## Seminar information archive

Seminar information archive ～04/18｜Today's seminar 04/19 | Future seminars 04/20～

### 2022/06/21

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Cosmetic surgeries on knots in the 3-sphere (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Kazuhiro Ichihara**(Nihon University)Cosmetic surgeries on knots in the 3-sphere (JAPANESE)

[ Abstract ]

A pair of Dehn surgeries on a knot is called purely (resp. chirally) cosmetic if the obtained manifolds are orientation-preservingly (resp. -reversingly) homeomorphic. It is conjectured that if a knot in the 3-sphere admits purely (resp. chirally) cosmetic surgeries, then the knot is a trivial knot (resp. a torus knot or an amphicheiral knot). In this talk, after giving a brief survey on the studies on these conjectures, I will explain recent progresses on the conjectures. This is based on joint works with Tetsuya Ito (Kyoto University), In Dae Jong (Kindai University), and Toshio Saito (Joetsu University of Education).

[ Reference URL ]A pair of Dehn surgeries on a knot is called purely (resp. chirally) cosmetic if the obtained manifolds are orientation-preservingly (resp. -reversingly) homeomorphic. It is conjectured that if a knot in the 3-sphere admits purely (resp. chirally) cosmetic surgeries, then the knot is a trivial knot (resp. a torus knot or an amphicheiral knot). In this talk, after giving a brief survey on the studies on these conjectures, I will explain recent progresses on the conjectures. This is based on joint works with Tetsuya Ito (Kyoto University), In Dae Jong (Kindai University), and Toshio Saito (Joetsu University of Education).

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

### 2022/06/20

#### Seminar on Geometric Complex Analysis

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

Constructions of CR GJMS operators in dimension three (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Taiji Marugame**(The University of Electro-Communications)Constructions of CR GJMS operators in dimension three (Japanese)

[ Abstract ]

CR GJMS operators are invariant differential operators on CR manifolds whose leading parts are powers of the sublaplacian. Such operators can be constructed by Fefferman's ambient metric or the Cheng-Yau metric, but the construction is obstructed at a finite order due to the ambiguity of these metrics. Gover-Graham constructed some higher order CR GJMS operators by using tractor calculus and BGG constructions. In particular, they showed that three dimensional CR manifolds admit CR GJMS operators of all orders. In this talk, we give proofs to this fact in two different ways. One is by the use of self-dual Einstein ACH metric and the other is by the Graham-Hirachi inhomogeneous ambient metric adapted to the Fefferman conformal structure. We also state a conjecture on the relationship between these two metrics.

[ Reference URL ]CR GJMS operators are invariant differential operators on CR manifolds whose leading parts are powers of the sublaplacian. Such operators can be constructed by Fefferman's ambient metric or the Cheng-Yau metric, but the construction is obstructed at a finite order due to the ambiguity of these metrics. Gover-Graham constructed some higher order CR GJMS operators by using tractor calculus and BGG constructions. In particular, they showed that three dimensional CR manifolds admit CR GJMS operators of all orders. In this talk, we give proofs to this fact in two different ways. One is by the use of self-dual Einstein ACH metric and the other is by the Graham-Hirachi inhomogeneous ambient metric adapted to the Fefferman conformal structure. We also state a conjecture on the relationship between these two metrics.

https://forms.gle/hYT2hVhDE3q1wDSh6

#### Number Theory Seminar

15:00-16:00 Hybrid

p-adic weight-monodromy conjecture for complete intersections (Japanese)

**Hiroki Kato**(Paris-Saclay University)p-adic weight-monodromy conjecture for complete intersections (Japanese)

### 2022/06/16

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers X (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers X (Japanese)

[ Abstract ]

Error-correcting of quantum computer

Error-correcting of quantum computer

### 2022/06/15

#### Number Theory Seminar

17:00-18:00 Hybrid

Steinberg symbols and reciprocity sheaves (JAPANESE)

**Junnosuke Koizumi**(University of Tokyo)Steinberg symbols and reciprocity sheaves (JAPANESE)

[ Abstract ]

The norm residue symbol and the differential symbol are known to satisfy the common relation $(a,1-a)=0$ which is called the Steinberg relation. Hu-Kriz showed that the Steinberg relation can be understood as a relation between certain morphisms in the stable motivic homotopy category. On the other hand, there is also an “additive variant” of the Steinberg relation, namely $(a,a)+(1-a,1-a)=0$, for which the classical motivic theory is no longer applicable. In this talk we will explain how the theory of reciprocity sheaves due to Kahn-Saito-Yamazaki can be utilized to generalize the theory of Hu-Kriz to include the additive Steinberg relation.

