## Commutative Algebra Seminar

University of Utah, Department of Mathematics

The seminar meets Fridays, 3:00--4:00 PM, inLCB 225.

## Spring, 2008

January 11, 2008:Le Tuan Hoa (Vietnamese Institute of Mathematics)

" Stability of associated primes of monomial ideals"

Abstract: Let $I$ be an ideal of a Noetherian ring. Brodmann and Eakin - McAdam showed that that the sequences $\{ \text{Ass} (I^n/I^{n+1})\}_{n\geq 1}$ and $\{ \text{Ass} (\overline{I^n}/\overline{I^{n+1}})\}_{n\geq 1}$ stabilize for large $n$. However, it is unknown from which number $n_0$ such a sequence stabilizes. The aim of this talk is to present a solution to this problem when $I$ is a monomial ideal of the polynomial ring over a field.

January 18, 2008:Irena Swanson (Reed College)

"An algorithm for integral closure "

January 25, 2008:Trung Dinh

"On growth of primary decomposition of Frobenius powers "

February 01, 2008:Mihnea Popa (UIC)

"Numerical inequalities via syzygies and generic vanishing"

Abstract: I will explain how a refinement of the Green-Lazarsfeld Generic Vanishing Theorem, and the Syzygy Theorem of Evans-Griffith, can be used to prove a higher dimensional analogue of the classical Castelnuovo-de Franchis inequality for surfaces. General related results on Fourier-Mukai transforms will be explained. Joint work with Giuseppe Pareschi.

February 08, 2008:Fumitoshi Sato (KIAS)

"Deformation theory of a smooth DM stack via differential graded Lie algebra "

February 15, 2008:TBA

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February 22, 2008:TBA

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February 29, 2008:TBA

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March 07, 2008:TBA

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March 07, 2008:TBA

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March 14, 2008:TBA

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March 21, 2008:TBA

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March 28, 2008:TBA

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April 04, 2008:TBA

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April 11, 2008:TBA

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April 18, 2008:TBA

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April 25, 2008:TBA

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## Past Seminars:

## Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Fall 2003

## Fall, 2007

August 23, 2007:Organizational meeting

August 31, 2007:Hailong Dao

"On injectivity of maps of Grothendieck groups induced by completion"

September 7, 2007:Anurag Singh

"Annihilators of Local Cohomology"

September 14, 2007:No seminar

September 21, 2007:No seminar

September 28, 2007:Hailong Dao

"Introduction to solid closure"

October 5, 2007:Hailong Dao

"On depths of Hom and tensor products"

October 12, 2007:Fall break

October 19, 2007:No seminar

October 26, 2007:No seminar

November 9, 2007:Paul Monsky (Brandeis)

"Tight closure and localization, a counter-example"

November 16, 2007:Peter Trapa (joint with Representation Theory seminar, 4pm in LCB 323)

"Primitive Ideals in the Enveloping Algebra of a Complex Semisimple Lie Algebra"

November 23, 2007:Thanksgiving break

November 30, 2007:Gretchen Rimmasch (BYU)

"A tropical Bezout's Theorem"

December 07, 2007:Christopher Hacon

TBA

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## Spring, 2007

January 12, 2007:Organizational Meeting

January 19, 2007:Hailong Dao

" Complexity of pair of modules"

January 26, 2007:Dan Ciubotaru (MIT)

"Kazhdan-Lusztig polynomials for p-adic groups"

Joint with Representation Theory Seminar.

February 2, 2007:Paul Roberts

"Arithmetic rank using etale cohomolgy"

February 9, 2007:Anurag Singh

"Arithmetic rank using etale cohomolgy, Part II"

February 16, 2007:No Seminar

February 23, 2007:Justin Sawon (Colorado State University)

"Existence of Lagrangian fibrations on holomorphic symplectic manifolds"

Joint with Algebraic Geometry Seminar.

March 2, 2007:Oana Veliche

"Bass numbers over artinian local rings"

March 9, 2007:No Seminar

March 16, 2007:Lars Winther Christensen (University of Nebraska-Lincoln)

"Vanishing of cohomology over AC-rings---conjectures of Auslander and Reiten"

March 19, 2007:Craig Huneke (University of Kansas)

"When does local cohomology have closed support?"

March 23, 2007:Spring Break

March 30, 2007:Sandy Spiroff (Seattle University)

"An algebraic proof of the commutativity of intersection with divisors"

April 6, 2007:Rahul Panharipande (Princeton University)

"Gromow-Witten theory and Noether-Lefschetz theory"

Joint with Algebraic Geometry Seminar.

April 13, 2007:Erin Chamberlain

"Modules with Prescribed Intersection Properties"

April 20, 2007:Florian Enescu (Georgia State University)

"Lower bounds for Hilbert-Kunz multiplicities"

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## Fall, 2006

August 25, 2006:Hailong Dao,"On superheights of ideals"

September 1, 2006:No Seminar

September 8, 2006:Rodney Y. Sharp (University of Sheffield),

"Uniform behaviour of Frobenius closures of parameter ideals"

September 15, 2006:Paul Roberts,

"Almost regular sequences"

September 22, 2006:Oana Veliche,

"A test complex for Gorensteiness"

September 29, 2006:No Seminar

October 6, 2006:October break (AMS Sectional Meeting)

October 13, 2006:No Seminar

October 20, 2006:Erin Chamberlain

"Modules of Finite Projective Dimension over Complete Intersections"

October 27, 2006:Hacon/McKernan

"Minimal models for varieties of log general type"

We will join the Algebraic Geometry Seminar in LCB 222 at 3:00 PM

November 3, 2006:No Seminar

November 10, 2006:Janet Striuli (University of Nebraska-Lincoln)

"A short proof of a Theorem of Braun"

