*A pigeonhole principle for countable linear orders*. Mathematics and computer science colloquium, Albion College, March 23, 2023. Abstract.*Coloring the smooth numbers*. Mathematics Colloquium, Miami University, Oxford, OH, April 5, 2018. Abstract.*Coloring the -smooth numbers with colors*. Mathematics and computer science colloquium, Albion College, March 22, 2018. Abstract.*Real-valued measurability and the extent of Lebesgue measure*. Logic seminar, University of Michigan, November 9 and 30, 2017. Abstract: Part 1, Part 2.*Real-valued measurability and Lebesgue measurable sets*. Logic seminar, University of Notre Dame, May 2, 2017. Abstract.*Ramsey theory and small countable ordinals*. Mathematics and computer science colloquium, Albion College, April 13, 2017. Abstract.*and squares*. Logic seminar, University of Michigan, March 16 and 23, 2017. Abstract: Part 1, Part 2.*Topological partition calculus of countable ordinals*. Logic seminar, University of Michigan. April 14, 2016. Abstract.*Topological partition calculus of countable ordinals*. Logic seminar, University of Illinois, Chicago. April 7, 2016. Abstract.*The Haddad-Sabbagh results in the partition calculus of small countable ordinals*. Logic seminar, University of Michigan. October 7 and 22, 2015. Abstract: Part 1, Part 2.*Topological partition properties of*. Set theory seminar, Boise State University, January 21 and 28, 2015. Abstract: Part 1. Part 2.*Co-analytic uniformization*. Set theory seminar, Boise State University, December 10, 2014. Abstract.*Ramsey theory of very small countable ordinals*. Set theory seminar, Boise State University, September 24 and October 1st, 2014. (The slides are the English version of the slides for the talk below.) Abstract: Part 1. Part 2.*Ramsey theory of very small countable ordinals*(in Spanish). Invited talk, Conference*50 años de la Carrera de Matemáticas*, Universidad de los Andes, September 18, 2014.*An absoluteness result*. Set theory seminar, Boise State University, February 18, 2014. Abstract.*Second incompleteness*. Set theory seminar, Boise State University, October 7, 2013. Abstract.*Finitary mathematics*. Set theory seminar, Boise State University, February 21, 2013. Abstract.*Is mathematics created or discovered*? Friday Forum, Honors College, Boise State University, February 15, 2013. See also here.*Determinacy from large cardinals. II*. Set theory seminar, Boise State University, February 7, 2013. Abstract.*Determinacy from large cardinals*. Set theory seminar, Boise State University, January 30, 2013. Abstract. Notes by Summer Kisner.*Aurichi’s notion of Selective ccc*. Set theory seminar, Boise State University, November 5, 2012. Abstract. Notes by Summer Kisner.*Forcing with over models of strong versions of determinacy*, Invited talk, Set theory session,*XV SLALM*, Universidad de los Andes, Bogotá, June 8, 2012.*Determinacy and inner model theory*, Tutorial,*XV SLALM*, Universidad Nacional, Bogotá, May 30-June 2, 2012.*Ramsey theory*,*Undergraduate Math Seminar*, Boise State University, March 22, 2012.*Ramsey theory*,*Graduate Student Seminar*, Boise State University, October 19, 2011.*Sets and games*,*Mathematics Colloquium*, Boise State University, September 1, 2011.*generic absoluteness*, Second conference on the core model induction and hod mice, (August 8-19, 2011), Institut für Mathematische Logik, WWU Münster, August 15, 2011.*consequences beyond*, Invited talk, Second conference on the core model induction and hod mice, (August 8-19, 2011), Institut für Mathematische Logik, WWU Münster, August 9, 2011.*Forcing with over models of determinacy*, Minicourse, Université Paris Diderot – Paris 7, July 13 and 20, 2011.*Projective well-orderings of the reals and forcing axioms*,*Invited talk (Special session in set theory)*, 2011 North American Annual Meeting of the Association for Symbolic Logic (March 24-27, 2011), University of California, Berkeley, March 27, 2011.*-dichotomies for -Borel sets*,*XI International Workshop on Set Theory*(October 4-8, 2010), Centre International de Rencontres Mathématiques, October 7, 2010.*Determinacy*,*Graduate Student Seminar*, Boise State University, September 8, 2010.*implies that there is a -definable well-ordering of the reals for some*,*Conference on the core model induction and hod mice*(July 19-August 6, 2010), Institut für Mathematische Logik, WWU Münster, August 4, 2010.*-dichotomies*,*Invited talk*, Special session in Set Theory, Logic Colloquium 2010, Université Paris Diderot – Paris 7, July 28, 2010.*-dichotomies*,*Logic/Set Theory Seminar*, University of California, Irvine, June 2, 2010.*Downward transference of mice*,*Contributed Talk*, XIX BEST conference, Boise State University, March 27, 2010. See also*-dichotomies*, by Richard Ketchersid.*On successors of*,*Workshop on Set Theory at ISLA 2010*, University of Hyderabad, Gachibowli, India, January 29, 2010.*Multiboard determinacy*,*Mathematics Colloquium*, Miami University, Oxford, OH, November 20, 2009.*Indeterminación y elección*,*Plenary Talk*, XVII Colombian Mathematical Congress, Cali, August 3-6, 2009.