The norm residue symbol and the differential symbol are known to satisfy the common relation $(a,1-a)=0$ which is called the Steinberg relation. Hu-Kriz showed that the Steinberg relation can be understood as a relation between certain morphisms in the stable motivic homotopy category. On the other hand, there is also an “additive variant” of the Steinberg relation, namely $(a,a)+(1-a,1-a)=0$, for which the classical motivic theory is no longer applicable. In this talk we will explain how the theory of reciprocity sheaves due to Kahn-Saito-Yamazaki can be utilized to generalize the theory of Hu-Kriz to include the additive Steinberg relation.

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room # Zoomによるオンライン開催 (Graduate School of Math. Sci. Bldg.)

This seminar is held on Wednesday.

Voxel-based fluid-structure interaction methods (日本語)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/82678271212?pwd=S05lczNlK2ZHM1BwMk5RRnhQTjcrdz09

This seminar is held on Wednesday.

**Kazuyasu Sugiyama**(Graduate School of Engineering Science, Osaka University)Voxel-based fluid-structure interaction methods (日本語)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/82678271212?pwd=S05lczNlK2ZHM1BwMk5RRnhQTjcrdz09

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

Please see the reference URL for details on the online seminar.

Cyclic polytopes and higher Auslander--Reiten theory 1 (English)

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

Please see the reference URL for details on the online seminar.

**Nicholas Williams**(The University of Tokyo)Cyclic polytopes and higher Auslander--Reiten theory 1 (English)

[ Abstract ]

In this series of three talks, we expand upon the previous talk given at the seminar and study the relationship between cyclic polytopes and higher Auslander--Reiten theory in more detail.

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNA/2021/Williams-Cyclic_polytopes_and_higher_AR.pdf

In the first talk, we focus on cyclic polytopes. We survey important properties of cyclic polytopes, such as different ways to construct them, the Upper Bound Theorem, and their Ramsey-theoretic properties. We then move on to triangulations of cyclic polytopes. We give efficient combinatorial descriptions of triangulations of even-dimensional and odd-dimensional cyclic polytopes, which we will use in subsequent talks. We finally define the higher Stasheff--Tamari orders on triangulations of cyclic polytopes. We give important results on the orders, including Rambau's Theorem, and the equality of the two orders.

[ Reference URL ]In this series of three talks, we expand upon the previous talk given at the seminar and study the relationship between cyclic polytopes and higher Auslander--Reiten theory in more detail.

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNA/2021/Williams-Cyclic_polytopes_and_higher_AR.pdf

In the first talk, we focus on cyclic polytopes. We survey important properties of cyclic polytopes, such as different ways to construct them, the Upper Bound Theorem, and their Ramsey-theoretic properties. We then move on to triangulations of cyclic polytopes. We give efficient combinatorial descriptions of triangulations of even-dimensional and odd-dimensional cyclic polytopes, which we will use in subsequent talks. We finally define the higher Stasheff--Tamari orders on triangulations of cyclic polytopes. We give important results on the orders, including Rambau's Theorem, and the equality of the two orders.

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

### 2022/06/14

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

Cartan calculi on the free loop spaces (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Katsuhiko Kuribayashi**(Shinshu University)Cartan calculi on the free loop spaces (JAPANESE)

[ Abstract ]

A typical example of a Cartan calculus is the Lie algebra representation of vector fields of a manifold on the derivation ring of the de Rham complex. In this talk, a `second stage' of the Cartan calculus is investigated. In a more general setting, the stage is formulated with a Lie algebra representation of the Andre-Quillen cohomology of a commutative differential graded algebra A on the endomorphism ring of the Hochschild homology of A in terms of the homotopy Cartan calculi in the sense of Fiorenza and Kowalzig. Moreover, the Lie algebra representation in the Cartan calculus is interpreted geometrically as a map from the rational homotopy group of the monoid of self-homotopy equivalences on a simply-connected space M to the derivation ring on the loop cohomology of M. An extension of the representation to the string cohomology and its geometric counterpart are also discussed together with the BV exactness which is a new rational homotopy invariant introduced in our work. This talk is based on joint work in progress with T. Naito, S. Wakatsuki and T. Yamaguchi.

