Recent talks by Jeffrey O. Shallit

I grant readers of this page the right to reproduce one copy of any of these talks for the purposes of research and self-study.

2024
- Developing Walnut Commands for Sequence Properties, guest lecture for a course, Automatic Sequences, for the Dutch national MSc programme in mathematics, run by Wieb Bosma and Robbert Fokkink, November 7 2024. The video is here.
- Using Automata to Prove Theorems about Sequences, talk for the One Flat World Seminar, May 8 2024. The video is here.
2023
- Proving Results in Combinatorics on Words and Number Theory using a Decidable Logic Theory, talk for the Selected Topics in Mathematics online seminar, University of Liverpool, November 22 2023. Here is the video.
- Proving Results About OEIS Sequences with Walnut, talk at CICM 2023 (16th Conference on Intelligent Computer Mathematics), September 5 2023.
- Doing Additive Number Theory with Logic and Automata, talk for the New York Number Theory Seminar, April 27 2023. Video here.
- New Results in Additive Number Theory via Combinatorics on Words, One World Combinatorics on Words Seminar, April 3 2023. Video is here.
- New results in additive number theory via automata theory and combinatorics on words, invited talk for GFSNP 2023, Antalya, Turkey, March 11 2023.
2022
- Using Walnut to Prove Results About Sequences in the OEIS, talk for the seqfan mailing list, October 18 2022.
  - Walnut code to prove the results in the talk.
  Video for the talk here.
- Using Automata and a Decision Procedure to Prove Results in Pattern Matching, invited talk for the CPM 2022 (Combinatorial Pattern Matching) conference, June 28 2022.
- The Ubiquitous Thue-Morse Sequence, invited talk for the Prison Mathematics Project, March 14 2022.
  - audio file for the music
  - the video on Youtube
2021
- Abelian and additive powers in the Tribonacci word, short talk for the One World Combinatorics on Words Seminar, November 22 2021. Video here.
- Adventures in Automata with a Theorem-Prover, Ng Kong Beng Public Lecture, IMS, Singapore (an invited talk), September 24 2021.
- Synchronized sequences, invited talk for the WORDS 2021 conference, Rouen, France, September 16 2021. Talk video is here.
- Say No to Case Analysis: Automating the Drudgery of Case-Based Proofs, invited talk for the CIAA 2021 conference, Bremen, Germany, July 20 2021.
- Additive Number Theory via Automata, invited talk for AAA 101--Arbeitstagung Allgemeine Algebra (101st Workshop on General Algebra), Department of Mathematics and Informatics, University of Novi Sad, Serbia, June 6 2021.
- Proving theorems in combinatorics on words with Walnut, part of a mini-symposium at CanaDAM 2021 (Canadian Discrete and Algorithmic Mathematics Conference), May 25 2021.
- The Walnut Tutorial: Using A Tool for Doing Combinatorics on Words, talk for the One World Combinatorics on Words Seminar, May 17 2021, 9:00 AM EDT.
  - text file with all the examples from the talk; you can just cut-and-paste these into Walnut
- Robbins and Ardila Meet Berstel, short talk for the One World Combinatorics on Words Seminar, March 22 2021. Video available here. Note: the Robbins-Ardila result was actually proved first by Tad White, On the coefficients of a recursion relation for the Fibonacci partition function, Fib. Quart. 24 (1986), 133-137.
2020
- Lazy Ostrowski Numeration and Sturmian Words, talk for the One World Seminar on Numeration Systems, September 15 2020. Video is available at that link.
2019
- Additive Number Theory via Automata Keynote lecture (the Sedgwick lecture) for the AARMS 2019 Conference for Mathematics, Statistics and Computer Science, Dalhousie University, October 26 2019.
- Critical exponent of infinite balanced words via the Pell number system, talk for the WORDS 2019 conference, Loughborough, England, September 10 2019.
- New results on pseudosquare avoidance, talk for the WORDS 2019 conference, Loughborough, England, September 13 2019.
- Determining Repetition Thresholds via Logic and Numeration Systems, invited talk for the Numeration 2019 conference, Erwin Schrödinger Institute, Vienna, Austria, July 8 2019.
2018
- Finite Automata and Additive Number Theory, invited talk for Highlights of Logic, Games, and Automata, Berlin, Germany, September 21 2018.
