Xavier's primary research interests reside in
the areas of
** linear algebra**,

Submitted

- S. M. Fallat,
**X. Martínez-Rivera**,__On the almost-principal minors of a symmetric matrix__,*submitted.*[arXiv:1807.07448].

- A. Abiad, B. Brimkov,
**X. Martínez-Rivera**, S. O, J. Zhang,__Spectral bounds for the connectivity of regular graphs with given order__,*Electronic Journal of Linear Algebra***34**(2018), 428-443. [DOI:10.13001/1081-3810.3675]. - S. M. Fallat,
**X. Martínez-Rivera**,__The quasi principal rank characteristic sequence__,*Linear Algebra and its Applications***548**(2018), 42-56. [arXiv:1711.01003], [DOI:10.1016/j.laa.2018.02.024]. **X. Martínez-Rivera**,__The signed enhanced principal rank characteristic sequence__,*Linear and Multilinear Algebra***66**(7) (2018), 1484-1503. [arXiv:1612.08940], [DOI:10.1080/03081087.2017.1363149].- A. Abiad, B. Brimkov, A. Erey, L. Leshock,
**X. Martínez-Rivera**, S. O, S.-Y. Song, J. Williford,__On the Wiener index, distance cospectrality and transmission regular graphs__,*Discrete Applied Mathematics***230**(2017), 1-10. [arXiv:1609.06911], [DOI:10.1016/j.dam.2017.07.010]. **X. Martínez-Rivera**,__The enhanced principal rank characteristic sequence over a field of characteristic 2__,*Electronic Journal of Linear Algebra***32**(2017), 273-290. [DOI:10.13001/1081-3810.3389].- S. Butler, M. Catral, H. T. Hall, L. Hogben,
**X. Martínez-Rivera**, B. Shader, P. van den Driessche,__The enhanced principal rank characteristic sequence for Hermitian matrices__,*Electronic Journal of Linear Algebra***32**(2017), 58-75. [DOI:10.13001/1081-3810.3249]. **X. Martínez-Rivera**,__Classification of families of pr- and epr-sequences__,

*Linear and Multilinear Algebra***65**(8) (2017), 1581-1599. [arXiv:1606.07495], [DOI:10.1080/03081087.2016.1248345].- M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben,
**X. Martínez-Rivera**, A. Ochoa,__Potentially eventually exponentially positive sign patterns__,

*Involve***6**(3) (2013), 261-271. [DOI:10.2140/involve.2013.6.261]. - M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben,
**X. Martínez-Rivera**, A. Ochoa,__Constructions of potentially eventually positive sign patterns with reducible positive part__,*Involve***4**(4) (2011), 405-410. [DOI:10.2140/involve.2011.4.405].

- M. Muñoz-Figueroa,
**X. Martínez-Rivera**, T. Seaquist, B. Crawford, A. Mubayi, K. Salau, C. Kribs-Zaleta.__Two strain competition: Trypanosoma cruzi__.*Written at the Mathematical and Theoretical Biology Institute (MTBI) REU*(2009). [mtbi.asu.edu/2009-7].