[ Reference URL ]A typical example of a Cartan calculus is the Lie algebra representation of vector fields of a manifold on the derivation ring of the de Rham complex. In this talk, a `second stage' of the Cartan calculus is investigated. In a more general setting, the stage is formulated with a Lie algebra representation of the Andre-Quillen cohomology of a commutative differential graded algebra A on the endomorphism ring of the Hochschild homology of A in terms of the homotopy Cartan calculi in the sense of Fiorenza and Kowalzig. Moreover, the Lie algebra representation in the Cartan calculus is interpreted geometrically as a map from the rational homotopy group of the monoid of self-homotopy equivalences on a simply-connected space M to the derivation ring on the loop cohomology of M. An extension of the representation to the string cohomology and its geometric counterpart are also discussed together with the BV exactness which is a new rational homotopy invariant introduced in our work. This talk is based on joint work in progress with T. Naito, S. Wakatsuki and T. Yamaguchi.

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

### 2022/06/09

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers IX (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers IX (Japanese)

[ Abstract ]

On stabilizer codes and toric codes

On stabilizer codes and toric codes

### 2022/06/08

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

Please see the reference URL for details on the online seminar.

超平面配置の特性準多項式 II (Japanese)

[ Reference URL ]

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

Please see the reference URL for details on the online seminar.

**Masahiko Yoshinaga**(Osaka University)超平面配置の特性準多項式 II (Japanese)

[ Reference URL ]

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

### 2022/06/07

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Kirchberg algebras sharing the same homotopy groups of their automorphism groups

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Taro Sogabe**(Univ. Tokyo)Kirchberg algebras sharing the same homotopy groups of their automorphism groups

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**早稲田大学**(Waseda University)Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups (JAPANESE)

[ Abstract ]

We discuss a relation between a dynamical zeta function defined by the geodesic flow on a 2-dimensional hyperbolic orbifold and the asymptotic behavior of the Reidemeister torsion for the unit tangent bundle over the orbifold. The unit tangent bundle over a hyperbolic orbifold is a Seifert fibered space with a geometric structure given by the universal cover of PSL(2, R). This geometric structure induces an SL(2, R)-representation of the fundamental group. Here the asymptotic behavior of the Reidemeister torsion means the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle over a hyperbolic orbifold and the SL(n, R)-representations induced by the SL(2, R)-one of its fundamental group. For a hyperbolic 3-manifold, we can derive the hyperbolic volume from the limit of the leading coefficient in the Reidemeister torsion with a dynamical zeta function according to previous works. For the unit tangent bundle over a 2-dimensional hyperbolic orbifold, which is not a hyperbolic 3-manifold, we can find the orbifold Euler characteristic of the orbifold in the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle from the relation with the dynamical zeta function defined by the geodesic flow on the orbifold.

[ Reference URL ]We discuss a relation between a dynamical zeta function defined by the geodesic flow on a 2-dimensional hyperbolic orbifold and the asymptotic behavior of the Reidemeister torsion for the unit tangent bundle over the orbifold. The unit tangent bundle over a hyperbolic orbifold is a Seifert fibered space with a geometric structure given by the universal cover of PSL(2, R). This geometric structure induces an SL(2, R)-representation of the fundamental group. Here the asymptotic behavior of the Reidemeister torsion means the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle over a hyperbolic orbifold and the SL(n, R)-representations induced by the SL(2, R)-one of its fundamental group. For a hyperbolic 3-manifold, we can derive the hyperbolic volume from the limit of the leading coefficient in the Reidemeister torsion with a dynamical zeta function according to previous works. For the unit tangent bundle over a 2-dimensional hyperbolic orbifold, which is not a hyperbolic 3-manifold, we can find the orbifold Euler characteristic of the orbifold in the limit of the leading coefficient in the Reidemeister torsion for the unit tangent bundle from the relation with the dynamical zeta function defined by the geodesic flow on the orbifold.