November 17, 2006:Hailong Dao

"Weak lifting of modules"

November 24, 2006:Thanksgiving break

December 1, 2006:No Seminar

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## Spring, 2006

February 3, 2006:Hailong Dao (University of Michigan),

"Vanishing of Chow groups and intersection properties of modules over hypersurfaces"

February 17, 2006:Ravi Ramakrishna (Cornell University),

"Deforming global galois representations"

February 24, 2006:Joro Todorov,

"A-infinity algebras and superpotentials"

March 3, 2006:Erin Chamberlain,

"The Monomial Conjecture and Cohen-Macaulay canonical modules--a paper by Le Thanh Nhan"

March 6, 2006:Luchezar Avramov (University of Nebraska-Lincoln),

"Length of homology of finite free complexes"

March 10, 2006:Erin Chamberlain,

"The Monomial Conjecture and Cohen-Macaulay canonical modules--a paper by Le Thanh Nhan, Part II"

March 24, 2006:Greg Piepmeyer (University of Nebraska-Lincoln),

"Tame and wild type--last case"

March 31, 2006:Kazuma Shimomoto,

"Some calculations of Fontaine rings"

April 7, 2006:Paul Roberts,

"The commutativity of intersection with divisors"

April 14, 2006:Oana Veliche,

"Modules over local rings with m^3=0"

April 21, 2006:Esben Halvorsen (Copenhagen University),

"How to make complexes smaller within Grothendieck groups"

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## Fall, 2005

September 2, 2005:Paul Roberts,

"Fontaine rings of Noetherian rings"

September 9, 2005:Sandra Spiroff,

"Some results on divisor class groups"

September 16, 2005:No Seminar

September 23, 2005:Kazuma Shimomoto,

"Perfect rings in mixed characteristic"

September 30, 2005:Kazuma Shimomoto,

"Perfect rings in mixed characteristic, Part II"

October 14, 2005:Oana Veliche,

"Acyclicity over local rings with m^3=0"

October 21, 2005:No seminar.

October 28, 2005:Trung Dinh,

"Approximation rings and Artin's functions."

November 4, 2005:Anurag Singh,

"Big Cohen-Macaulay algebras: a new proof by Huneke & Lyubeznik"

November 11, 2005:Anurag Singh,

"Big Cohen-Macaulay algebras: a new proof by Huneke & Lyubeznik, Part II"

November 18, 2005:No seminar

December 2, 2005:Christine Cumming (Purdue University),

"Cohen-Macaulayness of residual intersections"

December 9, 2005:Brent Strunk (Tulane University),

"Castelnuovo-Mumford regularity, reduction numbers, and postulation numbers"

December 12, 2005:Lars Christensen (University of Nebraska-Lincoln),

"When are evaluation homomorphisms invertible?"

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## Spring, 2005

January 21, 2005:Kazuma Shimomoto,

"Frobenius Action in Mixed Characteristic"

January 28, 2005:Anurag Singh (Georgia Institute of Technology),

"A connectedness theorem in positive characteristic"

February 4, 2005:No seminar

February 11, 2005:Kazuma Shimomoto,

"Frobenius Action in Mixed Characteristic, Part II"

February 18, 2005:Oana Veliche,

"Stable Cohomology of Local Rings, Part I"

February 25, 2005:Claudia Miller (Syracuse University),

"Extremal Algebras"

March 4, 2005:Peter Trapa,

"Geometry of Primitive Ideals in Enveloping Algebras"

March 11, 2005:No seminar

March 18, 2005:Spring break

March 25, 2005:Lars Christensen (University of Nebraska-Lincoln),

"Stability of Gorenstein dimensions"

April 1, 2005:Oana Veliche,

"Stable Cohomology of Local Rings, Part II"

April 8, 2005:Kazuma Shimomoto,

"Almost Ring Theory"

April 15, 2005:Erin Chamberlain,

"Modules of Finite Length and Finite Projective Dimension-a paper by P. Roberts and V. Srinivas"April 22, 2005:No seminar

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## Fall, 2004

September 3, 2004:Sandra Spiroff,

"Growth of Ideals"

September 10, 2004:Paul Roberts,

"Constructing Modules from Cycles, Part I"

September 24, 2004:Paul Roberts,

"Constructing Modules from Cycles, Part II"

October 1, 2004:Kazuma Shimomoto,

"On the Minimality of Hilbert-Kunz Multiplicity"

October 22, 2004:Oana Veliche,

"Gorenstein Dimension for Modules"

October 29, 2004:Oana Veliche,

"Gorenstein Dimension for Modules, Part II"

November 12, 2004:Bo-Hae Im,

"Hilbert Irreducibility and its Application"

November 19, 2004:Tyler Evans (Westminster),

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## Fall, 2003

August 29, 2003:Florian Enescu,"Rings with small Hilbert-Kunz multiplicity"

September 5, 2003:Paul Roberts,

"Killing local cohomology with elements of small valuation (I)"

September 12, 2003:Paul Roberts,

"Killing local cohomology with elements of small valuation (II)"

September 19, 2003:Indranath Sengupta,

"Affine monomial curves"

September 26, 2003:Kazuma Shimomoto,

"Approximately Gorenstein rings (I)"

October 10, 2003:Kazuma Shimomoto,

"Approximately Gorenstein rings (II)"

October 24, 2003:Robert Lazarsfeld (University of Michigan),

"Asymptotic invariants of linear series"

October 31, 2003:Sandra Spiroff,

"The behavior of the restriction of divisor classes to sequences of hypersurfaces"

November 7, 2003:Sandra Spiroff,

"The behavior of the restriction of divisor classes of sequences of hypersurfaces (II)"

November 21, 2003:Florian Enescu,

"The structure of F-pure rings"

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