- Ph.D. in Applied Mathematics. Cornell University (1998)
- M.Sc. in Mathematics. UPR, Rio Piedras (1988)
- B.Sc. in Mathematics. UPR, Rio Piedras (1984)

## Research Areas

Finite Fields, Error Control Codes, Number Theory.

## Publications

**Books**

- Francis Castro, Ivelisse Rubio Canabal (2013)
*Diagonal Equations (book section in Handbook of Finite Fields)*. CRC Press
- I. Rubio, P. Pennance (1992)
*Laboratorios de Precalculo Utilizando DERIVE*. WCB Publisher International, Inc.

**Articles**

**Published**
- Francis Castro, Carlos J Corrada Bravo, Natalia Pacheco, Ivelisse Rubio Canabal (2017). Explicit formulas for monomial involutions over finite fields. To be published in
* Advances in Mathematics of Communications*

- Rafael A. Arce Nazario, Francis Castro, Oscar González, Luis Medina, Ivelisse Rubio Canabal (2017). New families of balanced symmetric functions and a generalization of Cusick, Li and Stanica's conjecture. To be published in
* Designs, Codes and Cryptography*

- Ivelisse Rubio Canabal, Moss Sweedler, Chris Heegard (2016). Finding a Groebner basis for the ideal of linear recurrence relations on m–dimensional periodic arrays.
*Contemporary developments in finite fields and their applications*

- Jose R Ortiz Ubarri, Rafael A. Arce Nazario, Ivelisse Rubio Canabal, Cynthia Lucena (2016). EIP: Engaging Laboratory Experiences for the Introduction to Programming Course. To be published in
* Envisioning the future of undergraduate STEM education: Research and practice*

- Domingo Gomez, Oscar Moreno, Tom Hoholdt, Ivelisse Rubio Canabal (2015). Linear Complexity for Multidimensional Arrays – a Numerical Invariant.
*Proceedings of the IEEE International Symposium on Information Theory (ISIT 2015)*, 2697-2701

- F. Castro, I. Rubio (2015). Exact p–Divisibility of Exponential Sums via the Covering Method.
*Proceedings of the American Mathematical Society*, 143, 1043-1056

- Francis Castro, Heeralal Janwa, Gary L. Mullen, Ivelisse Rubio Canabal (2015). E–Perfect Codes.
*Bulletin of the Institute of Combinatorial Mathematics and its Applications*, 75, 83-90

- F. Castro, I. Rubio (2014). Construction of systems of polynomial equations with exact p–divisibility via the covering method.
*Journal of Algebra and its Applications*, 13, 6, 1450013-1-15

- R. Arce-Nazario, F. Castro, J. Cordova, K. Hicks, G. Mullen, I. Rubio (2014). Some Computational Results Concerning the Spectrum of Sets of Latin Squares.
*Quasigroups and related systems*, 22, 159-164

- F. Castro, G. Mullen, I. Rubio (2012). Some Enumerational Results Relating the Numbers of Latin and Frequency Squares of order n.
*Quasigroups and Related Systems*, 20, 1

- Francis Castro, Luis Medina, Ivelisse Rubio Canabal (2011). Exact Divisibility of Exponential Sums over the Binary Field via the Covering Method.
*Contemporary Mathematics*, 537, 129-136

- I. Rubio, F. Castro (2010). Solvability of Systems of Polynomial Equations with Some Prescribed Monomials.
*Contemporary Mathematics*, 518, 73-81

- F. Castro, H.F. Mattson, O. Moreno, H. Randriam, I. Rubio (2010). Divisibility of Exponential Sums via Elementary Methods .
*Journal of Number Theory*, 130, 1520-1536

- F. Castro, I. Rubio, P. Guan, R. Figueroa (2008). On systems of linear and diagonal equation of degree pi + 1 over finite fields of characteristic p.
*Finite Fields Appl.*, 14, 648-657

- I. Rubio, G. Mullen, C. Corrada and F. Castro (2008). Dickson permutation polynomials that decompose in cycles of the same length.
*AMS Contemporary Math*, 461, 229-239

- F. Castro, I. Rubio, J. Vega (2007). Divisibility of Exponential Sums and Solvability of Certain Equations Over Finite FIelds.
*Quarterly Journal of Mathematics*, 1-13

- F. Castro, I. Rubio, H. Randriam, O. Moreno, H.F. Mattson, Jr. (2006). An Elementary Approach to Ax-Katz,.
*IEEE, ISIT*

