**ALGEBRAIC GEOMETRY SEMINAR**

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**Time: Wednesday, 3:30-4:30 pm**

**Location: MATH 731**

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**Speakers/Abstracts:**

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**September 5th: Kenji Matsuki
(Purdue)**

*Title: ***A Kawamata-Viehweg type formulation of the
(logarithmic) Akizuki- Nakano Vanishing Theorem.**

*Abstract: *

**September 12th: Kenji Matsuki
(Purdue)**

*Title: ** ***A
Kawamata-Viehweg type formulation of the (logarithmic)
Akizuki- Nakano Vanishing Theorem.**

*Abstract: *Continuation of last week's talk.

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**September 19th: Donu Arapura
(Purdue)**

*Title: ***Chow groups and cycle maps**.

*Abstract: *This talk is entirely expository. I'll review basic
facts about Chow groups and cycle maps to usual/etale
(co)homology.
(This talk will be in preparation
for T. Saito's Lecture series next week).

*Takeshi Saito will will give a series of three Lectures during
the week of September 25. The first will be a special AG
seminar, the second during the usual AG seminar, and the third
in the sutomorphic forms seminar.

**September 25th: Takeshi Saito
(Tokyo)**

*Title: ***Characteristic cycle of an Žtale sheaf and its
functoriality (Lecture 1)**

*Abstract: *For an Žtale sheaf on a smooth algebraic variety over
a perfect field of characteristic p > 0, the characteristic
cycle is defined as a cycle supported on the singular support,
which is defined by Beilinson as a closed conical subset of the
cotangent bundle. The characteristic cycles are characterized by
and satisfy some functorial properties. I will explain basic
definitions and properties of the singular support and
characteristic cycle.

**Note: This talk will be from 1:30-2:30 in Univ. 317.**

**September 26th: Takeshi Saito (Tokyo)**
*Title: ***Characteristic cycle of an Žtale sheaf and its
functoriality (Lecture 2)**

*Abstract: *This will be a continuation of the
first lecture.

**September 27th: Takeshi Saito
(Tokyo)**
*Title: ***Characteristic cycle of an Žtale sheaf and its
functoriality (Lecture 3)**

*Abstract: *This will be a continuation of the
second lecture.

**Note: This talk will be in the
Automorphic forms seminar, from 1:30-2:30 in BRNG B238**

**October 3rd: No Seminar**

*Title: *

*Abstract: *

**October 10th: ****Ziwen Zhu (University of Utah)**

*Title:* **Higher Codimensional Alpha Invariants and
Characterization of**** Projective Spaces.**

*Abstract: *Recent work of Kento Fujita, Yuji Odaka and Chen Jiang
shows that among K-semistable Fano manifolds, the projective
space can becharacterized in terms of either the alpha invariant
or the volume. In this talk, I will generalize the definition of
alpha invariant to arbitrary codimension, and show that we can
characterize projective spaces among all K-semistable Fano
manifolds in terms of higher codimensional alpha invariants.
This result also demonstrates the relation between alpha
invariants and volumes in the characterization problem of
projective spaces among K-semistable Fano manifolds.

**October 17th: **

*Title: *

*Abstract: *

**October 24th: Yordanka Kovacheva
(University of Chicago)**
*Title: ***Intersection pairing of cycles and biextensions**

*Abstract: *We study the intersection of two cycles on a variety
in a situation similar to the Bloch-Beilinson height pairing and
Arakelov theory. The main question we answer is as follows. For
a fixed cycle, find conditions on it, such that whenever we pair
it with two rationally equivalent cycles (with possible multiple
equivalences), we get the same equivalence between the images of
the pairing. This question relates to the question of a
biextension, associated to a paring of cycles. In particular, we
show that Bloch's biextension of homologically trivial cycles
cannot be extended to a biextension of numerically trivial
cycles. As part of the proof we give an explicit expression of
the Suslin-Voevodsky's isomorphism.

**October 31st: **

*Title: *

*Abstract: *

**November 7th: Donu Arapura (Purdue
University)**

*Title: ***Cohomology of local systems on the moduli space
of abelian varieties**

*Abstract: *In
this expository talk I want to explain the Faltings-Chai method
for computing the cohomology of local systems on the above
moduli spaces. The answer is expressed in terms of the
cohomology of certain vector bundles over toroidal
compactifications. It has the advantage over some alternative
methods of giving some information on the mixed Hodge structure.

**November 14th: Michael Groechenig
(University of Toronto)**

*Title: ***De Rham epsilon lines and the epsilon connection**

*Abstract: *De Rham epsilon lines for holonomic D-modules on
curves were introduced by Deligne and Beilinson-Bloch-Esnault.
This formalism includes a product formula, expressing the
determinant of cohomology of a holonomic D-module as a tensor
product of the epsilon lines computed with respect to a non-zero
rational 1-form. Patel generalised the theory of de Rham epsilon
factors to arbitrary dimensions. A curious feature of BBEÕs
1-dimensional theory, is the epsilon connection which appears
when studying the variation of the epsilon lines on the space of
non-zero 1-forms. In this talk I will explain how properties of
algebraic K-theory yield a conjectural candidate for the epsilon
connection in arbitrary dimensions.

November 28th: Linquan Ma (Purdue University)
*Title: *

*Abstract: *

**December 5th: David Hansen
(University of Notre Dame)**

*Title: *

*Abstract: *

**December 12th:**

*Title: *

*Abstract: *

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