Monica Nevins, Associate Professor

Teaching - Research - Workshops - Students - Publications and Research Talks - Outreach/High School Students - About me - Fun

Teaching

• Winter 2012: MAT1325: Calculus II and an Introduction to Analysis. We discover why Calculus works, meet the real numbers honestly for the first time, and get our first taste of higher mathematics. Paradoxes, discoveries, logic, intuition, epsilon and delta --- all the drama of Calculus in one course. Plus some geometry in 3D and the beginnings of multivariable Calculus.
• Fall 2011: MAT1320: Calculus I, Section A. Your first glimpse of the Fundamental Theorem of Calculus and how it changed science forever.
• Fall 2011: MAT3166: Elementary Number Theory. This is what you might have thought studying math was about, back in high school. Prime numbers, numerical magic, big open questions and a little cryptology.
• Winter 2011: MAT4154/MAT5330 : Algebraic Geometry. An absolute must for all serious students in pure mathematics --- algebraic geometry combines ideas from topology, geometry and algebra to give us powerful new tools with which to approach problems in both geometry and algebra.
• Winter 2010: MAT3343: Applied Algebra. This course further develops your algebraic skills in the context of applications such as classical (and not-so-classical) symmetry groups, and error-correcting codes.
• Hiver 2009: MAT2543: Structures algébriques. C'est un cours exigeant et absolument satisfaisant; on y découvre les structures algébriques qui sous-viennent les mathématiques depuis le mi-19ième siécle.
• Winter 2009: Mathematical Cryptography. We discuss the current trends and successes of cryptography, with particular emphasis on those techniques with strong mathematical foundations. The cryptographic systems we will focus on include Elliptic Curve Cryptography, as well as more classical RSA and more recent NTRU.
• Fall 2008: MAT1341: Introduction to Linear Algebra. A challenging and fascinating introductory course for students in Engineering and the Physical Sciences.
• For previous teaching assignments, please see here.

Research

Workshops - My area

I am part of the very large and active Algebra and Lie Theory Research Group, within the Ottawa-Carleton Institute of Mathematics.

Workshops and Conferences Organized

• The University of Ottawa hosted the Fields Institute Workshop on Geometry Related to the Langlands Programme from May 27-31, 2009. This five-day workshop was the third of a series, and offered both mini-courses and a weekend conference. Co-organizer: Clifton Cunningham.
• I co-organized, with Isabelle Déchène and Ariane Masuda, a Special Session on Cryptography and Coding Theory, in the CMS Winter Meeting, Ottawa, December 2008.
• I was a member of the organizing committee of the 4th Connecting Women in Mathematics Across Canada (CWiMAC) workshop, held prior to the CMS Winter Meeting at the University of Ottawa, December 2008.
• The University of Ottawa hosted the Fields Institute Workshop on New Directions in Cryptography from June 25-27, 2008. Organisers: Ian Blake, Ali Miri and Monica Nevins.
• The University of Ottawa hosted the Fields Institute Workshop on the Representation Theory of Reductive Algebraic Groups from January 18-21, 2007. Organisers: Clifton Cunningham and Monica Nevins.
• The Fields Institute Workshop on the Representation Theory of p-adic Groups was held here May 5th through 9th, 2004. Organizers: Jason Levy and Monica Nevins.
• Special Session on real and p-adic groups at the CMS Winter meeting in Ottawa, December 2002. Organizers: Jason Levy and Monica Nevins.

Area of Specialization

• My principal area of interest is the representation theory of algebraic groups. One of my long-standing goals is to apply the method of coadjoint orbits (a philosophy for classifying unitary representations of real and complex Lie groups) to p-adic algebraic groups. Here is a nontechnical description of this research area.
• Over the past several years, I have been exploring branching rules, specifically, decompositions of representations of reductive p-adic groups upon restriction to a maximal compact subgroup. The goal is to gain insight into the structure of these representations, and their types.
• My secondary interests are in applications of representation theory and algebra to coding theory and cryptology. I have benefitted particularly from a collaboration with Dr. Ali Miri, now at Ryerson University.

Students

Undergraduate - Graduate - Current and Past Students

Undergraduate Research

I am very supportive of undergraduate research, and typically employ one or two upper level math students through the NSERC USRA, U of Ottawa Work-Study, or co-op programmes each summer. Research projects can take on many forms. Some students prefer more structure, and I will set out specific tasks to help you learn some graduate-level mathematics and to work out examples and find patterns. Other students thrive on the freedom of open-ended questions, where you let your interests and enthusiasm dictate what examples you work out and what patterns you discover.

Some recent project areas include: representation theory of finite groups, orthogonal designs for space-time codes, p-adic numbers, orbits of matrix groups acting on their Lie algebras, finite fields and constructibility of the 17-gon, algebraic topology.

Here's a little guide to get started on the mechanics of mathematical research and mathematical writing with LaTeX.

Graduate Research

I generally accept one or two master's students each year, often with co-supervisors. You apply to do a master's through the university; there is no official deadline but do appreciate that it is more or less first-come, first-serve in terms of accepting students each year. If you wish to work with me specifically, do contact me directly.

