H.J. Kenna Associate Professor
B.S., University of Illinois at Chicago, 1998
Ph.D., University of Illinois at Chicago, 2003
Office: 202 Hayes-Healy Hall
Phone: (574) 631-9591
Fax: (574) 631-6579
For additional information see Nero Budur’s Personal Page.
My work is in the general area of Algebraic Geometry. This is the study of geometric objects of a somewhat more rigid nature then topological or analytical objects since they are solutions of systems of polynomial equations. My focus is on singularities, which are the peculiar places where these objects are not smooth, and on their effect on the local and global geometry of these shapes.
Among my interests are topics connected with topology (Milnor fibrations, local systems), number theory (Igusa local zeta functions), representation theory (D-modules), combinatorics (hyperplane and subspace arrangements), differential geometry (geometric stability).
- On Hodge spectrum and multiplier ideals, Math. Ann. 327, no. 2, 257-270 (2003).
- (with M. Casanellas and E. Gorla) Hilbert functions of integral standard determinantal schemes and integral arithmetically Gorenstein schemes, J. Algebra 272, no. 1, 292-310 (2004).
- (with Morihiko Saito) Multiplier ideals, V-filtration, and spectrum, J. Algebraic Geom. 14 (2005), 269-282.
- On the V-filtration of D-modules, in “Geometric methods in algebra and number theory”, F. Bogomolov, Y. Tschinkel (Eds.), Progress in Mathematics 235, Birkhäuser (2005).
- (with Mircea Mustaţă and Morihiko Saito) Roots of Bernstein-Sato polynomials for monomial ideals: a positive characteristic approach, Math. Res. Lett. 13, no. 1, 125-142 (2006)
- (with Mircea Mustaţă and Morihiko Saito) Bernstein-Sato polynomials of arbitrary varieties, Compositio Math. 142, 779-797 (2006)
- (with Mircea Mustaţă and Morihiko Saito) Combinatorial description of the roots of the Bernstein-Sato polynomials for monomial ideals. Comm. Algebra 34 , no. 11, 4103-4117 (2006)
- Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers. Adv. Math. 221, 217-250 (2009)
- Jumping numbers of hyperplane arrangements. To appear in Comm. Algebra.
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