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Seminar information archive
Seminar information archive ～01/22｜Today's seminar 01/23 | Future seminars 01/24～
2026/01/22
thesis presentations
9:15-10:30 Room #118 (Graduate School of Math. Sci. Bldg.)
山本 寛史 (東京大学大学院数理科学研究科)
Computing the local 2-component of a non-selfdual automorphic representation of GL3
（GL3の非自己双対保型表現の局所2進成分の計算）
山本 寛史 (東京大学大学院数理科学研究科)
Computing the local 2-component of a non-selfdual automorphic representation of GL3
（GL3の非自己双対保型表現の局所2進成分の計算）
thesis presentations
11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)
高梨 悠吾 (東京大学大学院数理科学研究科)
On the Hiraga-Ichino-Ikeda conjecture on formal degrees for G2
（G2の形式次数における平賀・市野・池田予想について）
高梨 悠吾 (東京大学大学院数理科学研究科)
On the Hiraga-Ichino-Ikeda conjecture on formal degrees for G2
（G2の形式次数における平賀・市野・池田予想について）
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
三神 雄太郎 (東京大学大学院数理科学研究科)
(φ,Γ)-modules over relatively discrete algebras
（相対離散的な環上の(φ,Γ)加群）
三神 雄太郎 (東京大学大学院数理科学研究科)
(φ,Γ)-modules over relatively discrete algebras
（相対離散的な環上の(φ,Γ)加群）
thesis presentations
14:45-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)
軽部 友裕 (東京大学大学院数理科学研究科)
A study on Bridgeland stability conditions and the noncommutative minimal model program for blowup surfaces
（ブローアップ曲面に対するBridgeland 安定性条件と非可換極小モデルプログラムの研究）
軽部 友裕 (東京大学大学院数理科学研究科)
A study on Bridgeland stability conditions and the noncommutative minimal model program for blowup surfaces
（ブローアップ曲面に対するBridgeland 安定性条件と非可換極小モデルプログラムの研究）
thesis presentations
11:00-12:15 Room #122 (Graduate School of Math. Sci. Bldg.)
村上 聡梧 (東京大学大学院数理科学研究科)
On the shadowing property of differentiable dynamical systems beyond structural stability
(構造安定性を持たない可微分力学系の擬軌道追跡性について)
村上 聡梧 (東京大学大学院数理科学研究科)
On the shadowing property of differentiable dynamical systems beyond structural stability
(構造安定性を持たない可微分力学系の擬軌道追跡性について)
thesis presentations
13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)
前田 航志 (東京大学大学院数理科学研究科)
On the square integrability of regular representations on reductive homogeneous spaces
（簡約型等質空間上の正則表現の二乗可積分性について）
前田 航志 (東京大学大学院数理科学研究科)
On the square integrability of regular representations on reductive homogeneous spaces
（簡約型等質空間上の正則表現の二乗可積分性について）
thesis presentations
9:15-10:30 Room #126 (Graduate School of Math. Sci. Bldg.)
石倉 宙樹 (東京大学大学院数理科学研究科)
Decomposition of Borel graphs and cohomology
（ボレルグラフの分解とコホモロジー）
石倉 宙樹 (東京大学大学院数理科学研究科)
Decomposition of Borel graphs and cohomology
（ボレルグラフの分解とコホモロジー）
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
神田 秀峰 (東京大学大学院数理科学研究科)
Studies on Oeljeklaus–Toma manifolds
(Oeljeklaus–Toma多様体についての研究)
神田 秀峰 (東京大学大学院数理科学研究科)
Studies on Oeljeklaus–Toma manifolds
(Oeljeklaus–Toma多様体についての研究)
thesis presentations
14:45-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
粟津 光 (東京大学大学院数理科学研究科)
Amenability of group actions on compact spaces and the associated Banach algebras
（コンパクト空間への群作用の従順性と、作用に付随するバナッハ環の従順性に関して）
粟津 光 (東京大学大学院数理科学研究科)
Amenability of group actions on compact spaces and the associated Banach algebras
（コンパクト空間への群作用の従順性と、作用に付随するバナッハ環の従順性に関して）
thesis presentations
9:15-10:30 Room #128 (Graduate School of Math. Sci. Bldg.)
