ASARC Regular Seminar Fall and Winter 2009
We generally meet at Room 1409, Natural Sciences (E6-1) from 4:30PM to 5:30PM, Tuesdays, unless specified otherwise. Beginning Fall 2009, we plan to have seminars every week, if possible. If you would like to recommend speakers, please contact Jinhyun Park at jinhyunZZ@mathsciZZ.kaist.ac.kr (remove ZZ).

1. On September 1st, 2009, Kuerak Chung from KIAS will speak on Canonical delooping machine. Here is the abstract:
   How can we recognize mapping spaces from other spaces? We can use natural operations on them as a universal algebra and we may use this to recognize mapping spaces up to weak equivalence. In the case of mapping spaces, n-fold loop spaces, of pointed maps from the n-sphere, we can show that any space X having such a universal algebra structure is weakly equivalent to the n-fold loop space of B(X), delooping space. I will explain its categorical frame so that it may be applicable to other problems, e.g.,moduli spaces, deformation problems etc..
   
   
2. On September 8th, 2009, No seminar.
   
   
3. On September 15th, 2009, Jinhyun Park from KAIST will speak on Introduction to higher Chow groups : an analogue of singular homology for algebraic varieties Here is the abstract:
   This is an introductory talk on higher Chow groups. It will be understandable for graduate students in algebra and geometry. A Chow group is used by various mathematicians in various fields. For complex geometers, Chow groups are the place where the fundamental cohomology classes originate. For number theorists, Chow groups are equal to the ideal classes groups. For some people, the group of line bundles, so called the Picard groups, is given by this. For those work in Riemann surfaces, a subgroup of a Chow group is named the Jacobian variety. I will explain how this object is related to these, and how one can see this object as an analogue of singular homology for algebraic varieties.
   
   
4. On September 22th, 2009, Donghoon Hyeon from Postech will speak on Compact moduli space of commuting nilpotents. Here is the abstract:
   I will construct a moduli space of $q$ pairwise commuting nilpotents of $\mathfrak gl_d$ and give a natural compactification of it for the case $d = 3$.
   
   
5. On September 29th, 2009, Kentaro Ihara from Postech (PMI) will speak on Derivations and Automorphisms on the algebra of noncommutative power series. Here is the abstract:
   We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim in the talk is the explicit description of the automorphisms which are corresponding to the derivations via exponential map. (Note: Dr. Kentaro Ihara wrote the famous Compositio Math. paper with. Don Zagier on multi-zeta function, and number theorists are particularly welcomed to come.)
   
   
6. On October 6th, 2009, Sukmoon Huh from KIAS will speak on Vector bundles on a smooth quadric surface. Here is the abstract:
   It is a classical result due to Grothendieck that every vector bundles on the projective line is a direct sum of line bundles. Using this, there have been many attempts to understand vector bundles on the projective space, for example, by W.Barth and K.Hulek. In this talk, we introduce this idea in the case of smooth quadric surface. In the first half of the talk, we explain the basic notions in the algebraic geometry that will be used in the talk and recall several results on the projective space. In the second, we introduce the notion of jumping conics and prove that the set of jumping conics associated to a stable vector bundles on a smooth quadric surface forms a hypersurface in a 3-dimensional projective space. Using this, we explicitly describe the moduli spaces of stable vector bundles in two cases and see how these description can be applied to prove other classical results.
   
   
7. On October 13th, 2009, Shintaro Kuroki from KAIST (ASARC) will speak on Equivariant cohomology determines hypertoric manifold. Here is the abstract:
   The hypertoric manifold is defined by the hyperKahler analogue of symplectic toric manifolds. In usually, the toric manifold is a 2n-dim manifold with an n-dim torus action. On the other hand, the hypertoric manifold is a 4n-dim manifold with an n-dim torus action. However, we can apply the method of toric geometry or toric topology to analyze the hypertoric manifolds. In this talk, I introduce the hypertoric manifold and the method to analyze it from topological point of view, and prove that its equivariant diffeomorphism type is determined by the equivariant cohomology.
   
   
8. On October 20th, 2009, No seminar. Midterm exam week.
   
   
9. On October 27th, 2009, at E6-1 Room 2413, Junho Lee from KAIST (ASARC) will speak on Waring's problem for polynomials. Here is the abstract:
   In 1770, Lagrange proved that every nonnegative integer is the sum of four squares. Waring's problem is the generalization of Lagrange's theorem. More generally, we will introduce Waring's problem for polynomials and talk about the asymptotic order of a set of some polynomials.
   
