## Seminar information archive

Seminar information archive ～06/12｜Today's seminar 06/13 | Future seminars 06/14～

### 2023/12/26

#### Tokyo-Nagoya Algebra Seminar

15:00-16:30 Room #ハイブリッド・002 (Graduate School of Math. Sci. Bldg.)

t-structures on the equivariant derived category of the Steinberg scheme (English)

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

**Ivan Losev**(Yale University)t-structures on the equivariant derived category of the Steinberg scheme (English)

[ Abstract ]

The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.

[ Reference URL ]The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2023/12/21

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Quantum Computing and Cryptography (Japanese)

**Takashi Yamakawa**(NTT)Quantum Computing and Cryptography (Japanese)

[ Abstract ]

I explain several topics on quantum computing and cryptography including quantum money and verification of quantum computation based on cryptography.

I explain several topics on quantum computing and cryptography including quantum money and verification of quantum computation based on cryptography.

### 2023/12/20

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)

**Jinhyun Park**(KAIST)Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)

[ Abstract ]

The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.

Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.

The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.

Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.

### 2023/12/19

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

Topological quantum computing, tensor networks and operator algebras (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Yasuyuki Kawahigashi**(The University of Tokyo)Topological quantum computing, tensor networks and operator algebras (JAPANESE)

[ Abstract ]

Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.

[ Reference URL ]Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2023/12/15

#### Algebraic Geometry Seminar

13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)

**Shihoko Ishii**(University of Tokyo)On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)

[ Abstract ]

In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.

In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.

#### Colloquium

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)

https://forms.gle/42wEF5c2pqsqrHqR7

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Mikiya Masuda**(Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)

[ Abstract ]

Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.

[ Reference URL ]Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.

https://forms.gle/42wEF5c2pqsqrHqR7

#### Infinite Analysis Seminar Tokyo

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)

**Laszlo Feher**(University of Szeged, Hungary)Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)

[ Abstract ]

We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models

built on collective spin variables.

Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,

as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,

which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation

from an associated Heisenberg double.

Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the

corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped

with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives

a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.

We also show that

a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context

of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.

Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,

without realizing the bi-Hamiltonian aspect.

Finally, if time permits, the degenerate integrability of some of the reduced systems

will be explained as well.

[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$

to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).

[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).

[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,

Nonlinearity 35, 2971-3003 (2022).

[4] L. Feher and B. Juhasz,

A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,

Lett. Math. Phys. 112:45 (2022).

[5] L. Feher,

Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of

compact Lie groups, arXiv:2309.16245

We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models

built on collective spin variables.

Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,

as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,

which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation

from an associated Heisenberg double.

Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the

corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped

with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives

a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.

We also show that

a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context

of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.

Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,

without realizing the bi-Hamiltonian aspect.

Finally, if time permits, the degenerate integrability of some of the reduced systems

will be explained as well.

[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$

to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).

[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).

[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,

Nonlinearity 35, 2971-3003 (2022).

[4] L. Feher and B. Juhasz,

A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,

Lett. Math. Phys. 112:45 (2022).

[5] L. Feher,

Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of

compact Lie groups, arXiv:2309.16245

### 2023/12/14

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

Torus orbit closures in the flag variety (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Mikiya Masuda**(Osaka City University)Torus orbit closures in the flag variety (JAPANESE)

[ Abstract ]

The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.

[ Reference URL ]The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Functional encryption and attribute-based encryption (Japanese)

**Junichi Tomida**(NTT)Functional encryption and attribute-based encryption (Japanese)

[ Abstract ]

I will explain the basics and the recent progress of functional encryption and attribute-based encryption.

I will explain the basics and the recent progress of functional encryption and attribute-based encryption.

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

On exact dg categories (English)

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

**Xiaofa Chen**(University of Science and Technology of China)On exact dg categories (English)

[ Abstract ]

In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.

[ Reference URL ]In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2023/12/12

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

Multivariable knot polynomials from braided Hopf algebras with automorphisms (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)Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)

[ Abstract ]

We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.

[ Reference URL ]We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2023/12/11

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On Partial deformations and Bers embedding (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

**Ryo Matsuda**(Kyoto Univeristy)On Partial deformations and Bers embedding (Japanese)

[ Abstract ]

The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.

[ Reference URL ]The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

### 2023/12/07

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Cryptographic Program Obfuscation and Its Applications (Japanese)

**Ryo Nishimaki**(NTT)Cryptographic Program Obfuscation and Its Applications (Japanese)

[ Abstract ]

I will explain what cryptographically secure program obfuscation is, how to achieve it, and its applications in this talk.

I will explain what cryptographically secure program obfuscation is, how to achieve it, and its applications in this talk.

### 2023/12/06

#### Infinite Analysis Seminar Tokyo

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

This seminar has been cancelled.

