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, Konrad Lorenz University.
  • 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”.

Current

  • Jhony F. Caranguay Mainguez (Since June 2022). Co-advised with Professor Pedro Hernández Rizzo. Expected graduation date: July 2024.

Work on Progress

  • “Exact weights for triangulated categories”, with P. Bubenik.
  • “Applications of triangulated categories in topological data analysis”, with H. Giraldo & P. Rizzo

Selected Accepted and Published Articles

  1. “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
  2. “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
  3. “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
  4. “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
  5. “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
  6. “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
  7. “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
  8. “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
  9. “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
  10. “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.
  11. “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.
  12. “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 .
  13. “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
  14. “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
  15. “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

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