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Robert Osburn

Associate Professor

School of Mathematics & Statistics
G12
Science Centre North
UCD
Belfield
Dublin 4

Tel: +353 1 7162548
Email: robert.osburn@ucd.ie

Biography

  1. B.S. 1996, Ph.D. 2001: Louisiana State University, USA
  2. July 2001-June 2003: Postdoctoral Fellow, McMaster University, Canada
  3. July 2003-June 2004: Postdoctoral Fellow, Queen's University, Canada
  4. August 2004-June 2005: Invited Guest, MPIM, Germany
  5. Sept. 2005-May 2017: Lecturer, UCD   
  6. January-July 2007: Invited Guest, IHES, France
  7. June 3 - July 2, 2011: Invited Guest, Universite Paris Diderot - Paris 7
  8. June 1 - July 31, 2012: Invited Guest, IHES, France
  9. January 5 - March 5, 2015: Invited Guest, IHES, France
  10. March 6 - May 31, 2015: Invited Guest, MPIM, Germany
  11. May 2017 - current: Associate Professor, UCD

 

Professional

Honours and Awards

Year: 2014.
Title: Invited speaker, MFO Workshop Low-dimensional topology and number theory
Year: 2015.
Title: Professor, Section 25 - Mathematics, French Conseil National des Universites
Year: 2015.
Title: Research in Pairs, Mathematisches Forschungsinstitut Oberwolfach

Associations

Association: Irish Mathematical Society, Function/Role: member
Association: European Mathematical Society, Function/Role: member
Association: American Mathematical Society, Function/Role: member
     

