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CURRICULUM VITAE
Clinton Graydon McCrory
EDUCATION:
1968 BS in Mathematics, Massachusetts Institute of Technology
1970 MA in Mathematics, Brandeis University
1972 PhD in Mathematics, Brandeis University
Thesis: Poincaré Duality in Spaces with Singularities
Advisor: Jerome P. Levine
ACADEMIC HONORS:
1964 Presidential Scholar from South Carolina (A.C. Flora High School)
1968 Sigma Xi (M.I.T.)
1972 Leverhulme Fellow (University of Warwick)
1995 Beaver Teaching Award (University of Georgia)
1997 McCay Faculty Award (Mathematics Department, University of Georgia)
2007 General Sandy Beaver Teaching Professor (University of Georgia)
PROFESSIONAL APPOINTMENTS:
1972-73 Visiting Lecturer, University of Warwick
1973-74 Member, Institute for Advanced Study
1974-76 Tamarkin Instructor, Brown University
1976-80 Assistant Professor, Brown University
1980-86 Associate Professor, University of Georgia
1986-09 Professor, University of Georgia
2001-07 Director, Mathematics Department VIGRE Program, University of Georgia
2009 Professor Emeritus, University of Georgia
VISITING POSITIONS:
1980 (Spring) University of Warwick, University of Pisa
1981 (April) Institut des Hautes Études Scientifiques
1982 (September) University of Pisa
1986 (Fall) Mathematical Sciences Research Institute
1989 (Spring) University of Warwick
1990 (October) University of São Paulo at São Carlos
1992 (Fall) Mathematical Sciences Research Institute
1993 (November) University of Sydney
1994 (December) University of Sydney
1996 (December) University of Angers
1998 (Spring) University of Angers (Chercheur Associé, CNRS)
2000 (Spring) University of Warwick, University of Angers
2004 (Spring) Mathematical Sciences Research Institute, University of Angers
2005 (Fall) Institut Henri Poincaré
2008 (June) University of Angers
2010-2011 (October and April) University of Nice
GRADUATE STUDENTS:
Brown University:
Edwin Kokubun, MA 1975: The Schoenflies Theorem in Dimensions 2 and 3 in the Piecewise-Linear Category
Karen Roothaan, MA 1978: A Regular Cell Structure on G2R4
Janine Clookey, MA 1980: Introduction to Klein's Theory of the Icosahedron
James Sheehan, MA 1981: Knots and Singularities of Plane Curves
Barry Hill-Tout, PhD 1983: A Local Euler Invariant for Real Algebraic Singularities
University of Georgia:
Mark Faucette, MA 1983: Intersection of Manifolds and the Cup Product
Shoji Yokura, PhD 1984: Polar Classes and Segre Classes on Singular Projective Varieties
Janice Brown, MA 1986: Qualitative Properties of Autonomous Systems of First Order Differential Equations
Lazar Milin, PhD 1987: A Combinatorial Computation of the First Pontryagin Class of the Complex Projective Plane
Chris Sligar, PhD 1990: On the Minimal V-Degree of the Generalized Jones Polynomial
Scott Corley, MA 1995: A Discussion with Examples of the Relationship between the Euler Characteristic and Cusps of the Gauss Map
Mu Yeol Park, PhD 1997: Classification of Stable Cut Loci of Surfaces
Michelle LeMasurier, PhD 1998: Singularities of Second Order Implicit Differential Equations
Edgar Fuller, PhD 1999: The Geometry and Topology of Holonomic Knots
Valerie Hower, PhD 2007: Hodge Spaces of Real Toric Varieties
Emille Davie Lawrence, PhD 2007: Characterizing Right-Veering Homeomorphisms of the Punctured Torus via the Burau Representation
PUBLICATIONS:
1. Euler singularities and homology operations, Amer. Math. Soc. Proc. Symp. Pure Math. 27 (1975), 371-380. MR 51:14089.
2. Cone complexes and PL transversality, Trans. Amer. Math. Soc. 207 (1975), 269-291. MR 53:4078.
3. Cobordism operations and singularities of maps, Bull. Amer. Math. Soc. 82 (1976), 281-283. MR 54:3718.
4. Cone bundles, Trans. Amer. Math. Soc. 228 (1977), 157-163. MR 55:11261.
5. A characterization of homology manifolds, J. London Math. Soc. (2) 16 (1977), 146-159. MR 56:3846.
6. (with T. Banchoff) Whitney duality and singularities of projections, Geometry and Topology, Rio de Janeiro 1976, Springer Lecture Notes in Math. 597 (1977), 68-81. MR 56:6678.
