Curriculum Vitae

Education

  • Ph.D in Mathematics, University of Iowa, 2010. Thesis title: “Universal deformation rings of modules over self-injective algebras”. Thesis supervisor: Professor Frauke M. Bleher.

  • M.Sc. in Mathematics, University of Iowa, 2007.

  • M.Sc. in Mathematics, University of Puerto Rico at Mayagüez, 2005. Thesis title: “Some divisibility properties of polynomials over unique factorization domains”. Thesis supervisor: Professor Luis F. Cáceres.

  • B.Sc. in Mathematics, Universidad Nacional de Colombia, 2002. Thesis title: “Hilbert’s tenth problem” (in Spanish). Thesis supervisor: Professor Rodrigo de Castro Korgüi.

Academic and Professional Appointments 

  • Fall 2020 – Present: Professor (Tenured), Department of Mathematics, Valdosta State University.

  • Fall 2023 – Present: Research Faculty, Mathematics & Engineering, Foundation Universitaria Konrad Lorenz.
  • Fall 2022 : Visiting Scholar, Department of Mathematics, University of Florida, Gainesville, FL.
  • April 2023 : SOA Exam SRM Passed, Society of Actuaries

  • June 2022 : SOA Exam FM Passed, Society of Actuaries

  • November 2021: SOA Exam P Passed, Society of Actuaries.

  • Fall 2020 – Present: Fulbright Specialist , World Learning, U. S. Department of State

  • Fall 2015 – Summer 2020: Associate Professor (Tenured), Department of Mathematics, Valdosta State University.

  • June 2019: Visiting Scholar, Department of Mathematics, Universidad Nacional de Colombia in Bogotá.

  • March 2019: Visiting Scholar, Department of Mathematics, Université de Sherbrooke, Québec, Canada.

  • Summer 2015,2017,2018: Visiting Scholar, Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia

  • Summer 2016: Visiting Associate Professor, Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia.

  • November 2015: Coordinator at the XXXth Iberoamerican Mathematics Olympiad, Mayagüez, PR. 

  • Fall 2010 – Spring 2015: Assistant Professor, Department of Mathematics & Computer Science, Valdosta State University.

  • Fall 2010 – present: Undergraduate Mentor, National Alliance for Doctoral Studies in the Mathematical Sciences.

  • Fall 2008 – Summer 2010: Adjunct Faculty, Kirkwood Community College, Iowa City Campus.

  • Fall 2005 – Summer 2010: Teaching Assistant, Department of Mathematics, University of Iowa.

  • Fall 2007:  Research Assistant, Department of Mathematics, University of Iowa, supervised by Professor Frauke M. Bleher.

  • Fall 2002 – Spring 2005: Instructor/Teaching Assistant, Department of Mathematical Sciences, University of Puerto Rico at Mayagüez.

  • Spring 2003 – Summer 2005: Staff Member, Alliance for the Strengthening of Mathematics and Sciences Teaching (AfaMac) – Institute for the Strengthening of Mathematics Teaching (IFEM), University of Puerto Rico at Mayagüez.

  • Summer 2004: Trainee, Research Experience for Undergraduate Students (REU), University of Puerto Rico at Mayagüez, supervised by Professor Luis F. Cáceres.

M.Sc. Students Co-advised at the Universidad de Antioquia

  • Javier Rivera. Co-advised with Professor Hernán Giraldo. Thesis title: “Calculation of Auslander-Reiten Triangles in the Derived Category of Gentle Algebras” (in Spanish). Graduation date: June 2016.

  • Ricardo Rueda Robayo. Co-advised with Professor Hernán Giraldo. Thesis title: “The Happel’s Functor” (in Spanish).  Graduation date: June 2016.

Ph.D. Students Co-advised at the Universidad de Antioquia

Graduated

  • Yohny Calderón Henao: Ph.D. March 2020 (Supervision June 2016 to December 2020). Co-advised with Professor Hernán Giraldo. Thesis title: “Irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras” (in Spanish) with Magna Cum Laude distinction. 
  • Ricardo Rueda Robayo: Ph.D. July 2020 (Supervision June 2016 to December 2020). Co-advised with Professor Hernán Giraldo. Thesis title: “Auslander-Reiten components containing string and band complexes for a certain class of Brauer graph algebras” (in Spanish).
  • Adriana Fonce Camacho: Ph.D. July 2021 (Supervision July 2018 to July 2021). Co-advised with Professor Hernán Giraldo and Professor Pedro Hernández Rizzo. Thesis title: “Deformations of finite dimensional modules over a repetitive algebra” with Summa Cum Laude distinction.
  • Diego López García: Ph.D. December 2023 (Supervision July 2021 to December 2023). Co-advised with Professor Pedro Hernández Rizzo. Thesis title: “Deformations of finite dimensional modules over a certain class of infinite dimensional algebras”.
  • Jhony F. Caranguay Mainguez Ph.D. June 2024. (Supervision July 2022 to June 2024) Co-advised with Professor Pedro Hernández Rizzo. Thesis title: “Universal deformation rings of modules over generalized Brauer tree algebras”, with Summa Cum Laude distinction.