Conference Contributions

Osburn, R. (2002) Tame kernels and 4-rank densities. [Invited Lecture], K-theory of Number fields: from theory to algorithms, Metz, France , 25-JUN-02 - 28-JUN-02.
Osburn, R. (2002) Redei matrices and K-groups. [Invited Lecture], Quebec-Maine Number Theory Conference, Laval, Canada , 12-OCT-02 - 13-OCT-02.
Osburn, R. (2003) Representations of integers by certain binary quadratic forms. [Invited Lecture], PIMS Number Theory Day, Vancouver, Canada , 05-DEC-03 - 05-DEC-03.
Osburn, R. (2003) Traces of singular moduli. [Invited Lecture], CMS Winter Meeting, Vancouver, Canada , 06-DEC-03 - 08-DEC-03.
Osburn, R. (2004) Congruences for traces of singular moduli. [Invited Lecture], Workshop on Arithmetic and Geometry of Algebraic Varieties, The Fields Institute, Toronto, Canada , 27-MAR-04 - 28-MAR-04.
Osburn, R. (2004) Congruences for traces of singular moduli. [Invited Lecture], Quebec-Vermont Number Theory Seminar, Montreal, Canada , 15-APR-04 - 15-APR-04.
Osburn, R. (2004) Vanishing of eigenspaces and cyclotomic fields. [Invited Lecture], Workshop on Explicit Algebraic Number Theory, IHP, Paris, France , 11-OCT-04 - 15-OCT-04.
Osburn, R. (2004) Vanishing of eigenspaces and cyclotomic fields. [Invited Lecture], MPIM Number Theory Seminar, Bonn, Germany , 13-OCT-04 - 13-OCT-04.
Osburn, R. (2006) Two-dimensional lattices with few distances. [Invited Lecture], CNTA IX, University of British Columbia, Vancouver, Canada , 09-JUL-06 - 14-JUL-06.
Osburn, R. (2007) Two-dimensional lattices with few distances. [Invited Lecture], Clemson University Mathematics Colloquium, Clemson University, Clemson, South Carolina, USA , 14-FEB-07 - 14-FEB-07.
Osburn, R. (2007) Gaussian hypergeometric functions and supercongruences. [Invited Lecture], Palmetto Number Theory Series II, Clemson University, Clemson, South Carolina, USA , 17-FEB-07 - 17-FEB-07.
Osburn, R. (2007) Rank differences for overpartitions. [Invited Lecture], Recontres de theorie analytique et elementaire des nombres, IHP, Paris, France , 04-JUN-07 - 04-JUN-07.
Osburn, R. (2007) Ramanujan, partitions and overpartitions. [Invited Lecture], Irish Mathematical Society Annual Meeting, UCD, Dublin, Ireland , 03-SEP-07 - 04-SEP-07.
Osburn, R. (2007) Ramanujan, partitions and overpartitions. [Invited Lecture], UCC Colloquium Series, UCC, Cork, Ireland , 07-DEC-07 - 07-DEC-07.
Osburn, R. (2008) M2-rank differences for partitions without repeated odd parts. [Invited Lecture], Conference on Partitions, q-series and modular forms, University of Florida, Gainesville, Florida, USA , 08-MAR-08 - 16-MAR-08.
Osburn, R. (2008) Rank and crank moments for overpartitions. [Invited Lecture], The Hawaii workshop on the arithmetic of modular forms, Manoa, USA , 21-MAY-08 - 24-MAY-08.
Osburn, R. (2008) Gaussian hypergeometric series. [Invited Lecture], UCD-Nottingham Number Theory Day, Dublin, UCD, Ireland , 01-NOV-08 - 01-NOV-08.
Osburn, R. (2009) Gaussian hypergeometric series. [Invited Lecture], AMS Special Session on Automorphic and Modular Forms, Washington, D.C., USA , 05-JAN-09 - 08-JAN-09.
Osburn, R. (2009) Automorphic properties of generating functions for generalized rank moments and Durfee symbols. [Invited Lecture], Mock theta functions and applications in combinatorics, algebraic geometry and mathematical physics, MPIM, Bonn, Germany , 25-MAY-09 - 29-MAY-09.
Osburn, R. (2009) Automorphic properties of generating functions for generalized rank moments and Durfee symbols. [Invited Lecture], 26th Journees Arithmetiques, Saint-Etienne, France , 06-JUL-09 - 10-JUL-09.
Osburn, R. (2010) On computations of Shanks and Schmid. [Invited Lecture], University of South Carolina Number Theory Seminar, Columbia, South Carolina, USA , 20-MAR-10 - 20-MAR-10.
Osburn, R. (2010) Supercongruences. [Invited Lecture], Zeta and Limit Laws in Okinawa 2010, Okinawa, Japan , 06-OCT-10 - 09-OCT-10.
Osburn, R. (2011) Automorphic properties of combinatorial generating functions. [Invited Lecture], Cambridge Number Theory Seminar, University of Cambridge, UK , 01-FEB-11 - 01-FEB-11.