- Solving Problems in Additive Number Theory with Automata Theory, invited talk for CiE 2018, Kiel, Germany, August 1 2018
- Additive number theory and automata, talk for the Workshop on Words and Complexity, Lyon, France, February 20 2018
- Waring's theorem for binary k'th powers and palindromes, talk for the number theory seminar, University of Waterloo, February 6 2018
- Using automata to prove theorems in additive number theory, talk for the Knuth 80 conference, Piteå, Sweden, January 9 2018
2017
- Recent results in combinatorics on words using an automatic prover, talk for the Bridges between Automatic Sequences, Algebra and Number Theory workshop, May 4 2017
- 50 Years of Fine and Wilf, talk for the Oxford University department of computer science, April 10 2017
2016
- RISC Linz Sommerschool 2016 (ask me for password)
  - Walnut for Linz by Hamoon Mousavi
  - Slides for Lecture 1: Automatic sequences and k-regular sequences, August 1 2016
  - Slides for Lecture 2: Logic and automata, August 2 2016
  - Slides for Lecture 3: Proving claims about automatic sequences with Walnut, August 3 2016
  - Slides for Lecture 4: Enumeration and automatic sequences, August 4 2016
  - More exercises (also see the course notes for many more exercises!)
  - Slides for Lecture 5: Fibonacci- and Tribonacci-automatic sequences, and beyond, August 5 2016
- Experimental Combinatorics on Words Using the Walnut Prover, talk for the ACMES conference, Western University, May 12 2016
- Decision procedures for problems in combinatorics on words, talk at the University of Nebraska, March 11 2016
- Automatically Proving Theorems in Combinatorics on Words Using a Computer, talk at the University of Arizona computer science department, January 28 2016
- The Separating Words Problem, talk for the CCR 2016 conference, Honolulu, Hawaii, January 5 2016
2015
- 50 Years of Fine and Wilf, talk for the seminar at the Vrije Universiteit, Amsterdam, November 11 2015
- Subwords, regular languages, and prime numbers, talk for the seminar at the Université de Liège, November 5 2015
- Automatic subsets of rational numbers, talk for the seminar at the University of Nijmegen, November 3 2015
- Decidability and Automatic Sequences, talk for the workshop on Automatic Sequences, Number Theory, and Aperiodic Order, October 28 2015
- Continued Fractions: Old and New Results (slightly different from previous talk), talk for the seminar at TU Delft, October 27 2015
- Continued Fractions: New and Old Results, talk for the seminar at the Université de Lorraine, Nancy, France, October 23 2015
- Mechanical Proofs of Properties of the Tribonacci Word, talk (unabridged version!) at the WORDS 2015 conference, Kiel, Germany, September 17 2015
- Decision algorithms for problems from combinatorics on words, talk at NYU Polytechnic School of Engineering, July 23 2015
2014
- Results on Infinite Words Obtained with an Automatic Prover, AMS sectional meeting, Halifax, NS, October 19 2014
- 40 Years With Sloane's Integer Sequences, talk for the Sloane 75/OEIS 40 workshop, DIMACS, Rutgers, October 10 2014. Video: part 1; part 2.
- Decidability and enumeration for Fibonacci-automatic sequences, invited talk given at GASCOM 2014, Bertinoro, June 23 2014.
- Decidability in automatic sequences, talk at McMaster University, April 22 2014.
- Open problems in automata theory: an idiosyncratic view, LMS Keynote Address in Discrete Mathematics, BCTCS 2014, April 10 2014, Loughborough, England
  - Problem 10 on slide 37 has been solved, and I paid up 25 Euros at the WORDS 2015 conference!
- Critical exponents of k-automatic words and generalizations, Workshop on Reachability Problems for Infinite-State Systems, April 1 2014, Dagstuhl, Germany
2013
- Decidability and enumeration in automatic sequences, talk for the CSR (Computer Science in Russia) 2013 conference, Ekaterinburg, June 24 2013.
- The Frobenius problem and its generalizations, talk for the Colloquium Jacques Morgenstern, Université de Nice Sophia-Antipolis, France, June 20 2013.
- Avoiding circular repetitions, talk for the DLT (Developments in Language Theory) 2013 conference, Paris, June 18 2013. These slides were 90% prepared by my co-author Hamoon Mousavi.
- Subword complexity and k-synchronization, talk for the DLT (Developments in Language Theory) 2013 conference, Paris, June 18 2013.
- Decidability in automatic sequences, talk for the mini-symposium at the Canadam 2013 conference, June 11 2013. There were four other talks at this mini-symposium, and they were:
  - Daniel Goc, Automatic theorem-proving in automatic sequences
  - Narad Rampersad, Extremal words in the shift orbit closure of a morphic sequences
  - James Currie, Abelian powers and patterns in words: problems and perspectives
  - Luke Schaeffer, Abelian powers in automatic sequences are not always automatic
- Automata and nested recurrences, talk for the Canadam 2013 mini-symposium on nested recurrences, June 10 2013.
