Robert Osburn

School of Mathematics and Statistics
University College Dublin

Contact Information:

School of Mathematics and Statistics
University College Dublin
Dublin 4

Office: Science Center North, G12
Phone: +353 1 716 2548
Fax: +353 1 716 1172

robert dot osburn at ucd dot ie

Seminar and Teaching:

Algebra and Number Theory Seminar

Past seminars: here and here and here

Math 10040: Numbers and Functions

SCI 10010: Principles of Scientific Enquiry

Upcoming Events:

PhD defense of Jehanne Dousse, LIAFA, Paris 7, September 23, 2015

SeoulTech + KIAS, October 4-10, 2015

Automatic sequences, number theory and aperiodic order, TU Delft, October 28-30, 2015

MFO, Research in Pairs, March 13-26, 2016

Modular forms in String Theory, BIRS, Banff, September 26-30, 2016

Past Events:

Low-dimensional Topology and Number Theory, MFO, August 17-23, 2014 (invited speaker)

Workshop on L-functions and Modular Forms, ICTP, Trieste, September 7-12, 2014 

Séminaire tournant de théorie des nombres, ICJ, Lyon, November 6, 2014

LMS Prospects in Mathematics, Oxford, December 18-19, 2014

Functional equations and special functions, Grenoble, February 16-19, 2015

AKLS Seminar, Cologne, March 11, 2015

Characters of representations and modular forms, MPIM, Bonn, March 23-27, 2015

Workshop on vertex operator algebras and mock modular forms, NUI Galway, May 22-23, 2015

Automorphic forms: advances and applications, CIRM, Marseille, May 25-29, 2015

IHÉS, January 5 to March 5, 2015

MPIM, March 6 to May 31, 2015



research statement

teaching statement

student comments


38. in preparation.

37. in preparation.

36. S. H. Chan, R. Mao and R. Osburn, "On recursions for coefficients of mock theta functions",

35. J. Lovejoy and R. Osburn, "Mock theta double sums",

34. L. Long, R. Osburn and H. Swisher, "On a conjecture of Kimoto and Wakayama",

33. A. Keilthy and R. Osburn, "Rogers-Ramanujan type identities for alternating knots",
Journal of Number Theory, Special issue dedicated to Winnie Li, accepted for publication.

32. G. E. Andrews, S. H. Chan, B. Kim and R. Osburn, "The first positive rank and crank moments for overpartitions",
Annals of Combinatorics, accepted for publication.

31. R. Osburn, B. Sahu and A. Straub, "Supercongruences for sporadic sequences",
Proceedings of the Edinburgh Mathematical Society, accepted for publication.

30. R. Osburn and W. Zudilin, "On the (K.2) supercongruence of Van Hamme",
Journal of Mathematical Analysis and Applications, 433, no. 1, (2016), 706-711.

29. J. Lovejoy and R. Osburn, "Real quadratic double sums",
Indagationes Mathematicae, 26, no. 4, (2015), 697-712.

28.  J. Lovejoy and R. Osburn, "On two 10th order mock theta identities",
The Ramanujan Journal, 36, no. 1-2, (2015), 117-121.

27. R. Osburn, "q-hypergeometric series, alternating knots and identities",
Oberwolfach Reports, 11, no. 3, (2014), 2164-2167.

26.  J. Lovejoy and R. Osburn, "Mixed mock modular q-series",
Journal of the Indian Mathematical Society, New Series. Special volume to commemorate the 125th birth anniversary of Srinivasa Ramanujan, (2013) 45-61.

25.  J. Lovejoy and R. Osburn, "q-hypergeometric double sums as mock theta functions",
Pacific Journal of Mathematics, 264, no. 1, (2013) 151-162.

24.  R. Osburn and B. Sahu, "A supercongruence for generalized Domb numbers",
Functiones et Approximatio Commentarii Mathematici, 48, no. 1, (2013) 29-36.

23.  J. Lovejoy and R. Osburn, "The Bailey chain and mock theta functions",
Advances in Mathematics, 238 (2013) 442-458.

22.  D. Brink, P. Moree, and R. Osburn, "Principal forms X^2 + nY^2 representing many integers",
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 81, no. 2, (2011) 129-139.

21.  R. Osburn and B. Sahu, "Supercongruences for Apéry-like numbers",
Advances in Applied Mathematics, 47, no. 3, (2011) 631-638.

20.  R. Osburn and B. Sahu, "Congruences via modular forms",
Proceedings of the American Mathematical Society, 139, no. 7, (2011) 2375-2381.

19.   J. Lovejoy and R. Osburn, "Quadratic forms and four partition functions modulo 3",
Integers, 11, no. 1, (2011) 47-53.

18.  H. Chan, A. Kontogeorgis, C. Krattenthaler and R. Osburn, "Supercongruences satisfied by coefficients of 2F1 hypergeometric series",
Annales des sciences mathématiques du Québec, 34, no. 1, (2010) 25-36.

17.  J. Lovejoy and R. Osburn, "M2-rank differences for overpartitions",
Acta Arithmetica, 144, no. 2, (2010) 193-212.

16.  K. Bringmann, J. Lovejoy, and R. Osburn, "Automorphic properties of generating functions for generalized rank moments and Durfee symbols",
International Mathematics Research Notices, no. 2, (2010) 238-260.

15.  K. Bringmann, J. Lovejoy, and R. Osburn, "Rank and crank moments for overpartitions",
Journal of Number Theory, 129, (2009) 1758-1772.