Osburn, R. (2011) Automorphic properties of combinatorial generating functions. [Invited Lecture], 25th Automorphic Forms Workshop, Corvallis, Oregon, USA , 23-MAR-11 - 26-MAR-11.
Osburn, R. (2011) Automorphic properties of combinatorial generating functions. [Invited Lecture], LIAFA Seminaire Combinatoire enumerative et analytique, Paris, France , 09-JUN-11 - 09-JUN-11.
Osburn, R. (2012) Multisum mock theta functions. [Invited Lecture], AMS Special Session on Automorphic and Modular forms, Honolulu, USA , 03-MAR-12 - 04-MAR-12.
Osburn, R. (2012) The mock modularity of q-hypergeometric series. [Invited Lecture], Hypergeometric series and their generalizations in algebra, geometry, number theory and physics, IHP, Paris, France , 29-MAY-12 - 01-JUN-12.
Osburn, R. (2012) The mock modularity of q-hypergeometric series. [Invited Lecture], CNTA XII, Lethbridge, Alberta, Canada , 17-JUN-12 - 22-JUN-12.
Osburn, R. (2012) Ramanujan: his life, the last letter and beyond. [Invited Lecture], Oregon State University Special Seminar, Corvallis, Oregon, USA , 26-JUN-12 - 26-JUN-12.
Osburn, R. (2012) The mock and mixed mock modularity of q-hypergeometric series. [Invited Lecture], Collaborative Number Theory Seminar, CUNY Graduate Center, New York, USA , 07-SEP-12 - 07-SEP-12.
Osburn, R. (2012) The mock and mixed mock modularity of q-hypergeometric series. [Invited Lecture], Penn State Combinatorics/Partitions Seminar, University Park, Pennsylvania, USA , 11-SEP-12 - 11-SEP-12.
Osburn, R. (2012) The mixed mock modularity of q-hypergeometric series. [Invited Lecture], AMS Special Session on Harmonic Maass Forms and q-Series, Tucson, Arizona, USA , 27-OCT-12 - 28-OCT-12.
Osburn, R. (2012) On computations of Shanks and Schmid. [Invited Lecture], Emory Algebra and Number Theory Seminar, Atlanta, USA , 30-OCT-12 - 30-OCT-12.
Osburn, R. (2012) The modularity of q-hypergeometric series. [Invited Lecture], Ramanujan 125, New Delhi, India , 17-DEC-12 - 22-DEC-12.
Osburn, R. (2013) Supercongruences. [Invited Lecture], Analytic theory of automorphic forms, Chennai, India , 09-DEC-13 - 13-DEC-13.
Osburn, R. (2014) The mock modularity of q-hypergeometric series. [Invited Lecture], Seminaire de theorie des nombres de I'IMJ-PRG, Paris, France , 24-MAR-14 - 24-MAR-14.
Osburn, R. (2014) Supercongruences. [Invited Lecture], Applications of Automorphic Forms in Number Theory and Combinatorics, LSU, Baton Rouge, USA , 12-APR-14 - 15-APR-14.
Osburn, R. (2014) The mock modularity of q-hypergeometric series. [Invited Lecture], MSAM seminar, NUI Galway , 08-MAY-14 - 08-MAY-14.
Osburn, R. (2014) The mock modularity of q-hypergeometric series. [Invited Lecture], Warwick Number Theory Seminar, University of Warwick, Coventry, UK , 02-JUN-14 - 02-JUN-14.
Osburn, R. (2014) Rogers-Ramanujan type identities for alternating knots. [Invited Lecture], MFO Workshop on Low-dimensional topology and number theory, Oberwolfach, Germany , 17-AUG-14 - 23-AUG-14.
Osburn, R. (2014) Variations of hypergeometric functions and applications. [Invited Lecture], Advanced School and Workshop on L-functions and modular forms, ICTP, Trieste, Italy , 08-SEP-14 - 08-SEP-14.
Osburn, R. (2014) Rogers-Ramanujan type identities for alternating knots. [Invited Lecture], Seminaire tournant de theorie des nombres, Lyon, France , 06-NOV-14 - 06-NOV-14.
Osburn, R. (2015) Rogers-Ramanujan type identities for alternating knots. [Invited Lecture], AKLS Seminar, Cologne, Germany , 11-MAR-15 - 11-MAR-15.
Osburn, R. (2015) q-series and quantum knot invariants. [Invited Lecture], Korean Institute for Advanced Study Number Theory Seminar, Seoul, Korea , 08-OCT-15 - 08-OCT-15.
Osburn, R. (2015) q-series and quantum knot invariants. [Invited Lecture], Automatic sequences, Number Theory and Aperiodic Order, Delft, Netherlands , 28-OCT-15 - 30-OCT-15.
Osburn, R. (2016) q-series, modularity and knots. [Invited Lecture], Pacific Northwest Number Theory Conference, Oregon State University, Corvallis, USA , 14-MAY-16 - 15-MAY-16.

