Seminars will be in Avery 351, and will be held twice a week:
Wednesdays 3:30 - 4:20 pm
Thursdays 2:30 - 3:20 pm
6th and 7th December (Wednesday and Thursday). Janet Striuli, UNL.
Title: G-covers of residue fields of local rings, I and II.
4th December (Monday) Irena Peeva, Cornell University.
Time and Room: 3:30 -- 4:30 in Avery 112
Title: Hilbert Series
30th November (Thursday) Joseph Gubeladze, San Jose State University.
Title: K-theory of monoid rings
All nontrivial elements in K-groups of monoid rings over regular rings are annihilated by
iterations of the natural Frobenius type endomorphisms. This is a higher analog of the
triviality of vector bundles on affine toric varieties. In the talk I will assume no
K-theoretical background: the main K-theoretical concepts will be presented in an informal
and completely accessible way, without giving a single formal definition.
29th November (Wednesday) Lars W. Christensen, UNL.
Title: Descent of semidualizing complexes for rings with the approximation property
22nd and 23rd November. Give thanks.
16th November (Thursday). Kevin Knudson, Mississippi State University.
Title: Algorithms in Discrete Morse Theory
Given a finite simplicial complex K and a real-valued map f on the vertices of K, we show
how to extend f to a discrete Morse function on all of K in such a way that the
corresponding discrete gradient mirrors the large-scale behavior of f. We also present a
parametrized version of this problem. Several examples and applications will be
15th November (Wednesday) Hans-Bjoern Foxby, University of Copenhagen, Denmark.
Title: Intersection Theorems and Small Dimension
The New Intersection Theorem (NIT) by Peskine & Szpiro, Hochster, and Roberts and its
extensions will be compared to those of the Improved NIT by Evans & Griffith. This is
joint work with Yassemi.
13th November (Monday) Hans-Christian Herbig, University of Frankfurt, Germany.
Time and Room: 3:35 -- 4:30, in Avery 112
Title: A homological approach to singular reduction in deformation quantization
9th November (Thursday). Math Day. (No seminar)
8th November (Wednesday) Anders Frankild, University of Copenhagen, Denmark.
Title: When is a finitely generated module complete?
Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the
Let R be a commutative noetherian ring and I be an ideal in the Jacobson radical of R. Let
R^ be the I-adic completion of R. If M is a finitely generated R-module such that
Ext^i_R(R^,M) = 0 for all i >0, then M is I-adically complete.
One may think of this as a functorial way of detecting completeness of finitely generated
modules. This is joint work with Sean Sather-Wagsatff.
2nd November (Thursday). Sylvia Wiegand, UNL.
Title: Sums of 2 units and almost diagonal matrices
1st November (Wednesday) Andres Rosenschon, University of Alberta, Canada.
Title: Algebraic cycles on products of elliptic curves over p-adic fields.
We give examples of smooth projective varieties X over p-adic fields such that for
suitable l the Chow group in codimension 2 modulo l is infinite. This is joint work with
31st October (Tuesday), around 9:30 AM. Srikanth Iyengar, UNL. (This is not a seminar)
Title: Support of Koszul homology modules and positivity of Euler characteristics
26th October (Thursday). Zach Teitler, South Eastern Louisiana University.
Title: The intersection of the curves through a set of points in P^2
Given a set of points in the projective plane P^2, we consider the intersection of the
degree-d curves through the given set of points. This has applications to the computation
of the multiplier ideals of the original set of points. By using the Hilbert-Burch
theorem, we can "predict" what dimension and degree the intersection will have in terms of
the geometry of the given set of points; and we can show that for most arrangements of
points, these predictions come true.
25th October (Wednesday) Winfried Bruns, University of Osnabrueck, Germany.
Title: On the coefficients of Hilbert quasi-polynomials
18th and 19th October. Rest Cure.
12th October (Thursday). Chuck Weibel, Rutgers University.
Title: Hochschild homology and its cdh cousin describe K-theory of polynomials
We show that the groups NK_0(R), which describe projective modules over R[t] modulo
projectives over R, are direct sums of copies of cdh Hochschild homology except that the
seminormalization R+=H^0(R,O) is replaced by R+/R. Higher K-groups are direct sums of the
usual Hochschild homology groups. Thus many open questions in K-theory and Hochschild
homology are more closely related than we thought.
11th October (Wednesday) Hamid Rahmati, UNL.
Title: Contracting Endomorphisms and Gorenstein modules
We characterize Gorenstein modules when then ring has a finite contracting endomorphism.
4th and 5th October. No seminars.
27th and 28th September (Wednesday and Thursday). Roger Wiegand, UNL.
Title: Extended modules
Let (R,m) be a local ring, S a Noetherian ring and R--> S a faithfully flat extension.
Given a finitely generated S-module N, when is there a finitely generated R-module M such
that S\otimes_R M \cong N (or, more generally, a finitely generated R-module M such that N
is isomorphic to a direct summand of S\otimes_RM)? I will discuss these questions in
special cases, with particular emphasis on the case where S is the Henselization or
completion of R.
The talks will be partly a survey of known results, with some proofs when they are fun.
The talks should be accessible to graduate students.
20th and 21th September (Wednesday and Thursday). Mara Neusel, Texas Tech.
Title: Some things about invariant theory
14th September (Thursday). Rodney Sharp, University of Sheffield, U.K.
Title: Uniform behaviour of Frobenius closures of parameter ideals
13th September (Wednesday). Diana White, UNL.
Title: G_C projective dimension
In this talk, we introduce and investigate the notion of G_C-projectivity for modules over
(possibly non-noetherian) commutative rings, where C is a semidualizing module. This
extends the notion of G_C projectivity to the non-noetherian setting and generalizes
projectivity and G-projectivity within this setting. We then study the resulting modules
of finite G_C-projective dimension, showing in particular that they admit
G_C-projective approximations a' la Auslander and Buchweitz.
6th and 7th September (Wednesday and Thursday). Lucho Avramov and Srikanth Iyengar, UNL.
Title: A class inequality for differential modules
30th and 31st August (Wednesday and Thursday). Greg Piepmeyer and Mark Walker, UNL.
Title: A "new" proof of the New Intersection Theorem
We give a proof of Roberts' New Intersection Theorem in the mixed characteristic case that
uses Adams operations (as developed by Gillet-Soule) in lieu of the local Chern characters
used by Roberts.
24th August (Thursday). Ryo Takahasi, Meiji University, Japan.
Title: Uncountably many indecomposable totally reflexive modules
Several years ago, Huneke and Leuschke gave a theorem which proved a conjecture of
Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable
Cohen-Macaulay type which is complete or has uncountable residue field has at most a
one-dimensional singular locus. In this talk, I will verify that the assumption of the
excellent property can be removed, and consider the theorem over an arbitrary local ring.
I will prove that the existence of a certain prime ideal and a certain totally reflexive
module implies the existence of an uncountably infinite number of isomorphism classes of
indecomposable totally reflexive modules.
3rd August (Wednesday). Mark Rogers, Missouri State University.
Title: Gorenstein rings and irreducible parameter ideals
24th July (Monday). Jung-Chen Liu, National Taiwan Normal University.
Title: Buchsbaum-Rim Multiplicites as Hilbert-Samuel Multiplicities
Maintained by Srikanth Iyengar