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Seminar information archive
Seminar information archive ～10/22｜Today's seminar 10/23 | Future seminars 10/24～
2026/10/20
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Ken’ichi Ohshika (Gakushuin University)
Structures of unit tangent spheres of Thurston’s metric (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ken’ichi Ohshika (Gakushuin University)
Structures of unit tangent spheres of Thurston’s metric (JAPANESE)
[ Abstract ]
Thurston introduced in the 1980s a new metric on Teichmüller space using best Lipschitz maps instead of best quasi-conformal maps. Thurston’s metric is Finsler, and so we can consider the associated norm on tangent spaces of Teichmüller space. In this talk, we show how the unit sphere of this norm looks, regarded as a convex sphere. We in particular give a formula for dimensions of faces. This is a part of joint work with A. Papadopoulos.
[ Reference URL ]Thurston introduced in the 1980s a new metric on Teichmüller space using best Lipschitz maps instead of best quasi-conformal maps. Thurston’s metric is Finsler, and so we can consider the associated norm on tangent spaces of Teichmüller space. In this talk, we show how the unit sphere of this norm looks, regarded as a convex sphere. We in particular give a formula for dimensions of faces. This is a part of joint work with A. Papadopoulos.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/10/19
Operator Algebra Seminars
15:30-17:00 Room # 126 (Graduate School of Math. Sci. Bldg.)
Xin-Hai Tong (The University of Tokyo)
Clustering Theorem for Bose--Hubbard class Gibbs states
Xin-Hai Tong (The University of Tokyo)
Clustering Theorem for Bose--Hubbard class Gibbs states
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Ryota Kotani (Institute of Science Tokyo)
A Torelli-type theorem for hyperkähler quotients (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Ryota Kotani (Institute of Science Tokyo)
A Torelli-type theorem for hyperkähler quotients (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Tokyo Probability Seminar
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Kohki Sakamoto (The University of Tokyo)
Singularity of harmonic measure on Poisson-Voronoi tessellations in hyperbolic spaces
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Kohki Sakamoto (The University of Tokyo)
Singularity of harmonic measure on Poisson-Voronoi tessellations in hyperbolic spaces
[ Abstract ]
Poisson-Voronoi tessellations provide natural examples of invariant random tilings of homogeneous spaces. Benjamini, Paquette, and Pfeffer proved that the nearest-neighbor random walk on the Poisson-Voronoi tessellation of the hyperbolic plane has positive drift and hence converges to the boundary circle. They further conjectured that its hitting measure on the boundary is singular with respect to Lebesgue measure. I will explain how this follows from an ergodic-theoretic argument based on rerooting relations, and briefly discuss the higher-dimensional case as well.
Poisson-Voronoi tessellations provide natural examples of invariant random tilings of homogeneous spaces. Benjamini, Paquette, and Pfeffer proved that the nearest-neighbor random walk on the Poisson-Voronoi tessellation of the hyperbolic plane has positive drift and hence converges to the boundary circle. They further conjectured that its hitting measure on the boundary is singular with respect to Lebesgue measure. I will explain how this follows from an ergodic-theoretic argument based on rerooting relations, and briefly discuss the higher-dimensional case as well.
2026/10/16
Algebraic Geometry Seminar
13:15-14:45 Room #118 (Graduate School of Math. Sci. Bldg.)
Yutaro Naito (Nagoya University)
Symmetries of toric varieties over fields of characteristic zero
Yutaro Naito (Nagoya University)
Symmetries of toric varieties over fields of characteristic zero
Colloquium
15:30-16:30 Room #NISSAY Lecture Hall (Graduate School of Math. Sci. Bldg.)
Kouichi Taira (Graduate School of Mathematical Sciences, The University of Tokyo)
Spectral theory for the d'Alembertian on Lorentzian manifolds (日本語)
Kouichi Taira (Graduate School of Mathematical Sciences, The University of Tokyo)
Spectral theory for the d'Alembertian on Lorentzian manifolds (日本語)
[ Abstract ]
The spectrum of a linear operator on a Hilbert space may be regarded as an infinite-dimensional generalization of the notion of eigenvalues of matrices, and it has been studied extensively from the viewpoints of analysis and geometry. For example, the spectra of the Laplacian and Dirac operators on Riemannian manifolds are closely related to a variety of geometric phenomena.
