PETER R. W. MCNAMARA

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
Ph.D. in Pure Mathematics, June 2003
Thesis: Edge labellings of partially ordered sets
Advisor: Richard P. Stanley

TRINITY COLLEGE, DUBLIN, IRELAND, 1995–1999
B.A. in Mathematics


ACADEMIC POSITIONS

BUCKNELL UNIVERSITY, LEWISBURG, PENNSYLVANIA, August 2006–present
Professor of Mathematics, July 2017–present
Associate Professor of Mathematics, July 2012–June 2017
Assistant Professor of Mathematics, August 2006–June 2012

TRINITY COLLEGE, DUBLIN, IRELAND, June 2012–June 2013
Visiting Professor

MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS, June 2010–August 2010, January 2009–August 2009.
Visiting Scholar

UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA, August 2008–December 2008
Visiting Professor

INSTITUTO SUPERIOR TÉCNICO, LISBON, PORTUGAL, August 2005–July 2006
Postdoctoral Fellow
Mentor: Raul Cordovil

LABORATOIRE DE COMBINATOIRE ET D'INFORMATIQUE MATHÉMATIQUE, UNIVERSITÉ DU QUÉBEC À MONTRÉAL, CANADA, July 2003–July 2005
Postdoctoral Fellow
Mentors: François Bergeron and Christophe Reutenauer


HONORS AND AWARDS

Simons Foundation Collaboration Grant, 2012–2017

Sabbatical Salary Supplement, 2012–2013
Awarded by Bucknell’s Faculty Development Committee.

Project NExT (New Experiences in Teaching) Fellow, 2006–2007

Charles W. and Jennifer C. Johnson Prize, 2003
Awarded by the MIT Department of Mathematics to a graduate student for an outstanding research paper accepted for publication in a major journal.

Charles and Holly Housman Award for Excellence in Teaching, 2003
Awarded by the MIT Department of Mathematics to a graduate student on the basis of student and staff evaluations.

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,
Proceedings of the 8th International Conference on Lattice Path Combinatorics and Applications, 10pp., to appear.

The structure of the consecutive pattern poset, with Sergi Elizalde, International Mathematics Research Notices, 36 pp., to appear.

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.


PAPER UNDER REVIEW

From Dyck paths to standard Young tableaux, with Juan B. Gil, Jordan O. Tirrell and Michael D. Weiner, 19 pp., submitted.

Commutation and normal ordering for operators on symmetric functions, with Emmanuel Briand, Rosa Orellana and Mercedes Rosas, 23 pp., submitted.


PAPERS APPEARING IN PROCEEDINGS OF REFEREED CONFERENCES

On intervals of the consecutive pattern poset, with Sergi Elizalde,
Formal Power Series and Algebraic Combinatorics, Vancouver, July 2016.

The topology of the permutation pattern poset, with Einar Steingrímsson,
Formal Power Series and Algebraic Combinatorics, Chicago, June/July 2014.

The Möbius function of generalized subword order, with Bruce E. Sagan,
Formal Power Series and Algebraic Combinatorics, Nagoya, Japan, July/August 2012.

A Pieri rule for skew shapes, with Sami H. Assaf,
Formal Power Series and Algebraic Combinatorics, San Francisco, August 2010.

Infinite log-concavity: developments and conjectures, with Bruce E. Sagan,
Formal Power Series and Algebraic Combinatorics, Hagenberg, Austria, July 2009.

A combinatorial classification of skew Schur functions, with Stephanie van Willigenburg,
Formal Power Series and Algebraic Combinatorics, Tianjin, China, July 2007.

Positivity questions for cylindric skew Schur functions,
Formal Power Series and Algebraic Combinatorics, Taormina, Italy, June 2005.

Poset edge-labellings and left modularity, with Hugh Thomas,
Formal Power Series and Algebraic Combinatorics, Vadstena, Sweden, June 2003.