Committees

Committee : Ph.D. committee for Abhash Jha (NISER, Bhubaneswar), Doctoral Defense
Committee : Ph.D. committee for Jehanne Dousse (Paris 7), Doctoral Defense
Committee : Doctoral Studies Panel for Daniela Mueller
Committee : Doctoral Studies Panel for Stiofain Fordham
Committee : Ph.D. committee for Renrong Mao (NTU Singapore), Doctoral Defense
Committee : Doctoral Studies Panel for Richard Ellard
Committee : UCD Doctoral Defense for Anthony Brown
Committee : UCD Doctoral Defense Committee for Richard Moloney
Committee : UCD Master's Defense Committee for Caitriona Kellehan
Committee : UCD Master's Defense Committee for Vijay Singh
Committee : UCD Doctoral Defense Committee for Tao Liquin
Committee : UCD Master's Defense Committee for Ursula Finnegan
Committee : NSA Mathematical Sciences Grant Program
Committee : International Student Relations for UCD School of Mathematics and Statistics
Committee : Engineering Programme Board
Committee : Public relations committee for School of Mathematical Sciences
Committee : UCD Seed Funding
Committee : Exams for UCD School of Mathematical Sciences
Committee : Junior Year Abroad for UCD School of Mathematical Sciences
 

Education

Year 1996 Institution: Louisiana State University. USA
Qualification: BS Subject:
Year 2001 Institution: Louisiana State University. USA
Qualification: PhD Subject:
   

