iTHEMS Math Seminar
120 events
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Seminar
Thom polynomials relative to prescribed maps around the boundary
July 3 (Fri) 15:00 - 17:30, 2026
Masato Tanabe (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In the first half of this talk, I would like to recall their theory with introduction of algebro-topological materials. In the second half, I would also like to talk about applications of Thom polynomials to topology of non-singular maps. Since this century, various invariants of immersions/embeddings have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, those formulas are obtained in different forms and remain somewhat scattered. As the first step to unify them, I would like to introduce Thom polynomials relative to prescribed maps around the boundary. As a main result, we show a structure theorem of Thom polynomials relative to framable immersions. In fact, most earlier formulas are summarized as the vanishing of "correction terms" appearing in the structure theorem. This is an advanced seminar for mathematical researchers.
Venue: Seminar Room #359, Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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SeminarPrimitive Ideals and Hilbert Space Representations of Quantized Coordinate Algebras of Complex Semisimple Lie Groups
June 26 (Fri) 16:30 - 18:00, 2026
Heon Lee (Postdoc Researcher, Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Republic of Korea)
The primitive ideals of the coordinate algebra $ \mathcal{O} ( G ) $ of a complex semisimple Lie group $ G $ are in bijection with the points of $ G $, via the correspondence assigning to each point of $ G $ the kernel of the associated evaluation homomorphism on $ \mathcal{O} ( G ) $. This establishes a direct link between the algebraic structure of $ \mathcal{O} ( G ) $ and the geometry of $ G $. In this talk, we investigate the quantum analogue of this classical relationship for the $ q $-deformation $ G_q $. Specifically, we establish a sharp dichotomy: primitive ideals in homogeneous Joseph strata arise as kernels of irreducible representations of $ \mathcal{O} ( G_q ) $ by bounded operators on Hilbert spaces, which provide a quantum analogue of evaluation homomorphisms at points of $ G $, whereas those in inhomogeneous Joseph strata do not. This clarifies the extent to which the primitive spectrum of $ \mathcal{O} ( G_q ) $ can be accessed through operator-theoretic methods. We also analyze the semiclassical consequences of this result in light of the fact that the primitive ideals of $ \mathcal{O} ( G_q ) $ are parametrized by the symplectic leaves of the natural Poisson structure on $ G $. This talk is based on joint work with Christian Voigt.
Venue: via Zoom / Seminar Room #359
Event Official Language: English
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Seminar TomorrowClassification of certain actions of representation categories
June 5 (Fri) 15:00 - 17:00, 2026
Mao Hoshino (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
Last year I showed a classification theorem for certain classes of module categories over the representation category of quantum SU(n). Although its proof is elementary, the classification itself has a natural interpretation based on the concept of quantization.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Introduction to categorification and link homology
May 28 (Thu) 14:00 - 15:30, 2026
Mikhail Khovanov (Professor, Department of Mathematics, Johns Hopkins University, USA)
Quantum link invariants relate topology in 3 dimensions to mathematical physics and representation theory. They admit liftings to 4-dimensional structures, known as link homology. We will explain how the skein relations for quantum invariants turn into homological structures at this higher level and how semisimple representation theory turns into non-semisimple representations and homological algebra upon categorification.
Venue: Okochi Hall (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Singularities of differentiable maps and Thom polynomials
May 22 (Fri) 15:00 - 17:30, 2026
Masato Tanabe (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
Singularities are locations where something is exceptional. In particular, singularities of differentiable maps are mathematical concepts corresponding to stationary points of functions and apparent contours of surfaces under projection onto the retina. These are unavoidable in general, but important to study the shape of spaces and behavior of maps. The theory for them was initiated by R. Thom in 1950's, and have been deeply studied by many researchers.
Venue: Room 359, RIKEN Wako Campus (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Tropical geometry as a tool in algebraic geometry and beyond
May 13 (Wed) 15:30 - 17:00, 2026
Paul Alexander Helminck (Assistant Professor, Mathematical Institute of the Polish Academy of Sciences, Poland)
Tropical geometry is a field in mathematics that lies at the interface of algebraic geometry and combinatorics. One of the main goals in tropical geometry is to uncover the combinatorial patterns hidden in algebraic geometry. This basic principle can already be found in Bézout’s theorem, which counts the roots of sufficiently generic polynomial equations, and its generalization in the form of the BKK theorem, both of which can be proven tropically. The abstract combinatorial ideas that come out of this study have since also seen applications in economics, machine learning, chemical reaction networks and mathematical physics, among others. In this talk I will give an introduction to tropical geometry and I will discuss some of the main results. I will also discuss some of my latest work on finding the topology of an algebraic variety using tropical methods. In particular, I will discuss how this gives rise to a CW complex structure on a K3 surface. This structure for instance gives us a quick way to see various phenomena from mirror symmetry such as the monodromy of integral affine structures.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Six operations in differential topology
May 8 (Fri) 15:00 - 17:00, 2026
Takumi Maegawa (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
The formalism of six operations, pioneered by Grothendieck and Verdier, serves as a unifying framework for studying cohomological phenomena. This language realizes Poincaré-type duality and transfer maps as certain adjunctions between stable $\infty$-categories of sheaves. In this talk, we highlight the theory of six operations in topology and apply it to provide an intrinsic version of the Pontryagin-Thom construction. We then discuss the intrinsic construction of invariants coming from Seiberg-Witten theory, which is based on the speaker's previous work.
Venue: via Zoom / Seminar Room #359
Event Official Language: English
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Seminar
Quantum modular form and quantum invariants
March 13 (Fri) 14:00 - 16:00, 2026
Yuya Murakami (Research Scientist, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
Quantum invariants are invariants of knots and 3-manifolds which relate deeply to mathematical physics and representation theory. In recent years, it has become increasingly clear that it is also deeply related to number theory, that is, quantum modularity for quantum invariants. This topic is interesting from a topological viewpoint since this is a refinement of establishing asymptotic expansions of quantum invariants, which is an important problem in quantum topology, and is interesting from a number-theores[tic viewpoint since this gives examples of quantum modular forms, which are mysterious objects in number theory. I obtained two linked results on topology and number theory: Establishing explicit asymptotic expansions of quantum invariants for negative definite plumbed 3-manifolds and establishing quantum modularity of false theta functions in full generality. In this talk, I will outline previous progress on quantum modularity for quantum invariants and my results.
Venue: via Zoom / Seminar Room #359, Seminar Room #359
Event Official Language: English
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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
120 events