統計物理学メーリングリストの皆様、
東京大学物理学専攻の桂法称です。
立教大学の中山優氏の依頼により、
立教大学で、3/12(月)-14(水)に開催される
下記研究会の案内を代理投稿いたします。
よろしくお願い申しいたします。
桂 法称
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皆様、
立教大学数理物理学研究センターでは，下記日程で国際研究集会を開催致します。
International Symposium "Rikkyo MathPhys 2018"
日時：2018年3月12日(月)--14日(水)
場所：立教大学 池袋キャンパス 4342教室 (4号館3階)
詳細につきましてはホームページ
https://sites.google.com/a/rikkyo.ac.jp/rikkyo-mathphys-2018/home
を御覧ください。
https://sites.google.com/a/rikkyo.ac.jp/rikkyo-mathphys-2018/registration-1
で参加登録をお願い致します。
また、このメールに講演の概要を添付しておりますのでご参照ください。
皆様のご参加をお待ちしております。
世話人一同
March 12 (Mon)
Babak Haghighat (Tsinghua University)
Title: Landau-Ginzburg description of Little String theories
Abstract:
We will present a new set of coordinates which allow us to rewrite the
mirror geometry of certain Little String theories in terms a
Landau-Ginzburg model.
Ivan Ip (Kyoto University)
Title: Cluster realization and tensor product decomposition of
positive representations
Abstract:
For each simple Lie algebra g, a cluster realization of the
corresponding Drinfeld-Jimbo quantum groups Uq(g) has been found via
the positive representations, where an embedding into a quantum torus
algebra Xg is described by certain quiver diagram. Using this new
realization, we discuss its application towards the proof of the
tensor product decomposition of the positive representations of split
real quantum groups restricted to the Borel part, as well as the full
decomposition in type An found recently by Schrader-Shapiro related to
the spectral decomposition of the Hamiltonians of certain open
Coxeter-Toda system.
March 13 (Tue)
Yu-tin Huang (NTU)
Title: Theory space for effective field theories
Abstract:
In this talk I will talk about the "theory space" in terms of
coefficients of higher dimension operators in the infrared. For any
theory with a UV completion that has a perturbative parameter, these
coefficients are well defined. We will demonstrate that in this theory
space, the constraint of unitarity, locality and Lorentz invariance in
the UV carves out a subregion in which consistent theories can
possibly live. This region has well geometric structure similar,
albeit simpler, to that of the amplitudehedron of N=4 SYM. This
achieves the fascinating result in which all three principles are
unified in a geometric statement.
Masahito Yamazaki (Kavli IPMU)
Title: Gauge Theory and Integrability
Abstract:
In a celebrated paper in 1989, E. Witten discovered a beautiful
connection between knot invariants (such as the Jones polynomial) and
three-dimensional Chern-Simons theory. Since there are similarities
between knot theory and integrable models, it is natural to ask if
there is also a gauge theory explanation for integrable
models. The answer to this question was recently given by K. Costello
in 2013. In this talk I will describe my work with K. Costello and E.
Witten, which explains many results in integrable models from the
standard quantum field theory analysis of Costello's theory.
Katsushi Ito (Tokyo Institute of Technology)
Title: ODE/IM correspondece and Argyres-Douglas theory
Abstract:
The ODE/IM correspondence is a mysterious relation between the
spectral analysis approach to ordinary differential equation (ODE) and
functional relations in the 2d quantum integrable model (IM). In this
talk we first discuss the various functional relations obtained from
the linear problem associated with the modfied affine
Toda field equations, which reduces to the ODE in the conformal limit.
In particular we argue the Non-linear integral equation and derive the
effective central charge of the integrable model in the UV limit. We
next apply the ODE/IM correspondence to the quantum spectral curve of
a class of Argyres-Douglas theories in the Nekrasov-Shatashvili limit
of the Omega-background.
Daisuke Yamakawa (Tokyo Science University)
Title: Wild character varieties
Abstract:
It is well-known that the meromorphic connections on a compact Riemann
surface with prescribed irregular type at each singularity are
classified by the so-called monodromy/Stokes data. In this talk I will
construct the moduli spaces of monodromy/Stokes data as algebraic
Poisson varieties using the (twisted) quasi-Hamiltonian geometry.
