The MathNet Korea
Information Center for Mathematical Science

### 세미나

Information Center for Mathematical Science

#### 세미나

##### 한국천문연구원 콜로퀴움

The appearance of the first stars and galaxies at the cosmic dawn represents a transformational yet unexplored episode of the Universe's history. I will present the measurement of an absorption feature in the sky-averaged radio spectrum centered at 78 MHz by the EDGES Low-Band experiment. This feature is broadly consistent with the absorption of photons from the microwave background by neutral hydrogen gas in the intergalactic medium at z~17 due to significant star formation about 180 million years after the Big Bang. If independently verified, this measurement could correspond to the signature of the cosmic dawn. However, the large amplitude and sharp profile of the measured feature are in tension with standard physical models. In my talk I will describe the EDGES Low-Band measurement of the radio spectrum over the range 50-100 MHz, which was conducted from the desert of Western Australia, as well as some of the proposed physical implications if the signal is confirmed to be of cosmological origin.

##### KAIST 화학과 세미나

Interactions of peptides and surfactants with biological Interfaces such as cell membranes and skins play a key role in biological processes such as ion and biomolecule transport in cells. In this talk, I will present molecular dynamics (MD) simulation study of three different types of interactions between peptides or surfactants with biological interface. In the first part of my talk, energetic and dynamics of transport of ions and glucose through cyclic peptide nanotubes (CPNs) are addressed. Potential of mean force (PMF) profiles and position-dependent diffusion coefficients of Na+ and K+ are calculated to elucidate the translocation of ions and glucose through CPNs in water and in hydrated DMPC bilayers. The second part focuses on the thermodynamic and structural properties of Gram-negative outer membranes and interactions of CPNs with the outer membranes. In the last part, the micelle formation of a kind of surfactants and interactions of the surfactant micelles with ceramide bilayers, which is a model membrane of skin lipids, are briefly addressed.

##### KAIST 화학과 세미나

The subtleties of structure and bonding in compounds of the rare earths (Group 3 and the lanthanides) and uranium, the heaviest naturally occurring element, are still poorly-understood. However, their complexes can exhibit strong and tuneable Lewis acidity, high and tuneable reduction capacity, and the capacity for rapid ligand exchange reactions. Organometallic compounds of the lanthanides and actinides have shown many interesting small molecule activation reactions, including hydrocarbon C-H bond cleavage, over the last 25 years, and interest is increasing in their activity as catalysts, since the recognition that many rare earths are at least as abundant as iodine, and many are cheap and less toxic than iron. We will show new f-block organometallics that are capable of the reductive activation and functionalisation of CO, CO2, N2, and arenes, even using simple bulky ligands that have been previously overlooked. The dominance of single-electron redox reactivity is a potential drawback they share with the 3d metal catalysts. We will present some dinuclear f-block complexes supported by new platform ligands, and their multiple-electron redox chemistry and catalysis, with a particular focus on cerium and uranium.

##### KAIST 화학과 세미나

Visualization of ultrafast molecular dynamics is one of the ultimate purposes in physical chemistry because it leads to deep understanding of dynamic properties of molecules. A time-resolved (pump- probe) charged particle imaging for gas-phase molecules is one of the powerful approaches for such a purpose. However, there have been several difficulties in existing imaging techniques (e.g., the fixed camera angle and/or low count rate). In order to overcome the above mentioned difficulties and to take high-resolution snapshots of molecules, we developed a new “space-slice” tomographic imaging technique. Some details and performance of our apparatus will be shown in the presentation. By using the apparatus, rotational and vibrational motions of molecules can be visualized as nuclear wave packet dynamics. In our talk, “molecular movies” of the following two important cases will be screened and discussed. (1) Rotational wave packet dynamics of laser-kicked diatomic molecules Rotational wave packet was created upon irradiation of linearly polarized femtosecond laser pulses. The subsequent dynamics was tracked with time-resolved Coulomb explosion imaging. Owing to high-resolution of our imaging setup, we succeeded in observing highly complicated nodal structures, which govern the wavepacket dynamics. From the observed wavepacket, its component (eigenfunction including its sign) can be characterized. (2) Rotational/vibrational wave packet dynamics in molecular clusters Our imaging technique can be also used as a new tool for structural characterization. Nitrogen dimer (N2) 2 is one of the important systems in atmospheric chemistry, however, because of the small permanent dipole, spectroscopic studies are limited. We used femtosecond impulsive Raman pump-Coulomb explosion probe imaging to investigate the structure and dynamics of (N2)2. Observed images show periodic rotational and vibrational motions, from which spectroscopic data can be deduced. The static and dynamic structure of (N2) 2, which is governed by the weak intermolecular interaction, is discussed for the first time.

