**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**

**25th April (Wednesday). Cristiano Bocci, University of Milan, Italy.**

**Title: Secant varieties in phylogenetics - II**

**Special seminar: 23rd April (Monday). Ezra Miller, University of Minnesota.**

**Time and place: 10:30 ??**

**Title: Multiplier ideals of sums via cellular resolutions**

**19th April (Thursday). Mike Mandell, Indiana University.**

**Title: A Localization Sequence for the Algebraic K-Theory of Topological K-theory**

**Abstract:**

**While the K-theory of the integers is closely connected with number theory, the K-theory**

**of the "sphere spectrum" is closely connected with geometry. Waldhausen's "chromatic**

**tower" in K-theory interpolates between these. Conjectures of Rognes relate the layers in**

**this tower to the K-theory of ring spectra that are familiar to topologists, and at the**

**bottom is topological K-theory. This talk will describe this picture and explain what is**

**currently known.**

**18th April (Wednesday). Cristiano Bocci, University of Milan, Italy.**

**Title: Secant varieties in phylogenetics - I**

**Abstract:**

**I will talk about a recent result for phylogenetics which permits one to extend the result**

**of Lansberg and Manivel about the ideal of secant varieties of Segre varieties.**

**Iin the first one I will introduce some concepts of algebraic statistics, explain why**

**statistical models are algebraic varieties and then introduce general markov tree models.**

**This provides all the background needed for the second talk, on the particular subfield**

**(of algebraic statistics) of phylogenetic algebraic geometry.**

**12nd April (Thursday). Alexander Berglund.**

**Title: T.B.A.**

**11th April (Wednesday). Neil Epstein, University of Michigan. **

**Title: T.B.A.**

**Special seminar: 6th April (Friday). Dumitru Stamate.**

**Time and place: 10:30 AM, Avery 351.**

**Title: Koszul rings via sequentially Cohen-Macaulay posets**

**Koszul rings are graded algebras satisfying certain nice homological properties. In**

**particular, they are quadratic. Woodcock and Polo proved that the incidence algebra of a**

**finite graded poset P is Koszul if and only if each open interval in P is Cohen-Macaulay.**

**We study a possible extension of this result to arbitrary finite posets. We expect that in**

**this case, the associated graded ring of the incidence algebra of the poset play an**

**important role. We can describe the posets for which this associated ring is quadratic and**

**we'll present progress towards the conjectured result. This is joint work with Vic**

**Reiner, Univ. of Minnesota.**

**I'll start with Woodcock's approach on Koszul rings and introduce the incidence algebra of**

**a poset. All other notions will be introduced during the talk. Attending the previous**

**talk could be useful.**

**5th April (Thursday). Giuglio Cavaglia, Purdue University.**

**Title: How to compute generic initial ideals and extremal Betti numbers.**

**4th April (Wednesday). Dumitru Stamate.**

**Title: Sequentially Cohen-Macaulay modules and combinatorics**

**Abstract:**

**A module over a noetherian ring is called sequentially Cohen-Macaulay (seq-CM) if it has a**

**finite filtration of submodules whose quotients are CM modules of increasing Krull**

**dimension. The notion was introduced by Stanley starting from combinatorial**

**considerations, and it proved useful in commutative algebra. To begin with, I will survey**

**several characterizations and properties of seq-CM modules due to Schenzel, Peskine,**

**Herzog, Popescu,and Sbarra among others. Using the Stanley-Reisner correspondence, we**

**restrict to the case of face rings of simplicial complexes and give combinatorial and**

**homological characterizations of seq-CM complexes and posets, presenting results of Duval,**

**Bjorner, Wachs and Welker. In the end, I will present some important classes of seq-CM**

**modules.**

**29th March (Thursday). Liana Sega, University of Missouri, Kansas City.**

**Title: Cohomology over short local rings**

**28th March (Wednesday). Lars Winther Christensen, UNL.**

**Title: The Auslander Condition can be checked on the subcategory of maximal Cohen-Macaulay**

**modules**

**22nd March (Thursday). Kiriko Kato, Osaka Prefecture University, Japan.**

**Title: The quotient category of the homotopy category**

**21st March (Wednesday). Mustapha Lahyane.**

**Title: On Basic Rational Surfaces.**

**Abstract: In 1960, Masayoshi Nagata showed that the monoid of effective divisor classes of**

**a smooth projective rational surface may fail to be finitely generated. This phenomenon**

**began to be studied in detail in the 80s, beginning with work by Rosoff in 1980 and**

**Harbourne in 1985. The aim of this seminar is to discuss some complementary work**

**regarding this problem.