Work on Progress

  • “Applications of triangulated categories in topological data analysis”, with H. Giraldo & P. Rizzo
  • “A topological data analysis study on the causes of death among the general population and their correlation with the autistic population in the country of Colombia”, with Sebastian Garcia

Selected Accepted and Published Articles

  1. “A short note on deformations of (strongly) Gorenstein-projective modules over the dual numbers”, with Hector Suarez, accepted for publication in Sao Paolo J. Math. Sci.
  2. “A note on finite dimensional modules over k-algebras”, with P. Rizzo, accepted for publication in Commun. Algebra.
  3. “On irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras”, with Yohny Calderón-Henao and Hernán Giraldo, Algebr. Represent. Theory , Vol. 26, (2023), 2039-2055, DOI: 10.1007/s10468-022-10166-x
  4. “Singular equivalences of Morita type with level, Gorenstein algebras, and universal deformations rings”, J. Algebra, Vol. 630, (2023), 225-247, DOI: 10.1016/j.jalgebra.2023.03.041
  5. “On a deformation theory of modules over repetitive algebras”, with Adriana Fonce, Hernán Giraldo, and Pedro Rizzo, Algebr. Represent. Theory, Vol. 26, (2023), 1-22, DOI: 10.1007/s10468-021-10083-5
  6. “On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras”, with Hernán Giraldo and Ricardo Rueda-Robayo, Beitr. Algebra Geom., Vol. 63, (2022), 707-722, DOI: 10.1007/s13366-021-00607-x
  7. “Derived tame Nakayama algebras”,  with Viktor Bekkert and Hernán Giraldo, Proc. Amer. Math. Soc., Vol. 149 No. 11, (2021), 4555-4567, DOI: https://doi.org/10.1090/proc/15612
  8. “Universal deformation rings of modules over self-injective cluster tilted algebras are trivial”, with Isaias David Marin Gaviria, Algebra Colloq.,  Vol. 28 (2021), 269-280, DOI: 10.1142/S1005386721000213
  9. “On deformations of Gorenstein-projective modules over Nakayama and triangular matrix algebras”, J. Pure and Appl. Algebra, Vol. 225, No. 4,(2021), 106562, DOI: 10.1016/j.jpaa.2020.106562
  10. “Universal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional algebras”, with Viktor Bekkert and Hernán Giraldo, J. Pure and Appl. Algebra, Vol. 224, No. 5, (2020), 106223,  DOI: 10.1016/j.jpaa.2019.106223
  11. “A note on deformations of Gorenstein-projective modules over finite dimensional algebras”, Rev. Colombiana Mat., Vol. 53, No. E, (2019), 245-256, DOI: 10.15446/recolma.v53nsupl.84097
  12. “Universal deformation rings of string modules over a class of self-injective special biserial algebras”, with Hernán Giraldo, Yohny Calderón-Henao and Ricardo Rueda-Robayo,  Commun. Algebra, Vol. 47, No. 12, (2019) 4969-4988, DOI:10.1080/00927872.2019.1609010.
  13. “Deformation of complexes for finite dimensional algebras”, with Frauke M. Bleher, J. Algebra, Vol. 491, (2017), 90-140,  DOI:10.1016/j.jalgebra.2017.08.003.
  14. “String and band complexes over certain algebra of dihedral type”, with Hernán Giraldo, Algebr. Represent. Theory, Vol. 19, No. 2, (2016), 419-433, DOI:10.1007/s10468-015-9581-4 .
  15. “Universal deformation rings of modules over a certain symmetric special biserial algebra”, Beitr. Algebra Geom., Vol. 56, No. 1, (2015), 129-146, DOI:10.1007/s13366-014-0201-y
  16. “On the infinitude of prime elements”, with Luis F. Cáceres, Rev. Colombiana Mat., Vol 47, No. 2, (2013), 167-179. Available in http://www.scm.org.co/index.php/publicaciones/revista/contenido
  17. “Universal deformation rings of modules over Frobenius algebras”, with Frauke M. Bleher, J. Algebra, Vol. 367, (2012), 176-202. DOI:10.1016/j.jalgebra.2012.06.008 .

Preprints and Submitted Articles

  1. “Exact weights and path metrics for triangulated categories and the derived category of persistence modules“, with Peter Bubenik, submitted, available in https://arxiv.org/abs/2402.04242
  2. “Quasi-duo and weakly duo skew PBW extensions” with Hector Suarez, submitted.

