Text only print
Full screen print
Future seminars
Seminar information archive ～10/31｜Today's seminar 11/01 | Future seminars 11/02～
2025/11/04
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Kazuto Takao (Tohoku University)
Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kazuto Takao (Tohoku University)
Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups (JAPANESE)
[ Abstract ]
Casson-Gordon gave a criterion for Heegaard splittings of 3-manifolds to be strongly irreducible. By strengthening it, Lustig-Moriah gave a criterion for Goeritz groups of Heegaard splittings to be finite. Their criteria are based on Heegaard diagrams formed by maximal disk systems of the handlebodies. We generalize them for arbitrary disk systems, including minimal ones. As an application, we give Heegaard splittings with non-minimal genera and finite Goeritz groups. This is based on joint work with Yuya Koda.
[ Reference URL ]Casson-Gordon gave a criterion for Heegaard splittings of 3-manifolds to be strongly irreducible. By strengthening it, Lustig-Moriah gave a criterion for Goeritz groups of Heegaard splittings to be finite. Their criteria are based on Heegaard diagrams formed by maximal disk systems of the handlebodies. We generalize them for arbitrary disk systems, including minimal ones. As an application, we give Heegaard splittings with non-minimal genera and finite Goeritz groups. This is based on joint work with Yuya Koda.
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.)
Ryomei Iwasa (University of Copenhagen)
Descent and pro-excision
Ryomei Iwasa (University of Copenhagen)
Descent and pro-excision
[ Abstract ]
The theme of this talk is descent and excision of cohomology theories of schemes. We will start with a discussion of the canonical topology on spectral schemes. Unlike on classical schemes, this topology includes many other types of covers, such as h-covers. Then I will explain that THH and TC satisfy descent with respect to the canonical topology, which generalizes the flat descent by Bhatt—Morrow—Scholze. This in turn implies the cdh descent of K-theory on spectral schemes, despite its failure on classical schemes. Furthermore, this implies the cdh pro-excision of K-theory on spectral schemes, which generalizes the derived case by Kelly—Saito—Tamme (the original noetherian case is due to Kerz—Strunk—Tamme). Our proof of the cdh pro-excision is quite different from the previous ones and is more algebraic in nature. The results presented here are based on discussions with Antieau, Burklund, and Krause.
The theme of this talk is descent and excision of cohomology theories of schemes. We will start with a discussion of the canonical topology on spectral schemes. Unlike on classical schemes, this topology includes many other types of covers, such as h-covers. Then I will explain that THH and TC satisfy descent with respect to the canonical topology, which generalizes the flat descent by Bhatt—Morrow—Scholze. This in turn implies the cdh descent of K-theory on spectral schemes, despite its failure on classical schemes. Furthermore, this implies the cdh pro-excision of K-theory on spectral schemes, which generalizes the derived case by Kelly—Saito—Tamme (the original noetherian case is due to Kerz—Strunk—Tamme). Our proof of the cdh pro-excision is quite different from the previous ones and is more algebraic in nature. The results presented here are based on discussions with Antieau, Burklund, and Krause.
2025/11/06
Tokyo Probability Seminar
14:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
The lecture is on Thursday and start earlier. The classroom is 128. No teatime today.
Mo Dick Wong (Durham University) 14:00-15:30
On the limiting distribution of partial sums of random multiplicative functions
de Finetti Random Walks on a Hypercube and Gaussian Fields
The lecture is on Thursday and start earlier. The classroom is 128. No teatime today.
Mo Dick Wong (Durham University) 14:00-15:30
On the limiting distribution of partial sums of random multiplicative functions
[ Abstract ]
Consider a random walk associated with a Steinhaus multiplicative function (i.e. the increments are completely multiplicative and uniformly distributed on the complex unit circle): what can we say about its asymptotic behaviour? In his seminal work, Harper resolved a conjecture of Helson by showing that low fractional moments exhibit better-than-square-root cancellation, but the asymptotic distribution remained a mystery and was left as an open problem. In this talk, I will first explain some history and the number-theoretic motivations behind this model, and then present a central limit theorem that features a nonstandard renormalisation as well as a random variance described by the Riemann Zeta function on the critical line. I will highlight the probabilistic aspects of our proof, and in particular discuss a universality result for critical non-Gaussian multiplicative chaos. This is based on joint work with Ofir Gorodetsky.