Classical results include Weyl's law, which describes the asymptotic behavior of eigenvalues in terms of geometric quantities such as the volume of the manifold, and the index theorem, which relates the zero modes of the Dirac operator to characteristic classes of the manifold. These topics continue to be actively studied today.
On Lorentzian manifolds, which provide the geometric framework for relativity, the spectra of operators such as the d'Alembertian and the Dirac operator have also begun to attract increasing attention in recent years, partly because of applications to quantum theory. In contrast to the Riemannian setting, however, these differential operators are not elliptic, and many of the standard methods are therefore no longer directly applicable. As a result, even fundamental questions such as self-adjointness can be highly nontrivial.
In this talk, I will give an overview of known results on the spectra of differential operators on Riemannian and Lorentzian manifolds and, time permitting, present some of my own results.
The spectrum of a linear operator on a Hilbert space may be regarded as an infinite-dimensional generalization of the notion of eigenvalues of matrices, and it has been studied extensively from the viewpoints of analysis and geometry. For example, the spectra of the Laplacian and Dirac operators on Riemannian manifolds are closely related to a variety of geometric phenomena.
Classical results include Weyl's law, which describes the asymptotic behavior of eigenvalues in terms of geometric quantities such as the volume of the manifold, and the index theorem, which relates the zero modes of the Dirac operator to characteristic classes of the manifold. These topics continue to be actively studied today.
On Lorentzian manifolds, which provide the geometric framework for relativity, the spectra of operators such as the d'Alembertian and the Dirac operator have also begun to attract increasing attention in recent years, partly because of applications to quantum theory. In contrast to the Riemannian setting, however, these differential operators are not elliptic, and many of the standard methods are therefore no longer directly applicable. As a result, even fundamental questions such as self-adjointness can be highly nontrivial.
In this talk, I will give an overview of known results on the spectra of differential operators on Riemannian and Lorentzian manifolds and, time permitting, present some of my own results.
Seminar on Probability and Statistics
15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Krzysztof Bartoszek (Department of Computer and Information Science, Linköping University)
An introduction to quadratic stochastic operators (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/JjtHEBHOT6m4SvmAcXrtWQ
Krzysztof Bartoszek (Department of Computer and Information Science, Linköping University)
An introduction to quadratic stochastic operators (English)
[ Abstract ]
Markov chains are inherently linear processes and also are not elegant for describing interactions between agents. For this end, non-linear models are needed, and quadratic stochastic operators (QSOs) are a first step. They describe mixing of two populations, e.g., sexual reproduction, where one parent comes from the female class and the other from the male class. Studying the law, even in the limit, of a population evolving under a QSO is a challenging task due to the interaction component between the two classes of individuals. Restricting the class of QSOs, to the so-called centred quadratic stochastic operators, one is able to show that, in the case of hermaphroditic species, when the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits, one can represent the law of the trait in descendant populations through an appropriate sum of independent random variables. QSOs can be further generalized to an arbitrary number of parents, and cubic stochastic operators are the next step.
[ Reference URL ]Markov chains are inherently linear processes and also are not elegant for describing interactions between agents. For this end, non-linear models are needed, and quadratic stochastic operators (QSOs) are a first step. They describe mixing of two populations, e.g., sexual reproduction, where one parent comes from the female class and the other from the male class. Studying the law, even in the limit, of a population evolving under a QSO is a challenging task due to the interaction component between the two classes of individuals. Restricting the class of QSOs, to the so-called centred quadratic stochastic operators, one is able to show that, in the case of hermaphroditic species, when the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits, one can represent the law of the trait in descendant populations through an appropriate sum of independent random variables. QSOs can be further generalized to an arbitrary number of parents, and cubic stochastic operators are the next step.
https://u-tokyo-ac-jp.zoom.us/meeting/register/JjtHEBHOT6m4SvmAcXrtWQ
2026/10/13
Tuesday Seminar on Topology
16:00-17:30 Room #hybrid/123 (Graduate School of Math. Sci. Bldg.)
Joint with LMI colloquium. Pre-registration required. See our seminar webpage.
