iTHEMS Math Seminar
112 events
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Seminar
The Rectangular Peg Problem and microlocal sheaf theory
February 17 (Tue) 14:00 - 15:00, 2026
Yuichi Ike (Associate Professor, Graduate School of Mathematical Sciences, The University of Tokyo)
The Square Peg Problem asks whether every Jordan curve in the plane contains four distinct points that form the vertices of a square. This problem was proposed by Toeplitz in 1911 and remains unsolved in full generality. It can be generalized to the Rectangular Peg Problem, which concerns the existence of inscribed rectangles with a prescribed aspect ratio. Recently, Greene and Lobb successfully applied techniques in symplectic geometry to the problem and obtained new results. In this talk, I will explain how microlocal sheaf theory allows us to further extend their approach and affirmatively solve the Rectangular Peg Problem for a large class of Jordan curves, including all curves of finite length. This is joint work with Tomohiro Asano.
Venue: Seminar Room #359
Event Official Language: English
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Seminar
Persistent homology and its applications
February 17 (Tue) 11:00 - 12:00, 2026
Yuichi Ike (Associate Professor, Graduate School of Mathematical Sciences, The University of Tokyo)
Persistent homology is one of the main tools in topological data analysis (TDA), which encodes the topological features of given data into persistence diagrams. It has been successfully applied to various fields such as material science and computer graphics. In this talk, I will provide an overview of persistent homology and its applications. Furthermore, I will also discuss its integration with machine learning, specifically how persistent-homology-based loss functions can be used to regularize the topological structure of parameters.
Venue: Seminar Room #359
Event Official Language: English
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Seminar
Fracture squares and separable algebras
December 12 (Fri) 16:00 - 17:30, 2025
Luca Pol (Postdoctoral Researcher, Max Planck Institute for Mathematics in Bonn, Germany)
In this talk I will present a way to reconstruct a category from its subcategories of complete and local objects while retaining the symmetric monoidal structure. As an application of this machinery I will discuss how to calculate separable algebras in equivariant homotopy theory.
Venue: via Zoom / 3F 345-347 Seminar Room, Main Research Building
Event Official Language: English
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Seminar
From perturbations of operators to noncommutative condensers
December 11 (Thu) 16:00 - 17:00, 2025
Dan Voiculescu (Professor, Department of Mathematics, University of California, Berkeley, USA)
A numerical invariant, the quasicentral modulus underlies the multivariable generalizations of the classical Weyl-von Neumann-Kuroda and Kato-Rosenblum theorems. There are also connections to the Kolmogorov-Sinai dynamical entropy. I will also point out some of the open problems. Recently a noncommutative analogy with condenser capacity in nonlinear potential theory is emerging, that provides a new perspective on the subject.
Venue: via Zoom / #359, 3F, Main Research Building
Event Official Language: English
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Seminar
Graph polynomials and quantum field theory
December 9 (Tue) 15:00 - 17:00, 2025
Michael McBreen (Assistant Professor, Department of Mathematics, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong)
The Tutte polynomial was introduced in the 1940s as a two-variable generalisation of the chromatic polynomial of a graph. It is the universal matroid invariant satisfying a deletion-contraction relation, and is the subject of much recent work. I will describe a geometric realisation of the Tutte polynomial via the cohomology of a symplectic dual pair of hypertoric varieties. The same construction associates an interesting two-variable polynomial to any pair of symplectically dual spaces, whose one-variable specialisations recover the respective Poincare polynomials. Joint work with Ben Davison.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Full exceptional collections on Fano threefolds and the braid group action
December 5 (Fri) 16:00 - 17:30, 2025
Anya Nordskova (Postdoctoral researcher, Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU))
The bounded derived category D^b(X) of coherent sheaves on an algebraic variety X is a powerful tool that encodes a wealth of information about X. In some cases D^b(X) admits a particularly nice description via so-called full exceptional collections, which allow one to view D^b(X) as being glued from the simplest building blocks, each equivalent to the derived category D^b(pt) of a point. In this situation the set of all full exceptional collections admits an action of the braid group. In 1993, Bondal and Polishchuk conjectured that this braid group action is always transitive. After a short historical overview I will sketch the idea behind the proof of Bondal-Polishchuk's conjecture in the case when X is a Fano threefold of Picard rank 1 (e.g. the projective space P^3). This is the first 3-dimensional case where the transitivity of the braid group action has been verified. The talk is based on joint work with Michel Van den Bergh.
