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Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

한국고등과학원 세미나

Most searches for vector-like top partners (T) are concerned with the pair and single productions, strictly focusing on three conventional T decays (i.e. t Z, t h and Wb). As bounds become increasingly stringent, however, the utility of these channels greatly diminish. The null result at the LHC may hint at T hiding in new places. We consider a simplified renormalizable model with the SU(2) singlet T and an additional gauge singlet scalar S. A major implication is that the messenger S plays a role of linking the T and top quark, giving rise to non-standard decays or productions of T at loop-level. In the zero-mixing-angle limit, all conventional tree-level decays T → tZ, T → th and T → Wb vanish, while the S can mediate loop-level decays T → gt, T → γt and T → tZ, hence the decay pattern of the T can be significantly altered. In addition, the S can mediate loop-induced pp → T anti-t + t anti-T production, predicting a new signature of T at the LHC. We also explore a dark photon implication for T searches by introducing a new U(1) gauge group, which alters the T decay patterns and gives rise to new signatures.

한국고등과학원 세미나

Models of spontaneous baryogenesis have an interaction term ∂μθjμB in the Lagrangian, where jμB is the baryonic current and θ can be a pseudo-Nambu-Goldstone boson. Since the time component of this term, θ˙j0B, equals θ˙nB for a spatially homogeneous current, it is usually argued that this term implies a splitting in the energy of baryons and antibaryons thereby providing an effective chemical potential for baryon number. In thermal equilibrium, one {then obtains} nB∼θ˙T2. We, however, argue that a term of this form in the Lagrangian does not contribute to the single particle energies of baryons and antibaryons. We show this for both fermionic and scalar baryons. But, similar to some recent work, we find that despite the above result the baryon number density obtained from a Boltzmann equation analysis can be proportional to θ˙T2. Our arguments are very different from that in the standard literature on spontaneous baryogenesis.

한국고등과학원 세미나

It was unclear until recently whether the ergodicity of the geodesic flow on a given Riemannian manifold $M$ has any significant impact on the growth of the number of nodal domains of eigenfunctions of Laplace-Beltrami operator $\Delta_M$, as the eigenvalue $\lambda \to \infty$. In this talk, I'm going to explain my recent work with Steve Zelditch, where we prove that, when $M$ is a principle $S^1$-bundle equipped with a generic Kaluza-Klein metric, the nodal counting of eigenfunctions is typically $2$, independent of the eigenvalues. Note that principle $S^1$-bundle equipped with a Kaluza-Klein metric never admits ergodic geodesic flow. This, for instance, contrasts the case when $(M,g)$ is a surface with non-empty boundary with ergodic geodesic flow (billiard flow), in which case the number of nodal domains of typical eigenfunctions tends to $+\infty$ (proven in my paper with Seung Uk Jang). I will also present an orthonormal eigenbasis of Laplacian on a flat 3-torus, where every non-constant eigenfunction has exactly two nodal domains. This provides a negative answer to the question raised by Thomas Hoffmann-Ostenhof: For any given orthonormal eigenbasis of the Laplace--Beltrami operator, can we always find a subsequence where the number of nodal domains tends to $+\infty$?''

한국고등과학원 세미나

We discuss some algebraic invariants, alpha, beta, delta invariant, for K-stability of Fano variety. Giving examples, very explicit estimation of the invariants will be provided.

한국고등과학원 세미나

We discuss some algebraic invariants, alpha, beta, delta invariant, for K-stability of Fano variety. Giving examples, very explicit estimation of the invariants will be provided.

한국고등과학원 세미나

We discuss some algebraic invariants, alpha, beta, delta invariant, for K-stability of Fano variety. Giving examples, very explicit estimation of the invariants will be provided.

한국고등과학원 세미나

An arithmetic manifold is a type of Riemannian manifold constructed using number theoretical tools. In this talk, I want to introduce the audience to these spaces, to explain why I am interested on them and how this interplay between Geometry and Number Theory can motivate new questions. It is intended to be an introductory talk, so that every one is very welcome.

한국고등과학원 세미나

We discuss some algebraic invariants, alpha, beta, delta invariant, for K-stability of Fano variety. Giving examples, very explicit estimation of the invariants will be provided.

KAIST Discrete Math 세미나

Let H be a planar graph. By a classical result of Robertson and Seymour, there is a function f(k) such that for all k and all graphs G, either G contains k vertex-disjoint subgraphs each containing H as a minor, or there is a subset X of at most f(k) vertices such that G−X has no H-minor. We prove that this remains true with f(k)=ck log k for some constant c depending on H. This bound is best possible, up to the value of c, and improves upon a recent bound of Chekuri and Chuzhoy. The proof is constructive and yields the first polynomial-time O(log

KAIST 수리과학과 세미나
• Title : Syzygy schemes
• Speaker : EDOARDO SERNESI
• Data : 2018-12-08 16:20:00
• Host : KAIST
• Place :

will introduce the syzygy schemes of a canonical curve and compute a few examples.

KAIST 수리과학과 세미나

I will recall some basic facts in the syzygy theory, with emphasis on connections with Koszul cohomology, and I will present a vanishing result for Koszul modules.

KAIST 수리과학과 세미나

Let X be a compact Kahler manifold of dimension n > 0. Let G be a group of zero entropy automorphisms of X. Let G_0 be the set of elements in G which are isotopic to the identity. We prove that after replacing G by a suitable finite-index subgroup, G/G_0 is a unipotent group of derived length at most n-1. This is a corollary of an optimal upper bound of length involving the Kodaira dimension. We also study the algebro-geometric structure of X when it admits a group action with maximal derived length n-1. This is a joint work with Dinh and Oguiso.

2018 KAIST Physics Seminar

Detecting biomolecular interactions in the single-molecule level has been achieved using up-todate in vitro fluorescence-based single-molecule techniques. However, visualizing molecular dynamics of biomolecules in living cells has been tackled by some problems, like back-ground noise, diffraction-limit and toxicity of fluorescent probes. Here, to overcome the limitations, we developed a live-cell single-molecule imaging approach using photo-activated localization microscopy (PALM). To investigate gene expression in living cells, we labeled a photoactivatable fluorescent protein to RNA Polymerase II (Pol II) protein that directly synthesizes messenger RNA (mRNA) molecules from DNA during transcription, and also labeled mRNA molecules of a specific gene for dual-color live-cell imaging. We found that Pol II proteins form clusters at an active gene locus and moreover lifetime of Pol II cluster is proportional to the mRNA output. More recently, to address biological processes upstream of transcription, we developed a livecell assay to observe cooperative dynamics of enhancers, which are gene-expression regulatory DNA elements, and transcription sites. Gene activation is thought to involve a multistep process whereby transcription factors bind to distal enhancer sites and recruit a Mediator protein complex which contacts the Pol II protein at the gene loci. The interaction of Mediator and Pol II has yet to be observed in the nucleus of living cells and the dynamics of this interaction are not yet elucidated. We used quantitative PALM imaging and lattice-light-sheet imaging to study the organization and dynamics of Mediator and Pol II. We found that Mediator and Pol II form large stable clusters and also observed that these clusters have properties expected for phase-separated biomolecular condensates. Moreover, labeling a specific gene, we observed protein condensates dynamically contact with the active gene.