- A. Castillo,
*Distribution of the trace of Frobenius on average for rank 2 Drinfeld modules*, submitted (2015), 21 pages. - A. Castillo,
*The normal order of the divisor-counting function for rank 2 Drinfeld modules with nontrivial endomorphism ring*, submitted (2015), 18 pages. - A. Castillo and R. Dietmann,
*On Hilbert’s Irreducibility Theorem*, submitted (2015), 11 pages. - A. Castillo, C. Hall, R. J. Lemke Oliver, P. Pollack, and L. Thompson,
*Bounded gaps between primes in number fields and function fields*, Proc. Amer. Math. Soc.**143**(2015), no. 7, 2841–2856. - J. Berg, A. Castillo, B. Grizzard, V. Kala, R. Moy, and C. Wang,
*Congruences for Ramanujan's f and ω functions via generalized Borcherds products*, The Ramanujan Journal, November 2014, Volume 35, Issue 2, 327-338.

- "Distribution of the trace of Frobenius for Drinfeld modules", Illinois Number Theory Conference, University of Illinois at Urbana-Champaign, August 2015
- "Distribution of the trace of Frobenius for Drinfeld modules", Elementary, analytic, and algorithmic number theory: Conference in honor of Carl Pomerance’s 70th birthday, University of Georgia in Athens, June 2015
- "Bounded gaps between primes in number fields and function fields", Upstate Number Theory Conference, Cornell University, April 2015
- "Hilbert's Irreducibility Theorem and Galois resolvents", AMS Spring Southeastern Sectional Metting, University of Alabama in Huntsville, March 2015
- "Hilbert's Irreducibility Theorem and Galois resolvents", Automorphic Forms Workshop, University of Michigan, March 2015
- "Hilbert's Irreducibility Theorem and Galois resolvents", UIC-Northwestern Graduate Student Number Theory Day, Northwestern University September 2014
- "The normal order method and invariants of Drinfeld modules over finite fields", UIC Number Theory Seminar, October 2014
- "Distribution of the trace of Frobenius for Drinfeld modules", ENFANT, Hausdorff Center for Mathematics, July 2014
- "The normal order method and invariants of Drinfeld modules over finite fields", Midwest Number Theory Conference for Graduate Students and Recent PhDs, University of Illinois at Urbana-Champaign, June 2014

- Elementary, analytic, and algorithmic number theory: Research inspired by the mathematics of Carl Pomerance (In honor of Carl Pomerance’s 70th birthday), University of Georgia in Athens, June 8-11, 2015
- Upstate Number Theory Conference, Cornell University, April 10-12, 2015
- AMS Spring Southeastern Sectional Metting, University of Alabama, Huntsville, AL, March 27-29, 2015.
- Automorphic Forms Workshop, Ann Arbor, MI, March 2-5, 2015.
- Joint Math Meetings, San Antonio, TX, January 10-13, 2015.
- AIM Workshop: Bounded gaps between primes, American Institute of Mathematics, Palo Alto, CA, November 17-21, 2014.
- LMS-CMI Research School: Bounded gaps between primes, Clay Mathematics Institute, Oxford, UK, September 22-26, 2014.
- Workshop: Analytic Number Theory - ENFANT and ELEFANT, Hausdorff Center for Mathematics, Bonn, Germany, July 2014.
- Seminaire de Mathematiques Superieures 2014: Counting Arithmetic Objects, MSRI & CRM, Montreal, Canada, July 2014.
- Number Theory at Illinois: A Conference in Memory of the Batemans and Heini Halberstam, University of Illinois at Urbana-Champaign, June 2014.
- Midwest Number Theory Conference for Graduate Students and Recent PhDs, University of Illinois at Urbana-Champaign, June 2014.

- "Brun's Theorem towards twin primes and improvements: a survey", UIC Graduate Number Theory Seminar, January 2015
- "A survey of conjectures about the distribution of Frobenius for elliptic modules", UIC Graduate Number Theory Seminar, October 2014
- "Bounded gaps between primes and applications of the Maynard-Tao method", UIC Graduate Number Theory Seminar, September 2014
- "An introduction to function field arithmetic and Drinfeld modules", learning seminar lectures, Spring 2014, UIC
- "Effective versions of Hilbert's Irreducibility Theorem", Number Theory Working Seminar lectures, Spring 2013, UIC
- "Introduction to modular forms", learning seminar lectures, Winter 2012, UIC
- "Probabilistic Galois theory", Number Theory Working Seminar lectures, Fall 2012, UIC
- "Number fields", learning seminar lectures, Summer 2012, UIC
- "Local and global fields", learning seminar lectures, Spring 2012, UIC