Robert Griffiths (Monash University) 16:00-17:30Consider a random walk associated with a Steinhaus multiplicative function (i.e. the increments are completely multiplicative and uniformly distributed on the complex unit circle): what can we say about its asymptotic behaviour? In his seminal work, Harper resolved a conjecture of Helson by showing that low fractional moments exhibit better-than-square-root cancellation, but the asymptotic distribution remained a mystery and was left as an open problem. In this talk, I will first explain some history and the number-theoretic motivations behind this model, and then present a central limit theorem that features a nonstandard renormalisation as well as a random variance described by the Riemann Zeta function on the critical line. I will highlight the probabilistic aspects of our proof, and in particular discuss a universality result for critical non-Gaussian multiplicative chaos. This is based on joint work with Ofir Gorodetsky.
de Finetti Random Walks on a Hypercube and Gaussian Fields
[ Abstract ]
This talk will discuss a random walk on the infinite hypercube,
Xt+1 = Xt + Zt mod 2.
The increments (Zt) are i.i.d. with entries that form an infinite exchange- able {0,1} sequence, a de Finetti sequence. There is geometric killing in the random walk. A Gaussian free field (gx)x∈{0,1}∞ is associated with the random walk by taking the covariance function to be proportional to the Green function of the random walk. The Green function and a strong rep- resentation for (gx) are characterized by a negative binomial point process which involves the de Finetti measure of the increments of the random walk.
This talk will discuss a random walk on the infinite hypercube,
Xt+1 = Xt + Zt mod 2.
The increments (Zt) are i.i.d. with entries that form an infinite exchange- able {0,1} sequence, a de Finetti sequence. There is geometric killing in the random walk. A Gaussian free field (gx)x∈{0,1}∞ is associated with the random walk by taking the covariance function to be proportional to the Green function of the random walk. The Green function and a strong rep- resentation for (gx) are characterized by a negative binomial point process which involves the de Finetti measure of the increments of the random walk.
2025/11/10
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasufumi Nitta (Tokyo Univ. of Science)
(Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yasufumi Nitta (Tokyo Univ. of Science)
(Japanese)
[ Abstract ]
[ Reference URL ]https://forms.gle/gTP8qNZwPyQyxjTj8
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.
Yushi Hamaguchi (Kyoto University)
確率ヴォルテラ方程式のマルコフリフトの弱エルゴード性
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Yushi Hamaguchi (Kyoto University)
確率ヴォルテラ方程式のマルコフリフトの弱エルゴード性
[ Abstract ]
確率ヴォルテラ方程式の解は一般に非マルコフかつ非セミマルチンゲールであるような(有限次元)確率過程であるが、無限次元空間への持ち上げを考えることで、あるヒルベルト空間上のマルコフ過程(マルコフリフト)が得られる。
また、元の確率ヴォルテラ方程式の解は、このマルコフリフトのある種の射影として復元できる。
本研究の目的は、マルコフリフトの長時間漸近挙動を調べ、元の確率ヴォルテラ方程式の解に関する極限定理を得ることである。
そのうえで解決すべき難点は、マルコフリフトが満たす確率発展方程式が退化型であること、すなわち状態空間は無限次元であるが、ノイズを駆動するブラウン運動は有限次元であるという点である。
前回の東京確率論セミナー(2023年6月19日)では、マルコフリフトの漸近的対数ハルナック不等式、特に不変確率測度の一意性に関する結果を報告した。
本講演では、マルコフリフトの不変確率測度の存在性と指数型弱エルゴ―ド評価について、現在までに得られた研究成果を報告する。
確率ヴォルテラ方程式の解は一般に非マルコフかつ非セミマルチンゲールであるような(有限次元)確率過程であるが、無限次元空間への持ち上げを考えることで、あるヒルベルト空間上のマルコフ過程(マルコフリフト)が得られる。
また、元の確率ヴォルテラ方程式の解は、このマルコフリフトのある種の射影として復元できる。
本研究の目的は、マルコフリフトの長時間漸近挙動を調べ、元の確率ヴォルテラ方程式の解に関する極限定理を得ることである。
そのうえで解決すべき難点は、マルコフリフトが満たす確率発展方程式が退化型であること、すなわち状態空間は無限次元であるが、ノイズを駆動するブラウン運動は有限次元であるという点である。
前回の東京確率論セミナー(2023年6月19日)では、マルコフリフトの漸近的対数ハルナック不等式、特に不変確率測度の一意性に関する結果を報告した。
本講演では、マルコフリフトの不変確率測度の存在性と指数型弱エルゴ―ド評価について、現在までに得られた研究成果を報告する。
2025/11/11
Tuesday Seminar on Topology
9:30-10:30 Online
Pre-registration required. See our seminar webpage.