##### KAIST 화학과 세미나

Aromatic skeletons are usually considered as being unbreakable due to their aromatic resonance energy. Compared with exocyclic modifications of aromatic compounds, little is known about mutations of the endocyclic aromatic cores. I will talk about our endeavors to establish “aromatic metamorphosis”,[1,2] where heteroaromatic compounds are transformed into different ring systems using a multi-step strategy or ideally in one step. The following topics will be discussed: 1) Ni-Catalyzed Boron Insertion into the C2–O Bond of Benzofurans[3] 2) Cu-Catalyzed Ring-Opening Silylation of Benzofurans with Disilane[4] 3) Mn-Catalyzed Ring Opening of Benzofurans and Insertion of Heteroatoms into the C2–O Bond[5] 4) Reductive Cleavage and Boron Insertion of Indoles[6]

##### KAIST 화학과 세미나

This lecture will be devoted to a survey of the large advances made during the last two decades regarding synthesis of 5,10,15-triarylcorroles, the coordination chemistry of elements chelated by them, the corresponding spectroscopic, photophysical and electrochemical features, and applications that rely on the above [1]. This will be followed by the latest developments regarding the utility of utilization of metallocorroles for electro- and photo-catalysis and medicine-relevant applications [2-5]. Future prospects will be demonstrated by the newest achievements in the synthesis of 5,10,15-trialkylcorroles and the corresponding metal chelates [6-7], as well as by presenting yet unmatched challenges.

##### 고려대학교 수학과 세미나

During the past decade there was done a significant progress concerning sharp

##### 2018 고려대학교 수학과 Colloquium

Generative models have lately attracted tremendous attention due to the advances in performance empowered by deep learning. In this lecture, we will provide the nutshellsof learning theory and introduce recent deep generative models together with their applications. This lecture is for audiences who are familiar with basic statistical learning theory.

##### 2018 고려대학교 수학과 Colloquium

In biological systems, many species interact with multiple timescales. Because analysis and simulations of such multi-scale systems are challenging, various strategies to simplify the system has been developed. In this talk, I will describe a way to simplify deterministic and stochastic systems by projecting them to lower dimensional slow-manifold. I will also illustrate how we used such approach to solve two biological puzzles:1) accurate prediction of drug clearance in human liver and 2) molecular mechanisms for robust circadian rhythms against molecular noise.

##### 아주대학교 수학과 세미나

Stiebitz asked in 1995 the following question. For any two positive integers $s$ and $t$, does there exist a finite integer $f(s,t)$ such that every digraph with minimum outdegree at least $f(s,t)$ admits a bipartition $(A,B)$ such that $A$ induces a subdigraph with minimum outdegree at least $s$ and $B$ induces a subdigraph with minimum outdegree at least $t$? In this talk, we give an affirmative answer for tournaments, multipartite tournaments and digraphs with bounded maximum indegree. In particular, we show that for every $\varepsilon$ with $0<\varepsilon<1/2$, there exists an integer $\delta_{0}$ such that every tournament $T$ with minimum outdegree at least $\delta_{0}$ admits a bipartition $(A,B)$ satisfying that $-1\leqslant |A|-|B| \leqslant 1$ and each vertex of $T$ has at least $(1/2-\varepsilon)$ of its outneighbors in both $A$ and $B$.

##### 2018 아주대학교 수학과 colloquium

Toric topology is the study of topological spaces with "well-behaved" torus symmetry. It is deeply related with combinatorial objects such as polytopes and graphs. In this talk, we briefly review the real toric manifold de ned for a given simple graph, and see how to compute its cohomology ring using the structure of the graph. In particular, its Betti numbers are calculated using the graph invariant called a-number. I will try to keep the talk easy and understandable avoiding heavy use of topological methods.

##### 2018 서울대학교 수리과학부 세미나

We give a new definition of conjecturally integer-valued A^1 curves in a log Calabi-Yau surface (S,E), where S is a smooth projective surface and E is a smooth anticanonical divisor. These numbers are derived from the genus zero log Gromov-Witten invariants. We describe its conjectural relationship to genus zero BPS invariants and provide computational evidence.

##### 2018 서울대학교 수리과학부 세미나

We consider an optimal investment/consumption problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio which consists of one bond, one liquid risky asset (no transaction costs) and one illiquid risky asset (proportional transaction costs). We fully characterize the optimal trading and consumption strategies in terms of the solution of the free boundary ODE with an integral constraint. We find an explicit characterization of model parameters for the well-posedness of the problem, and show that the problem is well-posed if and only if there exists a shadow price process. Finally, we describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset.

##### 한국고등과학원 세미나

We study the connected correlator of 1/2 BPS winding Wilson loops in N=4 U(N) super Yang-Mills theory, where those Wilson loops are on top of each other along the same circle. We find the exact finite N expression of the connected correlator of such Wilson loops. We show that the 1/N expansion of this exact result is loops. We show that the 1/N expansion of this exact result is reproduced from the topological recursion of Gaussian matrix model. We also study the exact finite N expression of the generating function of 1/2 BPS Wilson loops in the symmetric representation.