The Commutative Algebra in the Southeast series of meetings represents a collaborative effort of commutative algebraists at
Georgia State University, University of South Carolina and University of Central Florida to increase exposure
of their research area in the Southeast through periodic meetings. Each academic year
GSU, USC and UCF organize two regional meetings and one national. A link with past meetings can be found
here. For some of the
past meetings, including national meetings held in Atlanta, see the following links
Spring 2010,
Atlanta National Meeting-Spring 2009,
Fall 2008,
Atlanta National Meeting-Spring 2008,
Spring 2007, Fall 2007 or Fall 2006 and earlier.
Florian
Enescu (Georgia State University) fenescu@gsu.edu
Yongwei Yao (Georgia State University) yyao@gsu.edu
Invited
speakers are:
Hailong Dao, University of Kansas
Sankar Dutta, University of Illinois at Urbana-Campaign
Andy Kustin, University of South Carolina
Alina Iacob, Georgia Southern University
Paul C. Roberts, University of Utah
Karl Schwede, University of Michigan
Anurag K. Singh, University of Utah
Adela Vraciu, University of South Carolina
Wenliang Zhang, University of Michigan
Updated schedule:
FRIDAY
3:00-4:00pm: Paul C. Roberts (colloquium at GSU)
The Arithmetic Case in Commutative Algebra
4:30-5:30pm: Hailong Dao
On the structure of Hom(M,N)
SATURDAY
9:00-10:00am: Adela Vraciu
The resolution of the Frobenius powers of the maximal ideal in a diagonal surface ring
10:15-11:15am: Anurag K. Singh
Local cohomology supported at determinantal ideals
11:30-12:30pm: Alina Iacob
Gorenstein flat complexes over noetherian rings
Lunch Break
2:30-3:30pm: Sankar Dutta
A connection between two sets of Conjectures
4:00-5:00pm: Karl Schwede
Surjectivity of the trace map and F-singularities
SUNDAY
9:00-10:00am: Paul C. Roberts
Fontaine Rings and Local Cohomology
10:15-11:15am: Wenliang Zhang
Quasilength, content of local cohomology, and
closure operations on ideals
11:30-12:30pm: Andy Kustin
Strata of Rational Plane Curves
Abstracts:
Hailong Dao, University of Kansas
On the structure of Hom(M,N): Let R be a regular local ring and
M,N be reflexive modules over R. In this talk we will describe
restrictions on the direct summands of Hom(M,N). Our results recover
classical ones
by Auslander, Auslander-Goldman, and a result by Griffith on simple
vector bundles of small rank on the punctured spectrum of R.
Sankar Dutta, University of Illinois at Urbana-Campaign
A connection between two sets of Conjectures
Andy Kustin, University of South Carolina
Strata of Rational Plane Curves:
Each rational plane curve is parameterized by an ordered triple of
homogeneous forms in two variables. We relate the
Zariski topology in the parameter space to the singularity configuration
on the curves. Our tool in this investigation is
the Hilbert-Burch matrix for the ordered triple of homogeneous forms.
This is joint work with David Cox, Claudia Polini, and Bernd Ulrich.
Alina Iacob, Georgia Southern University
Gorenstein flat complexes over noetherian rings:We show that over
a two sided noetherian ring the Gorenstein flat complexes are exactly
the complexes of Gorenstein flat modules. We use this to show that over
such rings the class of Gorenstein flat complexes is covering.
This is joint work with Edgar Enochs and Sergio Estrada.
Paul C. Roberts, University of Utah
The Arithmetic Case in Commutative Algebra: One of the aims of the field of Commutative Algebra
is to give a unified theory of the geometric
properties of rings that are used in Algebraic
Geometry and Number Theory. Nevertheless, there
are many instances where the arithmetic case,
where the ring does not contain a field,
requires different methods than the geometric
case, where the ring is defined over a field
such as the field of complex numbers.
In this talk I will survey some of the special
aspects of the arithmetic case and describe
how it has come up in recent work on several
conjectures in the field.
Fontaine Rings and Local Cohomology: The Fontaine ring is a construction which
allows one to apply methods of positive
characteristic, and in particular the
Frobenius map, to rings of mixed characteristic.
In this talk I will describe the construction
of the Fontaine ring and discuss recent progress
in applying it to questions of local cohomology
and the properties of the absolute integral
closure of a domain of mixed characteristic.
