**Conference Talks:**

- “On the adelic image of Galois representations attached to elliptic curves with complex multiplication,” Joint Math Meetings, Boston, 1/5/2023.
- “On the adelic image of Galois representations attached to elliptic curves with complex multiplication,” AMS Fall Sectional Meeting, 10/1/2022, UMass Amherst.
- “ell-adic Galois representations attached to elliptic curves with CM,” AMS Spring Sectional Meeting, 3/20/2022, Tufts University, Boston, MA (Online).
- “Towards a classification of adelic Galois representations attached to elliptic curves over Q,” IMBM Number Theory Seminars, 5/21/2021, Istanbul, Turkey (Online).
- “A classification of isogeny torsion graphs over Q,” (joint with Garen Chiloyan), 1/8/2021, Joint Math Meetings, Special Session on Algebraic and Arithmetic Geometry, Online.
- “Recent progress in the classification of torsion subgroups of elliptic curves“, 9/14/2019, Union College Mathematics Conference, Union College, Schenectady, NY.
- “Galois representations attached to elliptic curves with CM“, 6/28/2019, BU/Keio workshop, Boston University, Boston, MA.
- “A classification of p-adic Galois representations attached to elliptic curves with CM”, 3/22/2019, AMS Spring Central and Western Joint Sectional Meeting, University of Hawaii, Honolulu, HI.
- “Recent progress in the classification of torsion subgroups of elliptic curves“, 9/29/2018, Front Range Number Theory Day, Colorado State University, Front Collins, CO.
- “Recent progress in the classification of torsion subgroups of elliptic curves”, 5/22/2018, Diophantine Geometry, CIRM, Marseille (Luminy), France. (Video)
- “A probabilistic model for the distribution of ranks of elliptic curves”, 3/20/2018, Automorphic Forms Workshop, Tufts University, Medford, MA.
- “A probabilistic model for the distribution of ranks of elliptic curves”, 10/15/2017, Maine-Quebec Number Theory Conference, University of Maine, Orono, ME.
- “Bounds for the Mordell-Weil rank of jacobians of hyperelliptic curves over Q”, 9/23/2017, AMS Southeastern Fall Sectional Meeting, Orlando, FL.
- “A probabilistic model for the distribution of ranks of elliptic curves”, 5/6/2017, Upstate NY Number Theory Conference, Binghamton, NY.
- “On the minimal degree of definition of p-primary torsion subgroups of elliptic curves”, 3/5/2016, AMS Southeastern Spring Sectional Meeting, University of Georgia, Athens, GA.
- “On the minimal degree of definition of p-primary torsion subgroups of elliptic curves”, 10/4/2015, 2015 Maine-Quebec Number Theory Conference, University of Maine, Orono, ME.
- “Cuerpos de definición de puntos de torsión en curvas elípticas con ramificación minima”, 2/2/2015, Congreso RSME 2015, Granada, Spain.
- “Puntos de torsión en curvas elípticas”, 9/2/2014, Tercer Encuentro Conjunto RSME-SMM, Universidad Autónoma de Zacatecas, Mexico.
- “Uniform boundedness in terms of ramification”, 3/21/2014, AMS Southeastern Spring Sectional Meeting, University of Tennessee, Knoxville, TN.
- “Uniform boundedness in terms of ramification”, 10/6/2013, 2013 Maine-Quebec Number Theory Conference, University of Maine, Orono, ME.
- “Uniform boundedness in terms of ramification”, 6/1/2013, Pacific Northwest Number Theory Conference, 2013, University of Washington, Seattle, WA.
- “Uniform boundedness in terms of ramification”, 4/27/2013, Third Annual Upstate New York Number Theory Conference, Binghamton University, Vestal, NY.
- “On the field of definition of a p^n –th torsion point on elliptic curves over number fields”, 4/6/2013, AMS Spring 2013 Eastern Sectional Meeting, Boston College, Chestnut Hill, MA
- “Formal groups of elliptic curves with potential good supersingular reduction”, 9/29/2012, at the 2012 Maine/Québec Number Theory Conference, Université Laval, Québec City, Canada.
- “Are the real numbers really real? Really?”, 4/27/2012, plenary talk at the Spring 2012 MATYCONN meeting, Bridgeport, Connecticut.
- “Bounds on the torsion subgroup of an elliptic curve”, 10/2/2011, at the 2011 Maine/Québec Number Theory Conference, University of Maine, Orono, Maine.
- “On the field of definition of p-torsion points on elliptic curves over the rationals”, 5/1/2011, at the Upstate Number Theory Conference, Cornell University, Ithaca, New York.
- “On the field of definition of p-torsion points on elliptic curves over the rationals”, 4/9/2011, at the 2011 Spring Eastern Sectional Meeting, session on “Modular Forms, Elliptic Curves, L-functions, and Number Theory”, Worcester, Massachusetts.
- “The Quantitative Learning Center at UConn, and the effects of online homework in the study habits of students” (joint with Tom Roby), 1/14/2010, Joint Math Meetings, MAA Session on Developmental Mathematics Education: Helping Under-Prepared Students Transition to College-Level Mathematics, San Francisco, CA.
- “Bounds for the torsión subgroup of elliptic curves over fields with bounded ramification” (joint with Ben Lundell), 1/14/2010, Joint Math Meetings, AMS Special Session on Arithmetic Geometry, San Francisco, CA.
- “Bernoulli-Hurwitz numbers, Wieferich primes and Galois representations”, 4/25/09, AMS Sectional Meeting, special session on number theory, WPI, Worcester, MA.
- “Ranks of abelian varieties over infinite extensions of the rationals”, 10/11/08, AMS Sectional Meeting, special session on number theory, Wesleyan University, Middletown, CT.
- “Bounds for the torsion of elliptic curves over extensions with bounded ramification”, 10/11/08, (work presented by coauthor, Benjamin Lundell), AMS Sectional Meeting, special session on number theory, Wesleyan University, Middletown, CT.
- “Curvas elípticas de rango maximal”, 7/18/2007, Segundas Jornadas de Teoría de Números, Madrid.
- “Trivial bounds and elliptic curves of maximal rank”, 7/12/2006, CNTA IX, Vanc., BC.
- “Trivial bounds and elliptic curves of maximal rank”, 4/22/2006, AMS East Sec. Meet., Durham, NH.
- “Sobre unidades elípticas y representaciones p-ádicas de Galois”, 7/1/2005, Primeras Jornadas de Teoria de Numeros, Vilanova i la Geltru, Spain.
- “Elliptic Units and Galois Representations”, 12/11/2004, at the Canadian Mathematical Society – Winter Meeting, Arithmetic Geometry Session.

