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Seminar information archive
Seminar information archive ～01/14｜Today's seminar 01/15 | Future seminars 01/16～
2025/10/06
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuya Takeuchi (Univ. of Tsukuba)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuya Takeuchi (Univ. of Tsukuba)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
[ Abstract ]
The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
[ Reference URL ]The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
The lecture is starting late. No Tea Time today.
Hiroshi Kawabi (Keio University)
Riemann多様体上の排他過程に対する流体力学極限
The lecture is starting late. No Tea Time today.
Hiroshi Kawabi (Keio University)
Riemann多様体上の排他過程に対する流体力学極限
[ Abstract ]
(コンパクトとは限らない)完備なRiemann多様体をグラフで離散化し, その上の排他過程に対するスケール極限を考察する。
本講演では, 石渡 聡 氏 (山形大学), 角田 謙吉 氏 (九州大学)と現在進行中の共同研究に基づき, 流体力学極限について得られた成果を報告する。
(コンパクトとは限らない)完備なRiemann多様体をグラフで離散化し, その上の排他過程に対するスケール極限を考察する。
本講演では, 石渡 聡 氏 (山形大学), 角田 謙吉 氏 (九州大学)と現在進行中の共同研究に基づき, 流体力学極限について得られた成果を報告する。
2025/10/03
Seminar on Probability and Statistics
16:00-17:10 Room #123 (Graduate School of Math. Sci. Bldg.)
Freddy Delbaen (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
Freddy Delbaen (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
[ Abstract ]
With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
[ Reference URL ]With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
2025/09/25
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Fumihiko Onoue (Technische Universität München)
On the shape of fractional minimal surfaces (Japanese)
Fumihiko Onoue (Technische Universität München)
On the shape of fractional minimal surfaces (Japanese)
[ Abstract ]
Fractional perimeter (or fractional area) has been studied for more than a decade since Caffarelli, Roquejofffre, and Savin introduced its notion in 2010; however, there are still a lot of things unknown. In this talk, we discuss the shape of the boundary of sets minimizing their fractional perimeter under several boundary conditions, reviewing several interesting examples distinct from sets minimizing their classical perimeter. Moreover, if time permits, we present another notion of fractional area for smooth hypersurfaces with boundary, which was introduced by Paroni, Podio-Guidugli, and Seguin in 2018. Then we discuss the shape of critical points of their fractional area in several simple situations. This talk is partially based on a joint work with S. Dipierro and E. Valdinoci.
Fractional perimeter (or fractional area) has been studied for more than a decade since Caffarelli, Roquejofffre, and Savin introduced its notion in 2010; however, there are still a lot of things unknown. In this talk, we discuss the shape of the boundary of sets minimizing their fractional perimeter under several boundary conditions, reviewing several interesting examples distinct from sets minimizing their classical perimeter. Moreover, if time permits, we present another notion of fractional area for smooth hypersurfaces with boundary, which was introduced by Paroni, Podio-Guidugli, and Seguin in 2018. Then we discuss the shape of critical points of their fractional area in several simple situations. This talk is partially based on a joint work with S. Dipierro and E. Valdinoci.
2025/09/09
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Kang Li (FAU Erlangen-Nürnberg)
Dimension theories from groupoids to classifiable $C^*$-algebras, and back again
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/seminar/operalge/future.html
Kang Li (FAU Erlangen-Nürnberg)
Dimension theories from groupoids to classifiable $C^*$-algebras, and back again
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/seminar/operalge/future.html
2025/08/22
thesis presentations
16:00-17:15 Room #128 (Graduate School of Math. Sci. Bldg.)
HOSHINO Mao (東京大学大学院数理科学研究科)
A tensor categorical aspect of quantum group actions
(量子群作用のテンソル圏的様相)
HOSHINO Mao (東京大学大学院数理科学研究科)
A tensor categorical aspect of quantum group actions
(量子群作用のテンソル圏的様相)
2025/08/19
Algebraic Geometry Seminar
13:30-15:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Trung Tuyen Truong (University of Oslo)
Some new results concerning Tate's questions and generalisations
Trung Tuyen Truong (University of Oslo)
Some new results concerning Tate's questions and generalisations
[ Abstract ]
In the 1960s, Tate formulated (inspired by Weil's conjectures and a result of Serre on compact Kahler manifolds) a couple of questions concerning eigenvalues for pullback on cohomology of polarized endomorphisms. Grothendieck and Bombieri proposed Standard conjectures to solve these questions by Tate. The speaker, inspired by complex dynamics, proposed a generalisation of one of Tate's questions to rational maps and dynamical correspondences. This talk presents some new results and approaches (which are less demanding than the Standard conjectures, in that Standard Conjecture of Hodge type is not required) concerning these Tate's questions and generalisation. The talk includes joint works with Fei Hu and Junyi Xie.
