Notre Dame Algebraic Geometry SeminarFall 2008(11-12 on Tuesdays in DBTL 138 or
Thursdays in H 258)
|
|||
|
Date |
Time/Place |
Speaker |
Title |
|
Tu, Sept 2 |
11am DBTL 138 |
Alan Stapledon (U. |
|
|
Tu, Sept 16 |
11 am DBTL 138 |
Andy Kustin (U. |
|
|
Tu, Sept 23 |
11am DBTL 138 |
Nero Budur (Notre Dame) |
|
|
Th, Oct 9 |
11am H 258 |
Bonnie
Smith (Notre Dame) |
|
|
Tu, Oct 14 |
11 am DBTL 138 |
Izzet Coskun (U. Illinois -Chicago) |
|
|
Th, Oct 30 |
11am H 258 |
Kyungyong Lee (Purdue) |
|
|
Th, Nov 6 |
11am H 258 |
Yihuang
Shen (Purdue) |
|
|
Wed, Nov 19 !!! |
3pm HH 125 |
Giulio Caviglia (Purdue) |
|
Past
seminars: Spring 2008.
Abstract of Talks:
Sept 2. Alan Stapledon (U. Michigan): Weighted Ehrhart theory and orbifold
cohomology
Abstract: If P is a
lattice polytope, then one can define a polynomial $\delta_{P}(t)$, which encodes
the number of lattice points in any fixed dilation of P. The polynomial
$\delta_{P}(t)$ is a classical combinatorial invariant, called the Ehrhart
$\delta$-polynomial of $P$. We will present a new geometric interpretation of
the coefficients of $\delta_{P}(t)$. That is, they are sums of dimensions of
orbifold cohomology groups of a toric stack. As a combinatorial application, we
will prove a weighted version of Ehrhart Reciprocity.
Sept 16. Andy Kustin (U. South Carolina): Reduction numbers of planar ideals.
Abstract: We use the Socle Lemma of Huneke-Ulrich, a
characteristic zero result, to calculate reduction numbers. Our proof works in
all characteristics.
Sept 23. Nero Budur (Notre Dame): Singularities and Hodge filtrations.
Abstract: This talk consists of two parts. In the first part
we review various points of view on singularities: motivation, definitions,
relations, and computability. In the second part we discuss recent work on the
Hodge filtration for local systems. Applications include: computability of
invariants of singularities in the hyperplane arrangement case, and polynomial
periodicity of Hodge numbers for congruence covers.
Oct 9. Bonnie Smith
(Notre Dame): The Core of a Monomial Ideal.
Abstract: The core of an ideal I is the intersection of all reductions of
I--that is, the intersection of all sub-ideals of I which share certain
properties of I. The core arises naturally in the context of the
Briançon-Skoda Theorem, and there is also a connection (which was shown by Hyry
and Smith) between the core and a conjecture of Kawamata about the
existence of non-vanishing global sections of ample line bundles. For the
case of a monomial ideal I in a polynomial ring over a field k, we would like
to have a combinatorial description of the core of I which would reflect the
combinatorial properties of I itself. I will describe some results of
this type.
Oct 14. Izzet Coskun (U. Illinois- Chicago): The geometry of homogeneous spaces.
Abstract: Homogeneous spaces play a central role in geometry, representation theory and combinatorics. In this talk, I will explain how to solve enumerative problems involving homogeneous spaces such as Grassmannians, flag varieties and orthogonal flag varieties. I will describe a positive rule for intersecting Schubert varieties in flag varieties and explain some consequences of this rule. I will describe how to extend these rules to the orthogonal setting.
Oct 30. Kyungyong Lee (Purdue): Hilbert schemes of points.
Abstract : The famous n! conjecture can be stated in an
elementary language. In fact it asserts that the dimension of the vector space
spanned by all derivatives of a certain bivariate analogue of the n × n
Vandermonde determinant is equal to n!. This seemingly elementary conjecture
was solved by M. Haiman, with a highly nontrivial machinery. The proof is
closely related to the algebraic and geometric properties of isospectral
Hilbert schemes of points on the plane. I'll discuss how some of the results in
the plane case can or cannot be generalized to the higher dimensional case.
For problems with this page, email Nero Budur.