- Automata and rational numbers, talk for the Journée p-automatique, Institut Henri Poincaré, April 30 2013.
- Open problem: decidability of divisibility in automata, presentation at the Fields workshop on Challenges in Combinatorics on Words, April 22 2013.
2012
- Numerology, talk for the Eschaton 2012 conference, Ottawa, December 1 2012
- "Automata and Rational Numbers", talk for the Pure Mathematics Colloquium, University of Waterloo, November 26 2012
- Why I'm Still Using APL, talk for the APL @ 50 conference, York University, November 1 2012
- Alf van der Poorten and continued fractions, talk for the Memorial Conference, Newcastle, Australia, March 13 2012
2011
- Short course on decidable properties of automatic sequences, University of Turku, Finland, November 2011 (4 hours)
- 50 Years of Fine and Wilf, invited talk for the Department of Mathematics, University of Turku, Finland, November 10 2011
- Short course on decidable properties of automatic sequences, FSFLA 2011, Tarragona, Spain, November 2011
- Fife's theorem for 7/3-powers, talk at WORDS 2011, Prague, September 15 2011
- The critical exponent is computable for automatic sequences, talk at WORDS 2011, Prague, September 12 2011
- Enumeration and decidable properties of automatic sequences, talk at DLT 2011, Milan, Italy, July 22 2011
- Fife's theorem revisited, talk at DLT 2011, Milan, Italy, July 22 2011
- 50 Years of Fine and Wilf, talk for the Waterloo Workshop in Computer Algebra (in honor of Herb Wilf's 80th birthday), May 26 2011
- The Frobenius Problem and Its Generalizations, talk at Tulane University, April 7 2011
- Introduction to Combinatorics on Words, talk for the Dagstuhl workshop, February 20-26, 2011
2010
- Enumeration of Automata, Languages, and Regular Expressions, invited talk for the "Highlights of AutomathA" conference, Vienna, Austria, November 23 2010
- The Separating Words Problem, talk at McMaster University, optimization seminar, September 27 2010
- Open Problems in Automata Theory and Formal Languages, talk for the Theory Colloquium, MIT, May 11 2010.
- The Frobenius Problem and Its Generalizations, talk for the MAA New York Meeting, May 1, 2010.
2009
- Universality and prefixes, suffixes, and factors, invited talk for the WORDS 2009 conference, September 15 2009, Salerno, Italy
- Periodicity and Repetitions in Automatic Sequences (invited talk for the minisymposium on Words at the 2nd Canadian Discrete and Algorithmic Mathematics Conference (CANADAM), May 27 2009)
- The Frobenius Problem and Its Generalizations (Queen's Distinguished Seminar Series)
2008
- The Frobenius Problem and Its Generalizations, talk at LIAFA in Paris, France, May 16 2008
- The Frobenius Problem and Its Generalizations, talk at the University of Arizona, Department of Computer Science, February 7, 2008.
2006
- The Ubiquitous Thue-Morse Sequence, Invited talk for the Research Experiences for Undergraduates program at University of North Carolina, Greensboro, July 14 2006.
- New Directions in State Complexity, Invited talk for the DCFS 2006 conference, June 22 2006.
- A series of 4 expository talks for the Summer School CANT (Combinatorics, Automata, and Number Theory) at the University of Liège, Belgium, May 8-12 2006.
2005
- William Dembski and Intelligent Design, 15-minute talk for the Interdisciplinary Coffee Talk Society at the University of Waterloo, November 1 2005
- My Favorite Open Problems in Words, invited talk for the Words 2005 conference.
2004
- Regular Expressions: Enumeration and State Complexity, invited talk for the Conference on Implementation and Application of Automata (CIAA), Kingston, Ontario, July 23 2004.
- Avoidability in Words: New Results and Open Problems, invited talk for the Workshop on Word Avoidability, Complexity and Morphisms (WACAM), Turku, Finland, July 17 2004.
2003
- New results on avoidability in words, talk for the Computer Science Department, University of Western Ontario, October 3 2003.
- New results on avoidability in words, talk for the Tutte Seminar, University of Waterloo, July 4 2003.
- Periodicity, morphisms, and matrices, talk for the number theory seminar, University of Waterloo, February 27 2003.
2002
- Talk at the DCFS 2002 conference (Descriptional Complexity of Formal Systems), London, Ontario.
  Regular Expressions: New Results and Open Problems
- Three talks at MathCamp, Colorado Springs, Colorado, July 29-August 2 2002.