In the 1960s, Tate formulated (inspired by Weil's conjectures and a result of Serre on compact Kahler manifolds) a couple of questions concerning eigenvalues for pullback on cohomology of polarized endomorphisms. Grothendieck and Bombieri proposed Standard conjectures to solve these questions by Tate. The speaker, inspired by complex dynamics, proposed a generalisation of one of Tate's questions to rational maps and dynamical correspondences. This talk presents some new results and approaches (which are less demanding than the Standard conjectures, in that Standard Conjecture of Hodge type is not required) concerning these Tate's questions and generalisation. The talk includes joint works with Fei Hu and Junyi Xie.
Tokyo-Nagoya Algebra Seminar
15:00-16:30 Online
Naoya Hiramae (Kyoto University)
自己入射的代数のCartan行列の正定値性と$\tau$-傾有限性 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Naoya Hiramae (Kyoto University)
自己入射的代数のCartan行列の正定値性と$\tau$-傾有限性 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Geometric Analysis Seminar
16:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Hiro Lee Tanaka (Texas State University)
For Liouville sectors, Floer theory in families without Floer theory in families
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Hiro Lee Tanaka (Texas State University)
For Liouville sectors, Floer theory in families without Floer theory in families
[ Abstract ]
Numbers do not have automorphisms, but most other mathematical objects do.
So when Floer theory yields non-numerical invariants, one can hope for symmetries to act on such invariants. Typically, one realizes these actions by carefully setting up an analytical framework for Floer theory to vary over the fibers of some bundle. In the setting of Floer theory for a class of symplectic manifolds called Liouville sectors, we show that a completely different technique -- localization of infinity-categories -- achieves the same goals, and more! This talk is based on some old joint work with Oleg Lazarev and Zachary Sylvan.
[ Reference URL ]Numbers do not have automorphisms, but most other mathematical objects do.
So when Floer theory yields non-numerical invariants, one can hope for symmetries to act on such invariants. Typically, one realizes these actions by carefully setting up an analytical framework for Floer theory to vary over the fibers of some bundle. In the setting of Floer theory for a class of symplectic manifolds called Liouville sectors, we show that a completely different technique -- localization of infinity-categories -- achieves the same goals, and more! This talk is based on some old joint work with Oleg Lazarev and Zachary Sylvan.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
2025/07/31
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
The lecture is on Thursday. The classroom is 128. We are having teatime from 15:15 in the common room on the second floor. Please join us.
Xinyi Li (Peking University)
Analyticity of 3D Brownian intersection exponents
The lecture is on Thursday. The classroom is 128. We are having teatime from 15:15 in the common room on the second floor. Please join us.
Xinyi Li (Peking University)
Analyticity of 3D Brownian intersection exponents
[ Abstract ]
In this talk, we will discuss the boundary Harnack principle (BHP) of the domain in \mathbb{R}^3 with the trace of a 3D Brownian motion removed and how it implies the analyticity of the intersection exponents for 3D Brownian motion. Based on a joint work (available at arXiv:2411.14921) with Yifan Gao (CityU HK), Yifan Li, Runsheng Liu and Xiangyi Liu (PKU).
In this talk, we will discuss the boundary Harnack principle (BHP) of the domain in \mathbb{R}^3 with the trace of a 3D Brownian motion removed and how it implies the analyticity of the intersection exponents for 3D Brownian motion. Based on a joint work (available at arXiv:2411.14921) with Yifan Gao (CityU HK), Yifan Li, Runsheng Liu and Xiangyi Liu (PKU).
2025/07/30
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Bruno Chiarellotto (Dipartimento di Matematica "Tullio Levi-Civita", Universita' degli Studi di Padova)
The tempered tube and the tempered cohomology
https://www.math.unipd.it/~chiarbru/
Bruno Chiarellotto (Dipartimento di Matematica "Tullio Levi-Civita", Universita' degli Studi di Padova)
The tempered tube and the tempered cohomology
[ Abstract ]
We will discuss a recent joint work with F. Bambozzi and P. Vanni (https://arxiv.org/abs/2410.09473). In the derived analytic spaces in the non arch. setting there are opens where the sections not only converge but they have also some arithmetic properties (log-growth). We will discuss how to construct such a spaces and we will give some applications: to the classical log-growth transfer theorem and on a new interpretation of convergent cohomology where one can replace the classical tube of the rigid cohomology with a "tempered one".
