iTHEMS Math Seminar
121 events
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Seminar
Stability of ferromagnetism in many-electron systems
July 31 (Fri) 16:00 - 18:10, 2020
Tadahiro Miyao (Associate Professor, Department of Mathematics, Faculty of Science, Hokkaido University)
First part Title: Stability of ferromagnetism in many-electron systems Abstract: I construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems. Within the new framework, I reinterpret the Marshall-Lieb-Mattis theorem and Lieb’s theorem; in addition, from the new perspective, I prove that Lieb’s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. I also examine the NagaokaThouless theorem and its stability. These examples verify the effectiveness of the new viewpoint. Second part Title: Order preserving operator inequalities in many-electron systems Abstract: In this talk, I will introduce order preserving operator inequalities and explain how these inequalities are applied to the mathematical study of ferromagnetism. As examples of applications, Lieb's theorem of the Hubbard model and its stabilities will be discussed in terms of the inequalities.
Venue: via Zoom
Event Official Language: English
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Seminar
Topological data analysis from a practical and mathematical perspective
July 15 (Wed) 16:00 - 18:10, 2020
Yuichi Ike (Researcher, Artificial Intelligence, FUJITSU LABORATORIES LTD.)
1. Topological data analysis and its applications In this talk, I will explain some methods in topological data analysis (TDA) and their applications. First I recall persistent homology, which is a central tool to analyze the "shape" of a point cloud set. Then I show several applications to material science and time-series analysis. I also talk about our collaborative research with Inria on noise-robust persistent homology and an automated vectorization method of persistence diagrams. 2. Persistence-like distance on sheaf category and displacement energy In this talk, I will talk about relation among sheaf theory, persistence modules, and symplectic geometry. We introduce a persistence-like distance on Tamarkin sheaf category and prove a stability result with respect to Hamiltonian deformation of sheaves. Based on this result, we propose a new sheaf-theoretic method to give a lower bound of the displacement energy of compact subsets of a cotangent bundle. This is a joint work with Tomohiro Asano.
Venue: via Zoom
Event Official Language: English
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Seminar
Universal Error Bound for Constrained Quantum Dynamics
June 24 (Wed) 16:00 - 18:10, 2020
Ryusuke Hamazaki (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / RIKEN Hakubi Team Leader, Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR))
In quantum mechanics, the existence of large energy gaps allows us to trace out the degrees of freedom of irrelevant energy scale. Consequently, we can treat a system within a constrained subspace obtained by the projection of the total Hilbert space. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. In this talk, we show a universal and rigorous error bound for such a constrained-dynamics approximation in generic gapped quantum systems [1,2]. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. If time allows, I will briefly talk about generalizations of our result to e.g., quantum many-body systems and open quantum systems.
Venue: via Zoom
Event Official Language: English
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Seminar
Information geometry of operator scaling
June 17 (Wed) 16:00 - 18:10, 2020
Tasuku Soma (Research Associate, Graduate School of Information Science and Technology, The University of Tokyo)
Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently, a generalization of matrix scaling to completely positive maps called operator scaling has been found to appear in various fields of mathematics and computer science, and the Sinkhorn algorithm has been extended to operator scaling. In this study, the operator Sinkhorn algorithm is studied from the viewpoint of quantum information geometry through the Choi representation of completely positive maps. The operator Sinkhorn algorithm is shown to coincide with alternating e-projections with respect to the symmetric logarithmic derivative metric, which is a Riemannian metric on the space of quantum states relevant to quantum estimation theory. This talk is based on joint work with Takeru Matsuda.
Venue: via Zoom
Event Official Language: English
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Seminar
Knotted 2-spheres in the 4-space and Yang-Mills gauge theory
May 27 (Wed) 16:00 - 18:10, 2020
Masaki Taniguchi (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))
The classification problem of knots is one of the central topics in a study of topology. In the first part, we review classical knot theory and theory of 2-dimensional knots in the 4-dimensional space. In the second part, we focus on a problem considered in differential topology. In the studies of differential topology, people are interested in the difference between continuous and smooth. As the main result of this talk, we introduce a theorem that tells us the difference between continuous and smooth 2-dimensional knots. The proof uses Yang-Mills gauge theory for 4-manifolds obtained by the surgery of 2-knots.
Venue: via Zoom
Event Official Language: English
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Seminar
How many electrons can atoms bind?
May 13 (Wed) 16:00 - 18:10, 2020
Yukimi Goto (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))
In this talk, I will introduce the mathematical studies on the ionization problem. Some experimental & numerical evidences say that any doubly charged atomic ion X^{2-} is not stable. This 'fact' is called the ionization conjecture in mathematical physics literatures. My hope is to illustrates the interplay between mathematical and physical ideas. The talk is directed towards researchers on various aspects of quantum mechanics. In the first part, we will discuss the many-body aspects of quantum mechanics and introduce some basic notions. The second part will deal with the mathematical results in some approximation theories.