Some related information:

• An overview of some of the research projects I pursue.
• Some projects you could participate in as my graduate student include buildings, supercuspidal representations, space-time codes, and cryptography.
• Some help for new graduate students, including style files for your thesis, a primer on getting started with LaTeX, and some comments on mathematical writing.
• Here is a more general overview of the mechanics of getting started on mathematical research and writing.

Recent Publications and Research Talks

Journals - Submitted Papers - Conference Proceedings - Selected Talks

Publications in Journals

1. José Lima, A. Miri and M. Nevins, "Analysis of Relay Attacks on RFiD Systems," IEEE Latin America Transactions, Vol.:10, Iss.:1, Jan. 2012
2. Monica Nevins, "Patterns in Branching Rules for Irreducible Representations of SL_2(k), for k a p-adic field," to appear in Harmonic analysis on reductive, p-adic groups, edited by Robert S. Doran, Paul J. Sally, Jr., and Loren Spice, Contemp Math, to appear in 2011.
3. Peter S. Campbell and Monica Nevins, "Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic field", arXiv:0710.3263v1 [math.RT], Canad. J. Math. 62 (2010), no. 1, 34-51.
4. Monica Nevins, Camelia KarimianPour and Ali Miri, NTRU over Rings Beyond Z, Designs, Codes and Cryptography, Volume 56, Issue 1 (2010), page 65-78. DOI: 10.1007/s10623-009-9342-7
5. Peter S. Campbell and Monica Nevins, "Branching Rules for Unramified Principal Series Representations of GL(3) over a p-adic field", Journal of Algebra, 321(9), pp 2422-2444, May 2009.
6. Terasan Niyomsataya, Ali Miri and Monica Nevins, "An Application of the Bruhat Decomposition to the Design of Full Diversity Unitary Space-Time Codes", IEEE Transactions on Information Theory, Vol 55, Issue 1, pp 232-244, January 2009.
7. Monica Nevins, "On Nilpotent Orbits of SL(n) and Sp(2n) over Local Fields", arXiv:0708.1363v1 [math.RT], Journal of Algebras and Representation Theory, 2011, Volume 14, Number 1, Pages 161-190. DOI: 10.1007/s10468-009-9182-1
8. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Unitary space-time group codes: diversity sums from character tables," IEEE Transactions on Information Theory, Vol 54, Issue 11, pp 5203-5210, November 2008.
9. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Affine Reflection Group Codes", IEEE Transactions on Information Theory, Vol 54, Issue 1, pp 441-454, January 2008.
10. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Unitary Space-Time Constellation Designs from Group Codes,", IEEE Transactions on Information Theory, Vol 53, No 11, pp 4322-29, November 2007.
11. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Pairwise error probability of space-time codes for a keyhole channel", IET Communications, Volume 1, Issue 1, pp 101-105, February 2007.
12. Ali Miri, Monica Nevins and Terasan Niyomsataya, "Applications of Representation Theory to Wireless Communications", Designs, Codes and Cryptography, Volume 41, Number 3, pp307-318, December 2006.
13. Terasan Niyomsataya, Ali Miri and Monica Nevins, "A new unitary space-time code with high diversity product", IEEE Transactions on Wireless Communications, Vol 5, No 1, January 2006.
14. Monica Nevins, "Branching Rules for Principal Series Representations of SL(2) over a p-adic field", Canad. J. Math. 57 (2005), no. 3, 648--672.
15. Monica Nevins, "Admissible Nilpotent Orbits of Exceptional p-adic Lie groups", Represent. Theory (electronic) Vol 6., 2002.
16. Monica Nevins, "Admissible Nilpotent Orbits of p-adic Reductive Lie Groups," Represent. Theory (electronic) Vol 3., 1999.
17. Monica Nevins, "Admissible Nilpotent Orbits of p-adic Reductive Lie Groups," Ph.D. Thesis, MIT, 1998.

Submitted Publications

1. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Decoding Affine Reflection Group Codes with Trellises", 15 pages, submitted April 2011.
2. Nicholas Mailloux, Ali Miri and Monica Nevins, "COMPASS: Authenticated Group Key Agreement from Signcryption", 20 pages, submitted March 2011.