[ Reference URL ]We will discuss a recent joint work with F. Bambozzi and P. Vanni (https://arxiv.org/abs/2410.09473). In the derived analytic spaces in the non arch. setting there are opens where the sections not only converge but they have also some arithmetic properties (log-growth). We will discuss how to construct such a spaces and we will give some applications: to the classical log-growth transfer theorem and on a new interpretation of convergent cohomology where one can replace the classical tube of the rigid cohomology with a "tempered one".
https://www.math.unipd.it/~chiarbru/
2025/07/29
Numerical Analysis Seminar
16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Takashi Suzuki (Osaka University)
An analytic proof of the Hodge decomposition on bounded domains in Euclidean space and its applications (Japanese)
Takashi Suzuki (Osaka University)
An analytic proof of the Hodge decomposition on bounded domains in Euclidean space and its applications (Japanese)
2025/07/28
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Syota Esaki (Oita University)
Difference between n-dimensional Cauchy distribution and n-times product of Cauchy distribution from perspective of measure concentration
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Syota Esaki (Oita University)
Difference between n-dimensional Cauchy distribution and n-times product of Cauchy distribution from perspective of measure concentration
[ Abstract ]
確率解析と測度距離幾何学はそれぞれにおいて広く研究されているが，お互いの関わりはまだ深いとは言えない．ところが，両者ともに，極限定理，特に測度集中現象を通して深く関わりあうと考えることができる．本講演では確率論的な模型である多次元コーシー分布, または, 1次元コーシー分布の直積に基づく測度集中現象について述べ、それらの測度距離幾何的な相違点について述べる. 時間が許した場合には, これらに対応する安定分布の結果についても紹介する. この講演は東京都立大学の数川大輔氏と福岡大学の三石史人氏との共同研究に基づく．
確率解析と測度距離幾何学はそれぞれにおいて広く研究されているが，お互いの関わりはまだ深いとは言えない．ところが，両者ともに，極限定理，特に測度集中現象を通して深く関わりあうと考えることができる．本講演では確率論的な模型である多次元コーシー分布, または, 1次元コーシー分布の直積に基づく測度集中現象について述べ、それらの測度距離幾何的な相違点について述べる. 時間が許した場合には, これらに対応する安定分布の結果についても紹介する. この講演は東京都立大学の数川大輔氏と福岡大学の三石史人氏との共同研究に基づく．
2025/07/25
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
Izumi Okada (Graduate School of Mathematical Sciences, The University of Tokyo)
Recent Advances in Simple Random Walks (日本語)
Izumi Okada (Graduate School of Mathematical Sciences, The University of Tokyo)
Recent Advances in Simple Random Walks (日本語)
[ Abstract ]
A simple random walk is a stochastic process in which, for example in two dimensions, the walker moves at each time step to one of the four neighboring sites—up, down, left, or right—with equal probability 1/4. Although this model has been extensively studied for many years, a number of fundamental questions remain unsolved even in such a simple setting.In this talk, I will provide an overview of recent developments in the field, along with some of our recent results.
A simple random walk is a stochastic process in which, for example in two dimensions, the walker moves at each time step to one of the four neighboring sites—up, down, left, or right—with equal probability 1/4. Although this model has been extensively studied for many years, a number of fundamental questions remain unsolved even in such a simple setting.In this talk, I will provide an overview of recent developments in the field, along with some of our recent results.
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Akihiro Kanemitsu (Tokyo Metropolitan University)
Quintic del Pezzo threefolds in positive and mixed characteristic
Akihiro Kanemitsu (Tokyo Metropolitan University)
Quintic del Pezzo threefolds in positive and mixed characteristic
[ Abstract ]
We will show that, over any base scheme, (families of) quintic del Pezzo threefolds V5 are classified by non-degenerate ternary symmetric bilinear forms.
As applications, we will discuss (1) the geometry of quintic del Pezzo threefolds in positive characteristic, especially in characteristic two, and (2) finiteness results of V5 over number fields/rings of integers.
