Abhijit Dasgupta

Current Research Area

My primary research area is Topology, Real Analysis, and Measure Theory in the context of the Borel and Projective hierarchies in Polish spaces. This is part of an area known as Descriptive Set Theory, and involves Classifying Sets in Topology and Analysis. Alberto Marcone's talk having the same title gives an overview of the subject. Recently, I have also worked in Randomness in Sequences and Non-standard Analysis.

Selected Publications (refereed)

• A Set of Axioms for Nonstandard Extensions, Math. Logic Quarterly 57, No. 5 (2011), 485-493. doi:10.1002/malq201010025.

• Mathematical Foundations of Randomness, Philosophy of Statistics (Volume 7 of the Handbook of Philosophy of Science, ISBN 978-0-444-51862-0), North-Holland (2011), pp. 641-710. © Copyright 2011 Elsevier BV. Preprint, book (at Amazon).

• The Riemann Integrable Functions are Π⁰₃-complete in the Lebesgue Integrable Functions, J. Math. Anal. Appl. 332(2007), 700-708. doi:10.1016/j.jmaa.2006.09.080.

• Constructing Δ₃⁰ using topologically restrictive countable disjoint unions, Real Analysis Exchange 31(2), 2005/2006, 547-552.

• A Universal coanalytic linear ordering, Proc. Amer. Math. Soc. 129(12), December 2001, 3715-9.

• Borel complexity of the space of probability measures, Proc. Amer. Math. Soc. 129(8), August 2001, 2441-3.

• (with R. Cheng and others) When does f^-1 = f ?, Amer. Math. Monthly 105(8), October 1998, 704-717.

• Boolean operations, Borel sets, and Hausdorff's question, J. Symbolic Logic 61(4), December 1996, 1287-1304.

Talk (on Axiomatic Nonstandard Analysis)

• Logicless Nonstandard Analysis: An Axiom System (Abstract, Slides), presented in UltraMath 2008: Applications of Ultrafilters and Ultraproducts in Mathematics, Pisa, Italy, June 1--7, 2008.

Expository Articles (in Topology Atlas)

• Countable metric spaces without isolated points, in ``Topology Explained,'' June 2005, online at http://at.yorku.ca/p/a/c/a/25.htm.

• Limit points of discrete sets in metric spaces, in ``Topology Explained,'' July 2005, online at http://at.yorku.ca/p/a/c/a/26.htm.

• Ask a Topologist and Ask an Analyst Forum posts (200+ posts, mostly in summer 2005): Use Google search http://www.google.com/search?q=abhijit+dasgupta+site:at.yorku.ca