Venue: 3F 345-347 Seminar Room, Main Research Building (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Compact Association Schemes and Fourier Analysis
October 17 (Fri) 15:00 - 17:00, 2025
Akifumi Nakada (Ph.D. Student / JSPS Research Fellow DC, Graduate School of Advanced Science and Engineering, Hiroshima University)
Error-correcting codes are a fundamental tool in information and communication technologies. They can be viewed as collections of points in a space that are sufficiently far apart to allow error detection and correction. More broadly, coding theory studies good arrangements of points in spaces. This theory has been particularly developed in the frameworks of association schemes and compact homogeneous spaces, where harmonic analysis plays a central role. In this talk, we will begin with an introduction to error-correcting codes and then present compact association schemes, which we define as a generalization of these spaces in which harmonic analysis can be developed.
Venue: Hybrid Format (3F #359 and Zoom), Main Research Building
Event Official Language: English
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Seminar
Bonded Knotted Structures and Applications
October 16 (Thu) 16:00 - 18:00, 2025
Sofia Lambropoulou (Professor, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece)
We present the theory of bonded knots and bonded knotoids, as well as their algebraic counterparts, the theory of bonded braids and bonded braidoids. We also discuss some applications to the topological study of proteins.
Venue: via Zoom / Seminar Room #359
Event Official Language: English
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Seminar
Separability criteria for loops via the Goldman bracket
September 12 (Fri) 15:00 - 17:00, 2025
Aoi Wakuda (Ph.D. Student, Graduate School of Mathematical Sciences, The University of Tokyo)
In this talk, we give algebraic criteria using the Goldman bracket to determine whether two free homotopy classes of loops on an oriented surface have disjoint representatives. As an application, we determine the center of the Goldman Lie algebra of a pair of pants. We extend Kabiraj's method, which was originally limited to oriented surfaces filled by simple closed geodesics, and show that in this case, the center is generated by the class of loops homotopic to a point, and the classes of loops winding multiple times around a single puncture or boundary component.
Venue: via Zoom / #359, Seminar Room #359
Event Official Language: English
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Seminar
Geometry of 2d topological field theories and integrable hierarchies
September 4 (Thu) 15:00 - 17:00, 2025
Zhe Wang (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
In this talk, I will explain a mathematical formulation of 2d topological field theories making use of integrable hierarchies, which is a framework initiated by B. Dubrovin and developed by many other mathematicians. The talk is divided into two parts. The first 45 minutes is a gentle introduction on how the mathematical structure called Frobenius manifolds naturally appears from topological field theories. The remaining part of the talk is devoted to explaining relationships between Frobenius manifolds and integrable hierarchies via the example of the KdV hierarchy.
Venue: #359, Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Tamely Ramified Geometric Langlands Correspondence
August 22 (Fri) 15:00 - 19:00, 2025
Yuki Matsubara (Ph.D. Student, Centre for Quantum Mathematics, University of Southern Denmark, Denmark)
The geometric Langlands correspondence (GLC) is a geometric analogue of the Langlands conjecture in number theory, relating algebraic geometry, representation theory, and many other areas. Since A. Kapustin and E. Witten pointed out the relation between GLC and mirror symmetry, there have been various studies on GLC from a physics perspective as well as a mathematical perspective. First talk: An introduction to Langlands conjecture for everyone This is an entirely accessible overview of the Langlands conjecture. Starting from famous topics, such as the Pythagorean theorem and Fermat’s Last Theorem, I will introduce the statement and motivations behind the Langlands conjecture. No prior background will be assumed, and technical details will often be sketched rather than fully developed, so that anyone with a general mathematical curiosity can follow along. Second talk: On a certain tamely ramified geometric Langlands correspondence In this talk, I will present my research. Arinkin’s 2001 result established the geometric Langlands correspondence for the case G = SL2 on the complex projective line P1 with four fixed regular singularities. When one attempts to extend this to five or more singularities, it turns out to be more natural to decompose the correspondence into a Radon transform-type correspondence and a “GLC‑like” correspondence. I will report on the calculations of cohomology that support the proof of this GLC‑like correspondence in the P1 with five fixed regular singularities case.