Karl Schwede, University of Michigan
Surjectivity of the trace map and F-singularities:
Suppose that R is a normal domain with fraction field K and that L is a
finite separable extension of K. Set S to be the integral closure of R
in L. The trace map Tr : L \to K induces a map Tr : S \to R. If R
contains a field of charactersitic zero, then Tr is always surjective,
but in characteristic p > 0, this is not the case. In this talk we
will discuss conditions on the singularities of R and the branch locus
which guarantee
that Tr must be surjective (which generalizes a well known corollary of
Abhyankar's lemma). This is joint work with Kevin Tucker.
Anurag K. Singh, University of Utah
Local cohomology supported at determinantal ideals:We will
discuss a vanishing theorem for
local cohomology supported at (not necessarily generic) determinantal
ideals. This is based on work in progress with Uli Walther.
Adela Vraciu, University of South Carolina
The resolution of the Frobenius powers of the maximal ideal in a diagonal surface ring:
We let $R=k[x, y, z]/(x^n+y^n+z^n)$, where $k$ is a field, and
$I_N=(x^N, y^N, z^N)\subset R$. We study the $R$-free
resolution of $I_N$. We write $N=an+r$, with $0\le r < n$. Once the
characteristic of $k$ is fixed, the value of $a$ determines
whether $I_N$ has finite or infinite projective dimension. When the
projective dimension is infinite, the value of $r$, together
with the parity of $a$ determine the periodic part of the resolution.
This is joint work with Andy Kustin and Hamid Rahmati.
Wenliang Zhang, University of Michigan
Quasilength, content of local cohomology, and
closure operations on ideals:After a brief discussion of notions of
quasilength and content of local cohomology recently introduced by
Hochster and Huneke, I will explain how to use these ideas to define a
closure operation on ideals in
commutative rings of all characteristic that agrees with tight closure
in positive characteristic. This is a joint work with Mel Hochster.
Participants
Brett Barwick, University of South Carolina
Joe Brennan, University of Central Florida
Luis Nunez-Betancourt, University of Michigan
Ela Celikbas, University of Nebraska
Olgur Celikbas, University of Kansas
C-Y. Jean Chan, Central Michigan University
Cătălin Ciupercă, North Dakota State University
Hailong Dao, University of Kansas
Sankar Dutta, University of Illinois at Urbana-Champaign
Florian Enescu, Georgia State University
Daniel Hernández, University of Michigan
Jen-Chieh Hsiao, Purdue University
Ryan Karr, University of Central Florida
Andy Kustin, University of South Carolina
Alina Iacob, Georgia Southern University
Anton Leykin, Georgia Tech
Jinjia Li, University of Louisville
Laura Lynch, University of Nebraska
Sara Malec, Georgia State University
Chad Matthews, Georgia State University
Lance Miller, University of Utah
Anton Preslicka, Georgia State University
Paul Roberts, University of Utah
Karl Schwede, University of Michigan
Soumya Deepta Sanyal, University of Missouri, Columbia
Farbod Shokrieh, Georgia Tech
Anurag K. Singh, University of Utah
Bart Snapp, Ohio State University
Sandra Spiroff, University of Mississippi
Branden Stone, University of Kansas
Adela Vraciu, University of South Carolina
Roger Wiegand, University of Nebraska
Sylvia Wiegand, University of Nebraska
Emily Witt, University Of Michigan
Yongwei Yao, Georgia State University
Josephine Yu, Georgia Tech
Wenliang Zhang, University of Michigan
Applications for funding:
For those interested in attending the conference and need financial support, please complete our funding application/registration form..
We have limited
funds for financial support. We especially encourage graduate students
and junior faculty to apply for support by indicating this
on the form.
We ask everyone who intends to attend to still register for the
conference by using the above form (just leave blank the appropriate
items, if no
financial support is requested).
Deadline for the applications for funding: August 1, 2010. There is no deadline to register for the conference.
All talks will be in Classroom South (CLSO) 408. A campus map can be found here:
Map. The building is number 3 on the map.
On Saturday and Sunday there will be refreshments served at 8:30am.
Lodging:
We have reserved a block of rooms at Holiday Inn Downtown Atlanta.
This hotel is within short walking distance to the
Department as well as the MARTA station. One can book a room either
online or by phone by mentioning the Group Code: CAS. The rate is 94
dollars plus tax and fees. The deadline for reservations
is September 3.
Airport:
The Airport is served by MARTA and there is a MARTA station in the
terminal (SOUTH TERMINAL). The stop for the hotel is Peachtree Center
and the ride takes approximately 30-35 minutes.
The meeting is partially supported by the National Security Agency and Georgia State University Research Foundation.
Return to the
Commutative Algebra Meetings in the Southeast
home page.