Here is something close to a complete list of talks and research visits I've given, both invited and contributed. Further below is a list of slides which haven't been curated in some time.
2014/11/10 - London/Paris Number Theory Seminar - Jussieu
2014/9/29 - Number Theory Seminar - Torsion on CM Elliptic Curves over prime degree number fields - University of Warwick
2014/3/10 - Algebra and Topology Seminar - Palindromic Properties and Descent Obstructions - University of Copenhagen
2014/1/28 - Forschungsseminar "Arithmetische Geometrie" - Palindromic Properties and Descent Obstructions - Humboldt Universität zu Berlin
2014/1/16 - Algebra and Number Theory Seminar - Palindromic properties of curves and explicit descent obstructions - Pennsylvania State University
2013/11/1 - XM Seminar - Torsion on Elliptic curves - University of Copenhagen
2013/3/25 - Colloquium - From divergent series to a million-dollar puzzle - University of Louisiana Lafayette
2013/3/14 - 27th Automorphic Forms Workshop - Twists of Shimura Curves and Applications - University College Dublin
2013/2/5 - Reseach Visit - Massachusetts Institute of Technology
2013/2/1 - Student Seminar - The Frobenius Number - Eastern Connecticut State University
2013/1/22 - Job talk - University of Bristol
2012/10/3 - Math Club (Wide audience talk - ~50 student attendees) - Art and Mathematics: Escher, Lenstra, and 'The Print Gallery' - Bates College
2012/10/26 - Algebra Seminar - Twists of Shimura Curves 2: Embeddings and abelian varieties - Wesleyan University
2012/10/11 - Math Club - Art and Mathematics: Escher, Lenstra, and 'The Print Gallery' - Wesleyan University
2012/10/3 - Math Club - Art and Mathematics: Escher, Lenstra, and 'The Print Gallery' - University of Connecticut
2012/10/3 - Algebra Seminar - Twists of Shimura Curves and applications - University of Connecticut
2012/9/14 - Algebra Seminar - Twists of Shimura Curves and applications - Wesleyan University
2012/4/4 - Thesis Defense - University of Georgia
2012/2/24 - Impromptu Seminar - Twists of Shimura curves and applications - Graduate Center, City University of New York
2012/1/5 - Special Session:Rational Points on Varieties - Twists of Shimura curves and applications - Joint Meetings
2011/11/29 - Algebraic Geometry and Number Theory Seminar - Twists of Shimura curves - Johns Hopkins University
2011/11/18 - STAGE - Brandt Modules - Massachusetts Institute of Technology
2011/10/1 - Maine-Quebec Number Theory Conference - Twists of Shimura curves - University of Maine
2011/9/10 - PANTS XVI - Twists of Shimura curves - Emory University
2011/7/29 - Mock AMS Conference - Simultaneous embeddings into quaternion orders - University of Georgia
2011/5/19 - RAGE - Rational points on Atkin–Lehner twists of Shimura curves at ramified primes - Emory University
2010/12/4 - PANTS XVI - Some recent progress on the Frobenius problem - University of South Carolina
2010/7/28 - Mock AMS Conference - Twists of X0(14) and the inverse Galois problem - University of Georgia
2008/10/12 - PANTS VII - Torsion subgroups of CM elliptic curves - College of Charleston
2008/4/20 - SERMON - Torsion points on CM elliptic curves - Clemson University
Twists of Shimura Curves From the special session on Rational Points on Varieties at the 2012 Joint Meetings of the AMS and MAA. Beware that there's an error on page 8, corrected in my thesis.
Some recent progress on the Frobenius problem A talk given at the 14th meeting of the Palmetto Number Theory Series in December 2010 about some recent papers on the Frobenius Problem.
M.C. Escher and Maps Between Elliptic Curves This is a talk I gave in the graduate student seminar about some work of Lenstra on Elliptic curves and a painting of Escher. Beware that this pdf is over 5 megabytes as it contains a video showing the periodicity of Escher's lithograph.
Torsion Points on CM Elliptic Curves This is a talk I gave at the SouthEastern Regional Meeting On Numbers at Clemson in April 2008.
The Riemann-Roch Theorem This is a paper I did at the end of my class on Tate's Thesis in Spring 2007 at UConn. Notice that this is only Riemann-Roch for curves and even then since I use Weil's proof (adapted from Michael Rosen's Number Theory in Function Fields), there is not much Geometry to be seen on the surface.
The Semi-Stable Reduction Theorem This
is the hour presentation I did at the end of my Arithmetic Geometry class
in Fall 2007. This is based on some hopping around I did in Joseph
Silverman's The Arithmetic of Elliptic Curves although I do not
neccesarily assume that every field is perfect and thus expend some energy
checking polynomial GCDs to make sure that all the extensions described are separable so that we can work more easily with Discrete Valuations.
Quaternion Algebras and Modular Forms These are notes on a presentation I did in Jon Hanke's class on modular forms which pushes on towards Shimura Curves.
On the parametrization of rings of low rank This is a little something I wrote up for a presentation in the summer VIGRE Graduate Student Seminar about Bhargava's work parametrizing rings of low rank. This is an unedited set of notes, so caveat lector.
Geometric Invariant Theory and Toric Varieties These are the notes from a 35 minute presentation with (at the time) fellow UGA grad student Maxim Arap.
Theta Characteristics This is a 1 hour presentation on theta characteristics, ostensibly over the complex numbers, but with some sensitivity to arithmetic issues.