
Covering talk,
Talk on covering congruences (Joint Math Meetings, San Diego, January 2008).

Undergrad covering talk,
More elementary talk on covering congruences (Spuyten Duyvil Undergraduate
Mathematics Meeting, New York City, April, 2008; Ohio and Michigan
MAA Sections, Spring 2008).

Talk on Euler's function,
Talk at University of Georgia, February 2008 and Trinity University, March 2008.

Elementary primality talk,
Lucas Lecture at Fibonacci Association Meeting in Patras, Greece, July 2008.

Fields talk,
Counting Fields. At Canadian Number Theory Association Meeting
in Waterloo, Canada, July 2008. Version
for Berkeley Number Theory Seminar, February 2010.

Multiplicative order talk,
The multiplicative order mod n, on average.
At the Quebec/Maine number theory conference at Laval University,
Quebec, Canada, October, 2008.

Order and chaos,
At the PANTS meeting (yes, a "long PANTS talk"), University of
South Carolina, Columbia, SC, December, 2008.
Version of March, 2009,
Brigham Young University.
Version of April, 2009,
University of Rochester.

Sociable numbers: new developments on
an ancient problem,
Session on the Beauty and Power of Number Theory, Joint Mathematics
Meetings, Washington, DC, January, 2009.
Long version of March, 2009,
Brigham Young University undergraduate colloquium.
Long version of April, 2009,
Lorentz Center, Leiden, The Netherlands.
The first dynamical system?
AMS Special Session, Boston College, April, 2013.

A 1935 Erdős paper on prime numbers
and Euler's function,
at the AMS Central Section meeting, University of Illinois, Urbana, IL,
March, 2009.
Version of July, 2009, at the
University of Montreal and at the 41st Conference on Combinatorics,
Graph Theory and Computing,
Version of December, 2009,
at the West Coast Number Theory Conference.

Discrete Logarithms,
Dartmouth Number Theory Seminar, November 19, 2009.

Fixed points for discrete logarithms,
41st Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL,
March 2010.
Related talk: The Pólya–Vinogradov
inequality,
Illinois Number Theory Conference in Honor of Harold Diamond, May 21, 2010.
Related talk: Fixed points for discrete logarithms,
ANTS IX, Nancy, France, July 19–23, 2010.

Fibonacci integers,
Banff conference in honor of Cam Stewart, May 31, 2010 to June 4, 2010.

Counting in number theory, the Rademacher Lectures, U Penn, September, 2010:
Elementary number theory,
Finite cyclic groups,
Fibonacci integers,
Counting fields

Two problems in combinatorial number theory,
Number theory and its applications, Debrecen, Hungary, Oct. 4–8, 2010.

Elliptic curves: applications and problems,
IMA Abel Conference, Minneapolis, MN, January, 2011.

Order and chaos,
MSRI Arithmetic Statistics Introductory Workshop,
Berkeley, CA, January/February, 2011.
Undergrad version:
Order and chaos,
Hudson River Undergraduate Mathematics Conference,
Skidmore College, Saratoga Springs, NY, April 16, 2011.
Grad version:
Order and chaos,
Quebec Student Conference, University of Montreal,
May 20, 2011.
Short version:
A problem of Arnold on the average multiplicative order,
Maine/Quebec Number Theory Conference, University of Maine,
October 1,2, 2011.
Version of November, 2012
Version of December, 2013