PAPERS NOT INTENDED FOR PUBLICATION

Some positive differences of products of Schur functions, with François Bergeron, 24 pp., 2004


PRESENTATIONS

AMS Special Session on Applications of Partially Ordered Sets in Algebraic, Topological, and Enumerative Combinatorics, Joint Mathematics Meetings, Atlanta, January 2017
The structure of the consecutive pattern poset

Discrete Geometry and Combinatorics Seminar, Cornell University, April 2016
The structure of the consecutive pattern poset

Workshop on Positivity in Algebraic Combinatorics, Banff International Research Station, August 2015
Conjectures concerning the difference of two skew Schur functions

International Meeting of the American, European and Portuguese Mathematical Societies, June 2015
Comparing Skew Schur functions: a Quasisymmetric Perspective

Penn State Altoona Mathematics Colloquium, October 2014
Inequalities among Symmetric Polynomials

Formal Power Series and Algebraic Combinatorics, Chicago, July 2014
The Topology of the Permutation Pattern Poset

Stanley@70: A Conference in Honor of Richard P. Stanley's 70th Birthday, MIT, June 2014
Skew Schur Functions: Do Their Overlaps Determine Their F-supports (open problem presentation)

Bijective and Algebraic Combinatorics: in Honor of Bruce Sagan's 60th Birthday, University of Florida, March 2014
The Combinatorial Topology of the Permutation Pattern Poset

Canadian Mathematical Society Winter Meeting, Ottawa, December 2013
Comparing Skew Schur functions: a Quasisymmetric Perspective

Le Séminaire du LaCIM, Université du Québec à Montréal, November 2013
The Combinatorial Topology of the Permutation Pattern Poset

Bucknell University Student Colloquium Series, October 2013
The Art of Double Counting

Combinatorics Seminar, University of Strathclyde, Glasgow, April 2013
The Möbius Function of Generalized Subword Order

Mathematics Seminar, National University of Ireland Galway, March 2013
Symmetric Polynomials and the Skew Pieri Rule

Mathematics Colloquium, Dublin City University, February 2013
Symmetric Polynomials and the Skew Pieri Rule

Dublin University Mathematical Society, February 2013
Tilings from the Floor Up

Department of Mathematics & Statistics Colloquium, National University of Ireland Maynooth, November 2012
Symmetric Polynomials and the Skew Pieri Rule

Formal Power Series and Algebraic Combinatorics, Nagoya, Japan, July 2012
The Möbius Function of Generalized Subword Order

Combinatorics Seminar, University of Minnesota, April 2012
The Möbius Function of Generalized Subword Order

AMS Special Session on Enumerative and Algebraic Combinatorics, Joint Mathematics Meetings, Boston, January 2012
The Möbius Function of Generalized Subword Order

Workshop on Quasisymmetric Functions, Banff International Research Station, November 2010
Equality Questions for P-partition Quasisymmetric Functions (Preliminary Report)

Discrete Geometry and Combinatorics Seminar, Cornell University, August 2010
The Schur-Positivity Poset

Formal Power Series and Algebraic Combinatorics, San Francisco, August 2010
A Pieri Rule for Skew Shapes

Algebra Seminar, Bucknell University, April 2010
A Pieri Rule for Skew Shapes

Formal Power Series and Algebraic Combinatorics, Hagenberg, Austria, July 2009
Infinite Log-Concavity: Developments and Conjectures (poster)

Combinatorics Seminar, Dartmouth College, May 2009
The Schur-Positivity Poset

Combinatorics Seminar, University of Minnesota, April 2009
Infinite Log-Concavity

Combinatorics Seminar, MIT, February 2009
The Schur-Positivity Poset

Discrete Maths Seminar, University of British Columbia, November 2008
Infinite Log-Concavity

Mathematics Colloquium, San Francisco State University, October 2008
Infinite Log-Concavity

AMS Special Session on Combinatorics of Partially Ordered Sets, Claremont, California, May 2008
The Schur-Positivity Poset

Algebra Seminar, Bucknell University, September 2007
Two talks: An Introduction to Symmetric Functions and The Schur-Positivity Poset

Formal Power Series and Algebraic Combinatorics, Tianjin, China, July 2007
A Combinatorial Classification of Skew Schur Functions

Workshop on Combinatorial Hopf Algebras and Macdonald Polynomials, Centre de Recherches Mathématiques, Montreal, May 2007
A Combinatorial Classification of Skew Schur Functions

AMS Special Session on Algebraic Combinatorics, Fayetteville, Arkansas, November 2006
A Combinatorial Classification of Skew Schur Functions

Combinatorics Seminar, University of Michigan, September 2006
When Are Two Skew Schur Functions Equal?