Outreach Activities

Speaker at UCD Math Sparks program, 3/2016, "Groups and counting".
Speaker at the UCD Mathematical Society, 2/2016, "On irrational numbers".
Speaker at UCD School of Mathematics and Statistics one-day Research workshop, 12/2015, "q-series, modularity and knots".
Speaker at London Mathematical Society Prospects in Mathematics, Mathematical Institute, Oxford, "Rogers-Ramanujan identities, knots and UCD, December 18-19, 2014.
Speaker at UCD Summer School for High School Students, 7/2013,
"(Very) recent developments in number theory".
Speaker at UCD Mathematical Society, 1/2013, "The ABC Conjecture".
Speaker at Career afternoon, St. Joseph's College, Summerhill, Athlone, 11/2012, "Mathematical Sciences at UCD".
Speaker at UCD School of Mathematical Sciences Open Evening, 11/2011, "Research in mathematics at UCD".
Speaker at Public Lecture during Maths Week at UCD, 10/2011, "Ramanujan: his life, the last letter and beyond".
Speaker at the UCD/TCD Mathematics Summer School, 5/2011, "Topics in number theory".
Speaker at UCD Undergraduate Ambassadors Scheme Outreach Afternoon, "Paul Erdos".
Speaker at the UCD/TCD Mathematics Summer School, 6/2010, "Number theory".
Speaker at UCD Mathematical Society, 4/2009, "Erdos' 105 problem".
 

Other Activities

Invited speaker, 1/2017, tba, Hypergeometric motives and Calabi-Yau differential equations, Melbourne, Australia. 
Invited speaker, 9/2016, tba, Modular forms in String Theory, Banff, Canada.
Conference participant, 5/2015, Automorphic forms: advances and applications, CIRM, Marseille, France.
Conference participant, 3/2015, Characters of Representations and Modular Forms, MPIM, Bonn, Germany.
Conference participant, 2/2015, ANR Q-DIFF, Grenoble, France.
Conference participant, 7/2014, Building Bridges: 2nd EU/US Workshop on Automorphic Forms and Related Topics, University of Bristol, UK.
Conference participant, 7/2013, Special functions and special numbers, 60th birthday of Frits Beukers, Utrecht, Netherlands.
Conference participant, 3/2011, Conference on Modular forms and Mock modular forms and their applications in Arithmetic, Geometry and Physics, ICTP, Trieste, Italy.
Conference participant, 6/2010, Summer School on quasimodular forms and applications, Besse, France.
Conference participant, 5/2009, UCD-Nottingham Number Theory Day, University of Nottingham, UK.
Conference participant, 7/2007, 25th Journees Arithmetiques, University of Edinburgh, Scotland.
Conference participant, 9/2006, Conference in celebration of Bryan Birch's 75th birthday, University of Bristol, UK.
Conference participant, 6/2005, Gauss-Dirichlet conference, Goettingen, Germany.
Co-organizer of Algebra and Number Theory Seminar at UCD, 9/2005 - current.
5/2015, Co-organizer of Workshop on Vertex Operator Algebras and Mock Modular Forms (with Michael Tuite), NUIG, Ireland, see http://mathsci.ucd.ie/%7Eosburn/voasmmfs/ 
3/2013, Co-organizer of 27th Automorphic Forms Workshop (with Scott Ahlgren and Jeremy Lovejoy), Dublin, Ireland, see http://automorphicformsworkshop.org
7/2012, Co-organizer of Algebraic K-theory and Arithmetic: a conference in honor of Jurgen Hurrelbrink (with Grzegorz Banaszak, Jerzy Browkin, Manfred Kolster, Piotr Krason, Wieslawa Niziol, Robert Perlis, Kazimierz Szymiczek and Jerzy Urbanowicz), Bedlewo, Poland, see http://aka.wmi.amu.edu.pl/
7/2010, Co-organizer of Prospects in q-series and modular forms conference (with Jeremy Lovejoy and Sander Zwegers), Dublin, Ireland, see http://mathsci.ucd.ie/~osburn/pqsmf
11/2008, Co-organizer of UCD/Nottingham Number Theory Day (with Nigel Boston), Dublin, Ireland, see http://www.maths.nott.ac.uk/personal/ibf/duno.html
3/2008, Co-organizer of AMS Special Session on Number Theory and applications in other fields (with Jorge Morales, Robert Perlis and Helena Verrill), Baton Rouge, USA, see http://www.ams.org/meetings/sectional/2146_program_ss12.html
3/2003, Co-organizer of AMS Special Session on Algebraic Number Theory and K-theory (with Jurgen Hurrelbrink and Jorge Morales), Baton Rouge, USA, see http://www.ams.org/meetings/sectional/2086_program_ssa.html
1/2002 - 4/2003, Co-organizer of Algebra/Number Theory Seminar at McMaster University (with Manfred Kolster and Hui June Zhu), Hamilton, Ontario, see http://www.math.mcmaster.ca/talks/algebra_number_theory/sems.html
Project leader for Paul Beirne, UCD School of Mathematics and Statistics Undergraduate Research Projects, Summer 2015.
Project leader for Adam Keilthy, UCD School of Mathematics and Statistics Undergraduate Research Projects, Summer 2014.
Postdoctoral advisor for Brundaban Sahu, SFI Postdoctoral Fellow, 11/2008 - 10/2010.
Postdoctoral advisor for David Brink, Danish Research Fellow, 8/2009 - 8/2010.
Postdoctoral advisor for Marilyn Myers, IRCSET Postdoctoral Fellow, 12/2007 - 11/2009.
Reviewer for Book proposal, CRC Press, 3/2015.
Referee for the following journals: Acta Arithmetica, Acta Mathematica Scientia, Advances in Applied Mathematics, Advances in Mathematics, Annales des Sciences Mathematiques du Quebec, Annals of Combinatorics, Annali dell'Universita di Ferrara, Boletim da Sociedade Paranaense de Matematica, Bulletin of the Korean Mathematical Society, Bulletin of the London Mathematical Society, Communications in Number Theory and Physics, Contemporary Mathematics, Discrete Mathematics, Electronic Journal of Combinatorics, European Journal of Combinatorics, Finite Fields and their applications, Functiones et Approximatio, Commentarii Mathematici, Integers, International Journal of Mathematics and Mathematical Sciences, International Journal of Number Theory, Journal of Algebra and its Applications, Journal of Combinatorial Theory, Series A, Journal of Integer Sequences, Journal of Mathematical Analysis and Applications, Journal of Number Theory, LMS Journal of Computation and Mathematics, Mathematica Slovaca, Pacific Journal of Mathematics, Proceedings of the American Mathematical Society, Proceedings of the Edinburgh Mathematical Society, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Publicationes Mathematicae Debrecen, Quarterly Journal of Mathematics, Ramanujan Journal, Research in Number Theory, Rocky Mountain Journal of Mathematics, Seminaire Lotharingien de Combinatoire, Taiwanese Journal of Mathematics.
Reviewer for AMS Mathematical Reviews.

