# Nick Galatos

## Professor

303-871-3581 (Office)

Clarence M. Knudson Hall, 2390 S. York St. Denver, CO 80210

### What I do

I am happy to be teaching mathematics at all levels, from freshman Calculus to graduate courses and supervise PhD students. At the same time I enjoy doing research in Algebraic Logic.### Specialization(s)

mathematics, logic

### Professional Biography

BS from Aristotle University, Greece. MS and PhD from Vanderbilt University, TN. Postdocs and Visiting Asistant Professorships at Japan Advanced Institute of Science and Technology and at Vanderbilt University. Assistant Professor at DU during 2007-2010. Associate Professor at DU during 2010-2015. Professor at DU since 2015.

### Degree(s)

- Ph.D., Mathematics, Vanderbilt University, 2003
- MS, Mathematics, Vanderbilt University, 2000
- BS, Mathematics, Aristotle University, 1998

### Research

My area of research is Algebraic Logic. Mathematical logic is an important area in mathematics primarily because it provides the foundations for all of mathematics, a framework and the rules of inference that are used universally in all areas of Mathematics. Logic is applicable, however, to a wide range of disciplines extending past the natural sciences and spanning all the way to philosophy, law and psychology. Logical inferences in different disciplines naturally abide different laws, thus giving rise to different (but similar) logical systems. These logical systems can in turn be studied and compared using precise language and analysis, something that the discipline of mathematics naturally possesses. In my research I use tools from Abstract Algebra to study and compare different logical formalisms, establish general facts about them and bring to the surface differentiating features.

#### Areas of Research

Mathematics

Universal Algebra

Logic

Residuated lattices

Proof theory

#### Key Projects

- Algebra and Proof Theory
- BLAST 08 Conference

### Featured Publications

(2012). A category equivalence for odd Sugihara monoids and its applications. Journal of Pure and Applied Algebra, 216(10), 2177-2192.

. (2017). Algebraic proof theory for substructural logics: hypersequents. Annals of Pure and Applied Logic, 168(3), 639-737.

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

. (2015). Idempotent residuated structures: some category equivalences and their applications. Transactions of the AMS, 367(5), 3189–3223.

. (2008). From axioms to analytic rules in nonclassical logics. Proceedings of LICS'08, 229-240.

. ### Presentations

(2006). Algebraic cut elimination. Logic Summer School. Canberra, Australia: Australian National University.

. (2012). Algebraic Proof Theory (invited). 15th Latin Americal Symposium on Mathematical Logic Summer School. Bogota, Colombia: Association of Symbolic Logic, NSF.

. (2008). Axiomatizations for intersections of substructural logics. Shanks workshop on Proof Theory and Algebra. Vanderbilt University.

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

. (2013). Hyper-residuated frames (invited talk). Algebra and Coalgebra in Proof Theory. Utrecht, Holland.

. ### Awards

- The Bjarni Jónsson Prize for Research, , Vanderbilt University
- The B.F. Bryant Prize for Excellence in Teaching, Vanderbilt University
- Highest GPA of the decade, Aristotle University