Further details will be posted here as they become available. Or you may
contact the University of Illinois organizers

.

**Bruce Reznick (UIUC)** 11:00h-12:00h

** **

### Title: Steampunk canonical forms

Abstract: What is steampunk? It is a style based on combining 19th century

Victorian culture with bits of modern life, such as computers. What are

steampunk canonical forms? 19th century algebra plus the concept of vector

spaces plus Mathematica plus the hope that there is juice left in the

algebraic geometry of binary forms. One example: a general binary sextic

form can be written as the sum of a quadratic form cubed and a cubic form

squared. Numerical experiments suggest this can be done in 40 ways.

**Claudia Polini** (Notre Dame) 2:00h-3:00h

** **

### Title: Studies on curve singularities

Abstract: The goal of the talk is to relate the singularity types of a rational plane

curve to the syzygies of the forms parametrizing it. This is a report on

joint work with Cox, Kustin, and Ulrich.

More specifically, let C be a rational plane curve of degree d parametrized

by three forms, which can be assumed to be of degree d as well. The syzygy

matrix of this parametrization is a 2 by 3 matrix whose entries are forms

of degrees d_1 and d_2, where d_1 + d_2=d. Among other things we consider

curves of even degree d=2c; we show that if C has a singular point

(including an infinitely near singular

point) of multiplicity at least c, then the multiplicity of this singularity

is exactly c and furthermore d_1 = d_2 =c. We establish, essentially, a

correspondence between the constellation of multiplicity c singularities on

or infinitely near C on the one hand and the shapes of the syzygy matrices

on the other hand. Using this, we give a stratification of the space of

rational plane curves into irreducible locally closed sets, according to the

constellation of singularities of maximal multiplicity c.

**Wenbo Niu** (Purdue) 3:30h-4:30h

** **

### Title: Asymptotic Regularity of Ideal Sheaves

Abstract: Let $\sI$ be an ideal sheaf on $\nP^n$ . Associated to $\sI$ there are three elementary

invariants: the invariant $s$ which measures the positivity of $\sI$, the minimal number $d$

such that $\sI(d)$ is generated by its global sections, and the Castelnuovo-Mumford

regularity $\reg\sI$. In general one has $s\leq d\leq \reg\sI$. If we consider the asymptotic

behavior of the regularity of $\sI$, that is the regularity of $\sI^p$ when $p$ is

sufficiently large, then we could have a clear picture involving these invariants. We will

talk about two main theorems in this direction. The first one is the asymptotic regularity

of $\sI$ is bounded by linear functions as $sp\leq \reg \sI^p\leq sp+e$, where $e$ is a

constant. The second one is that if $s=d$, i.e., $s$ reaches its maximal value, then for $p$

large enough $\reg \sI^p=dp+e$ for some positive constant $e$.

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**Parking**: Please, park anywhere at the parking lot next to the IT building

(except for meters).

We will distribute the daily parking permits free of charge, which have to

be put on display in each car promptly.

**Lodging**: We put on hold a block of guestroom at University Place, see

http://www.iupui.edu/building/HO.htm

at the rate of $99 per night plus tax. Make reservations by calling

1-800-627-2700 (select Option #1)

or 317-231-5160. Please, identify your group affiliation: Algecom conference

to get the discounted rates.

The reservations have to be made by 5:00pm to September 29, 2011.

**Banquet**: An all you can eat 8 China buffet, see

http://www.8chinabuffet.com/

The approximate cost is $12 (alcohol extra).