Publications

     

Peer Reviewed Journals

Paul Beirne, Robert Osburn (2016) 'q-series and tails of colored Jones polynomials'. Indagationes Mathematicae-New Series, . [Details]
Jeremy Lovejoy, Robert Osburn (2016) 'Mock theta double sums'. Glasgow Mathematical Journal, . Available Online [DOI] Link to full text [Details]
Ling Long, Robert Osburn, Holly Swisher (2016) 'On a conjecture of Kimoto and Wakayama'. Proceedings of the American Mathematical Society, 144 (10):4319-4327. Available Online [DOI] Link to full text [Details]
George Andrews, Song Heng Chan, Byungchan Kim, Robert Osburn (2016) 'The first positive rank and crank moments for overpartitions'. Annals of Combinatorics, 20 (2):193-217. Available Online [DOI] Link to full text [Details]
Brundaban Sahu, Robert Osburn, Armin Straub (2016) 'Supercongruences for sporadic sequences'. Proceedings of the Edinburgh Mathematical Society, 59 (2):503-518. Available Online [DOI] Link to full text [Details]
Adam Keilthy, Robert Osburn (2016) 'Rogers-Ramanujan type identities for alternating knots'. Journal of Number Theory, 161 :255-280. Available Online [DOI] Link to full text [Details]
Robert Osburn, Wadim Zudilin (2016) 'On the (K.2) supercongruence of Van Hamme'. Journal of Mathematical Analysis and Applications, 433 (1):706-711. Available Online [DOI] Link to full text [Details]
Song Heng Chan, Renrong Mao, Robert Osburn (2015) 'On recursions for coefficients of mock theta functions'. Research in Number Theory, 1 (Article 29):1-18. Available Online [DOI] Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2015) 'Real quadratic double sums'. Indagationes Mathematicae-New Series, 26 (4):697-712. Available Online [DOI] Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2015) 'On two 10th order mock theta identities'. Ramanujan Journal, 36 (1-2):117-121. Available Online [DOI] Link to full text [Details]
Robert Osburn (2014) 'q-hypergeometric series, alternating knots and identities'. Oberwolfach Reports, 11 (3):2164-2167. Available Online [DOI] [Details]
Jeremy Lovejoy, Robert Osburn (2013) 'Mixed modular q-series'. Journal of the Indian Mathematical Society, Special volume :45-61. Available Online Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2013) 'q-hypergeometric double sums as mock theta functions'. Pacific Journal of Mathematics, 264 (1):151-162. Available Online [DOI] Link to full text [Details]
Robert Osburn, Brundaban Sahu (2013) 'A supercongruence for generalized Domb numbers'. Functiones et Approximatio, Commentarii Mathematici, 48 (1):29-36. Available Online [DOI] Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2013) 'The Bailey chain and mock theta functions'. Advances in Mathematics, 238 :442-458. Available Online [DOI] Link to full text [Details]
David Brink, Pieter Moree, Robert Osburn (2011) 'Principal forms X-2 + nY^2 representing many integers'. Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 81 :129-139. Available Online [DOI] Link to full text [Details]
Robert Osburn, Brundaban Sahu (2011) 'Supercongruences for Apery-like numbers'. Advances in Applied Mathematics, 47 :631-638. Available Online [DOI] Link to full text [Details]
Robert Osburn, Brundaban Sahu (2011) 'Congruences via modular forms'. Proceedings of the American Mathematical Society, 139 :2375-2381. Available Online [DOI] Link to full text [Details]
Jeremy Lovejoy and Robert Osburn; (2011) 'Quadratic forms and four partition functions modulo 3'. Integers, 11 (A4):47-53. Available Online [DOI] Link to full text [Details]
H. Chan, A. Kontogeorgis, C. Krattenthaler and R. Osburn; (2010) 'Supercongruences satisfied by coefficients of 2F1 hypergeometric series'. Annales des sciences mathematiques du Quebec, 34 (1):25-36. Available Online Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2010) 'M_2-rank differences for overpartitions'. Acta Arithmetica, 144 (2):193-212. Available Online [DOI] Link to full text [Details]
Kathrin Bringmann, Jeremy Lovejoy, Robert Osburn (2010) 'Automorphic properties of generating functions for generalized rank moments and Durfee symbols'. International Mathematics Research Notices, (2):238-260. Available Online [DOI] Link to full text [Details]
Kathrin Bringmann, Jeremy Lovejoy, Robert Osburn (2009) 'Rank and crank moments for overpartitions'. Journal of Number Theory, 129 (7):1758-1772. Available Online [DOI] Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2009) 'M_2-rank differences for partitions without repeated odd parts'. Journal de Theorie des Nombres de Bordeaux, 21 (2):313-334. Available Online [DOI] Link to full text [Details]
Robert Osburn, Carsten Schneider (2009) 'Gaussian hypergeometric series and supercongruences'. Mathematics of Computation, 78 (265):275-292. Available Online [DOI] Link to full text [Details]
Robert Osburn and Dermot McCarthy; (2008) 'A p-adic analogue of a formula of Ramanujan'. Archiv der Mathematik, 91 (6):492-504. Available Online [DOI] Link to full text [Details]
Jeremy Lovejoy, Robert Osburn (2008) 'Rank differences for overpartitions'. Quarterly Journal of Mathematics Oxford, 59 (2):257-273. Available Online [DOI] Link to full text [Details]
Robert Osburn (2007) 'Congruences for traces of singular moduli'. Ramanujan Journal, 14 (3):411-419. Available Online [DOI] Link to full text [Details]
Ram Murty, Robert Osburn (2007) 'Representations of integers by certain positive definite binary quadratic forms'. Ramanujan Journal, 14 (3):351-359. Available Online [DOI] Link to full text [Details]
Stefan de Wannemacker, Thomas Laffey, Robert Osburn (2007) 'On a conjecture of Wilf'. Journal of Combinatorial Theory - Series A, 114 (7):1332-1349. Available Online [DOI] Link to full text [Details]
P. Moree and R. Osburn; (2006) 'Two-dimensional lattices with few distances'. L'Enseignement Mathematique, 52 :361-380. Available Online [DOI] Link to full text [Details]
Stephen Choi, Angel Kumchev, Robert Osburn (2005) 'On sums of three squares'. International Journal of Number Theory, 1 (2):161-173. Available Online [DOI] Link to full text [Details]
Robert Osburn (2005) 'A remark on a conjecture of Borwein and Choi'. Proceedings of the American Mathematical Society, 133 (10):2903-2909. Available Online [DOI] Link to full text [Details]
Robert Osburn (2005) 'Vanishing of eigenspaces and cyclotomic fields'. International Mathematics Research Notices, 20 :1195-1202. Available Online [DOI] Link to full text [Details]
Robert Osburn (2004) 'A note on 4-rank densities'. Canadian Mathematics Bulletin, 47 :431-438. Available Online [DOI] Link to full text [Details]
Robert Osburn, Brian Murray (2003) 'Tame kernels and further 4-rank densities'. Journal of Number Theory, 98 (2):390-408. Available Online [DOI] Link to full text [Details]
Robert Osburn (2002) 'Densities of 4-ranks of K_2(O)'. Acta Arithmetica, 102 (1):45-54. Available Online [DOI] Link to full text [Details]
                                                                                                                     

