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Seminar information archive
Seminar information archive ～01/20｜Today's seminar 01/21 | Future seminars 01/22～
2026/01/20
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Takumi Maegawa (The University of Tokyo)
A six-functor construction of the Bauer-Furuta invariant (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takumi Maegawa (The University of Tokyo)
A six-functor construction of the Bauer-Furuta invariant (JAPANESE)
[ Abstract ]
Building on the pioneering works of Verdier and Grothendieck, and later developed by Kashiwara-Schapira, the six-functor formalism for sheaves enables us to understand cohomological duality theorems and transfer maps in terms of certain (stable) ∞-categorical adjunction. Following Gaitsgory-Rozenblyum, these six operations fit into a single (∞,2)-functor out of the 2-category of correspondences. In this talk, we will recall these modern points of view on the six-functor formalism, and as an application, we will see that the stable homotopy theoretic refinement of the Seiberg-Witten invariant defined for a closed spin c four-manifold, introduced by Furuta and Bauer, does correspond to a 2-morphism in that (∞,2)-functoriality.
[ Reference URL ]Building on the pioneering works of Verdier and Grothendieck, and later developed by Kashiwara-Schapira, the six-functor formalism for sheaves enables us to understand cohomological duality theorems and transfer maps in terms of certain (stable) ∞-categorical adjunction. Following Gaitsgory-Rozenblyum, these six operations fit into a single (∞,2)-functor out of the 2-category of correspondences. In this talk, we will recall these modern points of view on the six-functor formalism, and as an application, we will see that the stable homotopy theoretic refinement of the Seiberg-Witten invariant defined for a closed spin c four-manifold, introduced by Furuta and Bauer, does correspond to a 2-morphism in that (∞,2)-functoriality.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/01/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room # (Graduate School of Math. Sci. Bldg.)
Online only (No in-person).
Peiqiang Lin ( )
Lemma on logarithmic derivative over directed manifolds (English)
https://forms.gle/gTP8qNZwPyQyxjTj8
Online only (No in-person).
Peiqiang Lin ( )
Lemma on logarithmic derivative over directed manifolds (English)
[ Abstract ]
The lemma on logarithmic derivative is the key lemma of Nevanlinna theory in one variable. In several variables case, there is also a crucial lemma in Ahlfors’ proof, which we refer to as Ahlfors’ lemma on logarithmic derivative.
In this talk, we will give a generalization of Ahlfors’ lemma on logarithmic derivative to directed projective manifolds in the language of Demailly-Simple jet towers. We also give Algebraic-Geometric Version of Ahlfors’ lemma on logarithmic derivative and its transform. Finally, we show that these help us to obtain a better result in the specific case.
[ Reference URL ]The lemma on logarithmic derivative is the key lemma of Nevanlinna theory in one variable. In several variables case, there is also a crucial lemma in Ahlfors’ proof, which we refer to as Ahlfors’ lemma on logarithmic derivative.
In this talk, we will give a generalization of Ahlfors’ lemma on logarithmic derivative to directed projective manifolds in the language of Demailly-Simple jet towers. We also give Algebraic-Geometric Version of Ahlfors’ lemma on logarithmic derivative and its transform. Finally, we show that these help us to obtain a better result in the specific case.
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.