Invited talks

**2019 - March**,__The almost-principal minors and ap-rank of symmetric matrices__,*50*(Special Session on Combinatorial Matrix Theory), Florida Atlantic University, Boca Raton, FL, USA.^{th}Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC)**2019 - Jan.**,__The almost-principal minors and ap-rank of symmetric matrices__,*2019 Joint Mathematics Meetings*(AMS Special Session on If You Build It They Will Come: Presentations by Scholars in the National Alliance for Doctoral Studies in the Mathematical Sciences), Baltimore, MD, USA.**2017 - Dec.**,__The epr-sequence over a field of characteristic 2__,*Matrix Theory Seminar,*Georgia State University, Atlanta, GA, USA.**2017 - July**,__The signed epr-sequence__,*21*(Mini-symposium on Combinatorial Matrix Theory), Iowa State University, Ames, IA, USA.^{st}Conference of the International Linear Algebra Society**2017 - July**,__The sepr-sequence of a Hermitian matrix__,*Special Western Canada Linear Algebra Meeting (WCLAM)*, Banff International Research Station (BIRS), Banff, Alberta, Canada.**2017 - June**,__Principal rank characteristic sequences__,*Linear Algebra Seminar,*Auburn University, Auburn, AL, USA.**2016 - Oct.**,__The epr-sequence over a field of characteristic 2__,*AMS Fall Central Sectional Meeting*(Special Session on Combinatorial Matrix Theory), University of St. Thomas–Minnesota, Minneapolis, MN, USA.**2016 - April**,__Classification of families of pr- and epr-sequences__,*AMS Spring Central Sectional Meeting*(Special Session on Matrix and Operator Theory), North Dakota State University, Fargo, ND, USA.**2016 - March**,__Classification of families of pr- and epr-sequences__,*47*(Special Session on Combinatorial Matrix Theory, in honor of LeRoy Beasley), Florida Atlantic University, Boca Raton, FL, USA.^{th}Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC)

**2018 - May**,__The qpr-sequence__,*Western Canada Linear Algebra Meeting (WCLAM)*, Washington State University, Pullman, WA, USA.**2018 - March**,__The quasi principal rank characteristic sequence__,*XXXIII Seminario Interuniversitario de Investigación en Ciencias Matemáticas (SIDIM)*, University of Puerto Rico–Río Piedras, San Juan, PR, USA.**2017 - March**,__The signed enhanced principal rank characteristic sequence__,*XXXII Seminario Interuniversitario de Investigación en Ciencias Matemáticas (SIDIM)*, University of Puerto Rico–Ponce, Ponce, PR, USA.**2017 - Jan.**,__The epr-sequence over a field of characteristic 2__,*2017 Joint Mathematics Meetings*, Atlanta, GA, USA.**2016 - July**,__Classification of families of pr- and epr-sequences__,*20*, Katholieke Universiteit Leuven, Leuven, Belgium.^{th}Conference of the International Linear Algebra Society**2016 - May**,__Classification of families of pr- and epr-sequences__,*Western Canada Linear Algebra Meeting (WCLAM)*, University of Manitoba, Winnipeg, Manitoba, Canada.**2015 - Oct.**,__The principal rank characteristic sequence and the enhanced principal rank characteristic sequence__,*SIAM Conference on Applied Linear Algebra*, Atlanta, GA, USA.**2012 - July**,__Classification of potentially eventually exponentially positive sign patterns of small order__,*2012 SIAM Annual Meeting*, Minneapolis, MN, USA.

**2019 - Jan.**,__The almost-principal minors and ap-rank of symmetric matrices__,*Linear Algebra/Algebra Seminar*, Auburn University, Auburn, AL, USA.**2018 - Nov.**,__The qpr-sequence__,*Linear Algebra/Algebra Seminar*, Auburn University, Auburn, AL, USA.**2017 - Sept.**,__A new principal rank characteristic sequence__,*Linear Algebra/Algebra Seminar*, Auburn University, Auburn, AL, USA.**2015 - Oct.**,__The principal rank characteristic sequence and the enhanced principal rank characteristic sequence__,*SIAM ISU Student Chapter*, Iowa State University, Ames, IA, USA.

**2010 - Oct.**, (Joint with Rana Haber)__Classification of potentially eventually exponentially positive sign patterns of small order__,*2010 SACNAS National Conference*, Anaheim, CA, USA.**2010 - Feb.**,__Two strain competition: Trypanosoma cruzi__,*NEA Science Day*, University of Puerto Rico–Mayagüez, Mayagüez, PR, USA.**2009 - Oct.**,__Two strain competition: Trypanosoma cruzi__,*2009 SACNAS National Conference*, Dallas, TX, USA.**2009 - Sept.**,__Two strain competition: Trypanosoma cruzi__,*Ana G. Méndez University System (AGMUS) XX Undergraduate Research Symposium*, San Juan, PR, USA.