Léo Bénard (Aix-Marseille Université, FJ-LMI CNRS)
On a Langlands duality conjecture for character varieties of 3 manifolds (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with LMI colloquium. Pre-registration required. See our seminar webpage.
Léo Bénard (Aix-Marseille Université, FJ-LMI CNRS)
On a Langlands duality conjecture for character varieties of 3 manifolds (ENGLISH)
[ Abstract ]
Inspired by a similar conjecture for skein modules of 3 manifolds formulated by Ben-Zvi, Gunningham, Jordan and Safronov, we conjecture that for G complex reductive group and L(G) its Langlands dual, for a 3 manifold M, if the character varieties X(M, G) and X(M, L(G)) are finite, then they have the same cardinality counted with multiplicity. We will discuss examples, non-examples, non-reduced points, and describe the cases where we can prove this statement. This is joint work with Renaud Detcherry (Dijon).
[ Reference URL ]Inspired by a similar conjecture for skein modules of 3 manifolds formulated by Ben-Zvi, Gunningham, Jordan and Safronov, we conjecture that for G complex reductive group and L(G) its Langlands dual, for a 3 manifold M, if the character varieties X(M, G) and X(M, L(G)) are finite, then they have the same cardinality counted with multiplicity. We will discuss examples, non-examples, non-reduced points, and describe the cases where we can prove this statement. This is joint work with Renaud Detcherry (Dijon).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Dustin Clausen (IHES)
A refinement of Serre's conjecture
Dustin Clausen (IHES)
A refinement of Serre's conjecture
[ Abstract ]
Gaitsgory-Raskin proved a remarkable theorem: in the function field setting, a certain natural vector space of (everywhere unramified) automorphic forms for GL_n is isomorphic to the global sections of the dualizing sheaf on a natural stack of Langlands parameters. I will describe an attempt to translate the statement of this theorem to the number field context, in the setting of mod p automorphic forms. The resulting conjectural statement is a variant of conjectures of Emerton-Zhu; for GL_2 it is a refinement of Khare-Wintenberger's theorem (formerly, Serre's conjecture) relating modular forms and Galois representations mod p.
Gaitsgory-Raskin proved a remarkable theorem: in the function field setting, a certain natural vector space of (everywhere unramified) automorphic forms for GL_n is isomorphic to the global sections of the dualizing sheaf on a natural stack of Langlands parameters. I will describe an attempt to translate the statement of this theorem to the number field context, in the setting of mod p automorphic forms. The resulting conjectural statement is a variant of conjectures of Emerton-Zhu; for GL_2 it is a refinement of Khare-Wintenberger's theorem (formerly, Serre's conjecture) relating modular forms and Galois representations mod p.
2026/10/08
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Note that the seminar will be held on Thursday.
Marcus Grote (University of Basel)
Adaptive FEM with Explicit Time Integration For the Wave Equation
(English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Note that the seminar will be held on Thursday.
Marcus Grote (University of Basel)
Adaptive FEM with Explicit Time Integration For the Wave Equation
(English)
[ Abstract ]
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time integration [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving meshes and local time-stepping to overcome any overly stringent CFL stability restriction on the time-step due to local mesh refinement. Moreover, at each time-step the adaptive algorithm monitors the accuracy thanks to the error indicators and recomputes the current step on a refined mesh until the desired tolerance is met; meanwhile, the mesh is coarsened in regions of smaller errors. Leapfrog based local time-stepping is applied in all regions of local mesh refinement to incorporate adaptivity into fully explicit time integration with mesh change while retaining efficiency. Numerical results illustrate the optimal rate of convergence of the a posteriori error estimators on time evolving meshes.
