Robert Osburn





Contact Information:

School of Mathematics and Statistics
University College Dublin
Belfield
Dublin 4
Ireland

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 and 2015-2016


Second Semester 2017

Math 40240: Combinatorics



Upcoming Events:

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

Modular forms are everywhere, MPIM, Bonn, May 2017

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

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


Past Events:


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

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

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

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



cv.pdf

student comments



Publications:


40. in preparation.

39. in preparation.

38. R. Osburn, A. Straub and W. Zudilin, "A modular supercongruence for 6F5 : an Apéry-like story",
preprint.

37. J. Lovejoy and R. Osburn, "Mock theta double sums",
Glasgow Mathematical Journal, accepted for publication.

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.



Undergraduate Students:

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

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


Paul Beirne, PhD student, started September 2016, UCD
 

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.

Reader-F
National Institute of Science Education and Research
Bhubaneswar, India


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

Researcher
Akamai Technologies, Denmark



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




Grants:

UCD Seed Funding Scheme, February 2016
"q-series and quantum knot invarianrs"
1100

Irish Research Council New Foundations Scheme, March 2015
"VOAs+MMFs"
6000

SFI Conference and Workshop Programme, March 2013
"27th Automorphic Forms Workshop"
€2000

Number Theory Foundation, March 2013
"27th Automorphic Forms Workshop"
$5000

UCD Seed Funding Scheme, May 2012
"The Bailey chain and mock theta functions"
€1500

SFI Research Frontiers Programme, April 2008 - October 2011
"Arithmetic properties of coefficients of modular forms"
€116,300

Number Theory Foundation, January 2010
"Prospects in q-series and modular forms"
$1000


IRCSET France-Ireland Ulysses Programme, December 2007
"Ramanujan-type congruences for overpartitions and overpartition pairs"
€2500

UCD Seed Funding Scheme, December 2007
"Dyson's rank and overpartitions"
€2380

IRCSET Postdoctoral Fellowship Scheme (for Marilyn Myers), June 2007 - June 2009
"Variations of Kummer's conjecture"
€93,000

UCD Ad Astra Scholarship Programme (for Dermot McCarthy), September 2006 - August 2010
"Number theory, modular forms and combinatorics"
€48,000

UCD Seed Funding Scheme, August 2006
"Two-dimensional lattices with few distances"
€2093.73



Math Links:


UCD School of Mathematical Sciences 

MPIM

IHES

Number Theory Web

Math ArXiv




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