Robert Osburn

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: 2005-2012, 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2016-2017, 2017-2018, 2018-2019

Upcoming Events:

2nd VOAs+MMFs workshop, NUI Galway, June 2020

Modularity in Quantum Systems, KITP, November-December, 2020

Recent Events:

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

Pacific Northwest Number Theory Conference, Oregon State University, Corvallis, May 14-15, 2016

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

Hypergeometric motives and Calabi-Yau differential equations, MATRIX, Melbourne, January 8-28, 2017

Université Denis Diderot - Paris 7, March 12-17, 2017

University of Alberta, Edmonton, April 29-May 6, 2017

UCD Undergraduate Research Projects, Summer 2017

Low-dimensional Topology and Number Theory, MFO, August 20-26, 2017

Trends in Modular forms, NIMS, Daejeon, December 19-22, 2017

Periods in Number Theory, Algebraic Geometry and Physics, HIM, Bonn, January 3-19, 2018

Modular forms and quantum knot invariants, BIRS, Banff, March 11-16, 2018

AMS Special Session on Mock modular and quantum modular forms, Portland State, April 14-15, 2018

Antalya Algebra Days XX, Nesin Mathematics Village, May 16-20, 2018

UCD Undergraduate Research Projects, Summer 2018

Number Theory and Algebra Seminar, University of Zagreb, October 30, 2018

MPIM, Bonn, February 1-April 30, 2019

Modularity and 3-manifolds, ICERM, March 8-10, 2019

U.C. Berkeley, March 22-29, 2019

Algebra Seminar, TU Darmstadt, April 23, 2019

Number Theory Seminar, Queen's University, June 19, 2019

REU Colloquium, Oregon State University, Corvallis, July 22-25, 2019

James M. Flaherty Visiting Professor, McMaster University, May 17-August 9, 2019

KIAS and SeoulTech, August 12-17, 2019

2nd q-Day: q-series and related topics, KIAS, August 16, 2019

Fields Institute Undergraduate Summer Research Program, July 2-August 30, 2019

Colloquium and Flaherty Public Lecture, McMaster University, September 27, 2019


student comments


47. in preparation.

46. in preparation.

45. in preparation.

44.  R. Osburn, "Knot theory and Rogers-Ramanujan type identities",

43.  J. Lovejoy and R. Osburn, "The colored Jones polynomial and Kontsevich-Zagier series for double twist knots",

42.  J. Lovejoy and R. Osburn, "The colored Jones polynomial and Kontsevich-Zagier series for double twist knots, II",
New York Journal of Mathematics, accepted for publication.

41.  D. McCarthy, R. Osburn and A. Straub, "Sequences, modular forms and cellular integrals",
Mathematical Proceedings of the Cambridge Philosophical Society, accepted for publication.

40.  R. Osburn and A. Straub, "Interpolated sequences and critical L-values of modular forms",
Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
, 327-349, Texts & Monographs in Symbolic Computation, Springer, 2019.

39.  F. Luca, P. Moree, R. Osburn, S. Saad Eddin and A. Sedunova, "Constrained ternary integers",
International Journal of Number Theory, 15, no. 2, (2019), 407-431.

38.  R. Osburn, A. Straub and W. Zudilin, "A modular supercongruence for 6F5 : an Apéry-like story",
Annales de l'Institut Fourier (Grenoble), 68, no. 5, (2018), 1987-2004.

37.  J. Lovejoy and R. Osburn, "Mock theta double sums",
Glasgow Mathematical Journal, 59, no. 2, (2017), 323-348.

36.  P. Beirne and R. Osburn, "q-series and tails of colored Jones polynomials",
Indagationes Mathematicae, 28, no. 1, (2017), 247-260.

35.  L. Long, R. Osburn and H. Swisher, "On a conjecture of Kimoto and Wakayama",
Proceedings of the American Mathematical Society, 144, no. 10, (2016), 4319-4327.

34.  G. E. Andrews, S. H. Chan, B. Kim and R. Osburn, "The first positive rank and crank moments for overpartitions",
Annals of Combinatorics, 20, no. 2, (2016), 193-207.

33.  R. Osburn, B. Sahu and A. Straub, "Supercongruences for sporadic sequences",
Proceedings of the Edinburgh Mathematical Society (2), 59, no. 2, (2016), 503-518.

32.  A. Keilthy and R. Osburn, "Rogers-Ramanujan type identities for alternating knots",
Journal of Number Theory, 161, (2016), 255-280.

31.  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.

30.  S. H. Chan, R. Mao and R. Osburn, "On recursions for coefficients of mock theta functions",
Research in Number Theory, 1:29 (2015).

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.

0.  R. Osburn, "Densities of 4-ranks of K_2 of rings of integers",
Ph.D. thesis, LSU, 2001.

Undergraduate Students:

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

1.  Adam Keilthy, TCD
UCD SMS Undergraduate Research Project, Summer 2014

Graduate Students:

3.  Paul Beirne, PhD student,  PhD expected in summer 2020, UCD
IRC Postgraduate Scholarship

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

Associate Professor
Texas Tech University, Lubbock, Texas, USA

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

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

Postdoctoral Fellows:

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

Akamai Technologies, Denmark

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

Associate Professor
National Institute of Science Education and Research, Bhubaneswar, India

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

Assistant Professor
Calvin College, Michigan, USA

Conferences Organized:

Modular forms and quantum knot invariants, BIRS, Banff, March 11-16, 2018

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


James M. Flaherty Visiting Professor, Ireland Canada University Foundation, May 2019 - August 2019

IRC Postgraduate Scholarship (for Paul Beirne), October 2018 - September 2020
"Quantum knot invariants and modular forms"

UCD Seed Funding Scheme, April 2018
"Quantum knot invariants and modularity"

UCD Seed Funding Scheme, February 2016
"q-series and quantum knot invariants"

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 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:

UCD School of Mathematics and Statistics



Number Theory Web

Math ArXiv

Non-math Links:



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