[ Reference URL ]Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time integration [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving meshes and local time-stepping to overcome any overly stringent CFL stability restriction on the time-step due to local mesh refinement. Moreover, at each time-step the adaptive algorithm monitors the accuracy thanks to the error indicators and recomputes the current step on a refined mesh until the desired tolerance is met; meanwhile, the mesh is coarsened in regions of smaller errors. Leapfrog based local time-stepping is applied in all regions of local mesh refinement to incorporate adaptivity into fully explicit time integration with mesh change while retaining efficiency. Numerical results illustrate the optimal rate of convergence of the a posteriori error estimators on time evolving meshes.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2026/10/06
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yohance Osborne (Durham University)
Numerical approximation of mean field games systems (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yohance Osborne (Durham University)
Numerical approximation of mean field games systems (English)
[ Abstract ]
Mean field games (MFG) are models for Nash equilibria of competitive differential games of optimal control involving a continuum of players. MFG equilibria are often described by systems of partial differential equations, where a Hamilton–Jacobi–Bellman (HJB) equation for the representative player’s value function is coupled nonlinearly with a Kolmogorov–Fokker–Planck (KFP) equation that determines the player distribution. MFG systems are particularly challenging to approximate computationally because they exhibit the following difficulties all at once: nonlinear couplings between the HJB and KFP equations, a temporal forward–backward structure, non-negativity of absolutely continuous player distributions, as well as potential nondifferentiability of the Hamiltonian. This talk addresses the numerical approximation of MFG systems for two classes of numerical schemes: (1) monotone stabilized finite element methods for second-order MFG systems with nondifferentiable Hamiltonians, and (2) particle methods for first-order MFG systems under displacement monotonicity. I will present theorems on the strong convergence of these numerical schemes and their rates of convergence, along with discussion of some numerical experiments.
[ Reference URL ]Mean field games (MFG) are models for Nash equilibria of competitive differential games of optimal control involving a continuum of players. MFG equilibria are often described by systems of partial differential equations, where a Hamilton–Jacobi–Bellman (HJB) equation for the representative player’s value function is coupled nonlinearly with a Kolmogorov–Fokker–Planck (KFP) equation that determines the player distribution. MFG systems are particularly challenging to approximate computationally because they exhibit the following difficulties all at once: nonlinear couplings between the HJB and KFP equations, a temporal forward–backward structure, non-negativity of absolutely continuous player distributions, as well as potential nondifferentiability of the Hamiltonian. This talk addresses the numerical approximation of MFG systems for two classes of numerical schemes: (1) monotone stabilized finite element methods for second-order MFG systems with nondifferentiable Hamiltonians, and (2) particle methods for first-order MFG systems under displacement monotonicity. I will present theorems on the strong convergence of these numerical schemes and their rates of convergence, along with discussion of some numerical experiments.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kouichi Taira (The University of Tokyo)
Large eigenvalues and logarithmic Weyl law of the Connes-Moscovici operator (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kouichi Taira (The University of Tokyo)
Large eigenvalues and logarithmic Weyl law of the Connes-Moscovici operator (JAPANESE)
[ Abstract ]
The Bohr-Sommerfeld quantization condition is a principle that describes the semiclassical eigenvalues of a quantum system in terms of action integrals along closed trajectories of the corresponding classical system. A refined quantization condition incorporating the Maslov index as a correction term was independently discovered by Keller and Maslov, and a mathematically rigorous framework was subsequently developed by Arnold and Hörmander. On the other hand, for one-dimensional Sturm-Liouville systems under suitable boundary conditions, it may give rise to discrete eigenvalues even in situations where the usual Bohr-Sommerfeld picture based on closed classical trajectories does not directly apply. In this talk, we focus on the prolate operator recently introduced by Connes and Moscovici, and explain how eigenvalues arise when the corresponding classical system has no closed trajectories, as well as how these eigenvalues can be related to action integrals and Maslov index. As an application, we present a result concerning a Weyl law with a logarithmic term, conjectured by Connes and Moscovici, which describes the asymptotic behavior of the eigenvalue counting function. This is a joint work with M. Willems(Utrecht University) and M.Wrochna (Utrecht University).