(Based on joint work with Tetsushi Ito, Teppei Takamatsu, Yuuji Tanaka)
We will show that, over any base scheme, (families of) quintic del Pezzo threefolds V5 are classified by non-degenerate ternary symmetric bilinear forms.
As applications, we will discuss (1) the geometry of quintic del Pezzo threefolds in positive characteristic, especially in characteristic two, and (2) finiteness results of V5 over number fields/rings of integers.
(Based on joint work with Tetsushi Ito, Teppei Takamatsu, Yuuji Tanaka)
2025/07/22
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Giovanni Ferrer (Ohio State University)
Higher quantum symmetries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Giovanni Ferrer (Ohio State University)
Higher quantum symmetries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Alexis Marchand (Kyoto University)
Sharp spectral gaps for scl from negative curvature (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Alexis Marchand (Kyoto University)
Sharp spectral gaps for scl from negative curvature (ENGLISH)
[ Abstract ]
Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
[ Reference URL ]Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
thesis presentations
11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)
KATAYAMA Sho (東京大学大学院数理科学研究科)
On positive solutions to inhomogeneous elliptic problems
on unbounded domains
(非有界傾域上の非斉次楕円型問題の正値解について)
KATAYAMA Sho (東京大学大学院数理科学研究科)
On positive solutions to inhomogeneous elliptic problems
on unbounded domains
(非有界傾域上の非斉次楕円型問題の正値解について)
2025/07/15
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Anastasiia Tsvietkova (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Anastasiia Tsvietkova (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (ENGLISH)
[ Abstract ]
For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. The surfaces are all closed essential surfaces, oriented and connected. This is joint work with Marc Lackenby.
[ Reference URL ]For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. The surfaces are all closed essential surfaces, oriented and connected. This is joint work with Marc Lackenby.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tokyo-Nagoya Algebra Seminar
15:30-17:00 Online
Shunsuke Hirota (Kyoto University)
super category Oにおけるsemibrick (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Shunsuke Hirota (Kyoto University)
super category Oにおけるsemibrick (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Lie Groups and Representation Theory
14:30-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazuki Kannaka (Kanazawa University)
Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spaces
Kazuki Kannaka (Kanazawa University)
Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spaces
[ Abstract ]
In higher-dimensional Riemannian compact locally symmetric spaces, rigidity theory has been developed by Selberg, Weil, Mostow, Margulis, and so on. On the other hand, since the late 1980s, Toshiyuki Kobayashi initiated the study of deformation theory for locally symmetric spaces beyond the Riemannian setting. In particular, a family of pseudo-Riemannian compact locally symmetric spaces of arbitrarily high dimension without local rigidity were discovered. In this talk, we focus on a class of pseudo-Riemannian compact locally symmetric spaces known as standard ones. We explore questions such as the following: (1) Do they possess local rigidity? (2) Can they be continuously deformed into non-standard ones? For example, we show that compact space forms of constant negative curvature with signature (4, 3) in dimension 7 admit continuous deformations, analogous to hyperbolic compact Riemann surfaces. These deformations are constructed using the bending construction, originally introduced by Thurston. This talk is based on joint work (arXiv:2507.03476) with Toshiyuki Kobayashi.
In higher-dimensional Riemannian compact locally symmetric spaces, rigidity theory has been developed by Selberg, Weil, Mostow, Margulis, and so on. On the other hand, since the late 1980s, Toshiyuki Kobayashi initiated the study of deformation theory for locally symmetric spaces beyond the Riemannian setting. In particular, a family of pseudo-Riemannian compact locally symmetric spaces of arbitrarily high dimension without local rigidity were discovered. In this talk, we focus on a class of pseudo-Riemannian compact locally symmetric spaces known as standard ones. We explore questions such as the following: (1) Do they possess local rigidity? (2) Can they be continuously deformed into non-standard ones? For example, we show that compact space forms of constant negative curvature with signature (4, 3) in dimension 7 admit continuous deformations, analogous to hyperbolic compact Riemann surfaces. These deformations are constructed using the bending construction, originally introduced by Thurston. This talk is based on joint work (arXiv:2507.03476) with Toshiyuki Kobayashi.