Flat coordinates of algebraic Frobenius manifolds (ENGLISH)

**Misha Feigin**(University of Glasgow)This seminar has been cancelled.

Flat coordinates of algebraic Frobenius manifolds (ENGLISH)

[ Abstract ]

This seminar has been cancelled.

Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.

This seminar has been cancelled.

Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.

### 2023/12/05

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

On the Euler class for flat S

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Teruaki Kitano**(Soka University)On the Euler class for flat S

^{1}-bundles, C^{∞}vs C^{ω}(JAPANESE)
[ Abstract ]

We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S

[ Reference URL ]We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S

^{1}in terms of BΓ_{1}by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S^{1}bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2023/12/04

#### FJ-LMI Seminar

14:00- Room #056 (Graduate School of Math. Sci. Bldg.)

An introduction to Einstein constraints and the seed-to-solution method

https://fj-lmi.cnrs.fr/seminars/

**Philippe G. LEFLOCH**(Sorbonne University & CNRS)An introduction to Einstein constraints and the seed-to-solution method

[ Abstract ]

I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).

[ Reference URL ]I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).

https://fj-lmi.cnrs.fr/seminars/

### 2023/11/30

#### Applied Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Einstein spacetimes: dispersion, localization, collapse, and bouncing (English)

https://forms.gle/HPsYinKweUW3AQGv9

**Philippe G. LeFloch**(Sorbonne University and CNRS)Einstein spacetimes: dispersion, localization, collapse, and bouncing (English)

[ Abstract ]

I will overview recent developments on Einstein's field equations of general relativity, especially the global evolution problem from initial data sets. A variety of phenomena may arise in this evolution: gravitational waves, dispersion, collapse, formation of singularities, and bouncing. While many problems remain widely open and very challenging, in the past decades major mathematical advances were made for several classes of spacetimes. I will review recent results on the (1) nonlinear stability of Minkowski spacetime, (2) localization problem at infinity, (3) collapse of spherically symmetric fields, and (4) scattering through quiescent singularity. This talk is based on joint work with Y. Ma (Xi'an), T.-C. Nguyen (Montpellier), F. Mena (Lisbon), B. Le Floch (Paris), and G. Veneziano (Geneva).

Blog: philippelefloch.org

[ Reference URL ]I will overview recent developments on Einstein's field equations of general relativity, especially the global evolution problem from initial data sets. A variety of phenomena may arise in this evolution: gravitational waves, dispersion, collapse, formation of singularities, and bouncing. While many problems remain widely open and very challenging, in the past decades major mathematical advances were made for several classes of spacetimes. I will review recent results on the (1) nonlinear stability of Minkowski spacetime, (2) localization problem at infinity, (3) collapse of spherically symmetric fields, and (4) scattering through quiescent singularity. This talk is based on joint work with Y. Ma (Xi'an), T.-C. Nguyen (Montpellier), F. Mena (Lisbon), B. Le Floch (Paris), and G. Veneziano (Geneva).

Blog: philippelefloch.org

https://forms.gle/HPsYinKweUW3AQGv9

### 2023/11/28

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

An analogue of the Johnson-Morita theory for the handlebody group (ENGLISH)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Gwénaël Massuyeau**(Université de Bourgogne)An analogue of the Johnson-Morita theory for the handlebody group (ENGLISH)

[ Abstract ]

The Johnson-Morita theory provides an approach for the mapping class group of a surface by considering its actions on the successive nilpotent quotients of the fundamental group of the surface. In this talk, after an outline of the original theory, we will present an analogue of the Johnson-Morita theory for the handlebody group, i.e. the mapping class group of a handlebody. This is joint work with Kazuo Habiro; as we shall explain if time allows, our motivation is to recover the "tree reduction" of a certain functor on the category of bottom tangles in handlebodies that we introduced (a few years ago) using the Kontsevich integral.

[ Reference URL ]The Johnson-Morita theory provides an approach for the mapping class group of a surface by considering its actions on the successive nilpotent quotients of the fundamental group of the surface. In this talk, after an outline of the original theory, we will present an analogue of the Johnson-Morita theory for the handlebody group, i.e. the mapping class group of a handlebody. This is joint work with Kazuo Habiro; as we shall explain if time allows, our motivation is to recover the "tree reduction" of a certain functor on the category of bottom tangles in handlebodies that we introduced (a few years ago) using the Kontsevich integral.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### FJ-LMI Seminar

16:00- Room #117 (Graduate School of Math. Sci. Bldg.)

Some contributions on variable selection in nonlinear mixed-effects models

https://fj-lmi.cnrs.fr/seminars/

**Maud DELATTRE**(Université Paris-Saclay, INRAE)Some contributions on variable selection in nonlinear mixed-effects models

[ Abstract ]

In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.

