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PETER 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
Assistant Professor

MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS, January 2009 - August 2009
Visiting Scholar

UNIVERSITY OF CALIFORNIA, BERKELEY, August 2008 - December 2008
Visiting Scholar

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

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 of partially ordered sets

- P-partitions

- Matrix theory

PUBLICATIONS

Towards a combinatorial classification of skew Schur functions, with Stephanie van Willigenburg, Transactions of the American Mathematical Society, to appear, 34 pp.

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, 18pp. 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.

PAPERS UNDER REVIEW

Infinite log-concavity: developments and conjectures, with Bruce E. Sagan, 20 pp.

Positivity results on ribbon Schur differences, with Stephanie van Willigenburg, 20 pp.

PAPERS APPEARING IN PROCEEDINGS OF REFEREED CONFERENCES

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, 2004, 24 pp.

PRESENTATIONS

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

University of Michigan Combinatorics Seminar, 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

University of Minnesota Combinatorics Seminar, November 2004
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

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

McGill Discrete Mathematics and Optimization Seminar, 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

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

TEACHING AT BUCKNELL

Math 211 (Calculus III), Spring 2008

Math 320 (Introduction to Algebra), Spring 2008

Math 291 (Mathematical Problem Solving), Fall 2007
This new seminar course, which I proposed and designed, emphasized problems that appear in contests such as the Putnam Competition.

Math 343 (Numerical Analysis), Fall 2007

Math 240 (Combinatorics and Graph Theory for Secondary Mathematics), Spring 2007

Math 241 (Discrete Structures), Spring 2007

Math 202 (Calculus II), Fall 2006

Math 320 (Introduction to Algebra), Fall 2006

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
Compiled a short list of appropriate open problems and presented them to an undergraduate student. Through daily meetings, guided him on his chosen research project regarding the combinatorics of hyperplane arrangements.

SERVICE TO BUCKNELL UNIVERSITY

Member of Departmental Committees:
Mathematics Scholarships Selection Committee, February 2008 - April 2008
Student Liaisons and Resources, August 2007 - July 2008
Student Recruitment and Propaganda, August 2007 - July 2008
Ad Hoc Committee on Statistics, April 2007
Competitions, August 2006 - July 2008
Computer and Library Committee, August 2006 - July 2007

Organizer of student trip to the Conference on Undergraduate Research in Mathematics, Penn State University, November 2007

Presenter of a talk entitled "Tilings from the Floor Up," Student Colloquium Series, Mathematics Department, October 2007

Webmaster for Mathematics Department, August 2006 - July 2007

Presenter of a talk entitled "Tangrams, Chessboards and Dominoes: Exploring Tilings," Spring Open House, April 2007

Representative for Mathematics Department at the Fall University Fair, September 2006, and at the University Welcome Reception, August 2007

OTHER PROFESSIONAL ACTIVITIES

Session Chair at the Conference on Undergraduate Research in Mathematics, Penn 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 in 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 Journal of Combinatorial Theory (Series A), the Electronic Journal of Combinatorics, Order, the Central European Journal of Mathematics, Information Sciences, the European Journal of Combinatorics, the Annals of Combinatorics

Reviewer for Mathematical Reviews; six reviews completed

Member of the American Mathematical Society, the Mathematical Association of America, and the Association for Women in Mathematics

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