Eva Curry Associate Professor of Mathematics Department of Mathematics and Statistics Acadia University Adjunct Professor Department of Mathematics and Statistics and Faculty of Graduate Studies Dalhousie University

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Contact

Teaching

Research

Math for Social Justice

Curriculum Vitae

Links

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Contact

Office: Huggins Science Hall 155
Phone: (902) 585-1793
Email: eva.curry@acadiau.ca
Mailing Address:	Eva Curry Department of Mathematics and Statistics Acadia University 12 University Avenue Wolfville, Nova Scotia Canada B4P 2R6
Email is the best way to contact me.
Office hours: (Fall 2011)	TBA Or by appointment

Teaching

Current courses:	I will be on sabbatical for the 2012/2013 academic year.
Past courses:	Acadia University: Math1013 (Calculus I), Math1023 (Calculus II), Math1333 (Intro. Linear Algebra), Math 3303 (Algebra I), Math 3533 (Real Analysis I), Math3543 (Complex Variables), Math4513 (Intro. Topology), Math4763 (Signal Processing and Analysis), Math5843 (Complex Analysis), Math5863 (Topics in Dynamical Systems and Ergodic Theory I and II) Dalhousie University: Calculus I, Advanced Calculus I, Intro. Complex Variables, Functional Analysis Rutgers University: Differential Equations Math4ME Workshop on programming in StarLogo (University of Maine)

Students Supervised:

• Avra Laarakker, Master's student, thesis: "Topological Properties of Tiles and Digit Sets", Acadia University, Fall 2007 - Summer 2009.
• Nicolas Coombs, NSERC Undergraduate Summer Research Award, Acadia University, Summer 2010.
• Natasha Mandryk, Summer Research Assistant, Acadia University, Summer 2007.

Teaching Resources:

Sarah-Marie Belcastro's Project NExT talk on Using Class Time Well
Peer instruction
Dan Meyer's blog and TED talk


Research

I study digital representations for vectors, a research area at the intersection of ergodic number theory and topology, with connections to wavelet theory. A radix representation (also called a number system), such as base 10 or base 2 (binary) representations in one dimension, is one example of a digital representation. In a multidimensional radix representation, we have a base and a set of digits. The base must be an expanding, square matrix A with integer entries, called a dilation matrix. The digit set is a complete set of coset representatives of Zⁿ / AZⁿ. We consider integer vectors that can be written as a finite sum of positive powers of the base multiplied by digits, and real vectors that can be written as a (possibly infinite) sum of negative powers of the base multiplied by digits. Questions that I am interested in related to this construction include:

• investigating topological properties of the set of "fractions", which is the attractor of an iterated function system defined by the dilation matrix and digit set;
• investigating number theoretic properties of this representation based on different choices of digit sets;
• related multidimensional digit representations, such as multidimensional continued fraction algorithms, beta transformations, and others;
• connections to multidimensional wavelets and frames, and analysis on fractals.

My PhD was in multidimensional wavelet theory with probability, which led to my current research interests. In addition to this initial shift, since my research is very interdisciplinary (within mathematics - involving linear algebra, analysis and probability, topology and fractals, number theory, and even a little graph theory - and with some connections to theoretical computer science), I am continuously branching out into new areas of study. My other mathematical interests include:

• duality between the attractor and invariant measure of an IFS, Martin boundary; measurable and symbolic dynamics;
• analysis on fractals; wavelets, frames, and operators;
• voting theory, fair division, and mathematics applicable to questions of social justice;
• experimental mathematics;
• DNA and molecular computing, quantum computing.

Here is an overview of my research in slides.


