__Research__

Research
Interests Publications Presentations
Other Activities CV

*Universal Algebra, Ordered Algebraic
Structres and Algebraic Logic.*

Book.

* *

1.
*Residuated Lattices: an algebraic glimpse at
substructural logics,* with P. Jipsen, T. Kowalski and H. Ono, Studies in
Logics and the Foundations of Mathematics, Elsevier, pp. 509+ (2007). (web
site)

** **

Refereed papers.

*The undecidability of the word problem for distributive residuated lattices*,*Ordered Algebraic Structures (J. Martinez, ed.), Kluwer Academic Publishers, Dordrecht, 2002, 231-243*. (pdf)

*Cancellative residuated lattices*, with P. Bahls, J. Cole, P. Jipsen and C. Tsinakis, Algebra Universalis**50**(2003), no. 1, 83-106.*(pdf)*

*Equational bases for joins of residuated-lattice varieties*, Studia Logica**76**(2) (2004), 227-240. (pdf)

* *

*Adding involution to residuated structures*, with J. Raftery, Studia Logica**77**(2) (2004), 181-207.

*Generalized MV-algebras*, with C. Tsinakis, Journal of Algebra**283**(1) (2005), 254-291. (pdf)

*Minimal varieties of residuated lattices*, Algebra Universalis**52**(2) (2005), 215-239.

*Algebraization, paremetrized local deduction theorem and interpolation for substructural logics over FL*, with H. Ono, Studia Logica**83**(2006), 279-308. (pdf)

*Glivenko theorems for substructural logics over FL*, with H. Ono, Journal of Symbolic Logic**71**(4) (2006), 1353-1384. (pdf)

*Irreducible residuated semilattices and finitely based varieties*, with J. Olson and J. Raftery, Reports on Mathematical Logic**43**(2008), 85-108. (pdf)

* *

*From axioms to analytic rules in nonclassical logics*, with A. Ciabattoni and K. Terui,*Proceedings of LICS'08*, 229-240, 2008. (pdf)

* *

*Equivalence of closure operators: an order-theoretic and categorical perspective,*with C. Tsinakis, Journal of Symbolic Logic**74**(3) (2009), 780-810. (pdf)

*A survey of GBL-algebras (invited book chapter),*with P. Jipsen, Tributes vol.10 College Publications (2009), 303-328. (pdf)

*Cut elimination and strong separation for substructural logics: an algebraic approach*, with H. Ono, Annals of Pure and Applied Logic 161 (2010), no. 9, 1097--1133. (pdf)

*Generalized ordinal sums and translations,*Logic Journal of the IGPL (2011) 19 (3), 455-466. (pdf)

*MacNeille**completions of FL-algebras,*with A. Ciabattoni and K. Terui, Algebra Universalis**66**(4) (2011), 405-420. (pdf)

*Algebraic proof theory for substructural logics: cut-elimination and completions*, with A. Ciabattoni and K. Terui, Annals of Pure and Applied Logic**163**(3) (2012), 266-290. (pdf)

*A category equivalence for odd Sugihara monoids and its applications,*with J. Raftery, Journal of Pure and Applied Algebra**216**(2012), 2177-2192. (pdf)

*Periodic lattice-ordered pregroups are distributive,*with P. Jipsen, Algebra Universalis**68**(1-2) (2012), 145-150. (pdf)

*Residuated frames with applications to decidability,*with P. Jipsen, Transactions of the AMS**365**(3) (2013), 1219-1249. (pdf)

*Relation algebras as expanded FL-algebras,*with P. Jipsen, Algebra Universalis**69**(1) (2013), 1-12. (pdf)

*Cayley’s and Holland’s theorems for idempotent semirings and their applications to residuated lattices,*with R. Horcik,Semigroup Forum**87**(3) (2013), 569-589. (pdf)

*Idempotent residuated structures: some category equivalences and their applications,*with J. Raftery, Transactions of the AMS**367**(5) (2015), 3189-3223.

