Algecom1


 

Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day, informal meeting of mathematicians from the University of Illinois, Purdue University and nearby universities, with interests in algebra, geometry and combinatorics (widely interpreted).

Further details will be posted here as they become available. Or you may contact the University of Illinois organizers Hal Schenck and Alexander Yong, or the Purdue organizers Uli Walther and Saugata Basu .


First event : Fall, 2009

Date: September 26, 2009

Location: Department of Mathematics, Altgeld Hall, University of Illinois at Urbana-Champaign

The talks will held at 245 Altgeld Hall. Coffee-breaks  will be held down the hall in front of 273 Altgeld Hall.

List of participants

Purdue
 UIUC
Andrei Gabrielov *
Uli Walther *
Saugata Basu *
Giulio Caviglia * (s)
Manoj Kummini * P (s)
Kyungyong Lee * P
Peter Scheiblechner * P

Kuei-Nuan Lin S
Melissa Lindsey S
Lloyd West S
Christine Berkesch S
Amanda Kinzel S
Vita Kala S
Youngsu Kim S
Paolo Mantero S
Lan Nguyen S
Jonathan Montano S
Alex Yong *
Hal Schenck * (s)
Bruce Reznick *
Sheldon Katz *
Tom Nevins *
Li Li * P (s)
Andrew Schultz * P

Jimmy Shan S
Dominic Searles S
Jacob Hall S
Alex Seceleanu S
Ser-Wei Fu S
Ben Reinger S
Radoslav Kirov S
Matthew Yancey S
Immanuel McLaughlin S
Jinwon Choi S
Stephen Maguire S
 * faculty
P postdoc
S Graduate student
(s) Speaker

 



Speakers  and schedule:

Coffee and pastries          8h30   

Giulio Caviglia (Purdue)   9h30 - 10h30  


TBA

Manoj Kummini (Purdue) 11h - 12h

Title: Arithmetic rank of monomial ideals.

Abstract:

The arithmetic rank of an ideal $I$ (denoted $\mathrm{ara} I$)

in a polynomial ring $R = \Bbbk[x_1, \ldots, x_n]$ is the least number $r$

such that there exists polynomials $f_1, \ldots, f_r$ such that the ideals

$(f_1, \ldots, f_r)$ and $I$ have the same radical. It is the least number

of equations to required to define the variety of $I$. In this survey

talk, we will discuss combinatorial constructions that have been used to

determine arithmetic rank of various classes of monomial ideals.


Coffee and snacks          13h30

Li Li (UIUC)                     14h - 15h

Title: On the algebra and combinatorics of q,t-Catalan numbers.

Abstract:

Haiman proved that the q,t-Catalan number is the Hilbert series of the

graded vector space M=\oplus M_{d_1,d_2} spanned by a minimal set of

generators for the ideal of the diagonal locus of (C^2)^2. It is natural

to ask for a combinatorial construction of such generators. In this talk

we give upper bounds for the dimension of M_{d_1, d_2} in terms of

partition numbers, and find all bi-degrees (d_1,d_2) that acheive

equality. For these bi-degrees, we answer the aforementioned question.

This is joint work with Kyungyong Lee.


Hal Schenck (UIUC)         16h - 17h

Title:  Syzygies of plane curve singularities

Abstract:

Let C=V(Q) be a projective plane curve, reduced but not

irreducible. Question: when is the Jacobian ideal of Q arithemtically

Cohen-Macaulay? When Q is a product of linear forms, it is conjectured

that the combinatorics of the line arrangement determines the

Cohen-Macaulay property. In the case of lines, there is an inductive

operation, which corresponds to the algebraic geometry operation of

elementary modification of rank 2 bundles on a surface. When Q is

not a product of linear forms, subtle behavior of the singularities

enters the picture (quasihomogenity). I will report on recent work

on this problem, partly with S. Tohaneanu (CMH, 2009) and partly with

H. Terao and M. Yoshinaga.


Dinner Information

Dinner will be at 18h in  Mandarin Wok (approximate cost $10 per head).


Local Accomodation Information

Homewood Suites  (holding rooms for AlGeCom)
1417 S. Neil, Champaign, IL 217-352-9960


Other hotels in the area:
Hampton Inn
1200 W. University, Urbana, IL 217-337-1100
They have a shuttle to and from campus.

Eastland Suites
1907 N. Cunningham, Urbana, IL 217-367-8331
They have a shuttle to and from campus.

Hawthorne Suites
101 Trade Center, Champaign, IL 217-398-3400

I-Hotel
1900 S. First, Champaign, IL 217-819-5002
They have a shuttle to and from campus.

Hilton Garden Inn
1501 S. Neil, Champaign, IL 217-352-9970

Holiday Inn
1001 Killarney Rd, Urbana, IL 217-328-7900

Holiday Inn Express
1002 Killarney Rd., Urbana, IL 217-328-0328