Department of Mathematics | Office Phone: (570) 577-1901 | |
Bucknell University | Fax: (570) 577-3264 | |
Lewisburg, PA 17837 | peter.mcnamara@bucknell.edu | |
USA | http://www.facstaff.bucknell.edu/pm040 |
EDUCATION
MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS, 1999–2003
TRINITY COLLEGE, DUBLIN, IRELAND, 1995–1999
ACADEMIC POSITIONS
BUCKNELL UNIVERSITY, LEWISBURG, PENNSYLVANIA, August 2006–present
TRINITY COLLEGE, DUBLIN, IRELAND, June 2012–June 2013
MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS, June 2010–August 2010, January 2009–August 2009.
UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA, August 2008–December 2008
INSTITUTO SUPERIOR TÉCNICO, LISBON, PORTUGAL, August 2005–July 2006
LABORATOIRE DE COMBINATOIRE ET D'INFORMATIQUE MATHÉMATIQUE, UNIVERSITÉ DU QUÉBEC À MONTRÉAL, CANADA, July 2003–July 2005
HONORS AND AWARDS
Summer Research Session Grant, 2018
Simons Foundation Collaboration Grant, 2012–2018
Sabbatical Salary Supplement, 2012–2013
Project NExT (New Experiences in Teaching) Fellow, 2006–2007
Charles W. and Jennifer C. Johnson Prize, 2003
Charles and Holly Housman Award for Excellence in Teaching, 2003
MIT Presidential Fellowship, 1999–2000
Gold Medal for academic excellence upon graduation, Trinity College, 1999
Lloyd, Minchin and Roberts Prizes and Foundation Scholarship, Trinity College, 1996–1998
Individual winner, Irish Intervarsity Mathematics Competition, 1998
Honorable Mention, International Mathematics Olympiad, Toronto, 1995
RESEARCH INTERESTS
Combinatorics, often of an algebraic or order-theoretic nature. Specific topics include:
- Questions of Schur-positivity
- Relations among skew Schur functions
- Edge labellings, Möbius functions and topology of partially ordered sets
- P-partitions
- Matrix theory
PUBLICATIONS
Enumeration of colored Dyck paths via partial Bell polynomials, with Daniel Birmajer, Juan B. Gil and Michael D. Weiner, Lattice Path Combinatorics and Applications, G. Andrews, C. Krattenthaler, A. Krinik (Eds.), Springer, 11pp., to appear.
The structure of the consecutive pattern poset, with Sergi Elizalde, International Mathematics Research Notices, 2018 (7), 2099–2034.
The contributions of Stanley to the fabric of symmetric and quasisymmetric functions, with Sara C. Billey, chapter in The Mathematical Legacy of Richard P. Stanley, P. Hersh, T. Lam, P. Pylyavskyy, and V. Reiner (Eds.), American Mathematical Society, 2016, 83–104.
On the topology of the permutation pattern poset, with Einar Steingrímsson, Journal of Combinatorial Theory (Series A), 134 (2015), 1–35.
Comparing skew Schur functions: a quasisymmetric perspective, Journal of Combinatorics, 5 (1) (2014), 51–85.
Equality of P-partition generating functions, with Ryan E. Ward, Annals of Combinatorics, 18 (3) (2014), 489–514.
Maximal supports and Schur-positivity among connected skew shapes, with Stephanie van Willigenburg, European Journal of Combinatorics, 33 (6) (2012), 1190–1206.
The Möbius function of generalized subword order, with Bruce E. Sagan, Advances in Mathematics, 229 (5) (2012), 2741–2766.
A Pieri rule for skew shapes, with Sami H. Assaf and an appendix by Thomas Lam, Journal of Combinatorial Theory (Series A), 118 (1) (2011), 277–290.
Infinite log-concavity: developments and conjectures, with Bruce E. Sagan, Advances in Applied Mathematics, 44 (1) (2010), 1–15.
Positivity results on ribbon Schur differences, with Stephanie van Willigenburg, European Journal of Combinatorics, 30 (5) (2009), 1352–1369.
Towards a combinatorial classification of skew Schur functions, with Stephanie van Willigenburg, Transactions of the American Mathematical Society, 361 (8) (2009), 4437–4470.
Necessary conditions for Schur-positivity, Journal of Algebraic Combinatorics, 28 (4) (2008), 495–507.
Cylindric skew Schur functions, Advances in Mathematics, 205 (1) (2006), 275–312.
Poset edge-labellings and left modularity, with Hugh Thomas, European Journal of Combinatorics, 27 (1) (2006), 101–113.
P-partitions and a multi-parameter Klyachko idempotent, with Christophe Reutenauer, Electronic Journal of Combinatorics, 11 (2) (2005), #R21, 18 pp. Special volume in honor of Richard Stanley on the occasion of his 60th birthday.
Principal minor sums of (A+tB)^{m}, with Charles R. Johnson, Stefan Leichenauer and Roberto Costas, Linear Algebra and its Applications, 411 (2005), 386–389. Special issue on determinants and the legacy of Sir Thomas Muir.