*The finite embeddability property for non-commutative knotted extensions of RL*, with Riquelmi Cardona, Internat. J. of Algebra and Computation 25(3) (2015), 349–379.

*Modules over Quantaloids: Applications to the Isomorphism Problem in Algebraic Logic and $\pi$-institutions,*with Jose Gil-Ferez, Journal of Pure and Applied Algebra 221(1) (2016), 1-24. (pdf)

*Proof Theory for lattice-ordered groups*, with G. Metcalfe, Annals of Pure and Applied Logic, 167(8) (2016), 707-724.

*Algebraic proof theory for substructural logics: hypersequents,*with A. Ciabattoni and K. Terui, Annals of Pure and Applied Logic 168(3) (2017), 693-737. (pdf)

*Canonical formulas for k-potent commutative intergral residuated lattices,*with N. Bezhanishvili and L. Spada, Algebra Universalis 77(3) (2017), 321-343. (pdf)

*Distributive residuated frames and generalized bunched implication algebras,*with P. Jipsen, Algebra Universalis 78(3) (2017), 303-336. (pdf)

*The FEP for some varieties of fully-distributive knotted residuated lattices,*with R. Cardona, Algebra Universalis 78(3) (2017), 363-376. (pdf)

*Categories of models of R-mingle,*with W. Fussner, Annals of Pure and Applied Logic 170(10) (2019), 1188-1242. (pdf)

*The structure of generalized BI-algebras and weakening relation algebras*, with P. Jipsen, Algebra Universalis 81(3) (2020) paper #35, 35pp. (pdf)

*Weakening relation algebras and FL2 algebras*, with P. Jipsen, Lecture Notes in Computer Science 12062 (2020), 117-133. (pdf)

*Lattice-ordered pregroups are semi-distributive,*with P. Jipsen, M. Kinyon, and A. Prenosil, Algebra Universalis 82(1) (2021), paper #16, 6pp. (pdf)

*Theorems of alternatives for substructural logics*, with A. Colacito and G. Metcalfe, Outstanding Contributions to Logic, 21: Arnon Avron on semantics and Proof theory of nonclassical logics (2021), 91-105. (pdf)

*Densification via polynomial extensions*, with R. Horcik, Journal of Pure and Applied Algebra 222(3) (2022), paper #106852, 26pp.

*From distributive l-monoids to l-groups, and back again,*with A. Colacito, G. Metcalfe, S. Santchi, Journal of Algebra 601 (2022), 129–148. (pdf)

*Twist structures and Nelson conuclei,*with M. Busaniche and M. Marcos, Studia Logica 110(4) (2022), 949-987. (pdf)

*Most simple extensions of FLe are undecidabe,*with G. St. John, Journal of Symbolic Logic 87(3) (2022), 1156-1200. (pdf)

*Complemented MacNeille completions and algebras of fractions*, with A. Prenosil, Journal of Algebra 623 (2023), 288-357. (pdf)

*Gluings**in residuated lattices,*with S. Ugolini, Order 40 (2023), 623–664. (pdf)

*Distributive ℓ-pregroups: generation and decidability,*with Isis Gallardo, Journal of Algebra 648 (2024), 9-35.

*Semiconic**Idempotent Logic I: Structure and Local Deduction Theorems*, with W. Fussner, Annals of Pure and Applied Logic 175(7) (2024), paper no.103443, 30 pp.

*Decidability of lattice equations*, Studia Logica 112(3) (2024), 607-610.

*Unilinear**residuated lattices: axiomatization, varieties and FEP*, with Xiao Zhuang, Algebra Univeralis 85(3) (2024), paper no. 30, 33 pp.

*Almost minimal varieties of commutative integral residuated lattices,*with P. Agliano and M. Marcos, Int. J. Alg. Comput. 34(5) (2024), 807-836.