- I. Rubio and C. Corrada Bravo (2004). Cyclic decomposition of permutations of finite fields
obtained using monomials.
*Finite Fields and Applications, Lecture Notes in Computer
Science, 2948*, 254 - 261

- C. Corrada-Bravo and I. Rubio (2004). Algebraic Construction of Interleavers Using Permutation Polynomials.
*Proceedings of the 2004 IEEE International Conference on Communications*, 911-915

- C. J. Corrada Bravo and I. Rubio (2003). Deterministic interleavers for turbo codes with random-like performance and simple implementation.
*3rd International Symposium on TurboCodes*

- H. Medina, I. Rubio (1999). The Summer Institute in Mathematics for Undergraduates (SIMU): Aiming to In–.
*Council of Undergraduate Research Quarterly*

- I. Rubio, M. Sweedler, C. Heegard (1997). Groebner Bases for Linear Recursion Relations on m-D Arrays and Applications to Decoding.
*Proceedings of the IEEE International Symposium on Information Theory*

- K. Saints, I. Rubio, C. Heegard (1994). Decoding Algebraic-Geometric Codes Using Groebner Bases.
*Proceedings of the IEEE International Symposium on Information Theory*

- O. Moreno, I. Rubio (1990). Cyclic Decomposition of Monomial Permutations.
*Congressus Numerantium*, 147-158

- I.J. Dejter, I. Rubio (1989). Monomial Permutations with Uniform Cycle Decomposition.
*Congressus Numerantium *, 245-252

**Submitted**
- Francis Castro, Domingo Gómez, Oscar Moreno, Jose R Ortiz Ubarri, Ivelisse Rubio Canabal, Andrew Tirkel, Rafael A. Arce Nazario. Linear Complexity Analysis of Multidimensional Periodic Arrays
- Luis Medina, Francis Castro, Ivelisse Rubio Canabal. Exact Divisibility of Exponential Sums of Boolean Functions and Applications
- Francis Castro, Oscar Moreno, Ivelisse Rubio Canabal. A refinement of a theorem of Carlitz
- Oscar Moreno de Ayala, Tom Hoholdt, Ivelisse Rubio Canabal. Security of Multi–dimensional Arrays

## Professional Activities

**Awards and Recognitions**

*One of the best papers published in the JAA*, Journal of Algebra and its Applications (2014)
*Member of the Editorial Board of the American Mathematical Monthly*, Mathematical Association of America (2012)
*The Situation of Women and Minorities in Mathematics: A Civil Rights Issue*, Marjorie Lee Browne Colloquium, University of Michigan (2011)
*Gauss Research Foundation Award*, Seminario Interuniversitario de Investigacion Matematica (SIDIM) (2011)
*Dr. Etta Z. Falconer Award for Mentoring and Commitment to Diversity*, Infinite Possibilities Conference (IPC) (2010)
*US National Committe for Mathematics*, US National Academies (2010)
*Mathematics Programs that Make a Difference*, American Mathematical Society (2006)
*SACNAS Presidential Service Award (first time this award was given) for developing & leading the SACNAS Mathematics Program*, SACNAS Conference (2006)