**

**14th and 15th March. Spring Break.**

**8th March (Thursday). Tom Marley, UNL.**

**Title: Concerning the support of local cohomology modules**

**Abstract: **

**Let R be a Noetherian ring, I an ideal of R, and M a finitely generated R-module. In**

**general, it is unknown whether the supports of the local cohomology modules H^i_I(M) are**

**closed subsets of Spec R. In this talk, I will present some recent progress (done jointly**

**with Craig Huneke and Dan Katz) on this question.**

**Special seminar: 7th March (Wednesday). Hyman Bass, University of Michigan.**

**Time and place: 1 PM, Bessey Hall 108. **

**Title: The zeta function of a finite graph**

**Abstract:**

**This is a nice topic about a generating function to count "prime closed paths" in a finite**

**graph. It is defined as a formal power series, and the main theorem says that it is a**

**(very explicit) polynomial. This is really a discrete analogue of the Selberg zeta**

**function on a Riemann surface, but one doesn't need to know any of this to understand the**

**talk. In fact the talk should be understandable to grad students and even upper**

**undergraduates.**

**1st March (Thursday). White-out.**

**28th February (Wednesday). No seminar. **

**Special seminar: 23rd February (Friday) B. Purnaprajna, University of Kansas.**

**Time and place: 10:30 AM, Avery 351.**

**Title: Koszul rings from geometry.**

**Abstract:**

**Koszul rings have evoked interest among algebraists and geometers. To paraphrase Arnold**

**any homogeneous ring that has a serious reason for being quadratically presented is**

**Koszul. There are a large class of quadratic algebras arising from geometry where this**

**meta-principle always seem to hold. I will illustrate some vector bundle techniques that**

**are used to prove the above meta-principle.**

**22nd February (Thursday). B. Purnaprajna, University of Kansas.**

**Title: Mapping geography of surfaces of general type**

**Abstract: **

**The canonical map of a curve (that is the map induced by the canonical line bundle) of**

**genus $g\geq 2$ is well studied; either it gives an embedding or is a 2:1map onto a**

**rational normal curve. The higher dimensional analogue is much more subtle due to the**

**existence of higher degree covers, among other things. In this talk we show how the**

**geometry of canonical covers (that is the covers induced by the canonical map) is**

**intimately connected to various problems in algebraic and Kahler geometry. For example,**

**they appear in the determination of ampleness of a linear series on threefolds such as**

**Calabi-Yau, they also appear in the determination of generators of the canonical ring of**

**some varieties of general type. Most importantly, they play a role in mapping geography of**

**surfaces of general type, that is construction of surfaces of general type with prescribed**

**invariants such as first chern class, geometric genus and irregularity.**

**21st February (Wednesday). No seminar.**

**15th February (Thursday). Anurag Singh, University of Utah.**

**Title: Magic Squares**

**14th February (Wednesday). No seminar.**

**8th February (Thursday). S. Iyengar. UNL.**

**Title: Modules with prescribed cohomological varieties-II.**

**7th February (Wednesday). Lucho Avramov. UNL.**

**Title: Modules with prescribed cohomological varieties-I.**

**1st February (Thursday). Diana White. UNL.**

**Title: (Lack of) balance - II.**

**31 January (Wednesday). No seminar. **

**25th January (Thursday). Diana White. UNL**

**Title: (Lack of) balance - I.**

**24th January (Wednesday). No seminar. **

**18th January (Thursday). Frank Moore, UNL.**

**Title: Cohomology of fiber products of local rings.**

**Abstract:**

**The title says it all.**

**17th January (Wednesday) Henrik Holm, University of Copenhagen**

**Title: Aspects of precovering classes.**

**Abstract:**

**Informally speaking, a class of modules F over some ring is precovering (or**

**contravariantly finite) if every module admits a nice resolution consisting of modules**

**from F.**

**In general it is not easy to decide whether a given class is precovering or not. For**

**example, it was conjectured by Enochs in 1981 that for any ring R the class of flat**

**R-modules is (pre)covering. This conjecture remained open for twenty years until it was**

**finally settled by Bican, El Bashir, and Enochs in 2001.**

**The first part of the talk presents sources and examples of (pre)covering classes. In the**

**second part of the talk we look at some aspects of precovering classes in relative**

**homological algebra. More precisely, we relate the vanishing of Ext functors with the**

**vanishing of resolutions and Schanuel maps relative to a given precovering class.**

**This talk summarizes work of the speaker and of other people (proper references will be**

**given during the talk).**