*A dichotomy theorem in canonical models of , and an application to Scheeppers’s countable-finite game*,*Logic/Set Theory Seminar*, University of California, Irvine, June 1, 2009.*Scheepers’s countable-finite game in models of determinacy*,*Contributed Talk*, XVIII BEST conference, Boise State University, March 27, 2009. See also the companion talk,*A dichotomy theorem for models of*, by Richard Ketchersid.*Very large finite numbers*,*Graduate Student Seminar*, Boise State University, October 15, 2008.*Intersecting families and definability*,*Mathematics Colloquium*, Boise State University, September 19, 2008.*Regressive functions on pairs*,*Claremont Colleges Algebra/Number Theory/Combinatorics Seminar,*Pomona College, Claremont, May 9, 2008.*The extent of squares under*,*Invited talk*, ASL 2008 Annual Meeting, University of California, Irvine, March 29, 2008.*Forcing axioms and inner models*. Invited talk, Boise State University, February 27, 2008.*Intersecting families and definability*. Invited talk, William Patterson University, February 8, 2008.*Regressive functions*. Invited talk, Mills College, February 5, 2008.*Some results in finite combinatorics*,*Logic Colloquium*, University of California, Berkeley, November 2, 2007. Abstract.*Regressive functions on pairs*,*Logic Colloquium*, University of California, Los Angeles, October 19, 2007.*Combinatoria finita y lógica*,*Invited talk*, III Jornada conjuntística, Universidad Nacional, Bogotá, Colombia, August 22, 2007.*Admissible determinacy*,*Plenary talk*, XVI BEST conference, Idaho City, Idaho, March 25 and 26, 2007. See this related talk by Shehzad Ahmed (*Admissible determinacy*. Boise State University set theory seminar. June 14, 2013).*Elementary embeddings into the universe*,*Contributed talk,*Caltech-UCLA logic seminar, November 28, 2006.*Point set topology and determinacy*,*Invited talk,*Mathematics colloquium, Boise State University, Idaho, November 16, 2006.*Elementary embeddings into the universe*,*Invited talk,*Set theory seminar, Boise State University, Idaho, November 15, 2006.*Cardinal preserving elementary embeddings*,*Plenary talk*, XIII SLALM, Oaxaca, México, August 9, 2006.*Some consequences of the -ideal dichotomy*,*Contributed talk*, Caltech-UCLA logic seminar, April 14, 2006.*and a covering property that implies*,*Invited talk*, Set theory seminar, Fields Institute, Toronto, Canada, March 27, 2006.*Covering consequences of the proper forcing axiom*,*Invited talk*, UC Irvine-UCLA set theory seminar, March 18, 2006.*Strong forcing axioms and inner models*,*Invited talk*, MAMLS meeting in honor of Menachem Magidor 60-th birthday, University of California, Irvine, February 4, 2006.*Recent developments in the theory of the proper forcing axiom*,*Contributed talk*, Caltech-UCLA logic seminar, October, November 2005.*and the reals*. Kurt Gödel Research Center, University of Vienna. June 28, 2005. Abstract.*Preserving sequences of stationary subsets of*. Kurt Gödel Research Center, University of Vienna. May 3, 2005. Abstract.*Preserving sequences of stationary subsets of*,*Invited talk*, Université Paris 7-Denis Diderot, Paris, France, April 21, 2005.*Stationary subsets of and models of set theory*. Department colloquium, Boise State University, February 22, 2005.*Projective well-orderings of the reals*,*Invited ASL address*, Joint Mathematics Meetings, Atlanta, January 8, 2005.*Projective well-orderings and bounded forcing axioms*,*Logic Colloquium*, University of California, Los Angeles, December 10, 2004.*Bounded forcing axioms and projective well-orderings of the reals*. Kurt Gödel Research Center, University of Vienna. November 30, 2004. Abstract.*and the saturation of the nonstationary ideal on*. Kurt Gödel Research Center, University of Vienna. March 23, 2004. Abstract.*Cardinales Grandes y la Teoría de Primer Orden de los Reales*,*Graduate Seminar*, Universidad de los Andes, Bogotá, Colombia, February 12, 2004.*Real-valued measurable cardinals and -well-orderings of the reals*, Centre de Recerca Matemàtica, Bellaterra, Spain, December 18, 2003.*Real-valued measurable cardinals and definable well-orderings of the reals*,*Logic Colloquium*, Institut für Mathematische Logik und Grundlagenforschung of the University of Münster, Germany, December 5, 2003.*Well-Orderings of the Reals and Real-valued Measurability.*Kurt Gödel Research Center, University of Vienna. October 7 and 14, 2003. Abstract.

*Forcing axioms and inner models of*,*Greater Boston Logic Conference*, Massachusetts Institute of Technology, Cambridge, May 18, 2003.*Well-orderings of the reals*,*Mathematical Logic Seminar*, Carnegie Mellon University, Pittsburgh, November 13, 2002. Abstract.*Real-valued measurability and -well-orderings of the reals*. Set theory seminar, UC Berkeley, March 16 and April 6, 2001. Notes by Apollo Hogan.*What are super-real fields?*. Student logic colloquium, UC Berkeley, October 6, 2000. (An exposition of results of Dales and Woodin.) Abstract.*A brief introduction to forcing*. Student logic colloquium, UC Berkeley, November 10 and 17, 1999. Abstract: 1, 2.*Jerarquías de consistencia*. Universidad Nacional de Colombia. December, 1998.