**Talks**

- Finding a Groebner basis for the ideal of recurrence relations on m–dimensional periodic arrays, Fq 12 – International conference on Finite Fields and their applications (2015)
- Applications of the covering method for computing p–divisibility of exponential sums (invited), Mathematics Seminar, UPR–Mayaguez (2015)
- Construction and analysis of multidimensional periodic arrays (invited), Algebraic Number Theory Seminar of Pennsylvania State University (2015)
- An elementary method to compute exact p–divisibility of exponential sums (invited), invited talk at the session “Algebra: Much More Than Arithmetic!”, 2015 SACNAS Conference, Maryland (2015)
- Message without a bottle: coding to send and receive information safely (public lecture), Frontiers in Science Spring 2014 Public Lectures Series, Boca Raton, FL (2014)
- Applications of the covering method for computing p–divisibility of exponential sums (invited), Workshop on Polynomials over Finite Fields: Functional and Algebraic Properties, Centro de Investigación Matemática, Barcelona, España (2014)
- Construction of systems of polynomial equations with exact p–divisibility via the covering method (invited), The Fields Institute Ottawa–Carleton Discrete Mathematics Days, Carleton University, Canada (2014)
- Applications of exponential sums to solvability of equations, cryptography and coding (Plenary talk), Young Mathematicians Conference, The Ohio State University (2014)
- Exact p–Divisibility of Exponential Sums Using the Covering Method (plenary talk), 44th Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL (2013)
- Using the covering method to compute the p–divisibility of exponential sums and applications to coding theory (plenary talk), Combina–Texas, Southwestern University, Texas (2012)
- The Covering Method and the Number of Solutions of Equations over Finite Fields (invited talk), Blackwell–Tapia Conference, ICERM (2012)
- Latin and Frequency Squares, MSRI-UP, Berkeley, CA (2009)
- Solvability of Sysytems of Polynomial Equations with Some Prescribed Monomials, Int. Conf. on Finite Fields and Applications, Dublin, Ireland (2009)
- Solvability of Polynomial Equations Over Finite Fields, SACNAS Conference, Dallas, TX (2009)
- Turbo Encoders with Interleavers Constructed Using Dickson Polynomials, Aerospace Conference, UPR–RP (2009)
- New computational Solutions for Latin Square n=6 Orthogonality, UPR-RP (2009)
- The Mathematical Sciences Research Institute Undergraduate Program, SIDIM (2008)
- Solvability of Systems of Two Diagonal Equations of Finite Fields, SIDIM (2008)
- Dickson permutation polynomials that decompose in cycles of the same length, Finite Fields and Applications (Fq8), Melbourne, Australia (2007)
- An Elementary Approach to Ax–Katz, McEliece's Divisibility and Applications to Quasi–Perfect Binary 2–Error Correcting Codes, IEEE, 2006 ISIT, Seattle, Washington (2006)
- Algebraic Construction of Interleavers Using Permutation Monomials, 2004 IEEE International Conference on Communications, Paris, France (2004)
- Cyclic Decomposition of Permutations of Finite Fields Obtained Using Mono- mials and Applications to Turbo Codes, Finite Fields and Applications (Fq7), Toulouse, France (2003)
- Deterministic Interleavers for Turbo Codes with Random-like Performance and Simple Implementation, 3rd International Symposium on Turbo Codes, Brest, France (2003)

**Workshops Given**

- Everything you wanted to know about undergraduate summer programs in mathematics (but were afraid to ask), Panel at the Latinos in the Mathematical Sciences Conference, UCLA (2015)

**Synergistic Activities**

- Director of the research of over 27 undergraduate mathematics and computer science students over the last 17 years. Many of the results of these students have been presented and reported in undergraduate journals. Some of the students have won awards for their work at the national (USA) level.
- Co–PI and Co–Director, Mathematical Sciences Research Institute Undergraduate Program (MSRI–UP), Berkeley, 2007–2015.
- Member, Mathematical Sciences Research Institute (MSRI) Human Resources Advisory Committee, 2007– 2012.
- Member, Organizing Committee of the workshop Promoting Diversity at the Gradate Level in Math: a National Forum, MSRI, Berkeley, CA, Oct 14–17, 2008.
- Co–Organizer, several of the mathematics activities of the SACNAS Conference. Wrote grants, organized minicourses, plenary talks, mathematics sessions, workshops on career and development opportunities in mathematics. 2003–2013.
- Liason UPR–Río Piedras – PR–LSAMP, 2008–2011.
- Member, Organizing Committee of the Promoting Undergraduate Research in Mathematics Conference,
Chicago, Sept., 2006
- PI and Co–Director, REU–Summer Institute in Mathematics for Undergraduates (SIMU), 1998–2002.
- Referee, Finite Fields and Applications; IEEE Transactions on Information Theory; 2007 IEEE Wireless Communications and Networking Conference.
- Co–Organizer of the MSRI–SACNAS Workshop on Modern Mathematics (2006–present).
- Member of the Program Committee of the 2003–2006 SACNAS Conferences.
- Member of the Advisory Committee of the "Applied Mathematical Sciences Summer Institute (AMSSI)" at Cal Poly Pomona University, 2005–2007.
- Invited Faculty Member, Summer Program for Women in Mathematics at The George Washington University; July 2003 and July 2004.
- Co P.I. and Co–Director of the CSEMS program Humacao Research Scholarships: Increasing Student Achievement in Computational Mathematics (HRS); 2002–2005.
- Panelist, NSF–Course, Curriculum and Laboratory Improvement Program; July 2001;
- Panelist, NSF–Computer Science, Engineering and Mathematics Scholarships Program; April, 2002–2003;
- Panelist, NSF–NATO Postdoctoral Fellowships; February, 2000.
- Panelist of NSF–TUES, July, 2010
- Member, US National Committee for Mathematics, National Research Council, National Academies, 2010–present
- Workshop, Balancing Life and Graduate School, PROMISE Success Institute, University of Maryland Baltimore County (August, 2009)
- Workshop on Careers Using Mathematics, Nebraska Conference for Undergraduate Women in Mathematics (January, 2009)
- Panel, Random Bits of Advice, Nebraska Conference for Undergraduate Women in Mathematics (January, 2009)
- Workshop, Being A Woman Mathematician From An Underrepresented Minority Group, Nebraska Conference for Undergraduate Women in Mathematics (January, 2009)
- Member, Advisory Board for The EDGE Program at Bryn Mawr College and Spelman College, 2008–present
- Co–Organizer, Finite Fields and their Applications, Special Session at the 2013 Mathematical Congress of the Americas, Guanajuato, Mexico.
- Member, SACNAS’ Board Nomination Committee, 2013–2014.
- Member of the Editorial Board of (In)(Genios) an undergraduate research digital journal of the UPR–Río Piedras.
- Member of the Association of Women in Mathematics (AWM)/NSF Travel Grant Selection Committee 2014–15.
- AMS Representative to the AMS–MAA–SIAM Joint Committee on Employment Opportunities, 2012–2015.
- Member of the Editorial Board of the American Mathematical Monthly (2012–2016)
- Member of the Review Panel for the prize for children's books related to mathematics Mathical: Books for Kids from Tots to Teens, organized by the Mathematical Sciences Research Institute and the Children’s Book Council.
- Co–Organizer, Special session on Finite Fields, Forty–Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 7–11, 2015.
- Co–Organizer, Workshop on Mathematics in Communications, Santander, Spain, July 6–8, 2015.

