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Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

서울대학교 물리천문학부 COLLOQUIUM

실험실에서는 언제나 아직까지 인간이 경험하지 못한 영역을 탐구하고 있습니다. 예를 들어 CERN의 LHC는 지금까지 인간이 경험하지 못한 높은 에너지 상태를 만드는 실험입니다. 이와 같은 실험을 더 높은 에너지를 추구하는 (Energy Frontier)이라고 합니다. 최근 물리학자들은 상호작용이 작아서 좀체 관찰하기 어려운 사건에 관심이 많아졌습니다. 이런 사건을 탐구하려는 실험을 더 많은 사건을 추구하는 (Intensity Frontier) 실험이라고 합니다. 본 강연에서는 이러한 Intensity Frontier Physics 실험을 통해 어떤 물리학을 탐구하는지 알아보고, 앞으로 CERN에서 준비중인 새로운 intensity frontier 실험인 SHiP을 소개하겠습니다.

서울대학교 물리학과 세미나

Publication of research, including peer-review, is a vital and integral part of the scientific process. It remains the best method for disseminating and validating new knowledge in an open manner. However, for many researchers, the process can be unclear and somewhat daunting.Aimed at PhD students, post-docs and other early career researchers, Dr Thomas Miller will be describing the publication process and offering hints and tips on how to get your work published. He will also outline what IOP Publishing and JPhysD can do to promote your research and give your work the most visibility possible. This will be followed by a short session, where he will happy to answer any questions you might have about publishing your research.Dr Thomas Miller is Publisher for Journal of Physics D: Applied Physics. He has worked at IOP Publishing for more than 13 years and has been a publisher for more than 10. He has worked on many titles including Nanotechnology, Superconductor Science and Technology and most recently Publisher for Journal of Physics D: Applied Physics. Over 50 years old, Journal of Physics D: Applied Physics is a major international journal reporting significant new results in all aspects of applied physics research. We welcome experimental, computational (including simulation and modelling) and theoretical studies of applied physics. It has an Impact Factor of 2.373 and average receipt to first decision time of 42 days.

한국고등과학원 세미나

I would like to discuss a triangle of ideas in one-dimensional manifold diffeomorphism groups, which consist of analysis, dynamics and group theory. I will first state and prove the Slow Progress Lemma, which justifies a meta-statement “smoother diffeomorphisms are slower”. This lemma connects analysis to dynamics. Then I will illustrate how to justify another statement “slower representations have larger kernels”, connecting dynamics to group theory. Joint work with Thomas Koberda.

한국고등과학원 세미나

Consider an object of “dimension n” and the set of its subobjects of “dimension i”. For example, we might consider a polytope and its faces, or a partition and its subpartitions. Often the number of subobjects of “dimension i” is less than or equal to the number of objects of “dimension n-i”, for i between 0 and n/2. I will explain why this phenomenon is a shadow of the hard Lefschezt theorem. I will then explain the very interesting case of Coxeter group elements and Bruhat order, and try to describe what we do and don’t know.

한국고등과학원 세미나

Diffusion equations is one of most famous partial differential equations (PDEs). Lots of generalized diffusion equations have appeared on the basis of scientific meaning. For instance, degenerate diffusion equations appeared long time ago due to observation of stopping diffusion intermittently. In this talk, we mostly introduce the reason why we study generalized diffusion equations far beyond the heat equation and we are going to discuss the change of regularity of solutions depending on the degeneracy of diffusion if time is allowed.

한국고등과학원 세미나

Amdeberhan conjectured that the number of $(s, s + 2)$-core partitions with distinct parts for an odd integer $s$ is $2^{s-1}$. This conjecture was first proved by Yan, Qin, Jin, and Zhou, then subsequently by Zaleski and Zeilberger. Since the formula for the number of such core partitions is so simple one can hope for a bijective proof. We give the first direct bijective proof of this fact by establishing a bijection between the set of $(s, s + 2)$-core partitions with distinct parts and a set of lattice paths.