Venue: via Zoom
Event Official Language: English
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Seminar
From Eigenvalues to Resonances
May 1 (Fri) 16:00 - 18:10, 2020
Keita Mikami (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))
Resonance is one of the most studied object in mathematical study of Schrödinger operators. One possible reason is that resonance is appeared in many other fields like arithmetic, physics, and topography. This series of talks target both mathematicians and researchers in other fields. The goal of the talk is to introduce the study of resonances for two body Schrödinger operators. In the first part, we briefly review spectral theory and how we use it in the study of Schrödinger operators. The aim of this part is to introduce the audience some basic notions used in the study of Schrödinger operators. In the second part, we give brief introduction of resonances and its application to both mathematicians and researchers in other fields. We start from mathematical definition of resonances to its applications in the other fields.
Venue: via zoom
Event Official Language: English
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Seminar
Index of the Wilson-Dirac operator revisited: a discrete version of Dirac operator on a finite lattice
February 25 (Tue) 16:00 - 18:10, 2020
Mikio Furuta (Professor, The University of Tokyo)
The Wilson-Dirac operator is a discrete version of Dirac operator defined on regular lattices. When the discrete version is a fine approximation of the Dirac operator on a Z/2-graded Clifford module on a torus, it is known that (1) an integer-valued index is defined for the Wilson-Dirac operator, and (2) the index is equal to the Atiyah-Singer index of the Dirac operator on the torus. These have been well established up to around 2000. The strategy of all the previous works is to make use of the discrete version of the heat kernel for Neuberger's overlap Dirac operator. Therefore the strategy cannot be generalized to mod 2 index nor family version of index. In this talk I would like to explain a new approach to the index of Wilson-Dirac operator which can be immediately generalized to these various cases. Joint work with H. Fukaya, S. Matsuo, T. Onogi, S. Yamaguchi and M. Yamashita.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Solved and open problems regarding the neighborhood grid data structure
February 7 (Fri) 16:00 - 18:10, 2020
Martin Skrodzki (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Fellow, German Academic Scholarship Foundation, Germany)
February 7 at 16:00-17:00 17:10-18:10, 2020 In 2009, Joselli et al. introduced the neighborhood grid data structure for fast computation of neighborhood estimates for point clouds in arbitrary dimensions. Even though the data structure has been used in several applications and was shown to be practically relevant, it is theoretically not yet well understood even in the two-dimensional case. The purpose of this talk is to present the data structure, give a time-optimal building algorithm, and motivate several associated questions from enumerative combinatorics as well as low-dimensional (probabilistic) geometry. In case of questions that have been solved in the past, corresponding proofs will be provided. For the open question, the talk will list them as an outlook to possible future collaboration.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Semiclassical methods in mathematical quantum mechanics
January 23 (Thu) 16:00 - 18:10, 2020
Shu Nakamura (Professor, Gakushuin University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Talk 1: Semiclassical analysis, microlocal analysis and scattering theory. I plan to talk about overview on the semiclassical analysis and related topics, especially its intrinsic relationship with microlocal analysis and (microlocal) scattering theory. Roughly speaking, the microlocal analysis is an application of semiclassical idea to the analysis of singularities, and its analogue in momentum space is the microlocal scattering theory. We discuss basic notions of these, and mention several recent results. Talk 2: Microlocal structure of the scattering matrix with long-range perturbations. As an example of topics discussed in Talk 1, we discuss recent results on the scattering matrix with long-range perturbations. In particular, we show that the scattering matrix is expressed as a Fourier integral operator, and in some cases we can decide its spectral properties. Our approach is fairly geometric and abstract, and thus applies not only to usual Schrödinger operators but also to higher order operators and discrete Schrödinger operators.
Venue: #435-437, Main Research Building
Event Official Language: English
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Seminar
Multiple Zeta Values: Interrelation of Series and Integrals
December 17 (Tue) 16:00 - 18:10, 2019
Syuji Yamamoto (Associate Professor, Keio University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: This is an introduction to multiple zeta values (MZVs). Although the study of MZVs is related to various areas of mathematics, we will concentrate on the algebraic structures of MZVs themselves. The key point is that MZVs have two kinds of representations: nested series and iterated integrals. We present how these two representations yield rich algebraic relations among MZVs.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Noncommutative crepant resolutions and some higher dimensional flops
December 4 (Wed) 16:00 - 18:10, 2019
Wahei Hara (JSPS Research Fellow, Faculty of Science and Engineering, Waseda University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: We will talk about the theory noncommutative resolution of singularities. Noncommutative resolution is a noncommutative analog of usual (geometric) resolution of singularities, and allows us to generalise the idea of McKay correspondence to a large class of singularities. In the first part of the talk, we discuss the classical McKay correspondence, the definition of noncommutative crepant resolution, and some known results in lower dimensions. In the second half, we will discuss some concrete examples of noncommutative crepant resolutions in higher dimensions.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Some topics in projective geometry of algebraic varieties
November 8 (Fri) 16:00 - 18:10, 2019