Edge labellings of partially ordered sets, Ph.D. thesis, 2003.
EL-labelings, supersolvability and 0-Hecke algebra actions on posets, Journal of Combinatorial Theory (Series A), 101 (1) (2003), 69–89.
PREPRINTS
Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations, with Mark Dukes, 24 pp. From Dyck paths to standard Young tableaux, with Juan B. Gil, Jordan O. Tirrell and Michael D. Weiner, 22 pp.
PAPERS IN PREPARATION
Commutation and normal ordering for operators on symmetric functions, with Emmanuel Briand, Rosa Orellana and Mercedes Rosas.
PAPERS APPEARING IN PROCEEDINGS OF REFEREED CONFERENCES
On intervals of the consecutive pattern poset, with Sergi Elizalde,
The topology of the permutation pattern poset, with Einar Steingrímsson,
The Möbius function of generalized subword order, with Bruce E. Sagan,
A Pieri rule for skew shapes, with Sami H. Assaf,
Infinite log-concavity: developments and conjectures, with Bruce E. Sagan,
A combinatorial classification of skew Schur functions, with Stephanie van Willigenburg,
Positivity questions for cylindric skew Schur functions,
Poset edge-labellings and left modularity, with Hugh Thomas,
PRESENTATIONS
AMS Special Session on Applications of Partially Ordered Sets in Algebraic, Topological, and Enumerative Combinatorics, Joint Mathematics Meetings, Atlanta, January 2017
Discrete Geometry and Combinatorics Seminar, Cornell University, April 2016
Workshop on Positivity in Algebraic Combinatorics, Banff International Research Station, August 2015
International Meeting of the American, European and Portuguese Mathematical Societies, June 2015
Penn State Altoona Mathematics Colloquium, October 2014
Formal Power Series and Algebraic Combinatorics, Chicago, July 2014
Stanley@70: A Conference in Honor of Richard P. Stanley's 70th Birthday, MIT, June 2014
Bijective and Algebraic Combinatorics: in Honor of Bruce Sagan's 60th Birthday, University of Florida, March 2014
Canadian Mathematical Society Winter Meeting, Ottawa, December 2013
Le Séminaire du LaCIM, Université du Québec à Montréal, November 2013
Combinatorics Seminar, University of Strathclyde, Glasgow, April 2013
Mathematics Seminar, National University of Ireland Galway, March 2013
Mathematics Colloquium, Dublin City University, February 2013
Dublin University Mathematical Society, February 2013
Department of Mathematics & Statistics Colloquium, National University of Ireland Maynooth, November 2012
Formal Power Series and Algebraic Combinatorics, Nagoya, Japan, July 2012
Combinatorics Seminar, University of Minnesota, April 2012
AMS Special Session on Enumerative and Algebraic Combinatorics, Joint Mathematics Meetings, Boston, January 2012
Workshop on Quasisymmetric Functions, Banff International Research Station, November 2010
Discrete Geometry and Combinatorics Seminar, Cornell University, August 2010
Formal Power Series and Algebraic Combinatorics, San Francisco, August 2010
Algebra Seminar, Bucknell University, April 2010
Formal Power Series and Algebraic Combinatorics, Hagenberg, Austria, July 2009
Combinatorics Seminar, Dartmouth College, May 2009
Combinatorics Seminar, University of Minnesota, April 2009
Combinatorics Seminar, MIT, February 2009
Discrete Maths Seminar, University of British Columbia, November 2008
Mathematics Colloquium, San Francisco State University, October 2008
AMS Special Session on Combinatorics of Partially Ordered Sets, Claremont, California, May 2008
Algebra Seminar, Bucknell University, September 2007
Formal Power Series and Algebraic Combinatorics, Tianjin, China, July 2007
Workshop on Combinatorial Hopf Algebras and Macdonald Polynomials, Centre de Recherches Mathématiques, Montreal, May 2007
AMS Special Session on Algebraic Combinatorics, Fayetteville, Arkansas, November 2006
Combinatorics Seminar, University of Michigan, September 2006
Algebra Seminar, Universidade de Coimbra, Portugal, November 2005
Seminário do CAMGSD, Instituto Superior Técnico, Portugal, October 2005
Formal Power Series and Algebraic Combinatorics, Taormina, Italy, June 2005
Mathematics Seminar, Pomona College, February 2005
Mathematics Department Colloquium, Bucknell University, January 2005
Le Séminaire du LaCIM, Université du Québec à Montréal, October 2004
Retrospective in Combinatorics: Honoring Stanley's 60th Birthday, MIT, June 2004
Applied Algebra Seminar, York University, February 2004
Discrete Mathematics and Optimization Seminar, McGill University, November 2003
Le Séminaire du LaCIM, Université du Québec à Montréal, September 2003
Formal Power Series and Algebraic Combinatorics, Vadstena, Sweden, June 2003