Submitted papers.

*Semiconic**Idempotent Logic II: Beth Definability and Deductive Interpolation*, with W. Fussner, submitted.*Generation and decidability for periodic ℓ-pregroups,*with Isis Gallardo, submitted.*Classification for unilinear residuated lattices*, with Xiao Zhuang, submitted.

**Non-refereed conference
proceedings.**

·
*Involutive commutative distributive
residuated lattices*, proceedings of the 37^{th} Mathematical Logic
Group Meeting, Shizuoka, 2003.

·
*Extensions of Glivenko's theorem to
non-commutative substructural logics*, proceedings of the 39^{th}
Mathematical Logic Group Meeting, Gamagori, 2005.

**Theses.**

·
*Varieties of residuated lattices*, Ph.D.
thesis, Department of Mathematics, Vanderbilt Universisty, 2003. (pdf)

·
*Selected topics on residuated lattices*,
Qualifying paper, Department of Mathematics, Vanderbilt University, 2000. (pdf)

Edited volumes

- Special issue: Recent developments
related to residuated lattices and substructural logics
*,*with P. Jipsen and H. Ono, Studia Logica 100(6) (2012). - Outstanding contributions: Hiroakira Ono on Substructural
Logics, volume 23, with K. Terui, Trends in Logic, Springer, 2022.

Educational publication.

*From here to infinity: a
foundation for Calculus*, with J. Staples et al., Tomson Learning Custom
Publishing, 2001.

**Conference
Presentations and Seminar Talks**

* *

*Lattice-ordered groups
and pregroups,
Chapman, December 2023.*

*Lattice-ordered pregroups: generation and decidability, Siena Algebra Week, July, 2023.*

*Heyting** residuated
lattices and weakening relations (invited talk), *AMS sectional meeting, El
Paso, Texas, September 2022.

*Idempotent residuated
chains, *BLAST, Chapman, August 2022.

*Generalized bunched
implication logic, *PLS, Volos, July 2022.

*Lattice-ordered groups
and monoids, *TACL, Coimbra, June 2022.

*Theorems of the
alternatives (invited talk),* Seminario de Logica algebraica, Argentina,
online, April 2022.

*The structure of
idempotent residuated chains (invited talk),* Ordered Algebras and Logic,
Les Diablerets, Switzerland. March 2022.

*Interpolation and Beth
definability for conic idempotent Full Lambek calculus
(invited talk), *CLAM Latin American Congress of Mathematicians, Special
Session on Logic, Montevideo, Uruguay, September 2021.

*Lattice-ordered groups
and monoids (invited talk), *ACaCS conference on
semigroups Nis, Serbia, September 2021.

*Twist structures and
Nelson conuclei, *BLAST online at NMSU, Las Cruces
NM, June 2021.

*Almost minimal
varieties of commutative integral residuated lattices*, NMSU Algebra and
Logic seminar, May 2021.

*Nelson conucleus
algebras as semantics for paraconsistent logics and their twist-product
representation*, Alophis online seminar, Cagliari, Italy, May 2021.

*Distributive
lattice-ordered monoids*, Algebra and Coalgebra
online seminar, Amsterdam, May 2021.

*Amalgamation for conic idempotent residuated lattices, *Algebra and Logic online seminar, Boulder,
CO, April 2021.

*Strong amalgamation for a variety of idempotent semiconic residuated lattices, *Nonclassical Logic Webinar, Zoom, July
2020.

