* 강연순서

박종도 Jong-Do Park (경희대학교)

- Title: Explicit forms and zeros of the Bergman kernel function 
- Abstract:  The Bergman kernel function is a reproducing kernel for the Hilbert space of square-integrable holomorphic functions on a domain in $C^n$. It has been used as one of the main tools to study bounded domains in several complex variables. In this talk, we explain the methods of computing an explicit formula of the Bergman kernel function for various domains. As an application, we can determine whether the Bergman kernel has zeroes.

박희상 Heesang Park (건국대학교)

- Title: Symplectic fillings of quotient surface singularities

- Abstract: In this talk, I will introduce recent results on symplectic fillings of quotient surface singularities. That is, I will show that there is a one-to-one correspondence between minimal symplectic fillings and Milnor fibers associated to a quotient surface singularity, and I present explicit ways to compare them. This is joint work with Jongil Park, Dongsoo Shin and Giancarlo Urzua.

서검교 Keomkyo Seo (숙명여자대학교)

- Title: p-Laplacian operator and rigidity of complete minimal submanifolds

- Abstract: A complete minimal submanifold in a Riemannian manifold satisfies a fundamental second-order elliptic inequality which is called Simons's inequality. This inequality with additional geometric assumption enables us to find rigidity of such submanifolds in many cases. In this talk, we obtain the p-fundamental tone estimates of minimal submanifolds with certain conditions on the norm of the second fundamental form. Moreover, we discuss the connectedness at infinity of complete submanifolds by using the theory of p-harmonic function. For lower-dimensional cases, we are able to prove a rigidity of complete noncompact hypersurface without assuming minimality of the hypersurface.

오영탁 Young-Tak Oh (서강대학교)

- Title: The universal deformation of the Witt ring scheme

- Abstract: Witt vectors play an important role in several branches of mathematics. In this talk, I will introduce the universal deformation over reduced base rings of the Witt ring scheme enhanced by a Frobenius lift and Verschiebung. It agrees with a q-deformation introduced earlier by Christian Lenart and myself. I  also give a simpler description for this. This is joint work with Christopher Deninger. 

김준일 Joonil Kim (연세대학교)

- Title: Oscillatory Integrals over Global Domains.

- Abstract: For a class of oscillatory integrals  with phases $P$ over global domains $D$,  we establish a criterion to determine the convergence of these integrals and asymptotic expansions when they converge.  Next, we discuss about some applications to the problems of PDE, Number theory and Geometry.

이정연 Jungyun Lee (이화여자대학교)

- Title: Nonvanishing of Hecke L-functions for C.M fields at central point

- Abstract: We study relation between an interval in which Hecke L-function does not vanish and the unit rank of a number field. We prove there are infinitely many ray class character chi of a C.M field K such that  L_K(1/2, chi) is not zero. 

김현규 Hyun Kyu Kim (이화여자대학교)

- Title: Quantization of Teichmüller spaces

- Abstract: Quantization of Teichmüller space of a Riemann surface was first established in 1990's, as an approach to 2+1 dimensional quantum gravity in mathematical physics. It is a framework to assign to each smooth function on the Teichmüller space a self-adjoint operator on a Hilbert space, so that the operator commutator contains information on Poisson structure on the Teichmüller space. In this talk, I will introduce the basic setting, and mention its relationship to quantum gravity, 2d conformal field theory, mapping class group representations, 3-manifold invariant, and explain my works if time allows.

안재만 Jaeman Ahn (공주대학교)

- Title: The Degree-complexity of Curves and Surface

- Abstract: D.Bayer and D.Mumford introduced the degree complexity of a projective scheme X for the given term order as the maximal degree of the reduced Groebner basis of its defining ideal. The degree complexity depends on the choice of coordinates and on the monomial term orders. It is well-known that the degree complexity m(X) with respect to the graded reverse lexicographic order is equal to the Castelnuovo-Mumford regularity in generic coordinates. However, much less is known about the degree complexity M(X) with respect to the graded lexicographic order. We see from experience that the lexicographic Groebner basis tends to be extremely complicated and M(X) can climb to much higher degrees than m(X). In this talk, we will show the results on the degree complexity of low-dimensional smooth varieties with respect to the graded lexicographic order. Our main results give a relationship between the complexity of algebraic computations with the ideal of a smooth variety and the geometry of its generic projection. We use M. Green’s partial elimination ideals and careful work with Hilbert functions to achieve the result. We also provide some illuminating examples of our results via calculations done with Macaulay 2.