Thursday, May 6, 2021

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

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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.

2021-05-06 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - 대수기하학:

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Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties. We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese, and consider various techniques to provide equations on the secants. In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

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:

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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.

2021-05-06 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Sublinear expander and embeddings sparse graphs

by 홍 리우(워릭 대학교)

A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory, including e.g. the odd cycle problem of Erdos and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some of these developments.

Events for the 취소된 행사 포함