荒井 勇人 (東京大学大学院数理科学研究科)
Autoequivalences and stability conditions on a degenerate K3 surface
(退化K3曲面の自己同値と安定性条件)
荒井 勇人 (東京大学大学院数理科学研究科)
Autoequivalences and stability conditions on a degenerate K3 surface
(退化K3曲面の自己同値と安定性条件)
thesis presentations
13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)
吉田 淳一郎 (東京大学大学院数理科学研究科)
Quasi-Maximum Likelihood and Penalized Estimation for Non-Regular Models
(非正則モデルに対する擬似最尤推定および罰則付き推定)
吉田 淳一郎 (東京大学大学院数理科学研究科)
Quasi-Maximum Likelihood and Penalized Estimation for Non-Regular Models
(非正則モデルに対する擬似最尤推定および罰則付き推定)
thesis presentations
14:45-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
塩谷 天章 (東京大学大学院数理科学研究科)
Statistical inference for highly correlated point processes with applications to lead-lag analysis
(高相関点過程に対する統計推測とリード・ラグ解析への応用)
塩谷 天章 (東京大学大学院数理科学研究科)
Statistical inference for highly correlated point processes with applications to lead-lag analysis
(高相関点過程に対する統計推測とリード・ラグ解析への応用)
2026/01/21
Tuesday Seminar on Topology
16:00-17:00 Room #hybrid/118 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
Understanding the well-rounded deformation retraction of Teichmüller space (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
Understanding the well-rounded deformation retraction of Teichmüller space (ENGLISH)
[ Abstract ]
The term "well-rounded deformation retraction" goes back to a paper of Ash in which equivariant deformation retractions of the space of $n\times n$ positive-definite real symmetric matrices acted on by $SL(n,\mathbb{Z})$ were studied. An informal analogy between families of groups, such as $SL(n,\mathbb{Z})$, $Out(F_{n})$ and mapping class groups, suggests the existence of a similar equivariant deformation retractions of the actions of $Out(F_{n})$ and mapping class groups on well-chosen spaces. In all these examples, there are spaces on which the respective groups act with known equivariant deformation retractions onto cell complexes of the smallest possible dimension --- the virtual cohomological dimension of the group. The purpose of this talk is to explain that the equivariant deformation retraction of the action of the mapping class group on Teichmüller space can be understood to be a piecewise-smooth analogue of Ash's well rounded deformation retraction. The key idea is to understand the role of duality in correctly drawing this analogy.
[ Reference URL ]The term "well-rounded deformation retraction" goes back to a paper of Ash in which equivariant deformation retractions of the space of $n\times n$ positive-definite real symmetric matrices acted on by $SL(n,\mathbb{Z})$ were studied. An informal analogy between families of groups, such as $SL(n,\mathbb{Z})$, $Out(F_{n})$ and mapping class groups, suggests the existence of a similar equivariant deformation retractions of the actions of $Out(F_{n})$ and mapping class groups on well-chosen spaces. In all these examples, there are spaces on which the respective groups act with known equivariant deformation retractions onto cell complexes of the smallest possible dimension --- the virtual cohomological dimension of the group. The purpose of this talk is to explain that the equivariant deformation retraction of the action of the mapping class group on Teichmüller space can be understood to be a piecewise-smooth analogue of Ash's well rounded deformation retraction. The key idea is to understand the role of duality in correctly drawing this analogy.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/118 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Stavros Garoufalidis (Southern University of Science and Technology)
What are Lie superalgebras good for? (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Stavros Garoufalidis (Southern University of Science and Technology)
What are Lie superalgebras good for? (ENGLISH)
[ Abstract ]
I will try to answer, as honestly as I can, this question. Lie superalgebras are important in mathematical physics (supersymmetry), in representation theory, in categorification, in quantum topology, but also in classical topology. Namely, they may detect the genus of a smallest spanning surface of a knot. Come and listen about some theorems and experimental evidence, and decide for yourself if this is an accident, a conspiracy theory, or a manifestation of the truth!
[ Reference URL ]I will try to answer, as honestly as I can, this question. Lie superalgebras are important in mathematical physics (supersymmetry), in representation theory, in categorification, in quantum topology, but also in classical topology. Namely, they may detect the genus of a smallest spanning surface of a knot. Come and listen about some theorems and experimental evidence, and decide for yourself if this is an accident, a conspiracy theory, or a manifestation of the truth!
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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).
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