[ Reference URL ]The Bohr-Sommerfeld quantization condition is a principle that describes the semiclassical eigenvalues of a quantum system in terms of action integrals along closed trajectories of the corresponding classical system. A refined quantization condition incorporating the Maslov index as a correction term was independently discovered by Keller and Maslov, and a mathematically rigorous framework was subsequently developed by Arnold and Hörmander. On the other hand, for one-dimensional Sturm-Liouville systems under suitable boundary conditions, it may give rise to discrete eigenvalues even in situations where the usual Bohr-Sommerfeld picture based on closed classical trajectories does not directly apply. In this talk, we focus on the prolate operator recently introduced by Connes and Moscovici, and explain how eigenvalues arise when the corresponding classical system has no closed trajectories, as well as how these eigenvalues can be related to action integrals and Maslov index. As an application, we present a result concerning a Weyl law with a logarithmic term, conjectured by Connes and Moscovici, which describes the asymptotic behavior of the eigenvalue counting function. This is a joint work with M. Willems(Utrecht University) and M.Wrochna (Utrecht University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/10/05
Operator Algebra Seminars
15:30-17:00 Room # 126 (Graduate School of Math. Sci. Bldg.)
Takehiko Mori (Salesian Polytechnic)
The qx+r problem and the Cuntz algebra
Takehiko Mori (Salesian Polytechnic)
The qx+r problem and the Cuntz algebra
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Hisamoto (Nagoya Univ.)
Miyaoka–Yau inequality, delta invariant, and the Calabi functional (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Tomoyuki Hisamoto (Nagoya Univ.)
Miyaoka–Yau inequality, delta invariant, and the Calabi functional (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Tokyo Probability Seminar
16:50-18:20 Room #122 (Graduate School of Math. Sci. Bldg.)
The classroom is 122. No Tea Time today.
Dai Taguchi (Kansai University)
Euler–Maruyama scheme with unbounded Hölder drift
The classroom is 122. No Tea Time today.
Dai Taguchi (Kansai University)
Euler–Maruyama scheme with unbounded Hölder drift
[ Abstract ]
In this talk, we establish the strong rate of convergence of the Euler--Maruyama scheme for multidimensional stochastic differential equations with unbounded, uniformly locally Hölder continuous drift and multiplicative noise. Our approach relies on the Itô--Tanaka trick (Zvonkin-type transformation) adapted to unbounded drift. Furthermore, in order to apply the stochastic sewing lemma, we employ heat kernel estimates for the transition density of the Euler--Maruyama scheme. This talk is based on joint work with Tsukasa Moritoki (Okayama university).
In this talk, we establish the strong rate of convergence of the Euler--Maruyama scheme for multidimensional stochastic differential equations with unbounded, uniformly locally Hölder continuous drift and multiplicative noise. Our approach relies on the Itô--Tanaka trick (Zvonkin-type transformation) adapted to unbounded drift. Furthermore, in order to apply the stochastic sewing lemma, we employ heat kernel estimates for the transition density of the Euler--Maruyama scheme. This talk is based on joint work with Tsukasa Moritoki (Okayama university).
2026/10/02
Algebraic Geometry Seminar
10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
JongHae Keum (KIAS)
Automorphisms of Fermat quartic surface
JongHae Keum (KIAS)
Automorphisms of Fermat quartic surface
[ Abstract ]
In 1944 Beniamino Segre proved that the Fermat quartic surface in the 3-dimensional projective space has infinitely many discrete automorphisms. It was the first example of an algebraic surface with infinite discrete automorphism group. Since then, it has long been an open problem to find generators of its automorphism group.
On the other hand, any other Fermat hypersurface of dimension > 1 and degree > 2 admits only projectively linear automorphisms, and has finite automorphism group.
With Keiji Oguiso and Xun Yu, we solve this problem, finding 16 geometric generators of finite order.
I will present this result, along with history of computation of automorphism groups of other K3 surfaces.
In 1944 Beniamino Segre proved that the Fermat quartic surface in the 3-dimensional projective space has infinitely many discrete automorphisms. It was the first example of an algebraic surface with infinite discrete automorphism group. Since then, it has long been an open problem to find generators of its automorphism group.
On the other hand, any other Fermat hypersurface of dimension > 1 and degree > 2 admits only projectively linear automorphisms, and has finite automorphism group.
With Keiji Oguiso and Xun Yu, we solve this problem, finding 16 geometric generators of finite order.
I will present this result, along with history of computation of automorphism groups of other K3 surfaces.
2026/09/28
Tokyo Probability Seminar
14:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Stefan Junk ( Gakushuin University) 14:00-15:15
Some elements of the proof of equivalence of strong and very strong disorder for directed polymers (private seminar)
Dominik Schmid ( University of Augsburg) 16:00-17:30
The periodic directed landscape
We are having teatime from 15:20 in the common room on the second floor. Please join us.