Ryosuke Shimizu (Kyoto University)
Laakso-type fractal space上の解析学とSobolev空間の特異性
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Ryosuke Shimizu (Kyoto University)
Laakso-type fractal space上の解析学とSobolev空間の特異性
[ Abstract ]
近年のフラクタル上の解析学の進展により、Sierpinski gasketやSierpinski carpetといった典型的な自己相似集合上の(1,p)-Sobolev空間と対応する自己相似p-エネルギー形式が構成され、一階微分を捉えるためにp-walk次元という値が空間スケール指数として現れることが明らかになった。この値の挙動が種々の「特異性」と深く関係していると示唆されるが、そのような特異的現象の厳密な証明はSierpinski gasketの場合でも容易ではない。本講演では、Riku Anttila氏（University of Jyväskylä）とSylvester Eriksson-Bique氏（University of Jyväskylä）との共同研究（arXiv: 2503.13258）で得られた結果のうち、Laakso diamond spaceという空間上では、異なる指数p, qのSobolev空間の共通部分や、Sobolev空間とLipschitz関数の共通部分が定数関数のみになるという新たな特異的現象に関する結果を紹介する。
近年のフラクタル上の解析学の進展により、Sierpinski gasketやSierpinski carpetといった典型的な自己相似集合上の(1,p)-Sobolev空間と対応する自己相似p-エネルギー形式が構成され、一階微分を捉えるためにp-walk次元という値が空間スケール指数として現れることが明らかになった。この値の挙動が種々の「特異性」と深く関係していると示唆されるが、そのような特異的現象の厳密な証明はSierpinski gasketの場合でも容易ではない。本講演では、Riku Anttila氏（University of Jyväskylä）とSylvester Eriksson-Bique氏（University of Jyväskylä）との共同研究（arXiv: 2503.13258）で得られた結果のうち、Laakso diamond spaceという空間上では、異なる指数p, qのSobolev空間の共通部分や、Sobolev空間とLipschitz関数の共通部分が定数関数のみになるという新たな特異的現象に関する結果を紹介する。
2026/01/16
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Ryu Tomonaga (University of Tokyo)
On d-tilting bundles on d-folds
Ryu Tomonaga (University of Tokyo)
On d-tilting bundles on d-folds
[ Abstract ]
A d-tilting bundle is a tilting bundle whose endomorphism algebra has global dimension at most d. On d-dimensional smooth projective varieties, d-tilting bundles generalize geometric helices and play an important role in connections with tilting bundles on the total space of the canonical bundle (Calabi-Yau completion), non-commutative crepant resolutions and higher Auslander-Reiten theory.
In this talk, we prove the following results. First, if a d-dimensional smooth projective variety has a d-tilting bundle, then it is weak Fano. Second, every weak del Pezzo surface has a 2-tilting bundle. As an application, we show that every singular del Pezzo cone admits a non-commutative crepant resolution.
If time permits, we will also present a classification of d-tilting bundles consisting of line bundles on d-dimensional smooth toric Fano stacks of Picard number one or two.
A d-tilting bundle is a tilting bundle whose endomorphism algebra has global dimension at most d. On d-dimensional smooth projective varieties, d-tilting bundles generalize geometric helices and play an important role in connections with tilting bundles on the total space of the canonical bundle (Calabi-Yau completion), non-commutative crepant resolutions and higher Auslander-Reiten theory.
In this talk, we prove the following results. First, if a d-dimensional smooth projective variety has a d-tilting bundle, then it is weak Fano. Second, every weak del Pezzo surface has a 2-tilting bundle. As an application, we show that every singular del Pezzo cone admits a non-commutative crepant resolution.
If time permits, we will also present a classification of d-tilting bundles consisting of line bundles on d-dimensional smooth toric Fano stacks of Picard number one or two.
2026/01/15
Applied Analysis
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Tetsuya Kobayashi (Institute of Industrial Science, the University of Tokyo)
Chemical Reaction Network Theory through the Lens of Discrete Geometric Analysis (Japanese)
Tetsuya Kobayashi (Institute of Industrial Science, the University of Tokyo)
Chemical Reaction Network Theory through the Lens of Discrete Geometric Analysis (Japanese)
FJ-LMI Seminar
15:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
2026/01/14
Algebraic Geometry Seminar
13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Radu Laza (Stony Brook University)
Remarks on Lagrangian Fibrations on Hyperkähler Manifolds
Radu Laza (Stony Brook University)
Remarks on Lagrangian Fibrations on Hyperkähler Manifolds
[ Abstract ]
Hyperkähler manifolds are fundamental building blocks in the classification theory of algebraic varieties. A central problem is the finiteness of their deformation types, and, more ambitiously, the classification of these types. A natural approach to these questions is through the study of Lagrangian fibrations. In particular, the SYZ conjecture predicts that every deformation class of hyperkähler manifolds contains a member admitting a Lagrangian fibration.
In this talk, I will discuss several recent results on Lagrangian fibrations on hyperkähler manifolds. I will focus in particular on the special case of isotrivial Lagrangian fibrations, and on the striking fact that no such fibration exists in the exceptional OG10 deformation type. I will also briefly mention general boundedness results for Lagrangian fibrations, as well as results concerning the structure of their singular fibers. This latter part is largely based on the work of other authors, with some additional perspective and commentary of my own.
Hyperkähler manifolds are fundamental building blocks in the classification theory of algebraic varieties. A central problem is the finiteness of their deformation types, and, more ambitiously, the classification of these types. A natural approach to these questions is through the study of Lagrangian fibrations. In particular, the SYZ conjecture predicts that every deformation class of hyperkähler manifolds contains a member admitting a Lagrangian fibration.