*Lattice-ordered groups and their subreducts,
Shanks Workshop on Ordered Algebras and Logic, Vanderbilt University,
Nashville, March 2020.*

*Inverse-free subreducts of
lattice-ordered groups, Special AMS session on Algebras and Algorithms, Joint
Mathematical Meetings, Denver, January 2020.*

*Heyting** residuated lattices, Algebra and Logic seminar, Vanderbilt
University, Nashville, November 2019.*

*GBI-algebras and weakening relations (invited talk),
Logic Workshop, Amsterdam, Holland, October 2019.*

*Undecidability** for some
varieties of commutative residuated lattices, TACL, Nice, France, June 2019.*

*Generalized bunch implication algebras, BLAST, UC
Boulder, May 2019.*

*Decidability an undecidability
for residuated lattices, Algebra and Logic Seminar,
Vanderbilt University, April 2019.*

*Skew reflections, ASL winter meeting, Denver, February, 2019.*

*Is there a useful duality for residuate
lattices?(invited workshop talk), SYSMICS, Chapman
University, Orange, September 2018.*

*Embedding lattice-ordered bi-monoids in involutive commutative residuated
lattices (invited talk), LATD, Bern, Switzerland, August 2018.*

*Skew rotations, AbubL,
Cagliari, Italy, June 2018.*

*Undecidability** for some
varieties of commutative residuated lattices (invited talk), BLAST, Vanderbilt
University, Nashville, August 2017.*

*Generalized bunched implication algebras, TACL, Prague,
June 2017.*

*Residuated frames and applications (invited talk),
WoLC’16, Guanzhou, China, December 2016.*

*The FEP for residuated lattices via local finiteness of
the monoid reducts, Lattices Algebras and Truth
Degrees, Wits University, South Africa, June 2016.*

*Canonical formulas for k-potent commutative residuated lattces, Order
Algebras and Logic, Vanderbilt Univesity, Nashville,
February 2016.*

*The FEP for some noncommutative varieties of fully
distributive residuated lattices, *TACL 2015, Ischia, Italy, June 2015.

*Densification via polynomials (invited talk), *Shanks
workshop in ordered algebras and logic, March 2015.

*From display logic to nested sequents
via residuated frames (invited talk)*, Vienna
Summer of Logic, GetFun, July 2014.

*Embeddings** into BiFL-algebras and conservativity,
*Vienna Summer of Logic, LATD, July 2014.

*Proof theory for lattice-ordered groups (invited talk), *Brazilian
Logic Conference, Petropolis, Brazi, April 2014.

*A survey of residuated frames with connections to semirings and to display logic*, Prague seminar of substructural logics, March 2014.

*The finite embeddability
property for non-commutative knotted extension of RL*, Colloquium talk at
the Institute of CS, Czech Academy of Sciences, March 2014.

*Developments on higher levels of the substructural
hierarchy, *BLAST, Chapman University, Orange, August 2013.

*Cayley and Holland Theorems for Residuated Lattices, *TACL,
Nashville, July 2013.

*Hyper-residuated frames (invited talk), *ALCOP,
Utrecht, Holland. April, 2013.

*Distributive integral residuated lattices have the FEP
(invited talk)*, Special Session on Algebras, Lattice and Varieties, AMS
Sectional meeting, Boulder, April 2013.

*The finite embeddability
property for varieties of distributive, integral residuated lattices*,
Logic, Algebra and Truth Degrees, Kanazawa, Japan, September 2012.

*Rediscovering Structural Proof Theory: an algebraic
account *(invited seminar talk), Multi-dimension seminar, Japan Advanced
Institute of Science and Technology, September 2012.

*A categorical
equivalence of varieties and the Beth definability property, (invited talk), *15^{th}
Latin American Symposium on Mathematical Logic, Colombia, scheduled for June
2012.

*Algebraic Logic:
Algebraic Proof Theory, (invited tutorial),15 ^{th}* Latin American Symposium
on Mathematical Logic, Colombia, scheduled for June 2012.

