Ashvin A. Swaminathan

Presentations

Invited Talks

  1. Toward secondary terms for 2-Selmer groups in families of elliptic curves
    Algebraic and Number Theory Seminar, Dartmouth College, 2025.
  2. A positive proportion of hyperelliptic curves have no unexpected quadratic points
    Algebraic Geometry Seminar, Harvard University, 2025.
  3. A positive proportion of hyperelliptic curves have no unexpected quadratic points
    Algebraic Geometry Seminar, Boston College, 2024.
  4. A positive proportion of hyperelliptic curves have no unexpected quadratic points
    Informal Number Theory Seminar, University of Glasgow, 2024.
  5. A positive proportion of hyperelliptic curves have no unexpected quadratic points
    Number Theory Seminar, Tufts University, 2024.
  6. A positive proportion of hyperelliptic curves have no unexpected quadratic points
    Five College Number Theory Seminar, Amherst College, 2024.
  7. Geometry-of-numbers in the cusp, and class groups of orders in number fields
    Number Theory Seminar, Duke University, 2023.
  8. Affine symmetric spaces and class groups of cubic fields
    Québec Vermont Number Theory Seminar, McGill University, 2023.
  9. Geometry-of-numbers in the cusp, and class groups of orders in number fields
    Conference on Arithmetic Statistics, CIRM Luminy, 2023.
  10. Affine symmetric spaces and class groups of cubic fields
    Conference on Algebra, Algorithms, and Arithmetic, ICMS Edinburgh, 2023.
  11. Affine symmetric spaces and class groups of cubic fields
    Symposium on Arithmetic Geometry and its Applications, CIRM Luminy, 2023.
  12. The second moment of the size of the 2-Selmer group of elliptic curves
    Special Session on Arithmetic Statistics, JMM 2023.
  13. Geometry-of-numbers methods in the cusp, and class groups of orders in number fields
    Number Theory Seminar, MIT, 2022.
  14. 2-Selmer groups, 2-class groups, and the arithmetic of binary forms
    Online Number Theory Seminar, University of Debrecen, 2022.
  15. On the distribution of 2-Selmer groups of hyperelliptic Jacobians
    Workshop on Rational Points on Higher-Dimensional Varieties, ICMS Edinburgh, 2022.
  16. 2-Selmer groups, 2-class groups, and the arithmetic of binary forms
    Number Theory Seminar, Fields Institute, 2022.
  17. Geometry-of-numbers methods in the cusp, and applications to class groups
    Montreal Online Biweekly Inter-University Seminar on Analytic Number Theory (MOBIUS ANT), 2022.
  18. The second moment of the size of the $2$-Selmer group of elliptic curves
    Number Theory Seminar, Princeton University/IAS, 2021.
  19. $2$-Selmer groups, $2$-class groups, and the arithmetic of binary forms
    Palmetto Joint Arithmetic and Modularity Series (PAJAMAS) III, Invited Graduate Speaker, 2021.
  20. The second moment of the size of the $2$-Selmer group of elliptic curves
    Workshop on Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, 2021.
  21. Average $2$-torsion in the class groups of rings associated to binary $n$-ic forms
    Bhargava Seminar, Princeton University, 2020.
  22. Average $2$-torsion in the class groups of rings associated to binary $n$-ic forms
    Number/Representation Theory Seminar, University of Toronto, 2020.
  23. Most hyperelliptic curves are pointless
    Bhargava Seminar, Princeton University, 2019.
  24. Inflectionary invariants for plane curve singularities
    Special Session on Research in Mathematics by Undergraduates, JMM 2018.
  25. Surjectivity of Galois representations in rational families of abelian varieties
    Algebra, Geometry, and Number Theory Seminar, Tufts University, 2017.
  26. Inflection points of linear systems on families of curves
    Algebraic Geometry Seminar, Stanford University, 2017.
  27. Analysis on surreal numbers: functions and integration
    ASL Special Session, JMM 2016.
  28. Surreal analysis: an analogue of real analysis for surreal numbers
    Siemens Competition Regional Finals, California Institute of Technology, 2012.

Contributed Talks

  1. Toward secondary terms for 2-Selmer groups in families of elliptic curves
    Arithmetic Statistics Seminar, Harvard University. (Year not specified, assume recent)
  2. A positive proportion of monic odd hyperelliptic curves have no unexpected quadratic points
    Lightning Talk at conference on The Mordell conjecture: 100 years later, 2024.
  3. Most odd-degree binary forms fail to primitively represent a square
    Lightning Talk at Annual Meeting of Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, 2022.
  4. Counting lattice points in cusps of fundamental domains
    Number Theory Tea, Princeton University, 2020.
  5. Three lectures on the average size of $2$-Selmer groups of elliptic curves
    Bhargava Seminar, Stanford University, 2020.
  6. On the paucity of soluble superelliptic equations
    Bhargava Seminar, Stanford University, 2020.
  7. On the paucity of soluble superelliptic equations
    Bhargava Seminar, Princeton University, 2019.
  8. Inflectionary invariants for local complete intersection curve singularities
    Graduate Student Seminar, Princeton University, 2018.
  9. Inflectionary invariants for plane curve singularities
    LinkedIn Bangalore, 2018.
  10. Surjectivity of Galois representations in rational families of abelian varieties
    JMM 2017.
  11. Permutations that destroy arithmetic progressions in elementary $p$-groups
    JMM 2017.
  12. Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem
    JMM 2016.
  13. Permutations that destroy arithmetic progressions
    Harvard Math Table, 2016.
  14. On arboreal Galois representations of rational functions
    JMM 2015.
  15. How small is that prime?
    Harvard Math Table, 2015.
  16. Arboreal Galois representations of rational functions
    Harvard Math Table, 2014.
  17. Surreal analysis: an analogue of real analysis for surreal numbers
    Harvard Math Table, 2013.
  18. Surreal analysis: an analogue of real analysis for surreal numbers
    CMS Summer Meeting, 2013.