7. Stratified general position, Algebraic and Geometric Topology, Santa Barbara 1977, Springer Lecture Notes in Math. 664 (1978), 142-146. MR 80m:57016.
8. Geometric homology operations, Studies in Algebraic Topology, Advances in Math. Suppl. Studies, vol. 5 (1978), 119-141. MR 80j:57016.
9. Zeeman's filtration of homology, Trans. Amer. Math. Soc. 250 (1979), 147-166. MR 81b:55002.
10. (with T. Banchoff) A combinatorial formula for normal Stiefel-Whitney classes, Proc. Amer. Math. Soc. 76 (1979), 171-177. MR 80h:57031.
11. (with J. Blanton) An axiomatic proof of Stiefel's conjecture, Proc. Amer. Math. Soc. 77 (1979), 404-414. MR 80k:55052.
12. (with R. Hardt) Steenrod operations in subanalytic homology, Compositio Math. 39 (1979), 333-371. MR 82b:55019.
13. (with T. Banchoff and T. Gaffney) Cusps of Gauss Mappings, Research Notes in Mathematics, No. 55, Pitman Publishing Ltd., London 1982. MR 84a:48001. Second edition (with Daniel Dreibelbis): online publication http://www.emis.de/monographs/CGM/.
14. On the topology of Deligne's weight filtration, Amer. Math. Soc. Proc. Symp. Pure Math. 40 (1983), part 2, 217-226. MR 85f:14020.
15. (with T. Shifrin) Cusps of the projective Gauss map, J. Differential Geometry 19 (1984), 257-276. MR 85m:14070.
16. Massey products in singularity links, Duke Math. J. 51 (1984), 691-697. MR 86a:32038.
17. (with T. Banchoff and T. Gaffney) Counting tritangent planes of space curves, Topology 24 (1985), 15-23. MR 86m:58028a.
18. (with T. Shifrin and R. Varley) The Gauss map of a generic hypersurface in P4, J. Differential Geometry 30 (1989), 689-759. MR 91f:14039.
19. Configuration spaces of simplicial spheres, IV Convegno Nazionale di Topologia, Sorrento 1988, Rend. Circolo Mat. Palermo, Suppl. ser. II, no. 24 (1990), 159-168. MR 93b:57023.
20. (with M. Adams, T. Shifrin and R. Varley), Symmetric Lagrangian singularities and Gauss maps of theta divisors, Singularity Theory and its Applications, Part I, D. Mond and J. Montaldi, eds., Springer Lecture Notes in Math. 1462 (1991), 1-26. MR 92j:14033. [Errata in reference 29 below.]
21. (with T. Shifrin and R. Varley) The Gauss map of a genus three theta divisor, Trans. Amer. Math. Soc. 331 (1992), 727-750. MR 92h:14019.
22. (with M. Adams, T. Shifrin and R. Varley) Invariants of Gauss maps of theta divisors, Amer. Math. Soc. Proc. Symp. Pure Math. vol. 54, part 2 (1993) 1-8. MR 94a:00011.
23. (with Juan J. Nuno Ballesteros and M. Carmen Romero-Fuster) Self-translation surfaces, Matematica Contemporanea 5 (1993), 61-76.
24. (with G. Kennedy and S. Yokura) Natural transformations from constructible functions to homology, C. R. Acad. Sci. Paris, Série I, 319 (1994), 969-973. MR 96a:57059.