Richard Hain (Duke University)
Mapping class group actions on the homology of configuration spaces (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Richard Hain (Duke University)
Mapping class group actions on the homology of configuration spaces (ENGLISH)
[ Abstract ]
The action of the mapping class group of a surface S on the homology of the space F_n(S) of ordered configurations of n points in S is well understood when S has genus 0, but is not very well understood when S has positive genus. In this talk I will report on joint work with Clément Dupont (Montpellier) in the case where S is a surface of finite type of genus at least 2. We give a strong lower bound on the size of the Zariski closure of the image of the Torelli and mapping class groups in the automorphism group of the degree n cohomology of F_n(S). Our main tools are Hodge theory and the Goldman Lie algebra of the surface, which is the free abelian group generated by the conjugacy classes in the fundamental group of S.
[ Reference URL ]The action of the mapping class group of a surface S on the homology of the space F_n(S) of ordered configurations of n points in S is well understood when S has genus 0, but is not very well understood when S has positive genus. In this talk I will report on joint work with Clément Dupont (Montpellier) in the case where S is a surface of finite type of genus at least 2. We give a strong lower bound on the size of the Zariski closure of the image of the Torelli and mapping class groups in the automorphism group of the degree n cohomology of F_n(S). Our main tools are Hodge theory and the Goldman Lie algebra of the surface, which is the free abelian group generated by the conjugacy classes in the fundamental group of S.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Serban Matei Mihalache (The University of Tokyo)
Constructing solution of Polygon and Simplex equation (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Serban Matei Mihalache (The University of Tokyo)
Constructing solution of Polygon and Simplex equation (JAPANESE)
[ Abstract ]
The Polygon equation, formulated by Dimakis and Müller-Hoissen, can be interpreted as an algebraic equation corresponding to the Pachner (⌊(n+1)/2⌋+1, ⌈(n+1)/2⌉)-move on triangulations of n-dimensional PL manifolds, and is expected that this can be used to construct invariants of PL manifolds. In this talk, we show that solutions of higher-dimensional Polygon equations can be constructed from collections of "commutative" solutions of lower-dimensional Polygon equations, and we present explicit examples of such solutions. Furthermore, when a pair of solutions of the Polygon equation satisfies a condition called the mixed relation, we show that it gives rise to a solution of the Simplex equation, which is a higher-dimensional analogue of the Yang–Baxter equation. This talk is based on joint work with Tomoro Mochida.
[ Reference URL ]The Polygon equation, formulated by Dimakis and Müller-Hoissen, can be interpreted as an algebraic equation corresponding to the Pachner (⌊(n+1)/2⌋+1, ⌈(n+1)/2⌉)-move on triangulations of n-dimensional PL manifolds, and is expected that this can be used to construct invariants of PL manifolds. In this talk, we show that solutions of higher-dimensional Polygon equations can be constructed from collections of "commutative" solutions of lower-dimensional Polygon equations, and we present explicit examples of such solutions. Furthermore, when a pair of solutions of the Polygon equation satisfies a condition called the mixed relation, we show that it gives rise to a solution of the Simplex equation, which is a higher-dimensional analogue of the Yang–Baxter equation. This talk is based on joint work with Tomoro Mochida.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/11/12
FJ-LMI Seminar
15:00-15:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
This talk will provide an overview of a mini-course to be taught in January 2026 at the University of Tokyo, aimed at describing how Shannon entropy, a tool that was originally developed for and motivated by a rigorous mathematical analysis of communications engineering, later led to developments that can to some extent be viewed as taking place in a converse direction, where Shannon entropy provided insight into central basic questions in several fields of pure mathematics.
This talk will provide an overview of a mini-course to be taught in January 2026 at the University of Tokyo, aimed at describing how Shannon entropy, a tool that was originally developed for and motivated by a rigorous mathematical analysis of communications engineering, later led to developments that can to some extent be viewed as taking place in a converse direction, where Shannon entropy provided insight into central basic questions in several fields of pure mathematics.
Seminar on Probability and Statistics
10:30-11:40 Room #126 (Graduate School of Math. Sci. Bldg.)
