Professor Emerita of Mathematics
Finite groups and finite geometries, difference sets, quantum error correction
Mathematics professor Harriet Pollatsek loves mathematics and enjoys those times when she has managed to be "contagious" and help her students to love it too. She particularly relishes "the challenge of changing the opinion of someone who is sure she doesn't like mathematics."
Pollatsek's current research is related to ideas of symmetry. "Mathematicians formalize notions of symmetry by speaking of transformations. For example, instead of saying a valentine heart is symmetric, I can say that it looks the same when 'reflected' over a vertical line dividing it in half (but not the same when 'reflected' over any other line). These transformations are called 'symmetries,' and symmetries have a mathematical structure when they are 'combined.' Group theory is the study of these structures; it is essentially the study of symmetry, which is why it's so useful to physicists and chemists. My specific interests are in error correction and in difference sets. Arranging information 'symmetrically' can make it possible to detect and correct errors arising when the information is transmitted. Difference sets are combinatorial structures that correspond to geometric configurations with especially nice groups of symmetries. One of the reasons I enjoy studying difference sets is because it requires tools from many areas of mathematics: group theory, finite geometry, algebraic number theory, and combinatorics."
An active scholar, Pollatsek enjoys working with other scholars. Her collaboration with Mary Beth Ruskai on quantum error correction brings her into contact with researchers in computer science, engineering, and physics, and she enjoys this interdisciplinary contact.
Intellectual "cross-fertilization" is also facilitated by Mount Holyoke's membership in the Five College Consortium, which joins the resources of MHC with those of Amherst, Hampshire, and Smith Colleges, and the University of Massachusetts at Amherst. Says Pollatsek, "Mathematics is itself a community, and my department looks for many ways to connect our students to this larger community, from encouraging Five College activities to supporting student travel to meetings and conferences."
In addition to teaching, conducting her own research, and advising, Pollatsek has chaired the Committee on the Undergraduate Program in Mathematics (CUPM) of the Mathematical Association of America (MAA) and is a member of the editorial board for MAA's Illustrative Resources for the CUPM Curriculum Guide 2004.
"Quantum Error Correction: Classic Group Theory Meets a Quantum Challenge," an expository article by Pollatsek published in the American Mathematical Monthly
- Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004. Committee on the Undergraduate Program of the Mathematical Association of America, MAA (2004) (chair of CUPM and chair of Writing Group).
- "Permutationally invariant codes for quantum error correction." Linear Algebra and its Applications 392 (2004): 255-288 (with Mary Beth Ruskai).
- "Looking for Difference Sets in Groups with Dihedral Images." Designs, Codes, and Cryptography 28 (2003): 45–50 (with Emily Moore).
- "Quantum Error Correction: Classic Group Theory Meets a Quantum Challenge." American Mathematical Monthly 108 (2001): 932–962.
- "Ruling Out (160, 54, 18) Difference Sets in Some Nonabelian Groups." Journal of Combinatorial Designs 8 (2000): 221–231 (with [undergraduate authors] J. Alexander, R. Balasubramanian, J. Martin, K. Monahan, and R. Sen).
Grants, Honors, or Awards and Year Received
- Co-Project Director for NSF DUE grant 0218773 of $91,256 for "A National Agenda for Advancing the Undergraduate Mathematics Curriculum," awarded to the Mathematical Association of America on May 17, 2002. The period of the award is June 1, 2002 to May 31, 2004.
- $45,000 grant (for the same project above) received from the Calculus Consortium for Higher Education.