## Grants

**Submitted**

**STEM AWARE at Puerto Rico (AWARE-PR) Alliance, NSF**

Role: *Co-PI (Co-Principal Investigator)*

Funds: $250,000

**Current**

**Scholarship fund for excellence in Computer Science and Mathematics, NSF **

Role: *Co-PI (Co-Principal Investigator)*

Start date: September 1, 2014 | End date: August 1, 2017

Funds: $630,217
**Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP, NSA **

Role: *Co-PI (Co-Principal Investigator)*

Start date: May 1, 2013 | End date: May 1, 2015

Funds: $294,194
**Development of engaging and readily transferable laboratory experiences for the introductory programming course, NSF **

Role: *Co-PI (Co-Principal Investigator)*

Start date: September 15, 2013 | End date: September 14, 2013

Funds: $193,997

**Completed**

**Center for Undergradaute Research in Mathematics, NSF **

Role: *PI (Principal Investigator)*

Start date: June 1, 2013 | End date: December 31, 1969

Funds: $25,800
**Undergraduate Research in Mathematics as a Strategy to Increase Academic Achievement and Promote Students to Higher Education in Mathematics, NSA **

Role: *PI (Principal Investigator)*

Start date: April 1, 2005 | End date: April 1, 2008

Funds: $450,044
**Summer Institute in Mathematics for Undergraduates-1998-2002, UPR **

Role: *PI (Principal Investigator)*

Start date: April 1, 1998 | End date: April 1, 2003

Funds: $160,000
**REU-Summer Institute in Mathematics for Undergraduates-1998-2002, NSF **

Role: *PI (Principal Investigator)*

Start date: April 1, 1999 | End date: April 1, 2003

Funds: $407,000
**Summer Institute in Mathematics for Undergraduates-1998-2002, NSA **

Role: *PI (Principal Investigator)*

Start date: April 1, 1998 | End date: April 1, 2003

Funds: $560,000
**Humacao Research Scholarships: Increasing Student Achievement in Computational Mathemat-, NSF **

Role: *PI (Principal Investigator)*

Start date: April 1, 2002 | End date: April 1, 2005

Funds: $340,277
**Mathematics Mini-courses for Students at the 2003 and 2004 SACNAS Conferences, NSF **

Role: *PI (Principal Investigator)*

Start date: April 1, 2003 | End date: April 1, 2005

Funds: $29,531
**Enhancement of the Mathematics Component of the 2003-2006 SACNAS Conferences, NSA **

Role: *PI (Principal Investigator)*

Start date: April 1, 2003 | End date: April 1, 2006

Funds: $215,000
**MSRI Modern Mathematics Workshop, NSA **

Role: *PI (Principal Investigator)*

Start date: April 1, 2004 | End date: April 1, 2009

Funds: $125,000
**Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP), NSA **

Role: *PI (Principal Investigator)*

Start date: April 1, 2007 | End date: April 1, 2009

Funds: $400,000
**Applications of Permutation Monomials to Turbo Codes., Puerto Rico Space Grant Consortium **

Role: *PI (Principal Investigator)*

Start date: September 1, 2002 | End date: August 31, 2003

Funds: $50,000