Michael John Griffin

Research

Publications

• "Divisibility properties of coefficients of weight 0 weakly holomorphic modular forms." Electronic version of an article published as International Journal of Number Theory, Volume 7, Number 4, 2011, Pages 933-941 DOI No: 10.1142/S1793042111004599 © copyright World Scientific Publishing Company http://www.worldscinet.com/ijnt/.


• "On matrices arising in the finite field analogue of Euler's integral transform." (with Larry Rolen),
  Mathematics, 1, (2013), 3-8.


• "Properties of class polynomials for non-holomorphic modular functions." (With Larry Rolen),
  Journal of the Ramanujan Society, 30, no. 1 (2015), 83-99.


• "SU(2) Donaldson invariants of the projective plane." (with Andreas Malmendier and Ken Ono),
  Forum Mathematicum, 27 (2015), 2003-2023.


• "Ramanujan's mock theta functions." (with Ken Ono and Larry Rolen),
  Proceedings of the National Academy of Science, 110, no. 15, (2013) 5765-5768.


• "Singular moduli for a distinguished non-holomorphic modular function." (With Valerio Dose, Nathan Green, Tianyi Mao, Larry Rolen, and John Willis) Proceedings of the American Mathematical Society, 143, no. 3 (2015), 965-972


• "Weierstrass mock modular forms and elliptic curves." (With Claudia Alfes, Ken Ono, and Larry Rolen),
  Research in Number Theory, 1:24, (2015).


• "A framework of Rogers-Ramanujan identities and their arithmetic properties." (With Ken Ono and Ole Warnaar),
  Duke Mathematical Journal, 165 (2016), 1475-1527.


• "Moonshine." (With John Duncan and Ken Ono),
  Research in the Mathematical Sciences, 2:11, (2015).


• "Proof of the Umbral Moonshine conjecture." (With John Duncan and Ken Ono),
  Research in the Mathematical Sciences, 2:26, (2015).


• "On p-adic modular forms and the Bloch-Okounkov theorem." (With Marie Jameson and Sarah Trebat-Leder),
  Research in the Mathematical Sciences, 3:11 (2016).


• "A proof of the Thompson Moonshine conjecture." (With Michael Mertens),
  Research in the Mathematical Sciences, to appear.


• "On p-adic harmonic Maass functions." Preprint.


• TBD, (with Larry Rolen, Ken Ono, and Don Zagier), in preparation.

Presentations

• "Umbral Moonshine." Indefinite theta functions and applications in physcis and geometry, Trinity College. Dublin, 7 June 2017
• "Moonshine." School and Workshop on Modular Forms and Black Holes, NISER. Bhubaneswar India, 12 Jan. 2017
• "Thompson Moonshine." plenary talk, U. CONN. conference on elliptic curves, modular forms and related topics. Storrs CT, 13 Aug. 2016
• "Moonshine, Moonshine and mock modular forms, Umbral moonshine" KIAS number theory seminars. Seoul, 2-5 Feb. 2016
• "Moonshine." Princeton number theory working seminar. Princeton NJ, 8 Oct. 2015
• "Moonshine." Purdue automorphic forms and representation theory seminar. West Lafayette IN, 16 April 2015
• "Umbral moonshine." Automorphic forms workshop. Ann Arbor MI, 5 Mar. 2015
• "On the distribution of moonshine and umbral moonshine." UNC-Duke Number Theory Seminar. Durham NC, 21 Jan. 2015
• "Weierstrass mock modular forms and elliptic curves." Joint math meetings. San Antonio TX, 13 Jan. 2015
• "Algebraic units arising from a framework of Rogers-Ramanujan identities." Joint math meetings. San Antonio TX, 11 Jan. 2015
• "Weierstrass mock modular forms and elliptic curves." SASTRA Prize Conference. Kumbakonam India, 21 Dec. 2014
• "On the distribution of moonshine and other theorems at the interface of number theory and representation theory." Texas A&M Number Theory Seminar. College Station TX, 3 Dec. 2014
• "On the distribution of moonshine and other theorems at the interface of number theory and representation theory." BYU Number Theory Seminar. Provo UT, 18 Nov. 2014
• "Theorems at the interface of number theory and representation theory." University of Tennessee Algebra and Number Theory Seminar. Knoxville TN, 3 Nov. 2014
• "Theorems at the interface of number theory and representation theory." Penn State Number Theory Seminar. University Park PA, 27 Oct. 2014
• "Theorems at the interface of number theory and representation theory." University of FLorida Number Theory Seminar. Gainesville, 20 Oct. 2014
• "On the distribution of moonshine." Emory algebra and number theory seminar. Atlanta GA, 16 Sept. 2014
• "A framework of Rogers-Ramanujan identities and their arithmetic properties." 28th Automorphic forms workshop. Moab UT, 12 May 2014.
• "A framework of Rogers-Ramanujan identities and their arithmetic properties." AMS spring sectional meeting, Texas Tech University. Lubbock TX, 12 April 2014.
• "Weierstrass mock modular forms and elliptic curves." AMS spring sectional meeting, Texas Tech University. Lubbock TX, 11 April 2014.
• "A framework of Rogers-Ramanujan identities." University of South Carolina Number Theory Seminar. Clemson SC, 23 Oct. 2013.
• "Weierstrass mock modular forms and elliptic curves." Clemson number theory seminar. Clemson SC, 23 Oct. 2013.
• "Mock modular forms." TIFR number theory seminar. Mumbai India, 1 Aug. 2013.
• "Mock modular forms." IMSc number theory colloquium. Chennai India, 22-23 July. 2013.
• "Ramanujan's mock-theta runctions." BYU number theory seminar. Provo UT, 8 Jan. 2013.
• "SU(2) Donaldson invariants of the projective plane." Ramanujan 125 Conference. Gainesville FL, 6 Nov. 2012.
• "Properties of class polynomials for non-holomorphic modular functions." AMS Sectional Meeting. Honolulu HI, 3 Mar. 2012.
• "U_p congruences modulo powers of primes." 25th Automorphic Forms Workshop. Corvalis OR, 24 Mar. 2011.
• "Divisibility properties of coefficients of weight 0 weakly holomorphic Modular Forms." 24th Automorphic Forms Workshop. Honolulu HI, 23 Mar. 2010.
• "A new perspective on some non-simple periodic orbits." Spring Research conference, Brigham Young University College of Physical and Mathematical Sciences. Provo UT, 21 Mar. 2009.