In this talk, I will discuss several recent results on Lagrangian fibrations on hyperkähler manifolds. I will focus in particular on the special case of isotrivial Lagrangian fibrations, and on the striking fact that no such fibration exists in the exceptional OG10 deformation type. I will also briefly mention general boundedness results for Lagrangian fibrations, as well as results concerning the structure of their singular fibers. This latter part is largely based on the work of other authors, with some additional perspective and commentary of my own.
FJ-LMI Seminar
15:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Takuro Fukayama (University of Tokyo)
The number of cuspidal representations over a function field and its behavior under base changes
Takuro Fukayama (University of Tokyo)
The number of cuspidal representations over a function field and its behavior under base changes
[ Abstract ]
Cuspidal representations of a reductive group are largely determined by their local components. In the function field case, it is important to describe how the number of cuspidal representations with given local conditions changes under base changes. Assuming Arthur's simple trace formula for function fields, this number should be given by the sum of Gross's L-functions attached to some reductive groups. In this talk, I will explain the expression of the sum of L-functions and its behavior under base changes for some classical groups.
Cuspidal representations of a reductive group are largely determined by their local components. In the function field case, it is important to describe how the number of cuspidal representations with given local conditions changes under base changes. Assuming Arthur's simple trace formula for function fields, this number should be given by the sum of Gross's L-functions attached to some reductive groups. In this talk, I will explain the expression of the sum of L-functions and its behavior under base changes for some classical groups.
Tokyo Probability Seminar
15:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Xia Chen (University of Tennessee) 15:00-16:00
Hyperbolic Anderson equations and Brownian intersection local times
Moderate deviations for the capacity of the random walk range
Xia Chen (University of Tennessee) 15:00-16:00
Hyperbolic Anderson equations and Brownian intersection local times
[ Abstract ]
An idea recently merged from the investigation of hyperbolic Anderson equations is
to represent the chaos expansion of the solution in terms of Brownian intersection local
times. In this talk, I will address effeteness, current state, potentials and challenge about
this method.bPart of the talk comes from the work joined with Yaozhong Hu
Jiyun Park (Stanford University) 16:30-17:30An idea recently merged from the investigation of hyperbolic Anderson equations is
to represent the chaos expansion of the solution in terms of Brownian intersection local
times. In this talk, I will address effeteness, current state, potentials and challenge about
this method.bPart of the talk comes from the work joined with Yaozhong Hu
Moderate deviations for the capacity of the random walk range
[ Abstract ]
It is known that the capacity of the range of a random walk in d dimensions behaves similarly to the volume of the random walk in d-2 dimensions. In this talk, we extend this analogy to the moderate deviations of the capacity in dimension 5. In particular, we demonstrate that the large deviation principle transitions from a Gaussian tail to a non-Gaussian tail depending on the deviation scale. We also improve previously known results for dimension 4. Based on joint work with Arka Adhikari.
It is known that the capacity of the range of a random walk in d dimensions behaves similarly to the volume of the random walk in d-2 dimensions. In this talk, we extend this analogy to the moderate deviations of the capacity in dimension 5. In particular, we demonstrate that the large deviation principle transitions from a Gaussian tail to a non-Gaussian tail depending on the deviation scale. We also improve previously known results for dimension 4. Based on joint work with Arka Adhikari.
2026/01/13
Tuesday Seminar of Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Erbol Zhanpeisov (Tohoku University)
Blow-up rate for the subcritical semilinear heat equation in non-convex domains (Japanese)
Erbol Zhanpeisov (Tohoku University)
Blow-up rate for the subcritical semilinear heat equation in non-convex domains (Japanese)
[ Abstract ]
We study the blow-up rate for solutions of the subcritical semilinear heat equation. Type I blow-up means that the rate agrees with that of the associated ODE. In the Sobolev subcritical range, type I estimates have been proved for positive solutions in convex or general domains (Giga–Kohn ’87; Quittner ’21) and for sign-changing solutions in convex domains (Giga–Matsui–Sasayama ’04). We extend these results to sign-changing solutions in possibly non-convex domains. The proof uses the Giga-Kohn energy together with a geometric inequality that controls the effect of non-convexity. As a corollary, we obtain blow-up of the scaling critical norm in the subcritical range. Based on joint work with Hideyuki Miura and Jin Takahashi (Institute of Science Tokyo).
