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Seminar information archive ～01/13｜Today's seminar 01/14 | Future seminars 01/15～
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/
2026/01/16
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.
2026/01/19
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
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
2026/01/21
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
