Robert Osburn

Contact Information:

School of Mathematics and Statistics

University College Dublin

Belfield

Dublin 4

Ireland

Office: Science Center South, S0.99

Phone: +353 1 716 2548

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

Autumn 2023:

MST 10040: Combinatorics and Number Theory

MST 30020: History of Mathematics

SCI 10010: Principles of Scientific Enquiry

Upcoming Events:

Research visit, University of Geneva, December 13-17, 2023

Research visit and Colloquium talk, NISER, Bhubaneswar, January 5-12, 2024

School of Mathematical and Statistical Sciences Seminar, University of Galway, January 30, 2024

Plenary speaker, The Web of Modularity, Tulane University, February 22-25, 2024

2nd Vertex operator algebras and mock modular forms workshop, University of Galway, Summer 2024

(postponed from Summer 2022)

Recent Events:

Modular forms in String Theory, BIRS, Banff, September 25-30, 2016

Hypergeometric motives and Calabi-Yau differential equations, MATRIX Institute, Creswick, January 8-27, 2017

University of Alberta, April 29-May 6, 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

MPIM Number Theory Seminar, March 13, 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

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

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

UCD Undergraduate Research Projects, Summer 2020

Vanderbilt Number Theory Seminar, November 17, 2020

Warsaw Number Theory Seminar, November 30, 2020

EIMI Number Theory Seminar, December 8, 2020

SFB F50 Statusseminar, December 14-16, 2020

Modularity in Quantum Systems, KITP, November 30-December 18, 2020

Graduate Colloquium, University of Denver, April 23, 2021

New connections in number theory and physics, Isaac Newton Institute, Cambridge, May 24-28, 2021

Number Theory, Strings and Quantum Physics, Kavli IPMU, May 31-June 5, 2021

UCD Undergraduate Research Projects, Summer 2021 (come watch the student talks!)

Research visit, McMaster University, November 28 - December 5, 2021

MFO, Research in Pairs, January 9-22, 2022

MPIM Number Theory Seminar, March 30, 2022

MPIM, Bonn, March 1-31, 2022

Research visit, Institut Camille Jordan, Lyon, April 10-14, 2022

AMS Special Session on

Visiting Professor, Okinawa Institute of Science and Technology, June 9 - September 1, 2022

Kyushu Mathematical Physics Seminar, Fukuoka, July 20, 2022

Hao Dai's MSc defense, slides and thesis, September 5, 2022

Representation Theory XVII, Dubrovnik, October 3-8, 2022

Research visit, IRIF, Paris, December 4-17, 2022

MPIM Bonn, May 1-31, 2023

Research visit, IRIF, Paris, July 2-8, 2023

UCD Undergraduate Research Projects, Summer 2023 (come watch the student talks!)

Exact Asymptotics: From Fluid Dynamics to Quantum Geometry, OIST, Okinawa, August 28-September 15, 2023

Mathematical Sciences Seminar Series, UCC, November 29, 2023

cv

student comments

UCD profile

UCD Today article, Spring 2020 (see page 15)

UCD College of Science Research and Teaching Showcase

UCD Today article, Spring/Summer 2023 (see page 34)

OIST Theoretical Sciences Visiting Program Public Talk, Okinawa, July 7, 2022

Editorial Boards:

Journal of Combinatorial Theory, Series A

Canadian Journal of Mathematics and Canadian Mathematical Bulletin

Publications:

53. K. Allen and R. Osburn, "TBA",

in preparation.

52. B. Alinquant and R. Osburn, "On sporadic sequences",

preprint.

51. J. Lovejoy and R. Osburn, "Rank deviations for overpartitions",

submitted.

50. S. Crew, A. Goswami and R. Osburn, "Resurgence of Habiro elements",

submitted.

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

Encyclopedia of Ramanujan and his mathematics (Springer), accepted for publication.

48. A. Goswami, A. Jha, B. Kim and R. Osburn, "Asymptotics and sign patterns for coefficients in expansions of Habiro elements",

47. J. Dousse and R. Osburn, "A

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

Journal of Knot Theory and its Ramifications, 30, no. 5, (2021), 2150031.

45. A. Goswami and R. Osburn, "Quantum modularity of partial theta series with periodic coefficients",

Forum Mathematicum, 33, no. 2, (2021), 451-463.

44. S. H. Chan, R. Mao and R. Osburn, "Variations of Andrews-Beck type congruences",

Journal of Mathematical Analysis and Applications, 495, no. 2, (2021), 124771.

43. C. Bijaoui, H. Boden, B. Myers, R. Osburn, W. Rushworth, A. Tronsgard and S. Zhou, "Generalized Fishburn numbers and torus knots",

Journal of Combinatorial Theory, Series A, 178 (2021), 105355.

(See also the 2019 FUSRP final report)

42. D. McCarthy, R. Osburn and A. Straub, "Sequences, modular forms and cellular integrals",

Mathematical Proceedings of the Cambridge Philosophical Society, 168, no. 2, (2020), 379-404.

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

New York Journal of Mathematics, 25 (2019), 1312-1349.

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

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

Annales des sciences mathématiques du Québec, 34, no. 1, (2010), 25-36.

17. J. Lovejoy and R. Osburn, "M

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, "M

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

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:

7. Brendan Alinquant, UCD

UCD School of Mathematics and Statistics Undergraduate Research Project. Summer 2023

3.- 6. Colin Bijaoui (McMaster), Beckham Myers (Harvard), Aaron Tronsgard (Alberta), Shaoyang Zhou (Vanderbilt)

Fields Institute Undergraduate Summer Research Program, July 1-August 29, 2019

2. Paul Beirne, UCD

UCD SMS Undergraduate Research Project, Summer 2015

1. Adam Keilthy, TCD

UCD SMS Undergraduate Research Project, Summer 2014

MSc Students:

1. Hao Dai, MSc, Summer 2022

Thesis: Somos sequences and cluster algebras

PhD Students:

4. Kevin Allen, PhD student, 9/2021 to current, UCD

3. Paul Beirne, PhD 2020, UCD

IRC Postgraduate Scholarship

Thesis: Stability properties for the coefficients of the colored Jones polynomial

Senior Operations Executive

Irish Medicines Verification Organisation

2. Dermot McCarthy, PhD 2010, UCD

Ad Astra Research Scholarship.

Thesis:

Associate Professor

Texas Tech University, Lubbock, Texas, USA

1. Stefan de Wannemacker, PhD 2006, UCD

(co-advisor: David Lewis).

Thesis: Annihilating polynomials and Stirling numbers of the second kind

Senior Researcher

iTec, K.U. Leuven, Kortrijk, Belgium

Postdoctoral Fellows:

3. David Brink, August 2009-August 2010, UCD

Danish Research Fellowship

Researcher

Akamai Technologies, Denmark

2. Brundaban Sahu, Nov. 2008-Oct. 2010, UCD

SFI Postdoctoral Fellowship.

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:

AMS Special Session on

Workshop on Enumerative Combinatorics, UCD, March 10, 2021

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

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:

Enterprise Ireland, June 2021

"The modularity of quantum invariants for classical and virtual knots"

€16,000

UCD Seed Funding Scheme, April 2020

"Modular properties of quantum knot invariants"

€1800

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

"qKI+TQC"

€21,800

IRC Postgraduate Scholarship (for Paul Beirne), October 2018 - September 2020

"Quantum knot invariants and modular forms"

€48,000

UCD Seed Funding Scheme, April 2018

"Quantum knot invariants and modularity"

€1500

UCD Seed Funding Scheme, February 2016

"q-series and quantum knot invariants"

€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:

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