We generally meet at

- On June 12th, 2009 (Fri), from 16:00 to 17:00,
**Hee Jung Kim**from Louisiana State University will speak on Here is the abstract:*Knotting surfaces in 4-manifolds by twist-rim surgery.*

In this talk, we introduce a surgery operation to construct surfaces in simply-connected 4-manifolds with non simply-connected complements, that are topologically equivalent but not smoothly. This construction is based on the modification of "rim surgery" introduced by Fintushel and Stern. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In the case, we produce infinitely many smoothly inequivalent surfaces that are equivalent up to smooth s-cobordism and hence are topologically equivalent for good groups.

Host : Dong Yup Suh

- On June 19th, 2009 (Fri), from 16:30 to 17:30,
**Byungchul Cha**from Muhlenberg College will speak on Here is the abstract:*Linear independence of zeros of L-functions.*

We study Linear Independence (LI) assumption (sometimes called Grand Simplicity Hypothesis), which says that the ordinates of nontrivial zeros of zeta/L-functions do not satisfy any linear relation over rationals. LI has been used to study certain problems in analytic number theory, including the work of Rubinstein and Sarnak on prime number races and Ng on the growth rate of the summatory function of the Moebius function. We review the work of Rubinstein and Sarnak and that of Ng and consider the counterparts of their results in the function field setting.

Host : Sunghan Bae

- On June 22nd, 2009 (Mon), from 10:30 to 11:30, at Room 2411,
**Bernd Sturmfels**from the University of California at Berkeley will give his first (out of 2) talk on Here is the abstract:*An invitation to Algebraic Statistics*

Algebraic statistics is a maturing discipline whose main focus is the study of statistical inference using tools from algebraic geometry and computational algebra. Its underlying idea is that statistical models can be viewed as algebraic varieties. We discuss some of the basics in this field, with emphasis on topics covered in the speaker's recent book with Mathias Drton and Seth Sullivant, titled "Lectures on Algebraic Statistics".

- On June 22nd, 2009 (Mon), from 13:00 to 14:00, at Room 2411
**Bernd Sturmfelds**from the University of California at Berkeley will give his second (out of 2) talk on Here is the abstract:*Convex Algebraic Geometry*

Convex algebraic geometry is concerned with emerging interactions between convex optimization and algebraic geometry. A primary focus lies on the geometric underpinnings of semidefinite programming. This lecture offers a self-contained introduction. Starting with elementary questions concerning multi focal ellipses in the plane, we move on to discuss singularities and projections of spectrahedra, and new algorithms for real algebraic varieties.

- On July 9th, 2009 (Thu), from 16:00 to 17:00,
**Su Hu**from Tsinghua University will speak on Here is the abstract:*A note on global units and local units of function fields.*

Let K be a geometric Galois extension of the rational function field k=F_q (t). Let O_k be the integral closure of k=F_q[t] in K. Let U_k be the group of units of O_k and U_v be the group of local units of K_v. In this talk, we will consider the following problem: whether there exists a finite place P of F_q (t) such that the natural map U_K/U_K^d \to \rpdo_{v/P} U_v/U_v ^d is injective, where d>1 is a factor of q-1.

Host: Sunghan Bae

- On July 10th, 2009 (Fri) from 15:00 -16:00,
**Linsheng Yin**from Tsinghua University will speak on Here is the abstract:*Modular forms of weight one produced from Galois representations.*

We construct explicitly a variety of modular forms of weight 1 by computing the Artin L-functions of a class of non-abelian Galois number fields. This is a joint work with S. Bae and Y. Hu.

Host: Sunghan Bae

- On July 21st, 2009 (Tue),
**Abhishek Banerjee**from Johns Hopkins University/IHES will give his first (out of 3) talk on Here is the abstract:*Bivariant Chow groups and Motivic Filtrations (1).*

Our main objective is to extend the motivic filtration of Shuji Saito to bivariant Chow groups. We start by defining a cycle class map from the bivariant chow groups to the bivariant cohomology groups. The cycle class map enables us to define a filtration on the bivariant chow groups; in fact, we will have two possible definitions for this filtration, which we shall show later to be equivalent.

- On July 23rd, 2009 (Thu),
**Abhishek Banerjee**from Johns Hopkins University/IHES will give his second (out of 3) talk on Here is the abstract:*Bivariant Chow groups and Motivic Filtrations (2).*

In the second talk, we will define, using these ideas and "higher refined Gysin morphisms", objects that act as higher bivariant Chow groups.

- On July 27th, 2009 (Mon),
**Abhishek Banerjee**from Johns Hopkins University/IHES will give his last talk on Here is the abstract:*Hochschild Homology of Sheaves via Fibred Categories.*

We shall introduce a definition for Hochschild homology of a separated presheaf/sheaf of abelian groups on a small Grothendieck site C = (C, \tau ). The starting point is the well known one to one correspondence between presheaves on a category C and categories fibred in sets over C (due to SGA1). The method can also be extended to define Hochschild homology for a separated presheaf/sheaf of sets.

- On July 28th, 2009,
**Sug Woo Shin**from the University of Chicago will speak on Here is the abstract:*Modular forms and Galois representations.*

The mysterious relationship between modular forms (or more generally automorphic representations) and Galois representations has become one of the most interesting and fruitful research topic since more than 50 years ago. I will review some of the past success and report on some of the recent development.

- On August 4th, 2009, from 3:00PM to 4:00PM,
**Kazuma Morita**from Hokkaido University will give his first lecture (out of 3) on Here is the abstract:*p-adic Hodge theory: l-adic representations vs p-adic representations.*

This is an introductory lecture series on p-adic Hodge theory.

- On August 4th, 2009, from 4:30PM to 5:30PM,
**Kazuma Morita**from Hokkaido University will give his second lecture (out of 3) on*p-adic Hodge theory: Fontaine rings and basic facts of p-adic representations.*

- On August 5th, 2009, from 4:30PM to 5:30PM,
**Kazuma Morita**from Hokkaido University will give his last lecture on*p-adic Hodge theory: Comparison isomorphisms (etale cohomology vs crystalline cohomology).*

- On August 24th, 2009, Monday, from 4:30PM to 5:30PM,
**Dano Kim**from the University of Chicago will speak on Here is the abstract:*Adjoint section rings.*

Given a line bundle L on a projective variety, it is natural to consider the graded section ring R(L) given by all sections of multiples of L. We call R(L) a complete section ring. Then we define a general section ring to be a subring of R(L). We will define a certain class of (not necessarily complete) section rings associated to adjoint line bundles, which contains the usual canonical rings. We will discuss its properties and why we need those rings.