Honors, Awards and Grants

  • Fall 2023: VSU Presidential Excellence Award for Research, Valdosta State University
  • Fall 2022: Leave with Pay (sabbatical leave for one semester), College of Sciences & Mathematics, Valdosta State University
  • Summer 2021: NSF CBMS Conference Grant, PI, with Dr. Shaun V. Ault (co-PI), National Science Foundation (USD$ 35,000).
  • Fall 2021-Spring 2021: CoSM Faculty Scholarship, College of Sciences & Mathematics, Valdosta State University
  • Spring 2020: Nominated by the College of Sciences and Mathematics  for the VSU Presidential Award in Research, Office of Academic Affairs, Valdosta State University
  • Spring 2019: Reassigned Time for Research, Office of Academic Affairs, Valdosta State University
  • Fall 2018-present: Cluster algebras and theory of geometric invariants: Theoretical frame for the innovation in superconductivity and microbiological analysis, with Carlos Alzate, Germán Benitez, Pedro Hernandez Rizzo, and Hernán Giraldo, Universidad de Antioquia (COP$100,000,000 or about USD$30,000)
  • Summer 2016: VSU Migrant Student Summer Camp Grant, with Dean Connie L. Richards and Dr. Susan R. Wehling.  Georgia Department of Education (USD$25,148).
  • Summer 2012, 2015: Faculty Research Seed Grant, Office of Sponsored Programs & Research Administration, Valdosta State University (USD$5,000 each)
  • Spring 2014: Nomination for the Faculty Excellence Award in Teaching, Office of Vice President of Academic Affairs, Valdosta State University
  • Spring 2011-2016, 2019: Reassigned Time for Research, Office of Academic Affairs, Valdosta State University