We study the blow-up rate for solutions of the subcritical semilinear heat equation. Type I blow-up means that the rate agrees with that of the associated ODE. In the Sobolev subcritical range, type I estimates have been proved for positive solutions in convex or general domains (Giga–Kohn ’87; Quittner ’21) and for sign-changing solutions in convex domains (Giga–Matsui–Sasayama ’04). We extend these results to sign-changing solutions in possibly non-convex domains. The proof uses the Giga-Kohn energy together with a geometric inequality that controls the effect of non-convexity. As a corollary, we obtain blow-up of the scaling critical norm in the subcritical range. Based on joint work with Hideyuki Miura and Jin Takahashi (Institute of Science Tokyo).
FJ-LMI Seminar
15:15-17:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Sogo Murakami (The University of Tokyo)
On the shadowing property of differentiable dynamical systems beyond structural stability (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Sogo Murakami (The University of Tokyo)
On the shadowing property of differentiable dynamical systems beyond structural stability (JAPANESE)
[ Abstract ]
The shadowing property, which has been extensively studied in connection with hyperbolic differentiable dynamical systems, is a dynamical concept ensuring that approximate orbits with small errors (commonly referred to as pseudo-orbits) can be traced by a true orbit. This property is one of the fundamental notions closely related to structural stability. In this talk, I will present the conditions under which the shadowing property holds for differentiable dynamical systems that are not structurally stable, in both discrete-time and continuous-time settings. In the first part of the talk, conditions guaranteeing the shadowing property for Axiom A diffeomorphisms will be discussed. In particular, I will explain the T^{s,u}-condition, and its relationship with the C^0-transversality condition introduced by PetrovPilyugin. I will then give a sufficient condition for having the shadowing property for Axiom A diffeomorphisms. In the second part, results concerning the shadowing property on chain recurrent sets for flows will be presented. While Robinson (1977) showed that every hyperbolic set exhibits the shadowing property, it is known that no singular hyperbolic set with non-isolated hyperbolic singularity, such as the Lorenz attractor, admits the shadowing property (Wen-Wen, 2020). Motivated by this, Arbieto et al. conjectured that any chain recurrent set with attached (non-isolated) hyperbolic singularities cannot possess the shadowing property. In this talk, a counterexample to this conjecture will be constructed.
[ Reference URL ]The shadowing property, which has been extensively studied in connection with hyperbolic differentiable dynamical systems, is a dynamical concept ensuring that approximate orbits with small errors (commonly referred to as pseudo-orbits) can be traced by a true orbit. This property is one of the fundamental notions closely related to structural stability. In this talk, I will present the conditions under which the shadowing property holds for differentiable dynamical systems that are not structurally stable, in both discrete-time and continuous-time settings. In the first part of the talk, conditions guaranteeing the shadowing property for Axiom A diffeomorphisms will be discussed. In particular, I will explain the T^{s,u}-condition, and its relationship with the C^0-transversality condition introduced by PetrovPilyugin. I will then give a sufficient condition for having the shadowing property for Axiom A diffeomorphisms. In the second part, results concerning the shadowing property on chain recurrent sets for flows will be presented. While Robinson (1977) showed that every hyperbolic set exhibits the shadowing property, it is known that no singular hyperbolic set with non-isolated hyperbolic singularity, such as the Lorenz attractor, admits the shadowing property (Wen-Wen, 2020). Motivated by this, Arbieto et al. conjectured that any chain recurrent set with attached (non-isolated) hyperbolic singularities cannot possess the shadowing property. In this talk, a counterexample to this conjecture will be constructed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lectures
16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Nobuo Sato (National Taiwan University)
反復ベータ積分とその応用 (日本語)
Nobuo Sato (National Taiwan University)
反復ベータ積分とその応用 (日本語)
2026/01/09
FJ-LMI Seminar
10:00-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas Karam (Shanghai Jiao Tong University)
Contributions of information theory to pure mathematics (英語)
[ Abstract ]
Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
[ Reference URL ]Information theory, founded by Shannon (1948), was originally motivated by communications engineering and has since grown to occupy a key role in several major approaches to artificial intelligence, including machine learning and neural networks, among others. Lecture 1 shall discuss the origins and the definition of Shannon entropy, as well as two approaches naturally leading to that definition. Lecture 2 shall then cover the definitions of the main central information-theoretic quantities aside from the Shannon entropies of random variables, and the main identities and inequalities that they satisfy. Lecture 3 will then specialise these results to recover many of the standard identities and inequalities involving dimensions of groups, dimensions of linear spaces and sizes of sets.