This talk is based on joint work with Philip Boalch.
Yasuaki Hiraoka (Tohoku University)
Title: Topological data analysis and persistent homology
Abstract:
Topological data analysis is an emerging concept in applied
mathematics in which we characterize "shape of data" using topological
methods. In particular, the persistent homology and its persistence
diagrams are nowadays applied to a wide variety of scientific and
engineering problems including materials science, life science and
social networks etc. In my talk, I will give a survey of these
concepts both from mathematics and applications. If time is allowed, I
will show several future challenges which deepen the mathematical
understandings and possible applications.
March 14 (Wed)
Norio Konno (Yokohama National University)
Title: Stationarity, Locality, and Recurrence of Quantum Walks
Abstract:
The discrete-time quantum walk (QW) is a quantum version of the
classical random walk and has been largely investigated for the last
decade. The striking property of the QW is the spreading property of
the walker. The standard deviation of the walker's position grows
linearly in time, quadratically faster than classical random walk,
i.e., ballistic spreading. On the other hand, a walker stays at the
starting position: localization occurs. Interestingly, a quantum
walker has both ballistic spreading and localization [1,2]. In this
talk, we consider a relation between stationarity, locality, and
recurrence of discrete-time QWs on integer lattices [3-9].
References
[1] Venegas-Andraca (2012) Quantum Inf. Process., Vol.11, pp.1015-1106
[2] Portugal (2013) Quantum Walks and Search Algorithms, Springer
[3] Konno (2014) Quantum Inf. Process., Vol.13, pp.1103-1125
[4] Konno, Takei (2015) Quantum Inf. Comput., Vol.15, pp.1060-1075
[5] Endo, Kawai, Konno (2016) RIMS Kokyuroku 2010, pp.45-55
[6] Endo, Kawai, Konno (2017) Interdiscip. Inform. Sci., Vol.23, pp.57-64
[7] Kawai, Komatsu, Konno (2017) Yokohama Math. J. (in press),
arXiv:1702.01523
[8] Kawai, Komatsu, Konno (2017) arXiv:1707.04040
[9] Komatsu, Konno (2017) Quantum Inf. Process., Vol.16, 291
Kohei Iwaki (Nagoya University)
Titile: Topological recursion and Voros coefficients
Abstract:
Topological recursion, introduced by Eynard-Orantin, is a remarkable
algorithm which computes certain correlation functions and free energy
(of matrix models) from a given spectral curve. The correlation
functions are closely related to the wave function (WKB solution) for
a Schrodinger-type equation obtained as a "quantization" of the
spectral curve (cf. Gukov-Sułkowski, Bouchard-Eynard, etc). On the
other hand, the Voros coefficients are important quantity in the
theory of exact WKB analysis developed by Voros et al. A fundamental
result of exact WKB analysis allows us to describe the monodromy or
Stokes matrices of Schrodinger-type equations by the Voros
coefficients (cf. Aoki-Kawai-Takei-Sato). I'll show an explicit
formula which describes a relation between the Voros coefficient and
the free energy of the topological recursion, for a class of
Schrodinger-type equations. If time allows, I'll also show how the
isomonodoromic tau-functions of Painleve equations appear in this
context.
My talk is based on joint works (some of them are in progress) with T.
Koike, O. Marchal, A. Saenz and Y. Takei.
Tatsuhiro Misumi (Akita University)
Title: Application of Resurgence Theory to Quantum Physics
Abstract:
The application of resurgence theory to quantum physics has been
attracting a great deal of attention. Resurgence theory was originally
developed in ODE to obtain a solution from formal power-series
solutions by use of the nontrivial relation between power-series and
non-power-series formal solutions. This relation is called the
"resurgent structure", which is also expected to exist between
perturbative and nonperturbative contributions in quantum theory. In
quantum mechanics, matrix models and certain supersymmetric field
theories, the existence of resurgent structure has been verified,
where complex classical solutions and the associated Lefshcetz
thimbles play a vital role. The question whether it exists in
non-abelian gauge theory such as Yang-Mills theory and QCD has been
intensively investigated these days.
I will give a review on the recent progress in these topics.