Seminar

Galois representations and the Langlands correspondence

June 8 (Thu) at 13:30 - 14:30, 2017

Kazuki Tokimoto (Kyoto University)

The Langlands correspondence relates number-theoretic objects to completely different objects. While still largely conjectural, it has attracted interests of many mathematicians over the years. It is known that the local Langlands correspondence in a special case can be constructed in a geometric way (the non-abelian Lubin-Tate theory). In this talk, I will explain some basic concepts in mathematics (such as groups, representations and Galois groups) and then try to convey some flavor of my result related to the non-abelian Lubin-Tate theory.

Venue: Seminar Room #160

Event Official Language: English

Atypicality of most few-body observables

May 29 (Mon) at 13:30 - 14:30, 2017

Ryusuke Hamazaki (The University of Tokyo)

Understanding how isolated quantum systems thermalize has recently gathered renewed interest among theorists, thanks to the experimental realizations of such systems. The eigenstate thermalization hypothesis (ETH) is particularly investigated as a sufficient condition for the approach to thermal equilibrium. It states that diagonal matrix elements of an observable for the energy eigenstates are almost the same within a small energy shell. The ETH is justified for an observable and a Hamiltonian whose respective eigenbases are typically oriented to each other; i.e., for almost all unitary transformations of these two eigenbases with respect to the uniform Haar measure. In this seminar, we consider a Hamiltonian with few-body interactions and random observables without assuming the uniform Haar measure. These observables are chosen in an operational manner as random linear combinations of the operator basis of spins. We show that most few-body observables have atypical matrix elements when the energy width is not exponentially small with the system size. Namely, the maximum fluctuation for diagonal matrix elements is larger than that predicted by the uniform Haar measure.

Venue: #433, Main Research Building

Event Official Language: English

Guiding principles to develop tough polymer materials: An exactly solvable model

May 25 (Thu) at 10:30 - 11:30, 2017

Naoyuki Sakumichi (Project Assistant Professor, Soft Matter Center, Ochanomizu University)

Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump [1-3], i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies [4] over 35 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cutoff length for a continuum description [5]. With the exact solution, we elucidate the physical origin of the velocity jump: it emerges from a dynamic glass transition in the vicinity of the propagating crack tip. We further quantify the velocity jump together with slow- and fast-velocity regimes of crack propagation, which would stimulate the development of tough polymer materials.

Venue: Seminar Room #160

Event Official Language: English

Chaos, Quark, Black Hole

April 14 (Fri) at 14:30 - 15:30, 2017

Koji Hashimoto (Professor, Department of Physics, Osaka University)

Venue: Seminar Room #160

Event Official Language: English

HPC in precision medicine

April 11 (Tue) at 15:30 - 16:30, 2017

Tilo Wettig (Professor, Universität Regensburg, Germany)

In theoretical particle physics we have been using high-performance computing (HPC) for three decades to make scientific progress. Recent advances in next-generation sequencing, as well as the corresponding bioinformatics questions, generate an obvious need for HPC methods in the field of precision medicine. We have recently started to explore this field and believe that our HPC expertise can be used to speed up time-critical workflows, to better manage the large amount of data involved, and to lead to more cost- and energy-efficient solutions. I will discuss a few concrete examples, including interesting questions in single-cell sequencing.

Venue: #433, Main Research Building

Event Official Language: English

Geometry in condensed matter physics

April 8 (Sat) at 13:00 - 14:00, 2017

Naoto Nagaosa (Deputy Director, Group Director, Strong Correlation Theory Research Group, RIKEN Center for Emergent Matter Science (CEMS) / Professor, Department of Applied Physics, Graduate School of Engineering, The University of Tokyo)

Quantum geometry plays essential roles current condensed matter physics. Aharonov-Bohm effect and Berry phase as its generalization are the key concepts in electronic systems in solids, which are described by the Bloch wavefunctions and electron correlation effects on top of them. In this talk, I will describe how the geometry determines the physical properties of materials focising on the gauge structure and electomagnetic responses.

Venue: Seminar Room #160

Event Official Language: English

The local time of simple random walks and Gaussian free fields in two dimensions

April 6 (Thu) at 10:30 - 11:30, 2017

Izumi Okada

By using the method of probability analysis, we have researched the local time of a multidimensional-simple random walk. Note that the local time means the number of visits of a simple random walk to specific points in integer lattice. It is known that functionals of a local time and Gaussian free fields denote a variety of nonlinear and mathematical phenomena such as random media. Then, we are observing the relationship between two processes. As a first step, we especially observe favorite points (the singular sites where the local time is large) et al. By A.Dembo, Y.Peres, O.Zeitouni, J.Rosen, who are leading experts in this field, the importance of this point has been recently shown.

Venue: Seminar Room #160

Event Official Language: English

Fatgraph models for RNA molecules

March 23 (Thu) at 10:30 - 11:30, 2017

Hiroyuki Fuji (Associate Professor, Faculty of Education, Kagawa University)

Concepts of fatgraphs and partial chord diagrams occur in many branches of mathematics, including topology, geometry, and representation theory. During the last decade, some applications of these mathematical objects to the research of the molecular biology have been reported. Among them, in particular, a characterization by the genus in the fatgraph presentation of the RNA has been studied remarkably. In this talk, I will explain how the concepts of fatgraphs and partial chord diagrams are applied to the study of the secondary structure of the RNA with pseudoknots, and introduce the matrix model that is invented by basic techniques of the quantum field theory. If time permits, I shall discuss about the matrix model of the protein, and speculate about further developments.

Venue: Seminar Room #160

Event Official Language: English

T-DUALITY AND SCATTERING OF STRINGY STATES

December 12 (Mon) at 15:00 - 16:00, 2016

Jnan Maharana

I shall first review the salient features of T-duality, paying special attentions to the worldsheet perspective. The construction of vertex operators for Moduli will be discussed. The KLT formalism will be applied to show that the S-matrix for scattering of massless state arising from toroidal compactification of closed bosonic string is T-duality invariant.

Venue: Seminar Room #160

Event Official Language: English

Non-perturabative quantum analysis based on resurgence theory

November 11 (Fri) at 10:30 - 11:30, 2016

Tatsuhiro Misumi (Lecturer, Akita University)

Venue: Seminar Room #160

Event Official Language: Japanese