- Formal Languages and Number Theory, Distinguished Lecture Series, University of Victoria, May 16, 2002.
2001
- Periodicity, Morphisms, and Matrices, talk for the theory seminar, Department of Computer Science, University of Arizona, November 7 2001.
- Algorithmic number theory before computers, talk at Microsoft Research, July 13 2001.
2000
- Can a Computer Think?, talk for the Kitchener-Waterloo-Cambridge-Guelph Humanists, November 20, 2000. Also see this Reading List.
- Morphisms, Matrices, and Periodicity, talk at the Winnipeg Combinatorial Mathematics Conference, September 30, 2000.
- Number Theory and Formal Languages, talk at the Winnipeg Combinatorial Mathematics Conference, September 29, 2000.
- k-regular Sequences, talk at the Colloquium in Honor of Michel Mendes France, Bordeaux, September 12, 2000. The problem about b(n) on slide 18 has now been solved by Zhao Shen.
- Algorithmic number theory before computers, talk at the workshop on Algorithmic Number Theory, Mathematical Sciences Research Institute, August 17, 2000.
- The greatest common divisor, talk at the workshop on Algorithmic Number Theory, Mathematical Sciences Research Institute, August 14, 2000.
- State complexity and Jacobsthal's function, talk at the CIAA '2000 Conference, London, Ontario, July 25, 2000.
- Ten Problems I Can't Solve, talk for the University of Waterloo Pure Math Club, July 11 2000.
  Note: Problems 3 and 5 have been solved by Soroosh Yazdani and Sabin Cautis. Problem 8 was solved in 2002 by David Moews but never published in a journal.
- The Uneasy Mix: Internet + Libraries, invited talk for the University of Waterloo Librarians Association, June 7 2000.
- Formal Languages and Number Theory, talk at AMS meeting, Notre Dame, April 8, 2000.
- Formal Languages and Number Theory, invited talk at International Colloquium on Automata, Languages, and Combinatorics, Kyoto, Japan, March 16, 2000.
- Formal Languages and Number Theory, invited talk at workshop on Unusual Applications of Number Theory, DIMACS, Rutgers University, January 14, 2000.
1999
- Automaticity and Rationality, slides for invited talk at Workshop on Descriptional Complexity of Automata, Grammars, and Related Structures, Magdeburg, Germany, July 22, 1999.
- Issues in Internet Regulation, slides for talk at Wilfrid Laurier University, March 23 1999.
- A Skeptic Looks at Christian Science, slides for talk for Freethought Waterloo, March 4 1999. You can also look at my longer version, A skeptical examination of Christian Science, and Five Questions Christian Scientists Can't Answer.
- Separating words with automata and grammars, talk for the University of Waterloo Algorithms and Complexity seminar, February 16 1999.
1998
- The Future of Free Speech in Cyberspace, talk at the Kitchener Public Library, February 23 1998.
1997
- Analysis of de Rooij's Algorithm for the Greatest Common Divisor of n Numbers, talk for the AMS meeting, Milwaukee, Wisconsin, October 25 1997.
- Regulating the Internet: National Necessity or Global Folly, talk for the conference Global Markets, Global Morals? at Wilfrid Laurier University, October 24 1997.
- Continued Fractions and Automatic Sequences, talk for the SAMS/AMS/SAMSA/LMS Joint Mathematics Conference, University of Pretoria, Pretoria, South Africa, June 27 1997.
- Number Theory and Formal Languages, talk for Number Theory Day, University of the Witwatersrand, Johannesburg, South Africa, June 25 1997.
1996
- Polynomial Automaticity, Context-Free Languages, and Fixed Points of Morphisms, talk for Mathematical Foundations of Computer Science (MFCS '96), Krakow, Poland, September 2 1996.
- Automaticity, plenary talk for the conference ``Emerging Applications of Number Theory'' at the Institute for Mathematics and Its Applications (IMA), Minneapolis, MN, July 23 1996.
- Continued Fractions and Automatic Sequences, talk for the 8th SIAM Conference on Discrete Mathematics, Minisymposium on Automatic Sequences, June 17 1996.
- Automaticity, talk at the University of Western Ontario, June 5 1996.
- The real meaning of free speech in cyberspace, talk for the conference "The Internet: Beyond the Year 2000", University of Toronto, Canada, May 1 1996.
- Discovery of a lost factoring machine, talk for the American Mathematical Society, Orlando, FL, January 13 1996.
1995
- Remarks on Inferring Integer Sequences, talk for the Canadian Mathematical Society, Vancouver, BC, December 11 1995.

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