*Modules over quantaloids and the isomorphism problem in abstract
algebraic logic (invited talk), Symposium on Fuzzy Mathematics, Kent State University and Youngstown State University, Ohio,
October 2011.*

*Residuated lattices in
algebra and logic (invited colloquium talk), Colloquium, Department of Mathematical Sciences,
Kent State University, Ohio, October 2011.*

*Relativizing the substructural hierarchy (invited plenary talk), Topology, Algebra and
Categories in Logic, Marseilles, France, July 2011.*

*Interpolation and Amalgamation for Substructural
Logics and Residuated Lattices, 8 ^{th} Panhellenic Logic Symposium,
Ioannina, Greece, July 2011. *

*Beth definability for relevance logic with mingle **(invited plenary talk), Second
International Conference on Order, Algebra, and Logics: honoring R.
McKenzie, H. Ono, and A. Wroński, Krakow,
Poland, June 2011.*

*Holland-Type Embeddings for Residuated Lattices **(invited
talk), Algebra
and Proof Theory amplified by Frames and Category Theory, Vanderbilt
University, Nashville, March 2011.*

*Remarks on l-groups
and abelian l-groups: preliminary report (invited talk),* l-Groups and
MV-Algebras: Interaction and Impact on Algebras of Logic, Buenos Aires,
Argentina, October 2010.

*Tutorial on Algebraic
Proof Theory* (week-long invited tutorial), University of Milan, Italy, July 2010.

*Dedekind-MacNeille completions of residuated
lattices**, *BLAST 2010 conference on
Algebraic Logic, Set Theory and Universal Algebra, University of Colorado,
Boulder, June 2010.

*The Isomorphism
Problem for modules over quantaloids,*** **World
Congress and School on Universal Logic III, Lisbon, Portugal, April 2010.

*Residuated lattices with applications to logic,* 31st Linz Seminar
on Fuzzy Set Theory. (Topic: Lattice-Based Logic and its Applications.)
Linz, Austria, February 2010.

*Applications of
residuated frames to algebra and logic, *BLAST 2009 conference
on Algebraic Logic, Set Theory and Universal Algebra, New Mexico State
University, Las CrucesAugust 2009.

*Algebraic Proof Theory
*(invited plenary talk),* *7^{th} Panhellenic Logic
Symposium, Patras, Greece, July 2009.

*Cut elimination for distributive substructural logics*, Topology,
Algebra and Categories in Logic, Amsterdam, July 2009.

*Sequents, Hypersequents and beyond (invited talk), *Gentzen systems and Beyond
workshop associated with the TABLEAUX 2009
conference, Oslo, July 2009.* *

*Non-associative residuated lattices,* 2^{nd}
Mile Hight Conference on Nonassociative Mathematics, University of Denver,
June 2009.

*An N2-variety of
residuated lattices that is not closed under completions* (invited talk),
and 12th Annual ORD/OAL, Bowling
Green State University, June 2009.

*MV-algebras and l-groups
as residuated lattices *(invited
week-long series of lectures)*, Workshop on
lattice-ordered groups and MV-algebras*, Bowling Green State University, June 2009.

*Skew Relation Algebras*
(invited talk), Ordered
Groups in Logic, Vanderbilt University, March 2009.

*Generalized ordinal
sums and translations* (selected
40-min talk), Logic, Algebra and
Truth Degrees, Siena, Italy, September 2008.

*Residuated Lattices – a tutorial* (invited 3-hour tutorial), Summer school on General Algebra and
Ordered Sets, Trest, Czech Republic, September 2008.

*The finite
embeddability property for subvarieties of integral residuated lattices,* BLAST
2008 conference on Algebraic Logic, Set Theory and Universal Algebra,
University of Denver, August 2008.

*On the substructural hierarchy *(invited plenary
talk), International Conference on
Residuated Structures: Algebra and Logic, Buenos Aires, Argentina, April
2008.

*Axiomatizations for intersections of substructural logics*
(invited 50-min talk), Shanks
workshop on Proof Theory and Algebra, Vanderbilt University, March 2008.

*Structural rules in FL: expressive power and cut
elimination,* Algebraic and
Topological Methods in Non-classical Logics III, University of Oxford, UK,
August 2007.