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

### 2022/06/02

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers VIII (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers VIII (Japanese)

[ Abstract ]

Explanation of error correcting code of quantum computer

------stabilizer method

Explanation of error correcting code of quantum computer

------stabilizer method

### 2022/06/01

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

Please see the reference URL for details on the online seminar.

超平面配置の特性準多項式 I (Japanese)

[ Reference URL ]

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

Please see the reference URL for details on the online seminar.

**Masahiko Yoshinaga**(Osaka University)超平面配置の特性準多項式 I (Japanese)

[ Reference URL ]

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

### 2022/05/31

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Pointwise inner automorphisms of almost periodic factors

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Yusuke Isono**(RIMS, Kyoto University)Pointwise inner automorphisms of almost periodic factors

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Stable Fukaya categories of Milnor fibers (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Kazushi Ueda**(The Univesity of Tokyo)Stable Fukaya categories of Milnor fibers (JAPANESE)

[ Abstract ]

We define the stable Fukaya category of a Liouville domain as the quotient of the wrapped Fukaya category by the full subcategory consisting of compact Lagrangians, and discuss the relation between the stable Fukaya categories of affine Fermat hypersurfaces and the Fukaya categories of projective hypersurfaces. We also discuss homological mirror symmetry for Milnor fibers of Brieskorn-Pham singularities along the way. This is a joint work in progress with Yanki Lekili.

[ Reference URL ]We define the stable Fukaya category of a Liouville domain as the quotient of the wrapped Fukaya category by the full subcategory consisting of compact Lagrangians, and discuss the relation between the stable Fukaya categories of affine Fermat hypersurfaces and the Fukaya categories of projective hypersurfaces. We also discuss homological mirror symmetry for Milnor fibers of Brieskorn-Pham singularities along the way. This is a joint work in progress with Yanki Lekili.

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

#### Tuesday Seminar of Analysis

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

Convergence of Sobolev gradient trajectories to elastica (Japanese)

https://forms.gle/wkCbqdmNuz9zr3vA8

**OKABE Shinya**(Tohoku University)Convergence of Sobolev gradient trajectories to elastica (Japanese)

[ Abstract ]

In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).

[ Reference URL ]In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).

https://forms.gle/wkCbqdmNuz9zr3vA8

### 2022/05/30

#### Seminar on Geometric Complex Analysis

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

Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Yusaku Tiba**(Ochanomizu University)Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds (Japanese)

[ Abstract ]

In this talk, we study an asymptotic estimate of holomorphic sections of a positive line bundle. Let $M$ be a complex manifold and $L$ be a positive line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld condition, we prove a submean value theorem for holomorphic sections and we give an asymptotic estimate of $\inf_{x \in X}|f(x)|_{h^k}$ for $f \in H^0(M, L^k)$. This estimate provides an analog result about the leading term of the asymptotic series expansion formula of the Bergman kernel function.

[ Reference URL ]In this talk, we study an asymptotic estimate of holomorphic sections of a positive line bundle. Let $M$ be a complex manifold and $L$ be a positive line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld condition, we prove a submean value theorem for holomorphic sections and we give an asymptotic estimate of $\inf_{x \in X}|f(x)|_{h^k}$ for $f \in H^0(M, L^k)$. This estimate provides an analog result about the leading term of the asymptotic series expansion formula of the Bergman kernel function.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/05/26

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers VII (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers VII (Japanese)

### 2022/05/25

#### Number Theory Seminar

17:00-18:00 Hybrid

Torsion points of elliptic curves over cyclotomic fields (JAPANESE)

**Koji Matsuda**(University of Tokyo)Torsion points of elliptic curves over cyclotomic fields (JAPANESE)

[ Abstract ]

By Mordell--Weil theorem, the Mordell--Weil groups of elliptic curves over number fields are finitely generated, and in particular their torsion subgroups are finite. For a fixed elliptic curve, it is easy to compute its torsion subgroups. Conversely using modular curves, we can study the possible torsion subgroups of elliptic curves. More precisely, the existence of an elliptic curve with certain torsion points is essentially equivalent to the existence of certain rational points of a modular curve. In this talk, in order to study the rational points of modular curves over cyclotomic fields, we compute the Mordell--Weil ranks of their Jacobian varieties over cyclotomic fields.