Stefan Junk ( Gakushuin University) 14:00-15:15
Some elements of the proof of equivalence of strong and very strong disorder for directed polymers (private seminar)
Dominik Schmid ( University of Augsburg) 16:00-17:30
The periodic directed landscape
[ Abstract ]
The Kardar--Parisi--Zhang universality class is a central topic in mathematical physics and probability theory. In this talk, we discuss the conjectural scaling limit of periodic models in the Kardar--Parisi--Zhang universality class: the periodic directed landscape. We establish the convergence of periodic exponential last passage percolation to the periodic directed landscape and give a variational characterization of the periodic KPZ fixed point, recently constructed by Baik, Liao, and Liu. We also establish the convergence of periodic asymmetric simple exclusion processes to periodic KPZ fixed points, coupled through the same periodic directed landscape. A key ingredient is a gluing technique for combining overlapping directed landscapes, which may be of independent interest. This is based on joint work with Amol Aggarwal and Ivan Corwin.
The Kardar--Parisi--Zhang universality class is a central topic in mathematical physics and probability theory. In this talk, we discuss the conjectural scaling limit of periodic models in the Kardar--Parisi--Zhang universality class: the periodic directed landscape. We establish the convergence of periodic exponential last passage percolation to the periodic directed landscape and give a variational characterization of the periodic KPZ fixed point, recently constructed by Baik, Liao, and Liu. We also establish the convergence of periodic asymmetric simple exclusion processes to periodic KPZ fixed points, coupled through the same periodic directed landscape. A key ingredient is a gluing technique for combining overlapping directed landscapes, which may be of independent interest. This is based on joint work with Amol Aggarwal and Ivan Corwin.
2026/09/10
Tokyo Probability Seminar
14:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Lectures start earlier.
Sung-Soo Byun (Seoul National University) 14:00-15:30
Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
Lectures start earlier.
Sung-Soo Byun (Seoul National University) 14:00-15:30
Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
[ Abstract ]
Since the pioneering work of Johansson, geometric last passage percolation (LPP) has become one of the central models in integrable probability, with many remarkable properties established over the past two decades. Most existing results, particularly those admitting explicit formulae, however, concern homogeneous environments. In this talk, I will discuss geometric LPP in a particular inhomogeneous environment. Our approach is based on a duality with a q-deformed analogue of the classical Jacobi unitary ensemble. Exploiting recent developments in the asymptotic spectral analysis of this random matrix model, I will present recent results on the law of large numbers, an explicit characterisation of the shape function, and the fluctuation behaviour of the last passage time.
Jacek Wesolowski (Warsaw University of Technology) 16:00-17:30Since the pioneering work of Johansson, geometric last passage percolation (LPP) has become one of the central models in integrable probability, with many remarkable properties established over the past two decades. Most existing results, particularly those admitting explicit formulae, however, concern homogeneous environments. In this talk, I will discuss geometric LPP in a particular inhomogeneous environment. Our approach is based on a duality with a q-deformed analogue of the classical Jacobi unitary ensemble. Exploiting recent developments in the asymptotic spectral analysis of this random matrix model, I will present recent results on the law of large numbers, an explicit characterisation of the shape function, and the fluctuation behaviour of the last passage time.
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
[ Abstract ]
A map is independence preserving (IP) if there exists a product probability measure which is transferred by this map into to a product probability measures. Many classical examples of such maps and related probability laws are known probably the best known is the map (x,y)\mapsto (x+y, x-y) is an IP map for product of normal laws. Sasada and Uozumi (2024) identified IP a new family of parametric Yang-Baxter maps on positive quadrant together with related probability laws. In particular, the map H_{III,B}^{(\alpha,\beta)}, of this family was connected to the IP property of the GIG distributions. This IP property appears also naturally in probabilistic integrable models of discrete Korteweg de Vries type, as observed by Croydon and Sasada (2020). In the case of (\alpha,\beta)=(1,0), remarkably, this IP property reduces to the classical Matsumoto-Yor property rooted in the conditional structure of functionals of exponential Brownian motion.
