Talks

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.