2025/07/14
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Hirotatsu Nagoji (Kyoto University)
Singularity of solutions to singular SPDEs
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Hirotatsu Nagoji (Kyoto University)
Singularity of solutions to singular SPDEs
[ Abstract ]
We give a sufficient condition for the marginal distribution of the solution to singular SPDEs on the $d$-dimensional torus to be singular with respect to the law of the Gaussian measure induced by the corresponding linear equation. As applications we obtain the singularity of the $\phi^4_3$-quantum field measure with respect to the Gaussian free field measure and the border of parameters for the fractional $\phi^4$-measure to be singular with respect to the base Gaussian measure. Our approach is applicable to quite a large class of singular SPDEs. This talk is based on a joint work with S. Kusuoka (Kyoto University) and M. Hairer (EPFL).
We give a sufficient condition for the marginal distribution of the solution to singular SPDEs on the $d$-dimensional torus to be singular with respect to the law of the Gaussian measure induced by the corresponding linear equation. As applications we obtain the singularity of the $\phi^4_3$-quantum field measure with respect to the Gaussian free field measure and the border of parameters for the fractional $\phi^4$-measure to be singular with respect to the base Gaussian measure. Our approach is applicable to quite a large class of singular SPDEs. This talk is based on a joint work with S. Kusuoka (Kyoto University) and M. Hairer (EPFL).
Infinite Analysis Seminar Tokyo
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Danilo Lewański (University of Trieste)
A spin on Gromov-Witten / Hurwitz correspondence and integrability
(English)
Danilo Lewański (University of Trieste)
A spin on Gromov-Witten / Hurwitz correspondence and integrability
(English)
[ Abstract ]
Hurwitz numbers enumerate branched coverings of Riemann surfaces and provide a rich sandbox of examples for enumerative geometry and neighbouring areas. Surprisingly, there is a formula that connects them to the intersection theory of the moduli spaces of stable curves: the ELSV formula. Furthermore, these numbers enjoy an integrability of type 2D-Toda as they can be expressed as vacuum expectations in the Fock space, result that has been later employed in the GW/Hurwitz correspondence.
A spin-off from the research on the mirror symmetry on Calabi-Yau 3-folds led to the spin generation of Hurwitz numbers via topological recursion. Over time this result has been generalised in different directions, including the Hurwitz count of Riemann surfaces with a spin structure, which are conjecturally determining Gromov-Witten invariants of surfaces with smooth canonical divisor. This led once more to the link with integrability, this time of type BKP.
Hurwitz numbers enumerate branched coverings of Riemann surfaces and provide a rich sandbox of examples for enumerative geometry and neighbouring areas. Surprisingly, there is a formula that connects them to the intersection theory of the moduli spaces of stable curves: the ELSV formula. Furthermore, these numbers enjoy an integrability of type 2D-Toda as they can be expressed as vacuum expectations in the Fock space, result that has been later employed in the GW/Hurwitz correspondence.
A spin-off from the research on the mirror symmetry on Calabi-Yau 3-folds led to the spin generation of Hurwitz numbers via topological recursion. Over time this result has been generalised in different directions, including the Hurwitz count of Riemann surfaces with a spin structure, which are conjecturally determining Gromov-Witten invariants of surfaces with smooth canonical divisor. This led once more to the link with integrability, this time of type BKP.
2025/07/10
Geometric Analysis Seminar
14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jeff Viaclovsky (University of California, Irvine)
Fibrations on the $6$-sphere and Clemens threefolds (英語)
Jeff Viaclovsky (University of California, Irvine)
Fibrations on the $6$-sphere and Clemens threefolds (英語)
[ Abstract ]
Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex space. In other words, $Z$ can only possibly fiber over a curve. This result applies in particular to a class of threefolds, known as Clemens threefolds, which are diffeomorphic to a connected sum of $k$ copies of $S^3 \times S^3$ for $k > 1$. This result also gives a new restriction on any hypothetical complex structure on the $6$-sphere $S^6$. This is joint work with Nobuhiro Honda.
Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex space. In other words, $Z$ can only possibly fiber over a curve. This result applies in particular to a class of threefolds, known as Clemens threefolds, which are diffeomorphic to a connected sum of $k$ copies of $S^3 \times S^3$ for $k > 1$. This result also gives a new restriction on any hypothetical complex structure on the $6$-sphere $S^6$. This is joint work with Nobuhiro Honda.
2025/07/08
Numerical Analysis Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Masaki Imagawa (Kyoto Univsersity)
Convergence analysis of perturbed advection equations in a bounded domain (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Masaki Imagawa (Kyoto Univsersity)
Convergence analysis of perturbed advection equations in a bounded domain (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
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