Selected List of Invited Talks

  • XXIInd Colombian Congress of Mathematics. Talk: “Singular equivalences of Morita type with level, Gorenstein algebras and universal deformation rings”, June 2023, Universidad Pedagógica y Tecnológica de Colombia, Tunja, Boyacá, Colombia.
  • Maurice Auslander Distinguished Lectures and International Conference. Talk: “Exact weights for triangulated categories”, April 2023, Woods Hole, MA
  • Departmental Colloquium. Talk: “An approach to repetitive algebras and their applications”, December 2022, University of Iowa, Iowa, IA
  • TDA Seminar. Talk: “Persistence theory and derived categories”, November 2022, University of Florida, Gainesville, FL
  • Algebra Seminar. Talk: “Singular equivalences of Morita type with level, Gorenstein algebras, and universal deformations rings”, November 2022, University of Florida, Gainesville, FL
  • Maurice Auslander Distinguished Lectures and International Conference. Talk: “On irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras”, October 2022, Woods Hole, MA
  • 2021 Southern Regional Algebra Conference. Talk: “A deformation theory of finite dimensional modules over repetitive algebras” (Online), March 2021, Georgia College & State University, Milledgeville, GA
  • X Escuela Internacional de Matemáticas del Caribe. Talk: “Applications of topological data analysis and representation theory of quivers” (Online), November 2020, Universidad de Cartagena, Cartagena, Colombia
  • Homological Methods and Tilting Theory for Finite Dimensional Algebras. Talk: “Deformations of modules over finite dimensional Jacobian algebras”, August 2019, University of Iowa, Iowa City, IA
  • XXIIIrd Latino-American Algebra Colloquium. Talk: “Deformations of modules over finite dimensional Jacobian algebras”, July 2019, Colegio Nacional, Mexico City, Mexico
  • May 1st Algebra Workshop. Talk: “String and band complexes over certain Brauer graph algebras”, May 2019, Georgia Southern University, Statesboro, GA
  • Maurice Auslander Distinguished Lectures and International Conference. Talk: “Deformations of Gorenstein-projective Modules over Nakayama and Triangular Matrix Algebras “, April 2019, Woods Hole, MA
  • 2018 Migrant Student Education Day. Talk: “Some guidelines for succeeding in mathematics courses in College “, October 2018, Valdosta State University, Valdosta, GA
  • XXIXth Meeting on Representation Theory of Algebras. Talk: “Derived tame Nakayama algebras”, October 2018, Université de Sherbrooke, Sherbrooke, Québec, Canada
  • Colloquium of the Department of Mathematical Sciences. Talk: “Deformations of Gorenstein-projective Modules over Nakayama Algebras”, September 2018, Georgia Southern University, Statesboro, GA
  • 5th UN Encuentro de Matemáticas. Talk: “Deformations of Gorenstein-projective Modules over Nakayama Algebras”, June 2018, Universidad Nacional de Colombia, Bogotá, Colombia
  • Maurice Auslander Distinguished Lectures and International Conference. Talk: “Derived Tame Nakayama Algebras”, April 2018, Woods Hole, MA
  • 5th Conference on Geometric Methods in Representation Theory. Talk: “Derived Tame Nakayama Algebras”, November 2017, University of Iowa, Iowa City, IA
  • XXIInd Latino-American Algebra Colloquium. Talk: “Universal Deformation of Modules over Monomial Algebras with no Overlaps”, August 2017, Pontificia Universidad Católica de Ecuador, Quito, Ecuador
  • Second Mathematical Congress of the Americas. Talk: “Universal Deformation Rings of Modules over a Class of Self-injective Special Biserial Algebras”. July 2017, McGill Université, Montreal, QC, Canada.
  • XXth Colombian Congress of Mathematics. Talk: “Universal Deformation Ring of Complexes over Finite Dimensional Algebras”, June 2017, Universidad Nacional de Colombia in Bogotá, Bogotá, Colombia.
  • Maurice Auslander Distinguished Lectures and International Conference. Talk: “On Universal Deformation Rings of Gorenstein-projective modules over finite dimensional algebras”, April 2017, Woods Hole, MA
  • 2016 Migrant Student Education Day. Talk: “¡SI SE PUEDE!: Some guidelines for succeeding in mathematics courses in College “, October 2016, Valdosta State University, Valdosta, GA
  • XXVIIIth Meeting on Representation Theory of Algebras. Talk: “On Universal Deformation Rings for Gorenstein Algebras”, October 2016, Université Bishop’s, Sherbrooke, Québec, Canada
  • XVII International Conference on Representation of Algebras ICRA 2016. Talk: “Singular Equivalence of Morita Type and Universal Deformation Rings for Gorenstein Algebras”, August 2016, Syracuse, NY.
  • ALTENCOA7-2016. Talk: “On Universal Deformation Rings for Gorenstein Algebras”, July 2016, Bucaramanga, Santander, Colombia
  • 2015 Migrant Student Education Day. Talk: “¡SI SE PUEDE!: Some guidelines for succeeding in mathematics courses in College “, October 2015, Valdosta State University, Valdosta, GA
  • XXVIIth Meeting on Representation Theory of Algebras. Talk: “String and Band Complexes over Certain Algebra of Dihedral Type”, September 2015, Université Bishop’s, Sherbrooke, Québec, Canada
  • XX Colombian Congress of Mathematics. Talk: “String and Band Complexes over Certain Algebra of Dihedral Type”, July 2015, Universidad Nacional de Colombia, Manizales, Colombia
  • XX Colombian Congress of Mathematics. Short course: “An Introduction the the Representation Theory of Finite Dimensional Algebras”, July 2015, Universidad Nacional de Colombia, Manizales, Colombia
  • 2015 VSU Migrant Leadership Academy. Talk: “Mathematical Demonstrations”, June 2015, Valdosta State University, Valdosta, GA
  • 3rd Conference on Geometric Methods in Representation Theory. Talk: “Deformations and Derived Equivalence over Symmetric Algebras”, November 2014, University of Iowa, Iowa City, IA
  • 2014 Migrant Student Education Day. Talk: “¡SI SE PUEDE!: Some guidelines for succeeding in mathematics courses in College “, October 2014, Valdosta State University, Valdosta, GA
  • ALTENCOA6-2014. Talk: “Deformations and Derived Equivalence over Symmetric Algebras”, August 2014, Pasto, Nariño, Colombia
  • Joint Mathematics Meetings. Talk: “On the Infinitude of Prime Elements”, January 2014, Baltimore, MD
  • 2nd Conference on Geometric Methods in Representation Theory. Talk: “Deformations and Derived Equivalence over Frobenius Algebras”, November 2013, University of Missouri, Columbia, MO
  • 2013 Migrant Student Education Day. Talk: “¡SI SE PUEDE!: Some guidelines for succeeding in mathematics courses in College “, October 2013, Valdosta State University, Valdosta, GA
  • Conference on Geometric Methods in Representation Theory. Talk: “Universal Deformation Rings of Modules over a Certain Symmetric Tame Algebra”, November 2012, University of Missouri, Columbia, MO
  • Institutional Seminar on Algebra. Talk: “Universal Deformation Rings of Modules over a Frobenius Algebra”, August 2012, Universidad de Antioquia, Medellín, Colombia
  • Maurice Auslander Distinguished Lectures and International Conference. Talk: “Universal Deformation Rings of Modules over a Certain Symmetric Special Biserial Algebra”, April 2012, Woods Hole, MA
  • Science Seminar. Talk: “On Prime Numbers and the Goldbach Conjecture”, February 2012, Valdosta State University
  • 1069th American Mathematical Society Meeting, Central Section. Talk: “Universal Deformation Rings of Modules over Frobenius Algebras”, March 2011, University of Iowa
  • Science Seminar. Talk: “On Certain Divisibility Property of Polynomials”, October 2010, Valdosta State University