Work in Progress

1. Monica Nevins, "Branching Rules for Supercuspidal Representations of SL(2)"

Refereed Conference Proceedings

1. Jose Augusto Lima, Ali Miri and Monica Nevins, "Analysis of Relay Attacks on RFiD Systems", I2TS 2011, Florianopolis, Brazil, December 2011. Selected among 10 best papers presented at the conference.
2. Nicholas Mailloux, Ali Miri and Monica Nevins, "Forward Secure Identity-based Key Agreement for Dynamic Groups", PST 2011, Montreal, Canada July 2011.
3. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Efficient Decoding Algorithm for Affine Reflection Group Codes", 24th Queen's Biennial Symposium on Communications.
4. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Multiple Symbol Detection For Differential Unitary Space-Time Modulation Using a Stack Algorithm", 24th Queen's Biennial Symposium on Communications.
5. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Unitary space-time constellations based on finite reflection group codes", Proceedings of the Canadian Workshop on Information Theory, CWIT 2005, Montreal, Canada, June 2005.
6. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Full Diversity Unitary Space-Time Bruhat Constellations," 2004 IEEE Information Theory Workshop, Texas, USA, pp370-374, Oc 24-29, 2004.
7. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Unitary Space-Time Codes from Group Codes: Permutation Codes Variant II," 2004 IEEE Candaian Conference on Electrical and Computer Engineering (CCECE 2004), Niagara Falls, Vol 1, pp597-600, May 2004.
8. Terasan Niyomsataya, Ali Miri and Monica Nevins, "On the Construction of Space-time Hamiltonian Constellations from Group Codes", 2004 IEEE International Conference on Communications (ICC 2004), Paris, Vol 1 pp613-617, June 2004.
9. Terasan Niyomsataya, Ali Miri and Monica Nevins, "New Space-Time Code Design for Prime Number of Transmitter Antennas," 22nd Biennial Symposium on Communications, Queen's University, pp12-14, May 31-June 3, 2004.
10. Terasan Niyomsataya, Ali Miri and Monica Nevins, "Improving the Diversity Product of Space-Time Hamiltonian Constellations," 2004 IEEE International Symposium on Information Theory, (ISIT 2004), Chicago, p186, June 27-July 2, 2004.

Selected Talks

1. "On some irreducible representations of SL(2,O), where O is the integer ring of a p-adic field.", Special Session on Harmonic Analysis and Representations of Reductive p-adic Groups, AMS Joint Math Meetings, January 2010.
2. "Patterns in Branching Rules for Supercuspidal Representations", Session on Lie Groups and Automorphic Forms, CMS Winter Meeting, Windsor, Dec 5, 2009.
3. "Applications of the Representation Theory of Groups: How Representation Theory Underlies Everything", at the Ottawa Mathematics Conference, Ottawa, May 1-2, 2008.
4. "Representation Theory and Wireless Communications: Space-Time Codes", on joint work with Terasan Niyomsataya and Ali Miri, Department of Mathematics Colloquium and AWM Invited Lecture, University of Chicago, February 23rd, 2007.
5. Ibid, presented in the Group Theory Seminar at the University of Bristol, UK, June 2007.
6. "Branching Rules for Principal Series Representations", on joint work with Peter S. Campbell, Algebra Seminar, University of Chicago, February 22nd, 2007.
7. "Branching Rules for Unramified Principal Series Representations of p-adic GL(3)", on joint work with Peter S. Campbell, Special Session on Algebraic Groups, 2006 Spring Eastern Section Meeting, Durham, NH, April 22-23, 2006
8. Slides of my talk at the CMS Summer Meeting in Waterloo, in June 2005: "Branching Rules for Principal Series Representations of GL(3), on joint work with Peter S. Campbell.
9. "Decomposition of Restrictions of Principal Series Representations of p-adic GL(3) to a Maximal Compact Subgroup," joint with Peter S. Campbell, Special Session on Representation Theory of Reductive Groups, 2004 Fall Central Section Meeting, Evanston, IL, October 23-24, 2004.
10. Slides of my talk at the AMS Sectional Meeting at Northeastern University, Boston, in October 2002: pdf file.
11. Slides of my talk at the Joint Meetings in New Orleans, January 2001 (pdf).

Outreach

Programs I am actively involved in

• I participate in Workshops by the Centre for University Teaching for graduate student TAs in the Faculties of Science and Engineering.
• I give talks on applications of pure mathematics on University of Ottawa Day, and on request.
• I have given lectures at the CMS Summer Math Camp and the Math Horizons Day, two joint initiatives of the University of Ottawa and the Canadian Mathematical Society. These invitation-only activities offer a fun and lively introduction to upper level mathematics to mathematically talented high school students.

Talks for the general public

• On RSA (University of Ottawa Day, Octobers 2004, 2006 and 2007)
• CryptoSecrets: The Mathematics of Internet Security (Holiday Science Lecture Series, December 29, 2005) - Puzzles related to the talk - Solutions to puzzles
• Codes and Cryptography, an interactive talk with a Grade 3 class in Ottawa, February 20, 2006.

About me

• Percival High School, Val d'Or, QC, 1989
• B.Sc. in Mathematics and Computer Science, University of Ottawa, 1994
• Ph.D. in Pure Mathematics, MIT, 1998, under the supervision of David Vogan
• Killam Postdoctoral Fellow, University of Alberta, 1998-2000, as well as instructor in the (Faculté) Campus Saint-Jean
• Assistant Professor, University of Ottawa, 2000-2008
• Associate Professor, University of Ottawa, 2008-
• Assistant Chair, Department of Mathematics and Statistics, 2009-2011
• I'm married, with two beautiful children.

Fun

• More math music available with video, too.
• They've produced the character table for E₈! Cool news from the Lie world; check out BBC's site. More serious details available from the American Institute of Mathematics site.