Lars Winkelmann (Free University of Berlin)
Testing the Maximal Rank of Time-Varying Covariance Matrices in Noisy High-Frequency Data (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/eRqQutp7TTeKmqH2Vhm8Xg
Lars Winkelmann (Free University of Berlin)
Testing the Maximal Rank of Time-Varying Covariance Matrices in Noisy High-Frequency Data (English)
[ Abstract ]
We address the problem of testing the maximal rank of time-varying covariance matrices in high-frequency diffusion models observed with additive noise. Building on a spectral representation of the quadratic covariation operator, we construct test statistics based on empirical eigenvalues of localized spectral covariance matrices. The presence of observational noise and the rotation of the eigenspace introduce a fundamental bias-variance trade-off. We derive the optimal separation rate at which the tests retain power, showing its dependence on both the smoothness of the covariance process and the existence of a spectral gap. Our theoretical framework integrates matrix perturbation theory, concentration inequalities, and statistical lower bound approaches. Simulations illustrate the performance of our methods, and an application to portfolios of government bonds underscores their practical relevance in financial econometrics.
[ Reference URL ]We address the problem of testing the maximal rank of time-varying covariance matrices in high-frequency diffusion models observed with additive noise. Building on a spectral representation of the quadratic covariation operator, we construct test statistics based on empirical eigenvalues of localized spectral covariance matrices. The presence of observational noise and the rotation of the eigenspace introduce a fundamental bias-variance trade-off. We derive the optimal separation rate at which the tests retain power, showing its dependence on both the smoothness of the covariance process and the existence of a spectral gap. Our theoretical framework integrates matrix perturbation theory, concentration inequalities, and statistical lower bound approaches. Simulations illustrate the performance of our methods, and an application to portfolios of government bonds underscores their practical relevance in financial econometrics.
https://u-tokyo-ac-jp.zoom.us/meeting/register/eRqQutp7TTeKmqH2Vhm8Xg
FJ-LMI Seminar
15:45-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)
Raphaël LEFEVERE (Université de Paris Cité)
Macroscopic diffusion in random lattice Lorentz gases (英語)
https://fj-lmi.cnrs.fr/seminars/
Raphaël LEFEVERE (Université de Paris Cité)
Macroscopic diffusion in random lattice Lorentz gases (英語)
[ Abstract ]
I will present the general issues that have to be tackled when deriving macroscopic laws from microscopic deterministic laws of motion and a toy model where these issues may be solved.
[ Reference URL ]I will present the general issues that have to be tackled when deriving macroscopic laws from microscopic deterministic laws of motion and a toy model where these issues may be solved.
https://fj-lmi.cnrs.fr/seminars/
2025/11/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masanori Adachi (Shizuoka Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Masanori Adachi (Shizuoka Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/11/18
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Guanyu Zhou (University of Electronic Science and Technology of China)
The mixed methods for the variational inequalities (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Guanyu Zhou (University of Electronic Science and Technology of China)
The mixed methods for the variational inequalities (English)
[ Abstract ]
We propose new mixed formulations for variational inequalities arising from contact problems, aimed at improving the approximation of the stress tensor and displacement in numerical simulations. We establish the well-posedness of these mixed variational inequalities. Furthermore, we will present their finite element analysis.
[ Reference URL ]We propose new mixed formulations for variational inequalities arising from contact problems, aimed at improving the approximation of the stress tensor and displacement in numerical simulations. We establish the well-posedness of these mixed variational inequalities. Furthermore, we will present their finite element analysis.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2025/11/19
Infinite Analysis Seminar Tokyo
16:00-18:00 Room #156 (Graduate School of Math. Sci. Bldg.)
Hiroaki Karuo (Gakushuin)
Finite-dimensional irreducible representations of stated higher skein algebras and Fock--Goncharov algebras (JAPANESE)
Hiroaki Karuo (Gakushuin)
Finite-dimensional irreducible representations of stated higher skein algebras and Fock--Goncharov algebras (JAPANESE)
[ Abstract ]
The skein algebra is a quantum algebra defined from an oriented surface and $\mathfrak{sl}_2\mathbb{C}$. There is a
generalization with respect to $\mathfrak{sl}_n\mathbb{C}$, called the stated $\mathrm{SL}(n)$-skein algebra, related to higher Teich\"uller theory, which is compatible with splitting of a surface. To understand its algebraic structure, we would like to know finite-dimensional irreducible representations. Among its finite-dimensional irreducible representations, it is known that those with the highest dimension are one-to-one correspondence with the points of a subset of the maximal spectrum of its center. In this talk, I will start with basics of stated $\mathrm{SL}(n,\mathbb{C})$-skein algebras and explain how to use Fock--Goncharov algebras to understand the representations with the highest dimensions. This is a joint work with Zhihao Wang (KIAS).
