|Welcome to Uli Walther's Research Page|
The fourth year of my Diplom degree I actually spent at Sheffield University in the UK where I earned a Master's degree in Pure Mathematics. For this I wrote a Master's thesis called Local Cohomology: A Survey . My advisor in Sheffield was Rodney Sharp.
In the fall of 1998 I was a guest at the Mathematical Sciences Research Institute, MSRI. In 1999-2000 I was at MSRI as a postdoctoral fellow where my mentor was David Eisenbud.
2002/03 I was a guest at the Universitaet Leipzig and the Max-Planck-Institut in the same city where I was hosted by Juergen Stueckrad and Juergen Jost.
I am now faculty at Purdue University.
Algorithmic computation of local cohomology modules and the local cohomological dimension of algebraic varieties (JPAA (139), 1999.)
Algorithmic computation of de Rham cohomology of complements of complex affine varieties (JSC (29), 2000)
A localization algorithm for D-modules, (JSC (29), 2000). With T. Oaku, N. Takayama.
Switching Surfaces and Groebner bases With A. Tannenbaum and T. Georgiou.(IEEE Trans. Autom. Contr. (46), 2001).
On the Lyubeznik numbers of a local ring (PAMS (129:6), 2001.)
Computing the cup product structure for complements of complex affine varieties. (JPAA (164), 2001).
D-modules on smooth toric varieties With M. Mustata, G. Smith, H. Tsai. (JA (240), 2001)
Computing the rational cohomology of complex varieties (Contemp. Math. (286), 2001)
Computing homomorphisms between holonomic $D$-modules With H. Tsai. (JSC (32), 2001)
D-modules and cohomology of varieties (in "Computations in algebraic geometry with Macaulay 2", Eisenbud, Grayson, Sturmfels, Stillman edts., Springer, Algorithms + Computations in Mathematics 8, 2001)
Cohomology, stratifications and parametric Groebner bases (JSC (35), 2003)
Bernstein-Sato polynomials and Milnor fibers for generic hyperplane arrangements (Compositio Math. (141), 2005)
Algorithmic Stratification of RHom(M,N) for regular holonomic modules on C^n (JSC (39), 2005)
Arbitrary rank jumps of $A$-hypergeometric systems through Laurent monomials With L. Matusevich (J. LMS (75), 2007)
Homological methods for hypergeometric families With L. Matusevich and E. Miller (JAMS (18), 2005)
On the arithmetic rank of certain Segre products With A.~Singh (Contemp. Math. (390), 2005)
Experiments with the restriction functor (preprint)
Duality and reducibility of hypergeometric systems (Math. Ann. (338), 2007)
A connectedness result in positive characteristic With A. Singh (TAMS (360), 2008)
Irregularity of hypergeometric systems via slopes along coordinate subspaces With M. Schulze (Duke MJ (142.3), 2008).
Local cohomology and pure morphisms With A. Singh (Ill. J. Math., the Griffith issue (51), 2007)
24 hours of local cohomology: the Snowbird lecture notes With S. Iyengar, G. Leuschke, A. Leykin, C. Miller, E. Miller, A. Singh (AMS Graduate Studies in Math (87), 2007)
Cohen--Macaulayness and computation of Newton graded toric rings With M. Schulze (JPAA (213), 2009)
Hypergeometric D-modules and twisted Gauss--Manin systems With M. Schulze (JA (223), 2009)
Bockstein homomorphisms in local cohomology With A.K. Singh (Crelle (655) 2011 )
Restriction of $A$-hypergeometric systems to coordinate subspaces With M. Fernandez-Fernandez (PAMS (139) 2011)
Resonance equals reducibility for $A$-hypergeometric systems With M. Schulze (ANT (6) 2012)
Local cohomology of logarithmic forms With G. Denham, H. Schenck, M. Schulze and M. Wakefield (Ann. Inst. Fourier (63) 2013)
Local cohomology modules supported at determinantal ideals With G. Lyubeznik, A.K. Singh (JEMS (18) 2016)
Survey on the D-module generated by f^s with an appendix by A. Leykin (Math. Sci. Res. Inst. Publ., 67 on the special year in commutative algebra and noncommutative algebraic geometry 2012/13)
Singularities and holonomicity of binomial D-modules With C.B. Zamaere and L.F. Matusevich (JA 2015)
The Jacobian, the Milnor fiber, and the $D$-module generated by $f^s$ (to appear in Inventiones Math.)
Bernstein--Sato polynomials for maximal minors and sub-maximal Pfaffians With A. Lorincz, C. Raicu and J. Weyman (to appear in Advances Math.)
Current work is on local cohomology; hypergeometric systems; b-functions and homological properties of $D$-modules; zeta-functions.
Some notes and talks