Mathematical Publications:

• Avra S. Laarakker and Eva Curry, Digit sets for connected tiles via similar matrices I: Dilation matrices with rational eigenvalues, submitted.
  arXiv
• Eva Curry, Radix and Pseudodigit Representations in Zⁿ, to appear, Proc. AMS.
  arXiv (unrevised version)
• Eva Curry, Multidimensional Radix Representations and the Hot Spot Theorem. "Tapas in Experimental Mathematics: Papers from AMS Special Session on Experimental Mathematics; January 5, 2007 New Orleans, Louisiana", Contemporary Mathematics, 457. American Mathematical Society, Providence, RI, 2008.
  AMS Bookstore; Google Books
• Eva Curry, Low-Pass Filters and Scaling Functions for Multivariable Wavelets. Canadian J. Math. 60 (2008), no. 2, 334-347.
  Canadian J. Math.
• Eva Curry, Radix Representations, Self-Affine Tiles, and Multivariable Wavelets. Proc. AMS 134 (2006), no. 8, 2411-2418.
  arXiv; Proc. AMS

Recent Invited Talks:

• Introduction to Sage, Sage Days 45, ICERM, Providence, RI; February 2013.
• Probabilistic Approach to Radix Representations and Pseudodigits, International Conference on Advances on Fractals and Related Topics, Chinese University of Hong Kong, Hong Kong, HK; December 2012.
• Martin and Poisson Boundaries for Low-Pass Filters, Colloquium, Department of Mathematics, Chinese University of Hong Kong, Hong Kong, HK; November 2012.
• Pseudodigits,
  • AMS Spring Eastern Section Meeting, Special Session on Analysis of Wavelets, Frames, and Fractals, George Washington University, Washington, DC; March 2012.
  • 4th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, in conjunction with AMS Fall Eastern Section Meeting, Special Session on Analysis, Probability, and Mathematical Physics on Fractals, Cornell University, Ithaca, NY; September 2011.
  • Jonfest, workshop on Computational and Analytic Mathematics in honour of Jonathan Borwein's 60th birthday, Simon Frasier University, Burnaby BC; May 2011.
• A One-Step Test for Connectedness of Radix IFS Tiles, AMS 2011 Spring Southeastern Section Meeting, Special Session on Fractals and Tilings, Georgia Southern University, Statesboro, GA; March 2011.
• Similar Matrices and Topological Properties of Self-Affine Tiles, Analysis and Number Theory Seminar, Department of Mathematics and Statistics, Dalhouse University, Halifax, NS; March 2010.

Math Research with Social Justice Applications

There is a common perception, most famously expressed by the mathematician G.H.~Hardy, that applications of mathematics only "accentuate the existing inequalities in the distribution of wealth, or more directly promote the destruction of human life." [Hardy, "A Mathematician's Apology"] In other words, Hardy claimed that applied mathematics was antithetical to the pursuit of social justice, that is, working to change our political, economic, and social structures to achieve more even distributions of wealth and political power and to eliminate oppression. A glance at the non-academic employers in mathematical job listings reinforces this conclusion. That young mathematicians may find their non-academic job options either uninteresting or inconsistent with their personal ethics, as Hardy did, has serious consequences for the profession, and for the direction of applied mathematics research.

Yet applied mathematics research is, indeed, done in areas that could be considered supportive of social justice goals. Different funding levels for different applications combined with the fact that many are in newer areas, such as climate modeling or voting theory, mean that many mathematicians and students are less aware of such research. A few examples were presented at a panel discussion that I organized at the January, 2011 Joint Mathematics Meetings in New Orleans, LA. However, much work is still needed to identify open research problems and opportunities for mathematicians to collaborate with non-mathematicians on applied research projects that have a social justice focus.

Stay tuned for more information, including a web site dedicated to the Mathematics of Social Justice.


Links

Department of Mathematics and Statistics
Acadia University

Sage open source mathematics software
WeBWorK open source online homework system
SENCER, Science Education for New Civic Engagements and Responsibilities
ACMMaC Acadia Centre for Mathematical Modeling and Computation
ACEnet Atlantic Computational Excellence Network
Harrison McCain Award Fund (Acadia University)

Guide to Tenants Rights in Nova Scotia (maintained by Dalhousie Legal Aid)
Dalhousie Legal Aid Service