The skein algebra is a quantum algebra defined from an oriented surface and $\mathfrak{sl}_2\mathbb{C}$. There is a
generalization with respect to $\mathfrak{sl}_n\mathbb{C}$, called the stated $\mathrm{SL}(n)$-skein algebra, related to higher Teich\"uller theory, which is compatible with splitting of a surface. To understand its algebraic structure, we would like to know finite-dimensional irreducible representations. Among its finite-dimensional irreducible representations, it is known that those with the highest dimension are one-to-one correspondence with the points of a subset of the maximal spectrum of its center. In this talk, I will start with basics of stated $\mathrm{SL}(n,\mathbb{C})$-skein algebras and explain how to use Fock--Goncharov algebras to understand the representations with the highest dimensions. This is a joint work with Zhihao Wang (KIAS).
2025/11/20
Applied Analysis
16:00-17:30 Room # 128 (Graduate School of Math. Sci. Bldg.)
Daisuke Naimen (Muroran Institute of Technology)
On the infinite concentration and the oscillation phenomena of spherically symmetric blow-up solutions of two-dimensional supercritical semilinear elliptic equations (Japanese)
Daisuke Naimen (Muroran Institute of Technology)
On the infinite concentration and the oscillation phenomena of spherically symmetric blow-up solutions of two-dimensional supercritical semilinear elliptic equations (Japanese)
2025/11/25
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Lars Diening (Bielefeld University)
Sobolev stability of the $L^2$-projection (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Lars Diening (Bielefeld University)
Sobolev stability of the $L^2$-projection (English)
[ Abstract ]
We prove the $W^{1,2}$-stability of the $L^2$-projection on Lagrange elements for adaptive meshes and arbitrary polynomial degree. This property is especially important for the numerical analysis of parabolic problems. We will explain that the stability of the projection is connected to the grading constants of the underlying adaptive refinement routine. For arbitrary dimensions, we show that the bisection algorithm of Maubach and Traxler produces meshes with a grading constant 2. This implies $W^{1,2}$-stability of the $L^2$-projection up to dimension six.
[ Reference URL ]We prove the $W^{1,2}$-stability of the $L^2$-projection on Lagrange elements for adaptive meshes and arbitrary polynomial degree. This property is especially important for the numerical analysis of parabolic problems. We will explain that the stability of the projection is connected to the grading constants of the underlying adaptive refinement routine. For arbitrary dimensions, we show that the bisection algorithm of Maubach and Traxler produces meshes with a grading constant 2. This implies $W^{1,2}$-stability of the $L^2$-projection up to dimension six.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Katsuhiko Kuribayashi (Shinshu University)
Interleavings of persistence dg-modules and Sullivan models for maps (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Katsuhiko Kuribayashi (Shinshu University)
Interleavings of persistence dg-modules and Sullivan models for maps (JAPANESE)
[ Abstract ]
The cohomology interleaving distance (CohID) is introduced and considered in the category of persistence differential graded modules. As a consequence, we show that, in the category, the distance coincides with the the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category (IDHC) in the sense of Lanari and Scoccola. Moreover, by applying the CohID to spaces over the classifying space of the circle group via the singular cochain functor, we have a numerical two-variable homotopy invariant for such spaces. In the latter half of the talk, we consider extended tame persistence commutative differential graded algebras (CDGA) associated with relative Sullivan algebras. Then, the IDHC enables us to introduce an extended pseudodistance between continuous maps with such persistence objects. By examining the pseudodistance, we see that the persistence CDGA is more `sensitive' than the persistence homology. This talk is based on joint work with Naito, Sekizuka, Wakatsuki and Yamaguchi.
[ Reference URL ]The cohomology interleaving distance (CohID) is introduced and considered in the category of persistence differential graded modules. As a consequence, we show that, in the category, the distance coincides with the the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category (IDHC) in the sense of Lanari and Scoccola. Moreover, by applying the CohID to spaces over the classifying space of the circle group via the singular cochain functor, we have a numerical two-variable homotopy invariant for such spaces. In the latter half of the talk, we consider extended tame persistence commutative differential graded algebras (CDGA) associated with relative Sullivan algebras. Then, the IDHC enables us to introduce an extended pseudodistance between continuous maps with such persistence objects. By examining the pseudodistance, we see that the persistence CDGA is more `sensitive' than the persistence homology. This talk is based on joint work with Naito, Sekizuka, Wakatsuki and Yamaguchi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/11/27
Colloquium
15:30-16:30 Room #NISSAY Lecture Hall (大講義室) (Graduate School of Math. Sci. Bldg.)