After that, Lectures 4,5,6,7 shall each illustrate a way in which basic information theory has provided tools that have enabled first proofs or new enlightening proofs of several results in pure mathematics that have simple and accessible formulations and are central to their respective areas. In probability, we shall highlight an entropy proof of the central limit theorem and the underlying analogy between Shannon entropy and thermodynamic entropy. In geometry, we shall explore applications of entropy to higher-dimensional geometry, in particular through Shearer’s lemma (1986) and the resulting control of the size of a set by its projections. In pure combinatorics, we shall focus on a breakthrough of Gilmer (2022) on the infamous conjecture of Frankl (1979) on union-closed families of sets. In combinatorial number theory, we shall outline the solution by Gowers, Green, Manners, Tao (2024) to Marton’s conjecture, one of the central problems of the area.
Finally, Lecture 8 will be devoted to a brief glimpse of the mathematically beautiful theory of information geometry recognised last year (2025) by the award of the Kyoto Prize to its founder Amari, and conclude with some of its practical applications – to neural networks – as Shannon presumably would have.
https://fj-lmi.cnrs.fr/seminars/
2026/01/07
Algebraic Geometry Seminar
10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Jun-Muk Hwang (IBS Center for Complex Geometry)
Fundamental forms and infinitesimal symmetries of projective varieties
Jun-Muk Hwang (IBS Center for Complex Geometry)
Fundamental forms and infinitesimal symmetries of projective varieties
[ Abstract ]
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset P^n$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset P^n$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms. This is a joint work with Qifeng Li.
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset P^n$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset P^n$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms. This is a joint work with Qifeng Li.
2026/01/06
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Xiaokun Xia (The University of Tokyo)
Reflection vectors in the quantum cohomology of a blowup (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Xiaokun Xia (The University of Tokyo)
Reflection vectors in the quantum cohomology of a blowup (ENGLISH)
[ Abstract ]
Let $X$ be a smooth projective variety with a semi-simple quantum cohomology. It is known that the blowup $\operatorname{Bl}_{\rm pt}(X)$ of $X$ at one point also has semi-simple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ is a reflection group. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ depending only on the geometry of the exceptional divisor.
[ Reference URL ]Let $X$ be a smooth projective variety with a semi-simple quantum cohomology. It is known that the blowup $\operatorname{Bl}_{\rm pt}(X)$ of $X$ at one point also has semi-simple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ is a reflection group. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ depending only on the geometry of the exceptional divisor.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/01/05
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasufumi Nitta (Tokyo Univ. of Science)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yasufumi Nitta (Tokyo Univ. of Science)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/12/26
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Nao Moriyama (Kyoto University)
Remarks on the minimal model theory for log surfaces in the analytic setting
Nao Moriyama (Kyoto University)
Remarks on the minimal model theory for log surfaces in the analytic setting
[ Abstract ]
In 2022, Fujino introduced a complex analytic framework for discussing the minimal model theory, in particular the minimal model program for projective morphisms of complex analytic spaces.
In this talk, I will discuss the minimal model theory for log surfaces in this setting. More precisely, I will show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of complex surfaces that are projective over complex analytic varieties.
In 2022, Fujino introduced a complex analytic framework for discussing the minimal model theory, in particular the minimal model program for projective morphisms of complex analytic spaces.
In this talk, I will discuss the minimal model theory for log surfaces in this setting. More precisely, I will show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of complex surfaces that are projective over complex analytic varieties.
Colloquium
15:30-16:30 Room #NISSAY Lecture Hall (大講義室) (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (Graduate School of Mathematical Sciences, The University of Tokyo)
Singularities and differential forms in positive characteristic (日本語)
Tatsuro Kawakami (Graduate School of Mathematical Sciences, The University of Tokyo)
Singularities and differential forms in positive characteristic (日本語)
[ Abstract ]
In this talk, I will focus on the local aspects of differential forms on algebraic varieties. I begin by reviewing prior results in characteristic zero concerning the extension problem, which asks whether reflexive differential forms can be lifted to birational models such as resolutions of singularities. I will then introduce a new approach to the extension problem in positive characteristic using the Cartier operator. If time permits, I will also discuss a new class of singularities in positive characteristic, defined via the Cartier operator.