Productfree sets of integers,
Integers Conference, Carrollton, GA, October, 2011.
Sums and products,
Mathematics & Statistics Colloquium, U. Vermont, December 2, 2011.
Boston Meetings version,
Joint Mathematics Meetings, Boston, MA, 2012.
UC Irvine colloquium, February 9, 2012.
Sums and products
International Number Theory Conference in memory of
Alf van der Poorten, AM, March 15, 2012.
Sums and products
Dartmouth Mathematics Society, May 16, 2012.
Sums and products
U. Georgia VIGRE seminar, November 28, 2012.
Sums and products,
West Chester U., April 24, 2013, SUNY Albany, April 25, 2013.
Sums and products,
Arizona State U., February 27, 2014.
Sums and products,
Providence College, April 2, 2014.
What we still don't know about addition
and multiplication, Johns Hopkins Center for Talented Youth,
May 4, 2013.
What we still don't know about addition
and multiplication, Richard and Louise Guy Lecture, University
of Calgary, September 12, 2013.
What we still don't know about addition
and multiplication, Woods Lecture Series, Butler University,
December 3, 2013.
What we still don't know about addition
and multiplication, Fuzzy Vance Lecture, Oberlin College,
March 20, 2014.
What we still don't know about addition
and multiplication, Christie Lecture, Bowdoin College,
April 7, 2014.
What we still don't know about addition
and multiplication, Bay Area Mathematical Adventures, Santa Clara University,
January 23, 2015.

Sets of monotonicity for Euler's function,
West Coast Number Theory Conference, Asilomar Conference Center, Pacific Grove, CA, December, 2011.

The range of Carmichael's function,
AMS Sectional Meeting, U. Hawaii, Honolulu, March, 2012.

Balanced subgroups of the multiplicative group,
Dartmouth Number Theory Seminar, April 26, 2012.
Balanced subgroups of the multiplicative group,
CNTA, June, 2012.
Balanced subgroups of the multiplicative group,
Quebec/Maine Number Theory Conference, September, 2012.
Balanced subgroups of the multiplicative group,
Central Section AMS Meeting, U. Akron, Akron, OH, October, 2012.
Balanced subgroups of the multiplicative group,
Palmetto Number Theory Symposium, December 2, 2012.

Some statistical problems concerning the arithmetic
functions σ and φ,
Joint Mathematics Meetings, Special Session on Arithmetic Statistics,
San Diego, CA, January, 2013.

Erdős, van der Corput, and the birth
of covering congruences,
Joint Mathematics Meetings, Special Session on Covering Congruences,
San Diego, CA, January, 2013.

Paul Erdős and the rise of
statistical thinking in elementary number theory,
Erdős Centennial Conference, Budapest, July 1–5, 2013.
Paul Erdős and the rise of statistical
thinking in elementary number theory,
Version of 1/15/14 at the Joint Math Meetings, Baltimore.

The set of values of an arithmetic function,
Mathematical Congress of the Americas, Guanajuato, Mexico, August 9, 2013.
The set of values of an arithmetic function,
Integers Conference (marking the Erdős centennial), University of West Georgia,
Carrollton, GA, October 23–27, 2013.
The ranges of various familiar functions,
CNTA XIII, Carleton University, Ottawa, Canada, June 20, 2014.
The ranges of some familar arithmetic functions,
Maine/Quebec Number Theory Conference, Orono, ME, October 34, 2015.

Square values of Euler's function,
SCHOLAR conference in honour of M. Ram Murty, University of Montreal, October
15–17, 2013.

Amicable numbers,
Illinois Conference in Memory of Felice and Paul Bateman and
Heini Halberstam, June 57, 2014.
Amicable numbers,
Brown University Algebra Seminar, April 6, 2015.

The statistics of elementary number theory,
2014 NCTS Conference on the Impact of Computation in Number Theory,
30 July, 2014 to 3 August, 2014, National Tsing Hua University, Hsinchu, Taiwan.
Statistics in elementary number theory,
CRM Workshop on "Statistics and elementary number theory", Montreal, 1519 September, 2014.

The first function,
U. Georgia colloquium, December 3, 2014.
The first function,
Middlebury College Seminar, April 21, 2015.
The first function,
Connections in Discrete Mathematics, A celebration of the work of Ron Graham,
Simon Fraser U., June 15  19, 2015
The sumofproperdivisors function,
BC–MIT Number Theory Seminar, September 15, 2015.
The first function,
Cal State Chico Colloquium, February 5, 2016.
The first function,
Dartmouth Colloquium, May 26, 2016.
The first function,
Western Michigan U., Colloquium, October 14, 2016.

