Friday, May 7, 2021

2021-05-14 / 16:00 ~ 17:00

by 홍영훈(중앙대)

For the mass-critical/supercritical pseudo-relativistic nonlinear Schrödinger equation, Bellazzini, Georgiev and Visciglia constructed a class of stationary solutions as local energy minimizers under an additional kinetic energy constraint, and they showed the orbital stability of the energy minimizer manifold. In this talk, by proving its local uniqueness, we show the orbital stability of the solitary wave, not that of the energy minimizer set. The key new aspect is reformulation of the variational problem in the non-relativistic regime, which is, we think, more natural because the proof heavily relies on the sub-critical nature of the limiting model. By this approach, the meaning of the additional constraint is clarified, a more suitable Gagliardo-Nirenberg inequality is introduced, and the non-relativistic limit is proved. Finally, using the non-relativistic limit, we obtain the local uniqueness and the non-degeneracy of the minimizer. This talk is based on joint work with Sangdon Jin.

2021-05-11 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - Discrete Math:

by ()

A signed graph is a graph in which each edge has a positive or negative sign. Calling two graphs switch equivalent if one can get from one to the other by the iteration of the local action of switching all signs on edges incident to a given vertex, we say that there is a switch homomorphism from a signed graph $G$ to a signed graph $H$ if there is a sign preserving homomorphism from $G’$ to $H$ for some graph $G’$ that is switch equivalent to $G$. By reductions to CSP this problem, and its list version, are known to be either polynomial time solvable or NP-complete, depending on $H$. Recently those signed graphs $H$ for which the switch homomorphism problem is in $P$ were characterised. Such a characterisation is yet unknown for the list version of the problem. We talk about recent work towards such a characterisation and about how these problems fit in with bigger questions that still remain around the recent CSP dichotomy theorem.

2021-05-14 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 현동훈(서울대학교 수리과학부)

다중관점기하학(multiple view geometry)에서는 카메라 관점의 변화에 따라 피사체의 영상이 어떻게 변화하는 지를 분석하고, 여러 관점에서 얻은 2차원 영상으로부터 3차원 모델을 재구성하는 기법을 연구한다. 본 강연에서는 다중관점기하학의 기본적인 개념과 테크닉을 설명하고, 이를 의료영상, 자율주행, 스마트헬스케어 등 다양한 산업분야에 적용하는 것에 대하여 소개한다.

2021-05-07 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 대수기하학: Introduction to infinity-categories VI

by 조창연(QSMS Seoul National University)

This is part VI of the lectures on infinity-categories. I'll keep talking about the simplicial nerve construction in contrast to the ordinary nerve functor. To finish off this whole series, some overview of the theory of infinity-categories will be given, including how similar and different it is to the ordinary category theory.

2021-05-13 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 박사학위심사: 고차 시컨트 다양체의 마트료시카 구조와 일반화된 브로노프스키 추측

by 최준호(KAIST)

심사위원장: 곽시종, 심사위원: 이용남, 백상훈, 박의성(고려대 수학과), 박진형(서강대 수학과)

2021-05-07 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Motivic homotopy theory of logarithmic schemes I

by Doosung Park(University of Zürich, Switzerland)

Morel and Voevodsky constructed the A^1-motivic homotopy category SH(k). One purpose of motivic homotopy theory is to incorporate various cohomology theories into a single framework so that one can discuss relations between cohomology theories more efficiently. However, there are still lots of non A^1-invariant cohomology theories, e.g. Hodge cohomology and topological cyclic homology. There is no way to represent these in SH(k). In the first talk, I will explain the construction of logDM^{eff}(k) for a perfect field k, which is strictly larger than Voevodsky's triangulated categories of motives DM^{eff}(k) because Hodge cohomology is representable in logDM^{eff}(k). This work is joint with Federico Binda and Paul Arne Østvær.

2021-05-12 / 15:30 ~ 16:30

학과 세미나/콜로퀴엄 - 정수론:

by Joachim K¨onig()

Let G be a finite group. The minimal ramification problem famously asks about the minimal number µ(G) of ramified primes in any Galois extension of Q with group G. A conjecture due to Boston and Markin predicts the value of µ(G). I will report on recent progress on this problem, as well as several other problems which may be described as minimal ramification problems in a wider sense, notably: what is the smallest number k = k(G) such that there exists a G-extension of Q with discriminant not divisible by any (k + 1)-th power?, and: what is the smallest number m = m(G) such that there exists a G-extension of Q with all ramification indices dividing m? Apart from partial results over Q, I will present function field analogs. (If you would like to join the seminar, contact Bo-Hae Im to get the zoom link.)

2021-05-07 / 10:30 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by ()

The standard machine learning paradigm optimizing average-case performance performs poorly under distributional shift. For example, image classifiers have low accuracy on underrepresented demographic groups, and their performance degrades significantly on domains that are different from what the model was trained on. We develop and analyze a distributionally robust stochastic optimization (DRO) framework over shifts in the data-generating distribution. Our procedure efficiently optimizes the worst-case performance, and guarantees a uniform level of performance over subpopulations. We characterize the trade-off between distributional robustness and sample complexity, and prove that our procedure achieves this optimal trade-off. Empirically, our procedure improves tail performance, and maintains good performance on subpopulations even over time.

2021-05-14 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Infinitesimal regulators

by Sinan Ünver(Koc University, Istanbul, Turkey)

We will describe a construction of infinitesimal invariants of thickened one dimensional cycles in three dimensional space, which are the simplest cycles that are not in the Milnor range. This is an analog of a construction of J. Park in the context of additive Chow groups. The construction allows us to prove the infinitesimal version of the strong reciprocity conjecture for thickenings of all orders. Classical analogs of our invariants are based on the dilogarithm function and our invariant could be seen as their infinitesimal version. Despite this analogy, the infinitesimal version cannot be obtained from their classical counterparts through a limiting process.

Events for the 취소된 행사 포함