*The variety of involutive residuated lattices is generated
by its finite members* (invited plenary talk), International conference on
Order, Algebra and Logics, Vanderbilt University, USA, June 2007.

*Algebraic cut elimination *(invited seminar talk), Logic Summer School, Australian
National University, Canberra, Australia, December 2006.

*Residuated frames *(invited talk), Workshop on Algebra and
Substructural Logics III, Krakow, Poland, November 2006.

*Cut elimination for substructural logics from a
semantical perspective,* Colloquium talk, Vienna University of Technology,
November 2006.

*Semantics for substructural logics,* Colloquium talk, University of Milan, Italy, October 2006.

*Decidability for involutive residuated lattices,*
Colloquium talk, Univesity of Szeged,
Hungary, October 2006.

*Glivenko theorems for substructural logics,* Logic Colloquium 2006, Association for
Symbolic Logic European Summer Meeting, Nijmegen, Netherlands, scheduled for
July 2006.

*Lack of structural rules and algebraic semantics, *Ordered
structures in many-valued logics, Massa Lubrense, Sorrento, Italy, May
2006.

*Algebraic methods in substructural logics, *Logic Colloquium 2005, Association
for Symbolic Logic European Summer Meeting, Athens, Greece, July 2005.

*Equivalence of consequence relations: an order-theoretic
and categorical perspective,* Algebraic and topological
methods in non-classical logics II, Barcelona, Spain, June 2005.

*Non-associative residuated lattices,* AMS sectional
meeting, special session on Universal Algebra and Lattice Theory,
Vanderbilt University, October 2004.

*Translations in substructural logics, *Logic Colloquium 2004, ASL European Summer
Meeting, Torino, Italy, July 2004.

*Non-associative substructural logics: algebraization, cut
elimination and separation*, Conference on
Residuated Structures and Many-Valued Logics, Patras University, Greece, June 2004.

*Residuated lattices – an introduction*, Department of Mathematics, Aristotle
University of Thessaloniki, Greece, May 2004.

*Involutive commutative distributive residuated lattices*,
37th
Mathematical Logic Group Meeting, Shizuoka, Japan, December 2003.

*The join of finitely many varieties of residuated
lattices* (invited talk), Annual
Meeting of the Association for Symbolic Logic, special session on Algebraic
Logic and Universal Algebra, University of Illinois at Chicago, June 2003.

*Decision problems for commutative distributive residuated
lattices*, Colloquium talk, University
of Saskatoon, Canada, May 2003.

*Generalized MV-algebras*, Conference on Ordered
Algebraic Structures, Vanderbilt University, March
2003.

*A Priestley duality for bounded distributive residuated
lattices*, Annual
meeting of the American Mathematical Society, special session on The Many
Lives of Lattice Theory and the Theory of Ordered Sets, with Connections to
Combinatorics, Baltimore, January 2003.

*A categorical equivalence for integral GMV-algebras*, Workshop on Algebra and
Substructural Logics, Japan Advanced
Institute of Science and Technology, November 2002.

*Integral generalized MV-algebras*, Algebra Seminar, Vanderbilt University, October 2002.

*Some atomic varieties of residuated lattices*, Algebra
Seminar, Vanderbilt University,
September 2002.

*Continuum many idempotent minimal residuated-lattice
varieties*, International
Conference on Modern Algebra in conjunction with the 17th annual Shanks
Lectures, Vanderbilt University,
May 2002.

*Varieties of residuated lattices generated by positive
universal classes*, Conference
on Ordered Algebraic Structures, Vanderbilt
University, March 2002.

*The undecidability of the word problem for the variety of
distributive residuated lattices*, Conference on
Lattice-Ordered Groups and f-Rings, University
of Florida, March 2001.

*The subvariety lattice of residuated lattices*, Workshop on Ordered
Algebraic Structures, Vanderbilt
University, March 2000.