References

[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.

[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.

[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.

[ Reference URL ]In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.

References

[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.

[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.

[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.

https://fj-lmi.cnrs.fr/seminars/

### 2023/11/27

#### Seminar on Geometric Complex Analysis

11:00-12:30 Room #128 (Graduate School of Math. Sci. Bldg.)

On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

**Satoshi Ogawa**(Osaka Metropolitan University)On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)

[ Abstract ]

Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.

In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.

[ Reference URL ]Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.

In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

#### Tokyo Probability Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)

**Stefan Junk**(学習院大学)Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)

[ Abstract ]

We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time

polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show

that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.

We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time

polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show

that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.

### 2023/11/24

#### Algebraic Geometry Seminar

14:00-15:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

On Kawamata-Miyaoka type inequality

**Haidong Liu**(Sun Yat-sen University)On Kawamata-Miyaoka type inequality

[ Abstract ]

For klt projective varieties with nef and big canonical divisors, there exists a Miyaoka-Yau type inequality concerning the first and the second Chern classes. In this talk, I will present a Kawamata-Miyaoka type inequality for terminal Q-Fano varieties, which is a mirror version of the Miyaoka-Yau type inequality. This is a joint work with Jie Liu.

For klt projective varieties with nef and big canonical divisors, there exists a Miyaoka-Yau type inequality concerning the first and the second Chern classes. In this talk, I will present a Kawamata-Miyaoka type inequality for terminal Q-Fano varieties, which is a mirror version of the Miyaoka-Yau type inequality. This is a joint work with Jie Liu.

#### FJ-LMI Seminar

14:00-14:40 Room #117 (Graduate School of Math. Sci. Bldg.)

Surgery equivalence relations on 3-manifolds (English)

https://fj-lmi.cnrs.fr/seminars/

**Gwénaël MASSUYEAU**(Université de Bourgogne & CNRS)Surgery equivalence relations on 3-manifolds (English)

[ Abstract ]

By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.

[ Reference URL ]By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.

https://fj-lmi.cnrs.fr/seminars/

### 2023/11/22

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Torsion birational motives of surfaces and unramified cohomology (Japanese)

**Takao Yamazaki**(Chuo University)Torsion birational motives of surfaces and unramified cohomology (Japanese)

### 2023/11/21

#### Tuesday Seminar on Topology

17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

Shadows, divides and hyperbolic volumes (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Yuya Koda**(Keio University)Shadows, divides and hyperbolic volumes (JAPANESE)

[ Abstract ]

In 2008, Costantino and D.Thurston revealed that the combinatorial structure of the Stein factorizations of stable maps from 3-manifolds into the real plane can be used to describe the hyperbolic structures of the complement of the set of definite fold points, which is a link. The key was that the Stein factorizations can naturally be embedded into 4-manifolds, and nice ideal polyhedral decompositions become visible on their boundaries. In this talk, we consider divides, which are the images of a proper and generic immersions of compact 1-manifolds into the 2-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. By embedding a polyhedron induced from a given divide into the 4-ball as was done to Stein factorization, we can read off the ideal polyhedral decompositions on the boundary. We then show that the complement of the link of the divide can be obtained by Dehn filling a hyperbolic 3-manifold that admits a decomposition into several ideal regular hyperbolic polyhedra, where the number of each polyhedron is determined by types of the double points of the divide. This immediately gives an upper bound of the hyperbolic volume of the links of divides, which is shown to be asymptotically sharp. As in the case of Stein factorizations, an idea from the theory of Turaev's shadows plays an important role here. This talk is based on joint work with Ryoga Furutani (Hiroshima University).

[ Reference URL ]In 2008, Costantino and D.Thurston revealed that the combinatorial structure of the Stein factorizations of stable maps from 3-manifolds into the real plane can be used to describe the hyperbolic structures of the complement of the set of definite fold points, which is a link. The key was that the Stein factorizations can naturally be embedded into 4-manifolds, and nice ideal polyhedral decompositions become visible on their boundaries. In this talk, we consider divides, which are the images of a proper and generic immersions of compact 1-manifolds into the 2-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. By embedding a polyhedron induced from a given divide into the 4-ball as was done to Stein factorization, we can read off the ideal polyhedral decompositions on the boundary. We then show that the complement of the link of the divide can be obtained by Dehn filling a hyperbolic 3-manifold that admits a decomposition into several ideal regular hyperbolic polyhedra, where the number of each polyhedron is determined by types of the double points of the divide. This immediately gives an upper bound of the hyperbolic volume of the links of divides, which is shown to be asymptotically sharp. As in the case of Stein factorizations, an idea from the theory of Turaev's shadows plays an important role here. This talk is based on joint work with Ryoga Furutani (Hiroshima University).

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

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