   
10. On November 3rd, 2009, Heesook Park from KAIST (ASARC) will speak on Free groups in the second bounded cohomology. Here is the abstract:
    The second bounded cohomology of an amenable group is zero. On the other hand, the second bounded cohomology of a free group of rank greater than 1 is infinite dimensional as a vector space over R. Also it is known that no group which contains a free group on two generators can be amenable. It was conjectured that the second bounded cohomology of a discrete group is zero or infinite dimensional. Though it is shown that this conjecture is not true in general, but it holds for a group that has no nontrivial perfect normal subgroup, in particular, for a residually solvable group. So it seems natural to ask if there is some relationship between free groups and the dimension of the second bounded cohomology. In this talk, we prove that the second bounded cohomology of a residually solvable group G is infinite dimensional if and only if there is a finite ordinal n such that its n-th commutator subgroup G^(n) is free of rank greater than 1.
    
    
11. On November 12th (Thursday), 2009, 2:30PM - 3:30PM, Shuji Saito from the University of Tokyo will speak on A counter example of a conjecture of Bloch-Kato and infinite torsion in zero-cycles over a local field.
    
    Note: He will give also a colloquium talk Cohomological Hasse principle, higher higher class field theory, and special values of zeta functions from 4:30PM to 5:30PM at Room 1501, E6-1.
    
    
12. On November 17th, 2009, Soon Yi Kang from KAIST (ASARC) will speak on Mock modular forms with small half integral weights. Here is the abstract:
    A mock modular form is the holomprphic part of a harmonic weak Maass form. In particular, Ramanujan's mock theta function and the generating series of the traces of singular moduli are mock modular forms of weights 1/2 and 3/2, respectively. In this talk, we will survey some recent progress in these mock modular forms.
    
    
13. On November 24th, 2009, No Seminar due to ASARC 3rd year report presentation.
    
    
14. On December 1st, 2009, Kiryong Chung from Seoul National University will speak on Hilbert scheme of rational cubic curves via stable maps. Here is the abstract:
    The space of smooth rational cubic curves in projective space $\mathbb{P}^r$ ($r\geq 3$) is a smooth quasi-projective variety, which gives us an open subset of the corresponding Hilbert scheme, the moduli space of stable maps, or the moduli space of stable sheaves. By taking its closure, we obtain three compactifications $\mathbf{H}$, $\mathbf{M}$, and $\mathbf{S}$ respectively. In this talk, we compare these compactifications. First, we prove that $\mathbf{H}$ is the blow-up of $\mathbf{S}$ along a smooth subvariety parameterizing planar stable sheaves. Next we prove that $\mathbf{S}$ is obtained from $\mathbf{M}$ by three blow-ups followed by three blow-downs and the centers are described explicitly. Using this, we calculate the cohomology of $\mathbf{S}$.
    
    
15. On December 8th, 2009, from 3:30PM to 4:30PM, Jungpil Park from KAIST (ASARC) will speak on Almost reverse lexicographic ideals. Here is the abstract:
    We introduce almost reverse lexicographic ideals in a polynomial ring over a field of arbitrary characteristic.Then we give a criterion for a given sequence of nonnegative integers to be the Hilbert function of an almost reverse lexicographic ideal in the polynomial ring.
    
    
16. On December 8th, 2009, Kangjin Han from KAIST will speak on On the behavior of syzygies of a projective scheme under inner projection. Here is the abstract:
    First, we will review syzygies and some related notions of a scheme $X$ in the projective space $\mathbb{P}^N$. We also consider how do the linear syzygies of $X$ behave under inner projection, i.e. the projection taking its center inside the original scheme. This is a natural 'projection' analogue to 'Restricting linear syzygies' due to D. Eisenbud, M. Green, K. Hulek, and S. Popescu which tells us some infomation about linear syzygies in case of taking linear sections. Finally, we will end this talk by considering some applications of it.
    
    
17. On December 15th, 2009, No seminar. Final exam week.
    
    
18. On December 22nd, 2009, at Room 2411, Tullia Dymarz from Yale University will speak on Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated groups. Here is the abstract:
    In geometric group theory we are interested in studying finitely generated groups as geometric objects. A finitely generated group can be considered as a metric space when endowed with a `word metric'. This word metric depends on the choice of generating set but all such metrics are bilipschitz equivalent. Usually, however, finitely generated groups are studied up to `quasi-isometry'. This is a coarse version of bilipschitz equivalence that allows one to study these groups by studying proper geodesic metric spaces on which they act. I will give examples that show that these two notions are not equivalent. The proof will give a flavor of some of the various theorems and techniques used geometric group theory.
    
    
19. On December 29th, 2009, No seminar
    
20. On January 5th, 2010, No seminar
    
21. On January 12th, 2010, No seminar
    
22. On January 19th, 2010, No seminar
    
23. On January 26th, 2010, No seminar
    

Past/Future seminars : [Spr/Sum 2009][Spr/Sum 2010]