Research

Research Interests

Robert completed his Ph.D. in 2001 in the fields of algebraic K-theory and number theory under the direction of Jurgen Hurrelbrink. His recent work has focused on special functions, modular forms, combinatorics and quantum knot invariants. He was the co-supervisor of Stefan de Wannemacker (Ph.D., 2006) with Professor David Lewis, full supervisor of Dermot McCarthy (Ph.D., 2010) and postdoctoral advisor for Marilyn Myers (IRCSET), Brundaban Sahu (SFI RFP), David Brink (Danish Research Fellow). Finally, he has advised undergraduates Adam Keilthy (TCD) and Paul Beirne (UCD) during the School of Mathematics and Statistics Summer Research Projects in 2014 and 2015, respectively.

Research Projects

Sponsor : University College Dublin (UCD)
Title : q-series and quantum knot invariants
Start Date / End Date : 01-APR-16 / 30-SEP-17
Sponsor : Irish Research Council (IRC)
Title : Workshop on Vertex Operator Algebras and Mock Modular Forms (VOAs+MMFs)
Start Date / End Date : 27-FEB-15 / 27-NOV-15
Sponsor : Science Foundation Ireland (SFI)
Title : The 27th Automorphic Forms Workshop
Start Date / End Date : 01-MAR-13 / 31-AUG-13
Sponsor : University College Dublin (UCD)
Title : The Bailey chain and mock theta functions
Start Date / End Date : 01-MAY-12 / 31-OCT-13
Sponsor : Science Foundation Ireland (SFI)
Title : Arithmetic properties of coefficients of modular forms
Start Date / End Date : 01-MAY-08 / 30-OCT-11
Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Ramanujan- type congruences for overpartitions and overpartition pairs
Start Date / End Date : 01-JAN-08 / 31-DEC-08
Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Variations of Kummer's Conjecture
Start Date / End Date : 31-DEC-07 / 30-DEC-09

Recent Postgraduates

Stefan de Wannemacker, Ph.D. 2006, UCD, co-advisor: Professor David Lewis.

Title of thesis: "Annihilating polynomials and Stirling numbers of the second kind" 

Dermot McCarthy, Ph.D. 2010, UCD

Title of thesis: "p-adic hypergeometric series and supercongruences"
 

 

Teaching

Teaching Philosophy

I believe that it is important for research intensive faculty members to teach a balance of undergraduate (in particular, first year) and graduate modules. Students should see mathematical concepts presented in a clear, concise and enthusiastic manner by a researcher who is excited about their subject!
 

Enhancement of Teaching

For each course, I tailor the lectures to the audience. Each lecture is carefully structured (a 50 minute lecture requires at least 3 to 4 hours of preparation) and presented in real-time via a chalkboard or document camera. In first year modules, the emphasis is on working a plethora of examples. The easiest way for most students to learn concepts is to observe and understand worked examples and then solve an array of problems on their own. This gives students a foundation of basic skills in which to complete various types of continuous assessment. As the difficultly level of a module increases, I pose questions with more depth and discuss topics at the forefront of mathematical research. Additionally, students give oral presentations in order to gain confidence and provide an opportunity for interaction with the audience. As a graduate student in the U.S. and a postdoctoral fellow in Canada, I was fortunate in that student evaluations for courses are standard practice. Since 2005, I have continued this practice for each of my courses at UCD by creating a Questionnaire and Comment Form. This form provides me with necessary feedback in order to judge the quality of my teaching and clarify what tangible steps can be taken to improve the delivery of my modules. For example, based on a student's suggestion, I now make a conscientious effort to pause more frequently as I write in order to reflect and reinforce the key points and give students time to digest the material.