한국고등과학원 세미나

I present and discuss new results concerning the deformation theory of compact complex manifolds that are non-isotrivially fibered in irreducible holomorphic symplectic manifolds. I exemplify these results with twistor spaces.

KAIST 수리과학과 세미나

In part I, we present a short overview of typical data science (DS) and machine learning (ML) projects in Silicon Valley tech companies, using problems in transportation science and online advertising industry as examples. In part II, we present a few ways statisticians can contribute to the success of such projects, and how they can be more equipped to make positive impacts. In part III, we present a case study in anomaly detection, a massive-scale learning problem that is central to many applications in many businesses and science. We explore some of the challenges including modeling, scaling, methods for assessing and visualizing performance, probability calibration, and automated monitoring.

KAIST Discrete Math 세미나

The infamous Erdős-Szekeres conjecture, posed in 1935, states that the minimum number ES(n) of points on a plane in general position (that is, no three colinear points) that guarantees a subset of n points in convex position is equal to 2(n-2) + 1. Despite many years of effort, the upper bound of ES(n) had not been better than O(4n – o(n)) until Suk proved the groundbreaking result ES(n)≤2n+o(n) in 2016. In this talk, we focus on a variant of this problem by Erdős, Tuza and Valtr regarding the number ETV(a, b, n) of points needed to force either an a-cup, b-cap or a convex n-gon for varying a, b and n. They showed ETV(a, b, n) > \sum_{i=n-b}^{a-2} \binom{n}{i-2} by supplying a set of points with no a-cup, b-cap nor a n-gon of that many number, and conjectured that the inequality cannot be improved. Due to their construction, the conjecture is in fact equivalent to the Erdős-Szekeres conjecture. However, even the simplest equality ETV(4, n, n) = \binom{n+1}{2} + 1, which must be true if the Erdős-Szekeres conjecture is, has not been verified yet. To the best of our knowledge, the bound ETV(4, n, n) ≤ \binom{n + 2}{2} – 1, mentioned by Balko and Valtr in 2015, is currently the best bound known in literature. The talk is divided into two parts. First, we introduce the mentioned works on the Erdős-Szekeres conjecture and observe that the argument of Suk can be directly adapted to prove an improved bound of ETV(a, n, n). Then we show the bound ETV(4, n, n) ≤ \binom{n+2}{2} – C \sqrt{n} for a fixed constant C>0, improving the previously known best bound of Balko and Valtr.

KAIST Discrete Math 세미나

Counting problems on sets of integers with additive constraints have been extensively studied. In contrast, the counting problems for sets with multiplicative constraints remain largely unexplored. In this talk, we will discuss two such recent results, one on primitive sets and the other on multiplicative Sidon sets. Based on joint work with Peter Pach, and with Peter Pach and Richard Palincza.

서울대학교 화학과 세미나

Complex chemical systems, such as living organisms, have highly organized structures based on well designed molecules through dynamic interactions. In contrast, synthetic systems exhibit simpler properites. In this talk, I will specifically focus on rational molecular design principles and the utilizations of such principles for the creation of dynamic and complex artificial chemical systems, possesing new functions that cannot be realized by conventional approaches. Owing to the remarkable progress over the past two decades in supramolecualr chemistry, a variety of complex nanostructures can be designed and tailored through thermodynamic control. Despite recent advances, chemical systems under such thermodynamic control are still short of functionality and complexity comparing to living systems. In order to create dynamic and complex chemical systems that surpass our living matters, non-covalent interactions (supramolecular interactions) should be more precisely controlled and have non-equilibriated states. In this regard, this presentation begins with a rational molecular design strategy for the realization of precise non-covalent polymerization in solution[1], [2]. I believe that this achievement steps forward towards dynamic functional chemical systems. From the second part of my talk, a new class of polymer design capable of forming dynamically crosslinked complex network will be discussed[3]. Multiple distinct crosslinking bonds with different bonding strength exist in the network. Such newly observed network realized unsual mechanical properties such as high stretchability, high toughness and autonmous self-healability, whereas their mechanical responses were similar to those of human skin. Lastly, unprecedented applications in electronic systems will be presented using this new energy dissipating chemical system[4],[5]. Integration of the dynamic chemical system with electronic materials successfully imparts its intrinsic dynamicity to electronics such that mechanically tough and self-healable electronic skins are developed for the first time.