**Member of
the Editorial Board** for the
journal *Algebra Universalis*
and the journal *Mathematical Logic
Quarterly*.

** Referee **for the journals

· Journal of Pure and Applied Algebra

· Order

· Discussiones Mathematicae: General Algebra and Applications

· Annals of Pure and Applied Logic

· Archive for Mathematical Logic

· Reports on Mathematical Logic

· Mathematical Logic Quarterly

· Logic Journal of the Interest Group in Pure and Applied Logics

· Journal of Logic and Computation

· Lecture Notes in Computer Science

· Czechoslovak Mathematical Journal

**Conference Organization:**

- Program committee member for TACL, Barcelona, 2024
- Program committee member for ASL Annual Meeting, Iowa, 2024
- Program committee member for LATD, Tbilisi, 2023.
- Program committee member for AiML, Rennes, 2022.
- Co-organizer Spring Western Sectional AMS meeting, special session on Algebraic Logic, 2022.
- Program committee member for LATD, Tbilisi, 2020.
- Co-Chair of BLAST, Denver, August 2018.
- Program committee member for TACL, Prague, 2017.
- Co-organizer of special session of AMS Sectional meeting, University of Denver, October, 2016.
- Program committee member for LATD, 2016.
- Program committee member for WOLLIC, 2015.
- Program committee member for LATD, 2014.
- Co-chair of TACL, 2013.
- Program committee member for ALCOP (Algebra and Coalgebra Meet Proof Theory), April 2012.
- Program committee member for TACL, 2009.
- Co-chair of BLAST 2008 conference in Algebraic
Logic, Set Theory and Universal Algebra, University of Denver, August
2008.
- Co-organizer of the Workshop
in Algebra and Logic, JAIST, March 2007.

**Master’s and Ph.D. committees **

· Ph.D. supervisor for Xiao Zhang and Isis Gallardo, current.

· Ph.D. thesis examiner for Frederik Lauridsen, Amsterdam, Holland, October 2019.

· Postoctoral mentor for Sara Ugolini, September 2018-present.

·
Ph.D. supervisor for Gavin St John. *Decidability and Undecidability
in substructural logics*. Graduated (PhD), May 2019.

·
Ph.D. supervisor for Wesley D. Fussner. *Duality
theory for Sugihara monoids Graduated* (PhD), December
2018.

· Ph.D. thesis examiner of Karel Chvalovsky, Charles University, Czech Republic, May 2015.

·
Ph.D. supervisor for Riquelmi
Cardona. *The Finite Model Property for Substructural Logics with Exchange*. Graduated (PhD) in
2015.

·
Ph.D. committee member for Wilmari
Morton, University of Johannesburg, 2012.

·
Ph.D. committee member for Jenya
Kirstein, University of Denver, 2012.

· Ph.D. committee member for Topaz Dent, UC Boulder, 2011.

·
Ph.D. committee member for Jose Jil-Ferez, University of Barcelona, 2009.

·
Examiner of the Ph.D. thesis of Ai-ni Hsieh,
University of Natal, South Africa, 2009.

·
Ph.D. committee member for Dan Daly, University
of Denver, 2009.

·
Ph.D. committee member for Aditya Nagrath,
University of Denver, 2008.

·
Examiner of the Master’s thesis of Ai-ni Hsieh,
University of Natal, South Africa, 2005.

· Riquelmi Cardona (PhD 2015), Professor of Mathematics, University of El Salvador.

· Wesley Fussner (PhD 2018), Postoctoral Fellow, University of Bern.

· Gavin St. John (PhD 2019), Postdoctoral Fellow, University of Salerno.

· Xiao Zhuang (PhD 2023), Remotasks.

· Isis Gallardo (PhD exp. 2024).

· Kempton Albee (PhD exp. 2026)

· Sara Ugolini (Postdoc 2018-2020), AI Research Institute, Barcelona.