Review and Enhancement of Curriculum

On the first day of every module, I hand out a syllabus and take the time to highlight all of the main points. It is vital to give a module description which clearly defines the types of assessment (exercise sheets, weekly quizzes, in-class exams, final exam) and gives a detailed schedule of what is covered in each lecture. This information provides students with exactly what is expected of them and with not only a "local" glimpse of each lecture, but also a "global" picture of how the various pieces of the module fit together. Students will also see that I am strongly in favor of continuous assessment. I feel that as part of the transition from secondary to third level education students should understand that much more is expected from them and that they will be exposed early and often to the rigors of not only mathematics, but to higher academic learning. Math 10040 is a first year honors Science module which is an introduction to number theory and combinatorics. These two subjects are branches of pure mathematics which have important applications to physics, chemistry, biology, computing, engineering, coding and cryptography, communications and business. Typically, 90 to 100 students take this module every year. This means that I am one of the first faces that new UCD students regularly see. I take this responsibility seriously. As module coordinator and creator of Math 10040, I determine the course content, assessment strategies and learning outcomes. Math 40280 is a postgraduate module which exposes all graduate students to the fundamentals of Algebra (i.e., Group Theory, the Sylow's theorems, Rings, Modules over a PID, Field theory, Galois theory, Simple and Semisimple algebras). This module is a key component in our School's graduate programme and was created by my colleague Dr. Vincent Astier and myself.

Developing as a Teacher

I have improved my technological skill set by creating module webpages using the software package Nvu and in the successful implementation (with colleague Dr. Michael Mackey) of an online interface program for students in courses with large enrollments. For example, 335 students in my second semester 2009 Math 10070 Calculus module could quickly and effectively monitor their continuous assessment. I have also improved my interpersonal skills through interactions with students. In order to stimulate student interactions, I encourage questions not only during the lectures, but also afterwards. Students then feel comfortable to either stop by anytime (I do not have fixed office hours) or email me (I respond quickly to emails received, day or night). Also, I create all of the assessment (exercise sheets, solutions, weekly quizzes, in-class exams, final exams) and mark all of the exams thereby keeping close watch on student performance. A student from Math 10040 said "His availability outside lectures is a huge benefit towards his students. The way he encourages students to ask questions is a giant help." Finally, I contributed to the training of my graduate students and postdocs during weekly meetings in which I gave advice on teaching courses and giving research presentations.

Innovation & Leadership

Dr. Thomas Unger (colleague) and I held weekly meetings in order to share teaching advice, discuss best practices and monitor student progress for two vital first year Science modules. In addition to acting as module coordinator for ten courses, I served on two School committees. The first committee continued the tradition of excellence and collaboration with Arts while the second was a new venue concerning the development and implementation of first year Math modules for the Bachelor of Commerce degree.

Collaborators

Internal Collaborators

Paul Beirne, UCD School of Mathematics and Statistics

David Brink, UCD School of Mathematical Sciences

Thomas Laffey, UCD School of Mathematical Sciences

Dermot McCarthy, UCD School of Mathematical Sciences

Brundaban Sahu, UCD School of Mathematical Sciences 


External Collaborators

George Andrews, Penn State University

Song Heng Chan, Nanyang Technological University, Singapore 

Stephen Choi, Simon Fraser University, British Columbia, Canada 
 
Byungchan Kim, Seoul National University of Science and Technology, Korea 

Angel Kumchev, Towson University, Maryland, USA

Pieter Moree, Max Planck Institut fuer Mathematik, Bonn, Germany

Stefan de Wannemacker, Katholieke Universiteit Leuven, Belgium
 
Brian Murray, Department of Defense, USA 

Ram Murty, Queen's University, Ontario, Canada

Jeremy Lovejoy, CNRS, LIAFA, Universite Denis Diderot-Paris 7, France

Carsten Schneider, Research Institute for Symbolic Computation, J. Kepler University Linz, Austria

Heng Huat Chan, National University of Singapore, Singapore

Aristides Kontogeorgis, University of the Aegean, Greece

Christian Krattenthaler, Universitat Wien, Austria

Kathrin Bringmann, University of Cologne, Cologne, Germany 

Brundaban Sahu, NISER, Bhubaneswar, India 

Renrong Mao, School of Mathematical Sciences, Soochow University, China

Ling Long, Louisiana State University, USA
 
Holly Swisher, Oregon State University, USA 
 
Adam Keilthy, Trinity College Dublin, Ireland 
 
Armin Straub, University of South Alabama, USA
 
Wadim Zudilin, University of Newcastle, Australia