The CRM Aisenstadt Chair Lectures, December 8–12, 2014, Montréal.
The ranges of some familiar functions,
December 8, 2014.
The first function,
December 11, 2014.
Amicable numbers,
December 12, 2014
Letters from the master: my correspondence
with Paul Erdős,
Lecture at History of Mathematics
Special Interest Group of the Mathematical Association of America,
Joint Mathematics Meetings, San Antonio, TX, January 10, 2015.
Here are some sample letters that are
discussed near the end of the talk.
Random number theory,
Lecture at Random Roads: A celebration of Joel Spencer's 70th birthday,
NYU, April 30, 2016.
'Rithmetic revisited: what we still don't know about + and ×,
Math Encounters, National Museum of Mathematics, June 1, 2016.
The first function and the GuySelfridge conjecture,
CNTA Calgary, Guy Session, June 21, 2016.
The first dynamical system (with a short feature),
Summer school on fractal geometry and complex dimensions, Cal Poly San Luis Obispo, June 27, 2016.
Why the ABC conjecture,
Kummer classes and anabelian geometry, U. Vermont, September 1011, 2016.
Euclidean prime generators,
Dartmouth Number Theory Seminar, October 4, 2016 and Integers Conference,
U. West Georgia, October 6, 2016.
Euclidean prime generators,
West Coast Number Theory Conference, Pacific Grove, CA, December 2016.
What we still don't know about addition and
multiplication,
Undergraduate Lecture Series, Michigan State U., October 11, 2016.
The ranges of some familiar arithmetic functions,
Michigan State U. Colloquium, October 13, 2016.
The ranges of some familiar arithmetic functions,
Max Planck Institute for Mathematics, November 2, 2016.
The ranges of some familiar arithmetic functions, MSRI, May 7, 2017.
The first dynamical system,
Charles U. (Prague) Seminar, November 8, 2016.
Random number theory,
Charles U. (Prague) Colloquium, November 8, 2016.
 U. Georgia talks, March 2228, 2017
Random number theory,
Euclidean prime generators,
What we still don't know about addition and multiplication,
The first dynamical system.
New results on an ancient function,
Maine/Quebec Number Theory Conference, October 14,15, 2017.
New results on an ancient function,
Joint Math Meetings 2018, San Diego, Special Session on Computational
Methods in Combinatorics and Number Theory.
The aliquot constant,
West Coast Number Theory Conference, December 1620, 2017.
What we still don't know about addition and multiplication,
Leonard C. Sulski Memorial Lecture and MAA Northeastern Section Dinner Meeting,
College of the Holy Cross, Worcester, MA, April 23, 2018.
The Erdős problem on primitive sets,
CRM workshop on Probability in Number Theory, U. de Montreál,
May 28, 2018. (See draft of paper on this topic with some updated results.)
The Erdős problem on primitive sets,
Integer Conference, Augusta, GA, October 3, 2018.
The Erdős problem on primitive sets,
West Coast Number Theory Conference, Chico, CA, December 1519, 2018.
The Erdős problem on primitive sets,
Joint Mathematics Meetings, Baltimore, MD, January 1519, 2019.
Random number theory,
CMS Summer Meeting, U. New Brunswick, June 4, 2018.
What we still don't know about addition and multiplication,
Evans–Bourdon Lecture, Washington & Lee U., October 9, 2018.
Primality testing: then and now,
Celebrating 75 years of Mathematics of Computation, ICERM, November 1–3, 2018, Providence.
What we still don't know about addition
and multiplication,
Trjitzinsky Lecture 1, U. Illinois UrbanaChampaign,
November 27, 2018.
Random number theory,
Trjitzinsky Lecture 2, U. Illinois UrbanaChampaign,
November 28, 2018.
Primality testing: then and now,
Trjitzinsky Lecture 3, U. Illinois UrbanaChampaign,
November 29, 2018.