Ph.D. Thesis Defense, MIT, April 2003
AMS Special Session on Lattice Theory, Joint Mathematics Meetings, Baltimore, January 2003
Canadian Mathematical Society Summer Meeting, Québec City, June 2002
Combinatorics Seminar, MIT, December 2001
TEACHING AT BUCKNELL
Math 192 (Topics in Calculus), Spring 2018, Spring 2010
Math 201 (Calculus I), Fall 2018, Fall 2017, Fall 2015
Math 202 (Calculus II), Fall 2016, Spring 2015, Fall 2011, Fall 2010, Fall 2009, Fall 2006
Math 209 (Mathematical Problem Solving), Fall 2013, Fall 2007 (as Math 291)
Math 211 (Calculus III), Spring 2016, Fall 2013, Spring 2008
Math 212 (Differential Equations), Fall 2017, Spring 2014, Spring 2011
Math 240 (Combinatorics and Graph Theory for Secondary Mathematics), Spring 2015, Spring 2007
Math 241 (Discrete Structures), Spring 2015, Spring 2007
Math 245 (Linear Algebra), Fall 2016, Fall 2014
Math 280 (Logic, Sets, and Proofs), Fall 2010, Spring 2010
Math 319 (Topics in Advanced Mathematics: Combinatorics), Spring 2014
Math 320 (Introduction to Algebra), Fall 2015, Fall 2009, Spring 2008, Fall 2006
Math 343 (Numerical Analysis), Fall 2011, Fall 2007
RESEARCH MENTORING AT BUCKNELL
Nate Lesnevich '19, Summer 2018--present
Tung Phan '17, Fall 2014
Ryan Ward '11, Fall 2009–Spring 2011
Joseph Ruby '11, Fall 2009–Spring 2010
PREVIOUS TEACHING AND MENTORING EXPERIENCE
Mentor, Research Experiences for Undergraduates Program, College of William and Mary, Williamsburg, Virginia, Summer 2004
Instructor, Calculus, MIT, Summers 2001 and 2002
Recitation Instructor, MIT, 2000–2003
Mentor, Summer Program for Undergraduate Research, MIT, 2001
SERVICE TO BUCKNELL UNIVERSITY
Chair of committee at the university level:
Member of committee at the university level:
Chair of departmental committees:
Member of departmental committees:
Presenter of talks entitled "The Art of Double Counting," October 2013, "A Life and Death Application of Mathematics," September 2009, and "Tilings from the Floor Up," October 2007, all in the Mathematics Department's Student Colloquium Series.
Organizer of student trip to the Conference on Undergraduate Research in Mathematics, Penn State University, November 2007
Presenter of a talk entitled "Tangrams, Chessboards and Dominoes: Exploring Tilings," Admitted Student Open House, April 2007
OTHER PROFESSIONAL ACTIVITIES
Member of the organizing committee and Session Chair for the 30th International Conference on Formal Power Series and Algebraic Combinatorics, Hanover, NH, July 2018
Member of the program committee for the 28th International Conference on Formal Power Series and Algebraic Combinatorics, Vancouver, July 2016
Presenter at the Upper Susquehanna Valley Math Circle, Lewisburg PA, October 2014
Session Chair at Stanley@70: A Conference in Honor of Richard P. Stanley's 70th Birthday, MIT, June 2014
Member of the program committee for the 25th International Conference on Formal Power Series and Algebraic Combinatorics, Paris, June 2013
Instructor of Mathematics Enrichment Classes as training for the Irish Mathematical Olympiad, University College Dublin, Spring 2013
Member of the organizing committee for the 22nd International Conference on Formal Power Series and Algebraic Combinatorics, San Francisco, August 2010
Organizer of Special Session on Algebraic Combinatorics at the Fall Eastern Section Meeting of the American Mathematical Society, Pennsylvania State University, October 2009
Session Chair at the Conference on Undergraduate Research in Mathematics, Pennsylvania State University, November 2007
Organizer of Project NExT Session on "How to Increase the Number of Majors," San Jose, August 2007
Judge for the Mathematical Association of America Undergraduate Poster Session, Joint Mathematics Meetings, New Orleans, January 2007
Organizer of Special Session on Algebraic Combinatorics at the Winter Meeting of the Canadian Mathematical Society, Montreal, December 2004
Research Assistant, MIT and Whitehead Institute, Summer 2000
Referee for Annals of Combinatorics, Central European Journal of Mathematics, Discrete Applied Mathematics, Electronic Journal of Combinatorics, European Journal of Combinatorics, Formal Power Series and Algebraic Combinatorics (Proceedings), Information Sciences, Journal of Algebraic Combinatorics, Journal of Combinatorial Theory (Series A), Mathematische Zeitschrift, Order, Séminaire Lotharingien de Combinatoire
Panelist reviewing National Science Foundation grant proposals
Reviewer of grant proposals for National Security Agency
Reviewer for Mathematical Reviews; fourteen reviews completed