Joint Meeting of the Korean and American Mathematical Societies, Seoul, KOR 2009.
  33. Object reconstruction from multiple views, Air Force Office of Scientific Research AMOS Program Review, Maui 2004.
  34. Approximating eigenvalues of large stochastic matrices, 8th Copper Mt. Conference on Iterative Methods, Colorado 1998.

πŸ”— References

  1. Clifford Bergman*, Professor of Mathematics, Iowa State University
  2. Venanzio Capretta, Assistant Professor of Computer Science, University of Nottingham
  3. Ralph Freese, Professor of Mathematics, University of Hawaii
  4. Peter Jipsen, Professor of Mathematics, Chapman University
  5. George McNulty, Professor of Mathematics, University of South Carolina
  6. Peter Mayr*, Assistant Professor of Mathematics, University of Colorado, Boulder
  7. J.B. Nation, Emeritus Professor of Mathematics, University of Hawaii

(* teaching reference)