### Seminar Talks (outside of UConn):

- “On the adelic image of a Galois representation attached to an elliptic curve with CM,”
**Wesleyan University Number Theory Seminar**, 3/31/2023. - “El Ultimo Teorema de Fermat (para polinomios),”
**Universidad de Puerto Rico – Mayaguez, Colloquium**, 3/16/2023. - “Fermat’s Last Theorem (for polynomials),”
**Union College Colloquium**, 2/16/2023. - “The adelic image of a Galois representation attached to an elliptic curve with CM”
**Boston University Number Theory Seminar**, 1/30/2023. - “The adelic image of a Galois representation attached to an elliptic curve with CM”
**MIT Number Theory Seminar**, 11/29/2022. - “What is a Galois representation?”
**Charles University Number Theory Seminar – Prague**, 12/14/2022. - “From Diophantus to Bitcoin: Why are Elliptic Curves Everywhere?”, 11/1/2022, Center for Advanced Mathematical Sciences (American Univ. of Beirut). (Slides)
- “From Diophantus to Bitcoin: Why are Elliptic Curves Everywhere?”, Open Neighborhood Seminar 10/26/2022, Harvard University.
- “Una clasificacion de grafos de isogenia-torsion para curvas elipticas sobre Q”, Seminario Latinoamericano de Teoria de Numeros, 5/21/2020. (Presentacion/Slides) (Video)
- “Coincidences of Division Fields and Isogeny-Torsion Graphs”, UVM Number Theory Seminar, 2/20/2020,
**University of Vermont**. - “What is… an elliptic curve?”
**Colby College Colloquium**, 11/4/2019, Colby College, Waterville, ME. - “Bounds for the Mordell-Weil rank of jacobians of hyperelliptic curves over Q”, AGENTS, 10/19/2017,
**Tufts University**. - “A probabilistic model for the distribution of ranks of elliptic curves”, Group, Lie and Number Theory Seminar, 11/6/2017,
**University of Michigan**. - “A probabilistic model for the distribution of ranks of elliptic curves”, Five College Number Theory Seminar, 11/1/2016,
**Amherst College.** - “A probabilistic model for the distribution of ranks of elliptic curves”, NYU-CUNY-Columbia Number Theory Seminar, 10/20/2016,
**Courant Institute**. - “A probabilistic model for the distribution of ranks of elliptic curves”, 9/19/2016, Number Theory Seminar,
**Boston University**. - “Galois representations attached to elliptic curves and torsion subgroups”, 5/13/2016, Number Theory Seminar,
**UC Santa Cruz**. - “Uniform results in torsion subgroups of elliptic curves”, 4/16/2015, Colloquium,
**University of Georgia (UGA)**. - “Abelian Division Fields”, 4/15/2015, Number Theory Seminar,
**University of Georgia (UGA).** - “Abelian Division Fields”, 4/6/2015, Number Theory Seminar,
**Boston University**. - “Cotas Uniformes en Terminos de Ramificacion”, 3/17/2015, Algebra Seminar,
**Universidad Autonoma de Madrid**, Spain. - “Uniform Bounds in Terms of Ramification”, 11/3/2014, Number Theory Seminar,
**Brown University**. - “Division fields of elliptic curves with minimal ramification”, 11/1/2013, The Arithmetic Seminar, at
**Binghamton University.** - “Division fields of elliptic curves with minimal ramification”, 10/21/2013, Number Theory Seminar at
**Boston University**. - “Kubert-Lang units, Bernoulli-Hurwitz numbers, Wieferich places and Galois representations”, 11/14/2011, Number Theory Seminar at
**Yale University**. - “Serre’s uniformity question and bounds on torsion subgroups of elliptic curves”, 10/25/2011, at the
**Five College Algebra Seminar (Amherst College)**. - “Torsion points on elliptic curves defined over number fields”, 11/22/2010, Number Theory Seminar at
**Boston University**. - “A survey of modular curves, and applications to torsion points on elliptic curves.”, 10/28/2010, Colloquium at
**Wesleyan University**. - “An elementary proof of Fermat’s Last Theorem (for polynomials!)”, 6/11/2010, at the Student Mathematical Institute,
**Cornell University**. - “Improving B(E,N)’s bound on the torsion subgroups of elliptic curves”, 6/11/2010, Number Theory Seminar,
**Cornell University**. - “Bounds on the torsion subgroup of an elliptic curve”, 10/24/2008,
**Five College Algebra Seminar**. - “Master Leonardo Bigollo and an unsolved 2000-year-old problem”, 2/4/2008,
**Merrimack College**. - “Bernoulli-Hurwitz numbers and Galois representations”, 3/19/2007,
**Boston U**.**Algebra Seminar**. - “Cotas triviales y curvas elipticas de rango maximal”, 12/12/2005, Seminario de Algebra,
**Universidad Autonoma de Madrid****, Spain.** - “Elliptic Units and Galois Representations”, 9/18/2004, Brown; 12/08/2003,
**Stanford University**. - “Elliptic Units and Galois Representations”, 11/18/2003,
**Five Colleges Number Theory Seminar.**