Ahmed Abbes (IHES)
The p-adic Simpson correspondence (English)
Ahmed Abbes (IHES)
The p-adic Simpson correspondence (English)
[ Abstract ]
The classical Simpson correspondence describes complex linear representations of the fundamental group of a smooth complex projective variety in terms of linear algebra objects, namely Higgs bundles. Inspired by this, Faltings initiated in 2005 a p-adic analogue, aiming to understand continuous p-adic representations of the geometric fundamental group of a smooth projective variety over a p-adic local field. Although the formulation mirrors the complex case, the methods in the p-adic setting are entirely different and build on ideas from Sen theory and Faltings’ approach to p-adic Hodge theory.
In this talk, I will survey the p-adic Simpson correspondence with a focus on the construction developed jointly with M. Gros, and on more recent work with M. Gros and T. Tsuji. In this latter work, we develop a new framework for studying the functoriality of the correspondence. The key idea is a novel twisting technique for Higgs modules using Higgs-Tate algebras, which is inspired by our earlier approach and encompasses it as a special case. The resulting framework provides twisted pullbacks and higher direct images of Higgs modules, allowing us to study the functoriality of the p-adic Simpson correspondence under arbitrary pullbacks and proper (log)smooth direct images by morphisms that do not necessarily lift to the infinitesimal deformations of the varieties chosen to construct the p-adic Simpson correspondence. Along the way, we clarify the relation of our framework with recent developments involving line bundles on the spectral variety.
The classical Simpson correspondence describes complex linear representations of the fundamental group of a smooth complex projective variety in terms of linear algebra objects, namely Higgs bundles. Inspired by this, Faltings initiated in 2005 a p-adic analogue, aiming to understand continuous p-adic representations of the geometric fundamental group of a smooth projective variety over a p-adic local field. Although the formulation mirrors the complex case, the methods in the p-adic setting are entirely different and build on ideas from Sen theory and Faltings’ approach to p-adic Hodge theory.
In this talk, I will survey the p-adic Simpson correspondence with a focus on the construction developed jointly with M. Gros, and on more recent work with M. Gros and T. Tsuji. In this latter work, we develop a new framework for studying the functoriality of the correspondence. The key idea is a novel twisting technique for Higgs modules using Higgs-Tate algebras, which is inspired by our earlier approach and encompasses it as a special case. The resulting framework provides twisted pullbacks and higher direct images of Higgs modules, allowing us to study the functoriality of the p-adic Simpson correspondence under arbitrary pullbacks and proper (log)smooth direct images by morphisms that do not necessarily lift to the infinitesimal deformations of the varieties chosen to construct the p-adic Simpson correspondence. Along the way, we clarify the relation of our framework with recent developments involving line bundles on the spectral variety.
2025/12/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Rei Murakami (Tohoku Univ.)
TBA
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Rei Murakami (Tohoku Univ.)
TBA
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/12/09
Tuesday Seminar of Analysis
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Marco Squassina (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
Marco Squassina (Università Cattolica del Sacro Cuore)
Log-concave solutions of the log-Schrodinger equation in a convex domain (English)
[ Abstract ]
First, we discuss some recent results on power concavity for certain classes of quasi-linear elliptic problems. We then turn our attention to a new problem involving the so-called log-Schrödinger equation, which cannot be addressed within the standard framework. To handle this, we introduce new techniques that lead to the existence of log-concave solutions to the log-Schrödinger equation in convex domains. Finally, we conclude with a brief discussion of (quantitative) partial concavity results for both elliptic and parabolic problems, as well as some perspectives on future developments concerning (quantitative) quasi-radiality results for problems in the ball.
First, we discuss some recent results on power concavity for certain classes of quasi-linear elliptic problems. We then turn our attention to a new problem involving the so-called log-Schrödinger equation, which cannot be addressed within the standard framework. To handle this, we introduce new techniques that lead to the existence of log-concave solutions to the log-Schrödinger equation in convex domains. Finally, we conclude with a brief discussion of (quantitative) partial concavity results for both elliptic and parabolic problems, as well as some perspectives on future developments concerning (quantitative) quasi-radiality results for problems in the ball.
2025/12/22
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Keiji Oguiso (Univ. of Tokyo)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Keiji Oguiso (Univ. of Tokyo)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