Venue: via Zoom / #359, Seminar Room #359
Event Official Language: English
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Seminar
Birational Geometry, Iitaka Program, and Positivity of Canonical and Anticanonical Divisor
July 11 (Fri) 14:00 - 16:00, 2025
Chi-Kang Chang (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
In birational geometry, one of the very interesting question is the Iitaka Program, that is, we want to "factorize" a given variety into "basic type" varieties. "Basic type" varieties are varieties of general type (canonincal divisor is ample), varieties of Calabi-Yau type (canonical divisor is "trivial"), and Fano type (anti-canonical divisor is ample). The (anti)canonical divisor is one of the most important ingredients of (projective) algebraic varieties. Even if the canonical divisor or anticanonical divisor of a given variety is not ample, if it is "positive" in some sense, then the positivity of the (anti)canonical divisor will provide us with important information about the geometry structure of the variety. On the other hand, given a morphism, it is also interesting to study the relation between the (anti)canonical divisor of the source space and the target space. In this talk, we will introduce some conjectures and known results around the positivity about varieties with positive (anti)canonical divisor in the few decades.
Venue: via Zoom / Seminar Room #359
Event Official Language: English
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Seminar
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms
June 26 (Thu) 15:00 - 17:00, 2025
Taketo Sano (Research Scientist, Mathematical Application Research Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
Rasmussen’s s-invariant is an integer-valued knot invariant derived from Khovanov homology, and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture. Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically. In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan’s reformulation of Khovanov homology via tangles and cobordisms. This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot. As an application, we demonstrate that the s-invariants of 3-strand pretzel knots can be computed by hand.
Venue: #345-347, Main Research Building, RIKEN Wako Campus (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Spectral flow and applications
June 23 (Mon) 14:00 - 16:00, 2025
Christopher Bourne (Associate Professor, Institute of Liberal Arts and Sciences, Nagoya University)
Given a family of symmetric matrices indexed by a parameter (e.g. time, external field), changing this parameter will cause the eigenvalues to move along the real axis. The spectral flow tracks these eigenvalues and counts how many cross the point 0. This idea turns out to be very useful for both pure mathematics as well as applications to physics and elsewhere. In this talk, I will introduce the spectral flow and how it can be generalised to a variety of settings that are also relevant for applications in quantum physics.
Venue: Hybrid Format (3F #359 and Zoom), Main Research Building (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Categorification and K-theory
June 20 (Fri) 15:30 - 17:30, 2025
Vladimir Sosnilo (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
In this talk, I will explain and motivate the concept of categorification and present various examples. The Euler characteristic is an invariant of a topological space, that serves as a shadow of a more refined category theoretic invariant—homology—which retains significantly more information. The existence of such a categorical construction underlying a numerical one is a common phenomenon in topology and algebra. I will also discuss Khovanov's question on the existence of categorification of arbitrary rings.
Venue: Seminar Room #359
Event Official Language: English
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Seminar
Ubiquity of geometric Brascamp--Lieb data
February 21 (Fri) 15:00 - 17:00, 2025
Hiroshi Tuji (JSPS Research Fellow PD, Graduate School of Science and Engineering, Saitama University)
This talk is based on a joint work with Neal Bez (Nagoya university) and Anthony Gauvan (Saitama university). The Brascamp--Lieb inequality is a futher general inequality involving some data (we call it the Brascamp--Lieb datum), which has been studied in harmonic analysis and convex geometry. For instance, the Hölder inequality and the Young convolution inequality are particular cases. In this talk, we have an interest in geometric Brascamp--Lieb data, which are specific data satisfying nice properties, for which the best constant of the Brascamp--Lieb inequality is well-understood. Our goal in this talk is to show that geomtric Brascamp--Lieb data are dense in general Brascamp--Lieb data in certain sence. Our result substantially follows from the work by Garg, Gurvits, Oliveira and Wigderson.
Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359
Event Official Language: English
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Seminar
The Topology, Geometry and Physics of non-Hausdorff manifolds
February 19 (Wed) 15:00 - 17:00, 2025
O'Connell David (Ph.D. Student, Okinawa Institute of Science and Technology Graduate University (OIST))
Non-Hausdorff manifolds are manifolds containing "doubled points" that cannot be separated by disjoint open sets. In this talk we will survey some mathematical and physical results surrounding these unusual spaces. As a theme, we will start with their fundamental description as a topological space, and slowly add in more and more structure of interest until we can meaningfully phrase questions of physics. On the mathematical side, we will see descriptions of non- Hausdorff manifolds as colimits of ordinary manifolds, which allows us to describe their geometric features without appealing to arbitrarily- existent partitions of unity. On the physical side, we will consider the inclusion of non-Hausdorff manifolds in a naïve 2d Lorentzian path integral for gravity, and (time permitting) explain how construct quantum fields on a non-Hausdorff background. Ultimately, we will see that these latter two arguments suggest that non-Hausdorff manifolds may be more appropriate than the standard "Trousers space" for the modelling of topology change in Lorentzian signature.
Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359
Event Official Language: English
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Seminar
Operator-algebraic approach to point processes
February 14 (Fri) 15:00 - 17:00, 2025
Ryosuke Sato (JSPS Postdoctoral Research Fellow, Faculty of Science and Engineering, Chuo University)
A point process is a mathematical description of a particle system with random interactions, and it naturally appears in various areas of mathematical physics and mathematics, including statistical mechanics, random matrix theory, combinatorics, and representation theory. In particular, a random particle system with repulsive interactions is associated with a determinantal point process, in which the correlation of any number of particles is expressed in terms of the two-particle correlation via a determinant. Furthermore, this determinantal structure enables an algebraic analysis using CAR algebras, which are operator algebras determined by canonical anti-commutation relations. In the first half of the talk, we will review the relationship between determinantal point processes and operator algebras, with a focus on why operator algebras naturally lend themselves to analyses in probability theory and statistical mechanics. In the second half, based on recent work, we will examine the dynamic relationship between point processes and operator algebras, discussing how dynamics on CAR algebras give rise to stochastic processes on determinantal point processes.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
D-modules and the Riemann-Hilbert correspondence as a foundation for mixed Hodge modules
January 31 (Fri) 14:00 - 16:00, 2025
Takahiro Saito (Assistant Professor, Faculty of Science and Engineering, Chuo University)
Algebraic analysis is a field which began with the study of differential equations in an algebraic framework, known as D-modules. The Riemann-Hilbert correspondence lies at the heart of this field, which bridges the worlds of analysis and geometry. Thanks to this, some geometric problems can be studied by using D-module theory, and vice versa. Based on D-module theory, Morihiko Saito introduced the concept of mixed Hodge modules, realizing Hodge theory on constructible sheaves, which brings us a functorial treatment of Hodge theory and various applications. In this talk, we will begin with the linear differential equations on the complex plane and introduce monodromy, regularity and Deligne's Riemann-Hilbert correspondence. Then, as a generalization of it, I will explain the basics of the theory of D-modules and the Riemann-Hilbert correspondence. Finally, I will describe the role they play in the theory of Hodge modules and recent progress in this area. For the audience's background knowledge, I will assume basic complex function theory. I will start with a simple example, so people outside the field are welcome.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Probabilistic approach to discrete integrable systems
January 17 (Fri) 15:30 - 17:30, 2025
Makiko Sasada (Professor, Graduate School of Mathematical Sciences, The University of Tokyo)
The KdV equation and the Toda lattice are two central and widely studied examples of classical integrable systems, and many of their variations have been introduced to the present. In particular, the box-ball system (BBS) is a basic example of a discrete integrable system, which has been revealed to be an ultra-discrete version of the KdV equation and the Toda lattice. The BBS has been studied from various viewpoints such as tropical geometry, combinatorics, and cellular-automaton. As a new perspective, research on probabilistic approaches to this system has been rapidly expanding in recent years, including the application of the Pitman transform, analysis of invariant measures and its generalized hydrodynamics. More recently, we find that the application of the Pitman transform and the study of invariant measures of i.i.d.-type also work in the same manner for the discrete KdV equation and the discrete Toda lattice. Further research has begun on the relationship between the Yang-baxter maps and the existence of i.i.d.-type invariant measures for the discrete integrable systems. In this talk, I will introduce these new research topics that have been spreading over the past several years from the basics. This talk is based on several joint works with David Croydon, Tsuyoshi Kato, Satoshi Tsujimoto, Ryosuke Uozumi, Matteo Mucciconi, Tomohiro Sasamoto, Hayate Suda and Stefano Olla.
Venue: Seminar Room #359
Event Official Language: English
112 events