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Mathematical logic, and in particular, recursive function theory.
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2011: "When series of computable functions into the reals are computable" (with I. Kalantari), submitted for publication.
2008: "On degree-preserving homeomorphisms between trees in computable topology" (with I. Kalantari), Archive for Mathematical Logic 46 (2008), pp. 679-693.
2008: "On Turing degrees of points in computable topology" (with I. Kalantari), MLQ Mathematical Logic Quarterly 54 (2008), no. 5, pp. 470-482.
2007: "Turing Degrees & Topology" (with I. Kalantari), Computation and Logic in the Real World: Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007, Local Proceedings, edited by S. Barry Cooper, Thomas F. Kent, Benedikt Lowe, and Andrea Sorbi, pp. 210-218.
2006: "Specker's theorem, cluster points, and computable quantum functions" (with I. Kalantari), Logic in Tehran: Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic, held October 18-22, 2003, edited by Ali Enayat, Iraj Kalantari, and Mojtaba Moniri, in the series Lecture Notes in Logic, volume 26, Association for Symbolic Logic (2006), pp. 134-159.
2004: "A blend of methods of recursion theory and topology: A \Pi^0_1 tree of shadow points" (with I. Kalantari), Archive for Mathematical Logic 43 (2004), pp. 991-1008.
2004: "Density and Baire category in recursive topology" (with I. Kalantari), Mathematical Logic Quarterly, 50 (2004), No. 4/5, pp. 381-391.
2003: "A Blend of Methods of Recursion Theory and Topology" (with I. Kalantari), Annals of Pure and Applied Logic, 124 (2003), pp. 141-178.
2002: "Recursive Quantum Functions, Avoidable Points, & Shadow Points in Recursive Analysis" (with I. Kalantari), Electronic Notes in Theoretical Computer Science, 66 (1) (2002), Elsevier Science Publishers.
1999: "Recursive and nonextendible functions over the reals; filter foundation for recursive analysis. II" (with I. Kalantari), Annals of Pure and Applied Logic, 98 (1999), pp. 87-110.
1998: "Point-free topological spaces, functions and recursive points; filter foundation for recursive analysis. I" (with I. Kalantari), Annals of Pure and Applied Logic, 93 (1998), pp. 125-151.
1997: "On universal words for automorphism groups of linear orders" (with S. Adeleke), Ordered Algebraic Structures: Proceedings of the Curacao Conference, Sponsored by the Caribbean Mathematics Foundation, June 26-30, 1995, edited by W. Charles Holland and Jorge Martinez, Kluwer Academic Publishers, 1997.
1987: "Degrees of splittings and bases of recursively enumerable subspaces" (with R. G. Downey and J. B. Remmel), Transactions of the American Mathematical Society, vol. 302, no. 2, pp. 683-714, August 1987.
1986: "Splitting properties of r. e. sets and degrees" (with R. Downey), The Journal of Symbolic Logic, vol. 51, no. 1, pp. 88-109, March 1986.
1984: "A Hierarchy of Families of Recursively Enumerable Degrees", The Journal of Symbolic Logic, vol. 49, no. 4, pp. 1160-1170, December 1984.
1983: "Splitting Properties and the Recursively Enumerable Degrees," Abstracts of papers presented to the American Mathematical Society, p. 387, August 1983.
1981: A Hierarchy of Families of Recursively Enumerable Degrees and a Theorem on Bounding Minimal Pairs, doctoral thesis, University of Illinois at Unrbana-Champaign,
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2007, June 21: "Turing Degrees and Topology," Computation and Logic in the Real World: Third Conference on Computability in Europe, CiE 2007, Siena, Italy
2003, Jan. 16: "Interpolation for Quantum Recursive Functions in Computable Analysis," Joint Mathematics Meeting, Baltimore, MD
1997, Mar. 22: "Filters as a Foundation for Recursive Analysis: Codomains, Avoidable Sets of Points, and Uniformity," Association for Symbolic Logic Annual Meeting, MIT, Cambridge, MA
1987, Apr. 11: "Effective Topology II: Continuous Functions on a Point-Free Space," 4th Biennial Greater Boston Logic Conference, MIT, Cambridge, MA
1983, Apr. 23: "Decompositions of Recursively Enumerable Sets," 2nd Biennial Cambridge Logic Conference, MIT, Cambridge, MA
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1998, Feb.: "Filters as a foundation for computable analysis," Mathematics Colloquium, WIU
1991, Oct.: "Post's Program and incomplete recursively enumerable sets," (a series of lectures) Logic Seminar, Math. Dept., WIU
1989: "Pi(0,1) Trees," (a series of lectures) Logic Seminar, Math. Dept. WIU
1986, Oct. 9: "A Mathematical Magical Mystery Tour," Mathematics Colloquium, WIU
1985, Oct.: "Capturing points in point-free traps," Mathematics Colloquium, WIU
1985, Oct.: "Effective location of countably dense sets of points in point-free topological spaces" (a series of lectures), Logic Seminar, Math. Dept., WIU
1984, Oct.: "The 0''' priority method" (a series of lectures), Logic Seminar, Math. Dept., WIU
1983, Oct.: "A Look at Nonstandard Analysis," Mathematics Colloquium, WIU
1981, Oct.: "A hierarchy of families of recursively enumerable degrees" (a series of lectures), Logic Seminar, Math. Dept., WIU
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1997: "Between Scylla and Charybdis," The Grapes of Math, problem posed in the December 15th issue, answer in the May 20, 1998 issue.
1996: "As I was going to Saint Ives," The Undivided Graduate, problem posed in the April 12th issue, answer in the May 6th issue.
1995: "Ups and downs of functions," The Grapes of Math, problem posed in the March 20th issue, answer in the October 30, 1996 issue.
1983: "Alan in Computerland," The Pentagon, pp. 128-142, Spring 1983.
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2011, Oct. 19: "What can be computed? What can not?" Math Club, WIU
1987, Fall: "An Open Function Which is Nowhere Continuous," Math Club, WIU
1985, Oct.: "Magic Squares," Math Club, WIU
1982, Nov.: "Cyclic decimal expansions and primitive roots," Math Club, WIU
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My e-mail address: L-Welch@wiu.edu
Revision Date: November 28, 2011