In this talk, I will focus on the local aspects of differential forms on algebraic varieties. I begin by reviewing prior results in characteristic zero concerning the extension problem, which asks whether reflexive differential forms can be lifted to birational models such as resolutions of singularities. I will then introduce a new approach to the extension problem in positive characteristic using the Cartier operator. If time permits, I will also discuss a new class of singularities in positive characteristic, defined via the Cartier operator.
2025/12/23
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Mayuko Yamashita (Perimeter Institute for Theoretical Physics / RIKEN)
Geometric engineering in Topological Modular Forms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Mayuko Yamashita (Perimeter Institute for Theoretical Physics / RIKEN)
Geometric engineering in Topological Modular Forms (JAPANESE)
[ Abstract ]
I will explain my ongoing project to construct a functor from the category of conformal field theories to the TMF-module category, and realizing the symmetry of CFTs in genuine equivariance in TMF. I will explain the progress on the cases related to the K3 sigma model, with the motivation coming from the Mathieu moonshine.
[ Reference URL ]I will explain my ongoing project to construct a functor from the category of conformal field theories to the TMF-module category, and realizing the symmetry of CFTs in genuine equivariance in TMF. I will explain the progress on the cases related to the K3 sigma model, with the motivation coming from the Mathieu moonshine.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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)
Algebraic dynamics of Calabi-Yau manifolds of Wehler type (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Keiji Oguiso (Univ. of Tokyo)
Algebraic dynamics of Calabi-Yau manifolds of Wehler type (Japanese)
[ Abstract ]
A general hypersurface $X$ of multi-degree 2 in $(\Bbb P^1)^{d+1}$ is called a Calabi-Yau manifold of Wehler type (of dimension $d$). In this talk, after recalling some remarkable properties of $X$ found by Cantat and me, I would like to show that $X$ has a birational primitive automorphism, in particular a birational automorphism with Zariski dense orbit, in any $d \ge 2$.
[ Reference URL ]A general hypersurface $X$ of multi-degree 2 in $(\Bbb P^1)^{d+1}$ is called a Calabi-Yau manifold of Wehler type (of dimension $d$). In this talk, after recalling some remarkable properties of $X$ found by Cantat and me, I would like to show that $X$ has a birational primitive automorphism, in particular a birational automorphism with Zariski dense orbit, in any $d \ge 2$.
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo-Nagoya Algebra Seminar
16:30-18:00 Online
Riku Fushimi (Nagoya University)
siltingとsimple-minded collectionの双対性 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Riku Fushimi (Nagoya University)
siltingとsimple-minded collectionの双対性 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/12/20
Seminar on Probability and Statistics
10:30-17:10 Room # (Graduate School of Math. Sci. Bldg.)
- (-)
- (-)
[ Reference URL ]
https://sites.google.com/view/yuimatutorial2025/
- (-)
- (-)
[ Reference URL ]
https://sites.google.com/view/yuimatutorial2025/
2025/12/19
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Hokuto Konno (University of Tokyo)
On diffeomorphisms of complex surfaces
Hokuto Konno (University of Tokyo)
On diffeomorphisms of complex surfaces
[ Abstract ]
Many basic questions about the diffeomorphism groups of complex surfaces remain unresolved. For example, until recently it was unknown whether there exists a simply-connected complex surface admitting a diffeomorphism that acts trivially on the intersection form but is not isotopic to the identity. We have recently answered this question by showing that certain elliptic surfaces do admit such diffeomorphisms. These diffeomorphisms are obtained as suitable compositions of reflections along (-2)-curves. Moreover, this result also provides a negative answer to a question of Donaldson in symplectic geometry. This talk is based on joint work with David Baraglia, and with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
Many basic questions about the diffeomorphism groups of complex surfaces remain unresolved. For example, until recently it was unknown whether there exists a simply-connected complex surface admitting a diffeomorphism that acts trivially on the intersection form but is not isotopic to the identity. We have recently answered this question by showing that certain elliptic surfaces do admit such diffeomorphisms. These diffeomorphisms are obtained as suitable compositions of reflections along (-2)-curves. Moreover, this result also provides a negative answer to a question of Donaldson in symplectic geometry. This talk is based on joint work with David Baraglia, and with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
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