**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**

**Abstract: **

**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**

**discussed.**

**15th November (Wednesday) Hans-Bjoern Foxby, University of Copenhagen, Denmark.**

**Title: Intersection Theorems and Small Dimension**

**Abstract:**

**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?**

**Abstract:**

**Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the**

**following result:**

**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.**

**Abstract:**

**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**

**V. Srinivas.**

**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**

**Abstract:**

**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**

**Abstract: **

**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**

**Abstract:**

**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**

**Abstract: **

**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**

**Abstract:**

**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**

**Abstract:**

**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**

**Abstract: **

**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**

**Abstract:**

**24th July (Monday). Jung-Chen Liu, National Taiwan Normal University.**

**Title: Buchsbaum-Rim Multiplicites as Hilbert-Samuel Multiplicities**

**Maintained by **** Srikanth Iyengar**** **