서울대학교 물리학과 세미나

The physical, electronic, mechanical, and chemical connections that materials make to one another and to the outside world are critical. Just as the properties and applications of conventional semiconductor devices depend on these contacts, so do nanomaterials, many nanoscale measurements, and devices of the future. We discuss the important roles that these contacts can play in preserving key transport and other properties. Initial nanoscale connections and measurements guide the path to future opportunities and challenges ahead. Band alignment and minimally disruptive connections are both targets and can be characterized in both experiment and theory. I discuss our initial forays into this area in a number of materials systems.

서울대학교 물리학과 세미나

Renormalization Group (RG) is one of the most powerful tools to investigate interacting quantum many body systems. In condensed matter, scale invariance of electron wave-functions is often emergent, and the RG analysis becomes useful. In this talk, we review the RG analysis in semi-metals and superconductors and introduce recent new results including quantum criticalities with infinite anisotropy and non-Fermi liquid behaviors at topological phase transitions.

KAIST 화학과 세미나

Among fundamental issues in photophysics and photochemistry, charge generation and separation/recombination at material interfaces are a primarily important problem to be studied for high efficiency in photovoltaic application. Organic/inorganic hybrid solar cell (HSC) is one of the future generation photovoltaics where the charge separation takes place near the heterointerface. To unveil physical behavior of hybrid “Frenkel-Wannier exciton” at the organic/inorganic hybrid interface, I focus on a typical semiconducting material combination, gallium arsenide (GaAs) as inorganic absorber and copper phthalocyanine (CuPc) as organic counterpart. Ultrafast charge transport and separation dynamics are studied by using time-resolved two-photon photoemission spectroscopy (TR-2PPE). CuPc/p-GaAs shows hole injection behavior depending on light intensity [1]. In addition, the photo-generated carriers within GaAs exhibit a few different pathways of relaxation and transfer on picosecond time scale time. At the CuPc/p-GaAs interface, a “hybrid charge transfer exciton (HCTE) state” [2] evolves right after the hole injection from GaAs to CuPc. The initial HCTE state splits into relaxed HCTE states and triplet state (T1) in CuPc. The formation of T1 may be applied to a low power LED if the relaxation to HCTE states is blocked [3]. As another example of organic solar cell devices, we compare electron dynamics of ZnPc/C60 and CuPc/C60 interfaces. Control of CuPc molecular plane into lying-down orientation enhances charge separation and interface charge transfer exciton formation. However, actual solar cell performance is influenced largely by charge mobility and crystallinity of the molecules.

KAIST 화학과 세미나

In the past decade, lithium-enriched compounds, Li2MeO3 (Me = Mn4+, Ru4+ etc.), have been extensively studied for high-capacity positive electrode materials of lithium batteries. Although the origin of high reversible capacities was a debatable subject for a long time, recently it has been evidenced that charge compensation is partly achieved by solid-state redox of non-metal anions, i.e., oxide ions (anionic redox),[1] coupled with solid-state redox of transition metal ions (cationic redox), which is the basic theory used for classical lithium/sodium insertion materials. Competition between cationic and anionic redox reactions is often evidenced for the lithium-enriched materials because the energy level of oxygen 2p band is lowered by the presence of excess lithium ions with high ionic characters in the crystal lattice. Reversibility of anionic redox reactions is also influenced by ionic and covalent characters for chemical bonds of transition metal ions.[2, 3] In contrast, when the energy of metal 3d band is low enough than that of oxygen 2p, pure cationic redox is realized even for the lithium-excess system.[4, 5] Moreover, this concept is further extended to sodium battery applications.[6] From these findings, we discuss the stabilization and destabilization mechanisms and material design strategy with the concept of cationic and anionic redox reactions to develop new high-capacity lithium/sodium insertion materials for battery applications.