Seminars & Colloquia

2018-01
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2018-02
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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

Using elliptic regularity results, we construct for every starting point, weak solutions to SDEs in R^d with Sobolev diffusion and locally integrable drift coefficient up to their explosion times. Subsequently, we develop non-explosion criteria which allow for linear growth, singularities of the drift coefficient inside an arbitrarily large compact set, and an interplay between the drift and the diffusion coefficient. Moreover, we show strict irreducibility of the solution, which by construction is a strong Markov process with continuous sample paths on the one-point compactification of R^d. Joint work with Haesung Lee 

Host: 폴정     English     2017-11-30 11:22:15
We study localization occurring during high-speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition among Hadamard instability (caused by softening response) and the stabilizing effects of strain-rate hardening.  We consider a hyperbolic-parabolic system that expresses the above mechanism and construct self-similar solutions of localizing type that arise as the outcome of the above competition.
The existence of self-similar solutions is turned, via a series of transformations, into a problem of constructing a heteroclinic orbit for an induced dynamical system. The dynamical system is four-dimensional but has a fast-slow structure with respect to a small parameter capturing the strength of strain-rate hardening. Geometric singular perturbation theory is applied to construct the heteroclinic orbit as a transversal intersection of two invariant manifolds in the phase space. The recognized orbit is numerically captured as well. This is to numerically capture a saddle-saddle connection in the phase space. Method of continuation via software package AUTO is employed in the computation.
Host: 김용정     To be announced     2018-01-15 16:14:28

A chordless cycle in a graph G is an induced subgraph of G which is a cycle of length at least four. We prove that the Erdős-Pósa property holds for chordless cycles, which resolves the major open question concerning the Erdős-Pósa property. Our proof for chordless cycles is constructive: in polynomial time, one can find either k+1 vertex-disjoint chordless cycles, or c k^2 log k vertices hitting every chordless cycle for some constant c. It immediately implies an approximation algorithm of factor O(OPT log OPT) for Chordal Vertex Deletion. We complement our main result by showing that chordless cycles of length at least ℓ for any fixed ℓ≥ 5 do not have the Erdős-Pósa property. 

 

 

Host: 엄상일     To be announced     2018-01-05 11:33:32
Abstract: We discuss optimal transport maps between non-convex domains.
In the convex cases, an optimal map is the gradient of a potential function. Moreover, the potential function is a solution to a Monge-Ampere equation. 
In the general non-convex case, the map is a diffeomorphism between subsets of given domain, and the complements of the subsets are measure zero.
Then, the complements can be considered as free boundaries of the potential function. In this talk, we discuss how to apply the well-developed theory in free boundary problems for Monge-Ampere equations to this optimal transport maps.
Host: 이용남     Korean English if it is requested     2018-01-08 10:18:39

We prove that a class of graphs obtained by gluing complete multipartite graphs in a tree-like way satisfies a conjecture of Kohayakawa, Nagle, Rödl, and Schacht on random-like counts for small graphs in locally dense graphs. This implies an approximate version of the conjecture for graphs with bounded tree-width. We also prove an analogous result for odd cycles instead of complete multipartite graphs.

The proof uses a general information theoretic method to prove graph homomorphism inequalities for tree-like structured graphs, which may be of independent interest.
Host: 엄상일     To be announced     2018-01-02 09:42:58

I will explain some topics on positivity of line bundles in my research. I am planning to talk about syzygies on abelian surfaces, dual defects of toric varieties, and a relation between Okounkov bodies and Seshadri constants. 

Host: 이용남     English     2017-12-19 08:51:09

I will explain some topics on positivity of line bundles in my research. I am planning to talk about syzygies on abelian surfaces, dual defects of toric varieties, and a relation between Okounkov bodies and Seshadri constants. 

Host: 이용남     English     2017-12-19 08:52:13

I will explain some topics on positivity of line bundles in my research. I am planning to talk about syzygies on abelian surfaces, dual defects of toric varieties, and a relation between Okounkov bodies and Seshadri constants. 

Host: 이용남     English     2017-12-19 08:47:05

Okounkov bodies have become a very interesting and useful tool to understand the positivity of divisors. Although the Okounkov body carries rich positivity data of a divisor, it only provides information near a single point. In this talk, we introduce a new convex body of a divisor that is effective in handling the positivity theory in a multi-point setting. We study its various properties, and observe local positivity data via this convex body.

Host: 이용남     English     2017-12-19 08:48:24

I will explain our recent progress on the construction of exceptional vector bundles on surfaces when they admit Q-Gorestein degenerations to singularities of class T_d. This is a generalization of the result of Hacking who has studied the case d=1. We give the construction of block(=completely orthogonal exceptional collection) of length d when d>1. If the underlying spaces are del Pezzo surfaces, then our construction explains the paralleism between toric degenerations and three block collections in derived categories.

Host: 이용남     English     2017-12-19 08:49:50