Algebra Seminar, Universidade de Coimbra, Portugal, November 2005
A Combinatorial Lie Element for the Symmetric Group Algebra

Seminário do CAMGSD, Instituto Superior Técnico, Portugal, October 2005
Symmetric Functions and Cylindric Schur Functions

Formal Power Series and Algebraic Combinatorics, Taormina, Italy, June 2005
Positivity Questions for Cylindric Skew Schur Functions

Mathematics Seminar, Pomona College, February 2005
An Introduction to the Combinatorics of Symmetric Functions

Mathematics Department Colloquium, Bucknell University, January 2005
Symmetric Functions and Cylindric Schur Functions Cylindric Skew Schur Functions

Le Séminaire du LaCIM, Université du Québec à Montréal, October 2004
Positivity Questions for Generalised Schur Functions

Retrospective in Combinatorics: Honoring Stanley's 60th Birthday, MIT, June 2004
Cylindric Schur Functions

Applied Algebra Seminar, York University, February 2004
P-partitions and Quasi-Symmetric Functions

Discrete Mathematics and Optimization Seminar, McGill University, November 2003
Questions of Schur-Positivity

Le Séminaire du LaCIM, Université du Québec à Montréal, September 2003
Edge Labellings of Partially Ordered Sets and Their Implications

Formal Power Series and Algebraic Combinatorics, Vadstena, Sweden, June 2003
Poset Edge-Labellings and Left Modularity

Ph.D. Thesis Defense, MIT, April 2003
Edge Labellings of Partially Ordered Sets

AMS Special Session on Lattice Theory, Joint Mathematics Meetings, Baltimore, January 2003
Equivalent Characterizations of Lattice Supersolvability and Their Extensions

Canadian Mathematical Society Summer Meeting, Québec City, June 2002
Permutation Edge-Labellings of Partially Ordered Sets

Combinatorics Seminar, MIT, December 2001
Two New Characterizations of Lattice Supersolvability


TEACHING AT BUCKNELL

Math 192 (Topics in Calculus), Spring 2010

Math 201 (Calculus I), 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)
This new seminar course, which I proposed and designed, emphasized problems that appear in contests such as the Putnam Competition.

Math 211 (Calculus III), Spring 2016, Fall 2013, Spring 2008

Math 212 (Differential Equations), 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

Tung Phan '17, Fall 2014

Ryan Ward '11, Fall 2009–Spring 2011
Ryan successfully defended his honors thesis "Equality of P-partition generating functions" in April 2011, and entered the Ph.D. program in mathematics at Pennsylvania State University in Fall 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
As part of NSF-funded program, guided two undergraduate research projects in Matrix Analysis. Worked with students to improve the mathematical exposition in their writing and presentations.

Instructor, Calculus, MIT, Summers 2001 and 2002
Full responsibility for course. This was a component of Project Interphase, an intensive program for entering first-years from minority backgrounds.

Recitation Instructor, MIT, 2000–2003
Taught for courses in Calculus, Linear Algebra, Differential Equations, Multivariable Calculus and Complex Analysis. Responsibilities included leading recitations, holding office hours, grading exams and homework, and assigning final grades.

Mentor, Summer Program for Undergraduate Research, MIT, 2001
Through daily meetings, guided an undergraduate student on his research project regarding the combinatorics of hyperplane arrangements.


SERVICE TO BUCKNELL UNIVERSITY

Chair of committee at the university level:
Committee on Staff Planning, January 2014–June 2014

Member of committee at the university level:
Committee on Staff Planning, August 2009–December 2011, August 2013–June 2014

Chair of departmental committees:
Curriculum, July 2015–June 2016
Competitions, August 2009–June 2010, August 2014–June 2015
Student Liaisons and Resources, August 2010–June 2011
Web, Computer, and Library, August 2013–June 2014

Member of departmental committees:
Ad Hoc Committee on Statistics, April 2007
Assessment, August 2011–December 2011
Calculus Review, August 2016–December 2016
Competitions, August 2006–June 2008, August 2009–June 2010, August 2013–June 2015
Computer and Library Committee, August 2006–June 2007
Curriculum, August 2010–June 2011, August 2014–December 2016
External Review Subcommittee on Faculty, August 2010–December 2010
Mathematics Hiring, August 2010–June 2011
Mathematics Talks, August 2011–December 2011, August 2013–June 2014, July 2015–June 2016
Mathematics Scholarships Selection Committee, February 2008–April 2008
Scholarships, August 2009–June 2010
Student Liaisons and Resources, August 2007–June 2008, August 2010–June 2011
Student Recruitment, August 2007–June 2008
Webmaster, August 2006–June 2007, August 2009–June 2010

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 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
Member of the development team of a gene-finding program as part of the MIT and Whitehead Institute's contribution to the Human Genome Project

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