25. (with T. Shifrin and R. Varley) Siegel modular forms generated by invariants of cubic hypersurfaces, J. Algebraic Geometry, 4 (1995), 527-556. MR 95m:14018.
26. (with J. Fu) Stiefel-Whitney classes and the conormal cycle of a real analytic variety, Trans. Amer. Math. Soc. 349 (1997), 809-835. MR 97h:32009.
27. (with A. Parusiński) Complex monodromy and the topology of real algebraic sets, Compositio Math. 106 (1997), 211-233. MR 98d:14075.
28. (with A. Parusiński) Algebraically constructible functions, Ann. Sci. École Norm. Sup. Paris 30 (1997), 527-552. MR 98f:14047.
29. (with M. Adams, T. Shifrin, and R. Varley) Conic Lagrangian singularities, Topology and its Applications 88 (1998), 155-178. MR 99i:57049.
30. (with A. Parusiński) Topology of real algebraic sets of dimension 4: necessary conditions, Topology 39 (2000), 495-523. MR 2000m:14060.
31. How to show a set is not algebraic, in Algorithmic and Quantitative Real Algebraic Geometry (S. Basu and L. Gonzalez-Vega, eds.), DIMACS Series, vol. 60, Amer. Math. Soc. 2003, 77-82. MR 2004d:14085.
32. (with A. Parusiński) Virtual Betti numbers of real algebraic varieties, C. R. Acad. Sci. Paris, Ser. I, 336 (2003), 763-768. MR 2004e:14087.
33. (with F. Bihan, M. Franz, and J. van Hamel) Is every toric variety an M-variety?, Manuscripta Math. 120 (2006), 217-232. MR 2008b:14082a.
34. (with A. Parusiński) Algebraically constructible functions: real algebra and topology, Panoramas & Synthèses 23, Soc. Math. France 2007, 68-85. MR 2009k:14112.
35. (with A. Parusiński) The weight filtration for real algebraic varieties, in Topology of Stratified Spaces, MSRI Pub. 58, Cambridge University Press, New York 2011, 121-160. MR2796410. Correction, June 2014.
36. (with A. Parusiński) The weight filtration for real algebraic varieties II: classical homology, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 108 (2014), 63-94. MR3183108.
37. (with A. Parusiński) Real intersection homology, Topology and its Applications 234 (2018), 108-129. MR3739460.
38. (with A. Parusiński and L. Paunescu) Algebraic stratified general position and transversality, J. Algebraic Geometry 28 (2019), 139-152. MR3875363.
39. (with A. Parusiński) Real intersection homology II: A local duality obstruction, Topology and its Applications 271 (2020), 107050. MR4050745.
UNPUBLISHED NOTES AND TALKS:
1. Lectures on homology operations, Brown University 1976.
2. Profiles of surfaces, University of Warwick 1980.
3. Generic curves and surfaces in 3-space: contact with lines and planes, University of Warwick 1980.
4. Secant planes of space curves, MSRI 1992.
5. Homology of real algebraic varieties: products and singularities, UGA 2013.
6. References on Stiefel-Whitney classes, University of Nice 2013.
7. Hyperresolutions: complex and real, Cargèse 2019.
8. The intrinsic stratification of a semialgebraic set, Marseille 2021.
RECENT INVITED LECTURES:
2008 Workshop in Real Algebraic Geometry (University of Angers), MSRI Workshop on the Topology of Stratified Spaces
2009 Conference on Real Singularities in Analysis and Geometry (University of Rennes)
2010 Georgia Institute of Technology
2011 Kyoto University, Kagoshima University
2012 University of Nice, CIRM Conference on the Topology and Geometry of Singular Spaces (Luminy)
2013 Franco-Japanese-Vietnamese Symposium on Singularities (University of Nice)
2015 CIRM Conference: Thematic Month on Singularities and Applications (Luminy)
2019 Real and Complex Singularities in Cargèse (for Adam Parusiński's 60th birthday)
2021 Singularity Theory and Regular Stratifications (Marseille, for David Trotman's retirement)
(Revised March 10, 2024)