We will propose an extension of H_{III,B}^{(\alpha,\beta)} to a Yang-Baxter map on the cone of symmetric positive definite matrices of a fixed dimension. We will show that this extended map preserves independence of GIG random matrices. We will present a proof that the matrix GIG distribution is characterized by the IP property of this map.
A map is independence preserving (IP) if there exists a product probability measure which is transferred by this map into to a product probability measures. Many classical examples of such maps and related probability laws are known probably the best known is the map (x,y)\mapsto (x+y, x-y) is an IP map for product of normal laws. Sasada and Uozumi (2024) identified IP a new family of parametric Yang-Baxter maps on positive quadrant together with related probability laws. In particular, the map H_{III,B}^{(\alpha,\beta)}, of this family was connected to the IP property of the GIG distributions. This IP property appears also naturally in probabilistic integrable models of discrete Korteweg de Vries type, as observed by Croydon and Sasada (2020). In the case of (\alpha,\beta)=(1,0), remarkably, this IP property reduces to the classical Matsumoto-Yor property rooted in the conditional structure of functionals of exponential Brownian motion.
We will propose an extension of H_{III,B}^{(\alpha,\beta)} to a Yang-Baxter map on the cone of symmetric positive definite matrices of a fixed dimension. We will show that this extended map preserves independence of GIG random matrices. We will present a proof that the matrix GIG distribution is characterized by the IP property of this map.
Infinite Analysis Seminar Tokyo
14:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Motohico Mulase (UC Davis)
The SL(2) that relates Gaiotto's Conformal Limit and the Geometric Langlands Correspondence (English)
Motohico Mulase (UC Davis)
The SL(2) that relates Gaiotto's Conformal Limit and the Geometric Langlands Correspondence (English)
[ Abstract ]
The purpose of this talk is to show that Gaiotto's "conformal limit" construction of opers via the non-Abelian Hodge correspondence gives the same map that appears in the Geometric Langlands Correspondence for the case of opers. The resulting map is a unique canonical biholomorphic map from the moduli space of G-spectral curves to the moduli space of LG-opers, both defined over a smooth complex projective curve X with a complex simple algebraic group G and its Langlands dual LG.
The Structure of the Talk:
In the first hour of the talk I will present the main theorem and explain motivational materials, including:
・The differential equations interpreting the stability conditions in algebraic geometry of moduli spaces;
・Simpson's NAH map between the moduli spaces of Higgs bundles and connections on X;
・The moduli space of opers that forms a Lagrangian in the moduli space of local systems on X;
・From a spectral curve to an oper as a quantization procedure; and
・The idea of Gaiotto on taking a scaling limit of NAH that changes a transcendental topological map into a calculable algebraic map.
In the second hour, I will talk about the following subjects:
・The Geometric Langlands Correspondence for the case of opers due to Beilinson-Drinfeld;
・Kostant's TDS;
・The proof of Gaiotto's conformal limit for the case of sl(2);
・GLC for sl(2);
・The parallelism of these proofs going from sl(2) to the general case through Kostant's TDS.
The purpose of this talk is to show that Gaiotto's "conformal limit" construction of opers via the non-Abelian Hodge correspondence gives the same map that appears in the Geometric Langlands Correspondence for the case of opers. The resulting map is a unique canonical biholomorphic map from the moduli space of G-spectral curves to the moduli space of LG-opers, both defined over a smooth complex projective curve X with a complex simple algebraic group G and its Langlands dual LG.
The Structure of the Talk:
In the first hour of the talk I will present the main theorem and explain motivational materials, including:
・The differential equations interpreting the stability conditions in algebraic geometry of moduli spaces;
・Simpson's NAH map between the moduli spaces of Higgs bundles and connections on X;
・The moduli space of opers that forms a Lagrangian in the moduli space of local systems on X;
・From a spectral curve to an oper as a quantization procedure; and
・The idea of Gaiotto on taking a scaling limit of NAH that changes a transcendental topological map into a calculable algebraic map.
In the second hour, I will talk about the following subjects:
・The Geometric Langlands Correspondence for the case of opers due to Beilinson-Drinfeld;
・Kostant's TDS;
・The proof of Gaiotto's conformal limit for the case of sl(2);
・GLC for sl(2);
・The parallelism of these proofs going from sl(2) to the general case through Kostant's TDS.