**Seminar Talks (at UConn):**** **

- “From Diophantus to Bitcoin: Why are elliptic curves everywhere?” UConn REU Talk Series, 7/21/2023.
- “Math of Encryption,” UConn Math Club, 3/8/2023.
- “Galois Representations,” SIGMA seminar, 9/24/2021.
- “What is… an elliptic curve?”, SIGMA seminar, 10/20/2020.
- “Coincidences of Division Fields”, Algebra Seminar, 2/12/2020.
- “Hilbert’s 10th Problem”, UConn Math Club, 11/4/2019.
- “Pi is irrational”, UConn Math Club, 3/13/2019.
- “Master Leonardo Bigollo and a 1000-year-old unsolved problem”, Number Theory Day 2018, 4/11/2018.
- “MATH: What is it good for?”, Major Exploration Week, 2/14/2018.
- “What is Galois Theory?”, UConn SIGMA, 2/17/2017.
- “What groups arise from the theory of elliptic curves?”, UConn SIGMA, 5/1/2015.
- “Fermat’s Last Theorem… for Polynomials”, UConn Math Club, 11/3/2014.
- “Algebraic Number Theory VS Elliptic Curves”, Special Seminar, 5/13/2014
- “Are the real numbers really real? Really?”, SIGMA Seminar, 10/11/2013.
- “Formal groups of elliptic curves with good supersingular reduction”, Algebra Seminar, 9/19/2012.
- “Bounds on the torsion subgroup of an elliptic curve”, Algebra Seminar, 10/4/2011.
- “An Elementary Proof of Fermat’s Last Theorem (for polynomials)”, SIGMA seminar, 4/23/2010.
- “Iwasawa Theory (continued)”, Algebra Seminar, 2/23/2010.
- “Classical Iwasawa Theory”, Algebra Seminar, 2/9/2010.
- “The Bridge between Elliptic Curves and Modular Forms”, SIGMA Seminar, 3/18/09.
- “UConn’s Quantitative Learning Center: Research and Future Directions”, CRME Seminar, 2/18/09.
- “Peer Tutoring at the Quantitative Learning Center”, CRME Seminar, 2/11/09.
- “Master Leonardo ”Bigollo” and a 2000-year old unsolved problem”, Math Club, 10/22/08.
- “Ranks of elliptic curves over infinite extensions of the rationals”, Algebra Seminar, 9/30/08.
- “Bounds on the torsion subgroup of an elliptic curve”, Algebra Seminar, 9/23/08.