Atsushi Ito (Assistant Professor, Graduate School of Mathematics, Nagoya University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: We talk about Gauss maps and projective dual varieties, which are classical objects in projective geometry of algebraic varieties. In particular, we explain Gauss maps in positive characteristic and projective dual varieties of toric varieties in characteristic 0.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Atiyah-Hirzebruch spectral sequence in the band theory
October 24 (Thu) 16:00 - 18:10, 2019
Ken Shiozaki (Assistant Professor, Yukawa Institute for Theoretical Physics, Kyoto University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: The topological nature of the band theory in crystalline systems can be well described by the topological K-theory over the Brillouin zone torus. In the first part of my talk, I will present the band-theory understanding of the grading of the K-group, and how the exactness axiom and the Mayer-Vietoris sequence are naturally understood. In the second part, I discuss how to compute the differentials of the Atiyah-Hirzebruch spectral sequence associated with a cell decomposition.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Mean dimension of dynamical systems and information theory
October 21 (Mon) - 23 (Wed) 2019
Masaki Tsukamoto (Professor, Kyushu University)
Oct.21 15:30-16:30, 16:40-17:40, Okochi Hall Oct.22 13:30-14:30, room #435-437, Main Research Building Oct.23 13:30-14:30, room #435-437, Main Research Building
Venue: Okochi Hall / #435-437, Main Research Building
Event Official Language: Japanese
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Seminar
Complex analysis on a neighborhood of a complex submanifold and its applications
July 30 (Tue) 16:00 - 18:10, 2019
Takayuki Koike (Lecturer, Department of Mathematics, Graduate School of Science, Osaka City University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: We explain our recent study on the complex analytic structure of a small tubular neighborhood of a complex submanifold, which is based on T. Ueda's classification theory. We also explain how to apply them to: (i) a study on (non-) existence of a smooth Hermitian metric on a nef line bundle over a projective manifold with semi-positive curvature, and (ii) a study on non-projective and non-Kummer K3 surfaces.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Introduction to Schroedinger Operators
July 12 (Fri) 16:00 - 18:10, 2019
Keita Mikami (Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: In this seminar, I will talk about mathematical study of Schroedinger operators (or Schroedinger equation). Part 1: I will talk about what mathematicians do to find a solution to Schroedinger equation. The goal of the first part is to be able to check the existence of solutions of Schroedinger equations in terms of decay/growth rate of potentials. Part 2: I will talk about what can we say about solutions to Schroedinger equation constructed in the first part. Especially, the relationship to the corresponding classical mechanic is introduced.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Asymmetric metric and coarse geometry
June 20 (Thu) 16:00 - 18:10, 2019
Hiroki Kodama (Visiting Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Assistant Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: For most of mathematicians, metric is symmetric. However, we can define asymmetric metric without any difficulty. "Coarse" is a notion to describe some large scale viewpoint. For example, the set of real numbers is coarse equivalent to the set of integers (with respect to standard metric). I will discuss asymmetric metric space in "coarse" sense. Part 1: I will define metric space and asymmetric metric space. I will also explain a notion of coarse equivalence. Part 2: I will discuss what kind of asymmetric metric space is not coarse equivalent to (symmetric) metric space. I also would like to give other generalizations of metric.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Certain invariants as dimension
May 24 (Fri) 16:00 - 18:10, 2019
Genki Ouchi (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: In this talk, I would like to talk about certain invariants that look like dimension. This talk has independent two parts. In part 1, I will talk about finite metric spaces. In 2013, Leinster introduced the notion of magnitude of finite metric spaces. It measures effective number of points in finite metric spaces. Considering magnitude and scale transformation, Leinster and Willerton defined dimension of finite metric space with scale. I will explain the definition of magnitude of finite metric spaces and see examples. In part 2, I will talk about derived categories of smooth projective varieties or finite dimensional algebras. In 2014, Dimitrov, Heiden, Katzarkov and Kontsevich introduced the notion of entropy of endofunctors of derived categories. It measures complexity of endofunctors under iteration. Serre functor is an autoequivalence of derived category, that describes Serre duality. Entropy of Serre functor looks like dimension of derived categories. I will talk about known results for entropy of Serre functors and some related topics.
Venue: Seminar Room #160
Event Official Language: English
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Seminar
Introduction to Singularity Theory in Algebraic Geometry
May 16 (Thu) 16:00 - 18:10, 2019
Kenta Sato (Special Postdoctoral Researcher, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. In this talk, I will explain for all scientists how singularities are studied in algebraic geometry. In algebraic geometry, we study algebraic varieties, which are figures defined as the zero sets of polynomial equations. To study an algebraic variety, we often expect that the variety is smooth, that is, the variety locally resembles Euclidian spaces. However, even if we start from smooth varieties, we sometimes encounter non-smooth varieties. This is one of the reasons why we need to study singularities. Part I: In the first one hour, I will explain how singularities are studied. I will introduce two invariants of singularities by which we can compare singularities numerically. One invariant is defined in terms of resolution of singularities and the other is defined in terms of positive characteristic methods. I also explain a surprising relation of these invariants. Part II: In the second one hour, I will explain how singularity theory is used to study smooth projective varieties. I will introduce Minimal Model Program and explain the relation with singularity theory.
Venue: Seminar Room #160
Event Official Language: English
121 events