2026/09/09
FJ-LMI Seminar
11:15-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Léo BÉNARD (CNRS FJ-LMI)
Character varieties of knots, and the Reidemeister torsion function (英語)
https://fj-lmi.cnrs.fr/seminars
Léo BÉNARD (CNRS FJ-LMI)
Character varieties of knots, and the Reidemeister torsion function (英語)
[ Abstract ]
I will mainly motivate the study of Reidemeister torsion from a historical perspective, and highlight some recent related results and questions.
[ Reference URL ]I will mainly motivate the study of Reidemeister torsion from a historical perspective, and highlight some recent related results and questions.
https://fj-lmi.cnrs.fr/seminars
FJ-LMI Seminar
15:00-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Warm Up Session of the Workshop on Polylogarithms
Herbert GANGL (Durham University)
Introduction to polylogarithms, with connections to number theory and algebraic $K$-theory (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
Warm Up Session of the Workshop on Polylogarithms
Herbert GANGL (Durham University)
Introduction to polylogarithms, with connections to number theory and algebraic $K$-theory (英語)
[ Abstract ]
In this survey talk we discuss several basic properties of classical polylogarithms
$$ \mathrm{Li}_m(z)=\sum_{k\geq1}\frac{z^k}{k^m}
$$
in the unit disc, for $m \geq 1$, leading up to a beautiful connection to the algebraic $K$-theory of number
fields, motivated by an attempt to find a suitable generalisation of Dirichlet’s celebrated class number
formula. Bloch initiated this for the dilogarithm, and Zagier extended it to higher polylogarithms. It
turns out that an arguably even more suitable class of functions to describe this connection involves
multiple polylogarithms (MPLs = nested sums of classical ones, in several variables $z_1, \ldots , z_d)$. If time
allows, we will also try to give a glimpse of Goncharov’s highly relevant “depth reduction conjecture”
for MPLs and what is known about it.
[ Reference URL ]In this survey talk we discuss several basic properties of classical polylogarithms
$$ \mathrm{Li}_m(z)=\sum_{k\geq1}\frac{z^k}{k^m}
$$
in the unit disc, for $m \geq 1$, leading up to a beautiful connection to the algebraic $K$-theory of number
fields, motivated by an attempt to find a suitable generalisation of Dirichlet’s celebrated class number
formula. Bloch initiated this for the dilogarithm, and Zagier extended it to higher polylogarithms. It
turns out that an arguably even more suitable class of functions to describe this connection involves
multiple polylogarithms (MPLs = nested sums of classical ones, in several variables $z_1, \ldots , z_d)$. If time
allows, we will also try to give a glimpse of Goncharov’s highly relevant “depth reduction conjecture”
for MPLs and what is known about it.
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
FJ-LMI Seminar
16:15-17:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Warm Up Session of the Workshop on Polylogarithms
Luc PIRIO (CNRS FJ-LMI)
Polylogarithms and Webs
[ Reference URL ]
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
Warm Up Session of the Workshop on Polylogarithms
Luc PIRIO (CNRS FJ-LMI)
Polylogarithms and Webs
[ Reference URL ]
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
2026/08/21
Algebraic Geometry Seminar
13:15-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)
Heath Pearson (the University of Nottingham)
TBA
Heath Pearson (the University of Nottingham)
TBA
[ Abstract ]
TBA
TBA
2026/08/04
thesis presentations
16:15-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
朝永 龍 (東京大学大学院数理科学研究科)
d-Tilting bundles and applications to d-representation infinite algebras and non-commutative crepant resolutions
（d-傾束およびそのd-無限表現型代数と非可換クレパント特異点解消への応用）
朝永 龍 (東京大学大学院数理科学研究科)
d-Tilting bundles and applications to d-representation infinite algebras and non-commutative crepant resolutions
（d-傾束およびそのd-無限表現型代数と非可換クレパント特異点解消への応用）
2026/07/31
Algebraic Geometry Seminar
16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Adrian Langer (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
Adrian Langer (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
[ Abstract ]
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
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