14.  J. Lovejoy and R. Osburn, "M2-rank differences for partitions without repeated odd parts",
Journal de Théorie des Nombres de Bordeaux, 21, no. 2, (2009) 313-334.

13.  R. Osburn and C. Schneider, "Gaussian hypergeometric series and supercongruences",
Mathematics of Computation, 78, no. 265, (2009) 275-292. 

12.  D. McCarthy and R. Osburn, "A p-adic analogue of a formula of Ramanujan",
Archiv der Mathematik, 91, no. 6, (2008) 492-504.

11.  J. Lovejoy and R. Osburn, "Rank differences for overpartitions",
The Quarterly Journal of Mathematics, 59, no. 2, (2008) 257-273.

10.  R. Osburn, "Congruences for traces of singular moduli",
The Ramanujan Journal, 14, no. 3, (2007) 411-419.

9.  R. Murty and R. Osburn, "Representations of integers by certain positive definite binary quadratic forms",
The Ramanujan Journal, 14, no. 3, (2007) 351-359.

8.  S. de Wannemacker, T. Laffey, and R. Osburn, "On a conjecture of Wilf",
Journal of Combinatorial Theory, Series A, 114, no. 7, (2007) 1332-1349.

7.  P. Moree and R. Osburn, "Two-dimensional lattices with few distances",
L'Enseignement Mathématique, 52, (2006) 361-380.

6.  S. K. K. Choi, A. Kumchev, and R. Osburn, "On sums of three squares",
International Journal of Number Theory, 1, no. 2, (2005) 161-173.

5.  R. Osburn, "A remark on a conjecture of Borwein and Choi",
Proceedings of the American Mathematical Society, 133, no. 10, (2005) 2903-2909.

4.  R. Osburn, "Vanishing of eigenspaces and cyclotomic fields",
International Mathematics Research Notices, no. 20, (2005) 1195-1202.

3.  R. Osburn, "A note on 4-rank densities",
Canadian Mathematical Bulletin, 47, (2004) 431-438.

2.  R. Osburn and B. Murray, "Tame kernels and further 4-rank densities",
Journal of Number Theory, 98, (2003) 390-406.

1.  R. Osburn, "Densities of 4-ranks of K_2(O)",
Acta Arithmetica, 102, (2002) 45-54.

Undergraduate Students:

Paul Beirne, UCD
UCD SMS Undergraduate Research Project, Summer 2015

Adam Keilthy, TCD
UCD SMS Undergraduate Research Project, May 26 - July 7, 2014

Graduate Students:

Stefan de Wannemacker, PhD 2006, UCD
(co-advisor: David Lewis).

Senior Researcher
iTec, K.U. Leuven, Kortrijk, Belgium

Dermot McCarthy, PhD, June 2010, UCD
Ad Astra Research Scholarship.

Visiting Assistant Professor
Texas A&M, starting September 1, 2010.

Tenure-track assistant professor
Texas Tech, starting September 2013.

Postdoctoral Fellows:

Marilyn Reece Myers, Dec. 2007-Dec. 2009, UCD
IRCSET Postdoctoral Fellowship.

Tenure-track Assistant Professor
Calvin College, Michigan

Brundaban Sahu, Nov. 2008-Oct. 2010, UCD
SFI Postdoctoral Fellowship.

National Institute of Science Education and Research
Bhubaneswar, India

David Brink, August 2009-August 2010, UCD
Danish Research Fellowship

Conferences Organized:

Workshop on vertex operator algebras and mock modular forms, NUI Galway, May 22-23, 2015

27th Automorphic Forms Workshop, UCD, March 11-14, 2013

Algebraic K-theory and Arithmetic, Banach Center, Bedlewo, Poland, July 22-28, 2012

Prospects in q-series and modular forms, UCD, July 14-16, 2010

UCD/Nottingham Number Theory Day, UCD, November 1, 2008

AMS Special Session on Number Theory and applications in other fields, LSU, March 28-30, 2008

AMS Special Session on Algebraic Number Theory and K-theory, LSU, March 14-16, 2003


Irish Research Council New Foundations Scheme, March 2015

SFI Conference and Workshop Programme, March 2013
"27th Automorphic Forms Workshop"

Number Theory Foundation, March 2013
"27th Automorphic Forms Workshop"

UCD Seed Funding Scheme, May 2012
"The Bailey chain and mock theta functions"

SFI Investigator Award Programme, March 2012
"The modularity of q-series"
€282,776 (requested budget, "adminstratively withdrawn by SFI")*

*For more on this controversy in Ireland, see this, this, this
this, this, or  this.

SFI Research Frontiers Programme, April 2008 - October 2011
"Arithmetic properties of coefficients of modular forms"

Number Theory Foundation, January 2010
"Prospects in q-series and modular forms"

IRCSET France-Ireland Ulysses Programme, December 2007
"Ramanujan-type congruences for overpartitions and overpartition pairs"

UCD Seed Funding Scheme, December 2007
"Dyson's rank and overpartitions"

IRCSET Postdoctoral Fellowship Scheme (for Marilyn Myers), June 2007 - June 2009
"Variations of Kummer's conjecture"

UCD Ad Astra Scholarship Programme (for Dermot McCarthy), September 2006 - August 2010
"Number theory, modular forms and combinatorics"

UCD Seed Funding Scheme, August 2006
"Two-dimensional lattices with few distances"

Math Links:

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Math ArXiv

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