By Mordell--Weil theorem, the Mordell--Weil groups of elliptic curves over number fields are finitely generated, and in particular their torsion subgroups are finite. For a fixed elliptic curve, it is easy to compute its torsion subgroups. Conversely using modular curves, we can study the possible torsion subgroups of elliptic curves. More precisely, the existence of an elliptic curve with certain torsion points is essentially equivalent to the existence of certain rational points of a modular curve. In this talk, in order to study the rational points of modular curves over cyclotomic fields, we compute the Mordell--Weil ranks of their Jacobian varieties over cyclotomic fields.

### 2022/05/24

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Stability analysis for the surface diffusion flow on double bubbles using the Lojasiewicz-Simon (English)

https://forms.gle/Cam3mpSSEKKVppZr9

**Michael Goesswein**(The University of Tokyo/University of Regensburg)Stability analysis for the surface diffusion flow on double bubbles using the Lojasiewicz-Simon (English)

[ Abstract ]

Many strategies for stability analysis use precise knowledge of the set of equilibria. For example, Escher, Mayer, and Simonett used center manifold analysis to study the surface diffusion flow on closed manifolds. Especially in higher dimensional situations with boundaries, this can cause problems as the set of equilibria will have a lot of degrees of freedom. In such situations approaches with a Lojasiewicz-Simon inequality gives an elegant way to avoid this problem. In this talk, we will both explain the general tools and ideas for this strategy and use them to prove the stability of standard double bubbles with respect to the surface diffusion flow. The talk is based on joint work with H. Garcke.

[ Reference URL ]Many strategies for stability analysis use precise knowledge of the set of equilibria. For example, Escher, Mayer, and Simonett used center manifold analysis to study the surface diffusion flow on closed manifolds. Especially in higher dimensional situations with boundaries, this can cause problems as the set of equilibria will have a lot of degrees of freedom. In such situations approaches with a Lojasiewicz-Simon inequality gives an elegant way to avoid this problem. In this talk, we will both explain the general tools and ideas for this strategy and use them to prove the stability of standard double bubbles with respect to the surface diffusion flow. The talk is based on joint work with H. Garcke.

https://forms.gle/Cam3mpSSEKKVppZr9

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Polynomial functors associated with beaded open Jacobi diagrams (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Christine Vespa**(IRMA, Université de Strasbourg / JSPS)Polynomial functors associated with beaded open Jacobi diagrams (ENGLISH)

[ Abstract ]

The Kontsevich integral is a very powerful invariant of knots, taking values is the space of Jacobi diagrams. Using an extension of the Kontsevich integral to tangles in handlebodies, Habiro and Massuyeau construct a functor from the category of bottom tangles in handlebodies to the linear category A of Jacobi diagrams in handlebodies. The category A has a subcategory equivalent to the linearization of the opposite of the category of finitely generated free groups, denoted by $\textbf{gr}^{op}$. By restriction to this subcategory, morphisms in the linear category $\textbf{A}$ give rise to interesting contravariant functors on the category $\textbf{gr}$, encoding part of the composition structure of the category A.

In recent papers, Katada studies the functor given by the morphisms in the category A from 0. In particular, she obtains a family of polynomial functors on $\textbf{gr}^{op}$ which are outer functors, in the sense that inner automorphisms act trivially.

In this talk, I will explain these results and give extensions of Katada’s results concerning the functors given by the morphisms in the category A from any integer k. These functors give rise to families of polynomial functors on $\textbf{gr}^{op}$ which are no more outer functors. Our approach is based on an equivalence of categories given by Powell. Through this equivalence the previous polynomial functors correspond to functors given by beaded open Jacobi diagrams.

[ Reference URL ]The Kontsevich integral is a very powerful invariant of knots, taking values is the space of Jacobi diagrams. Using an extension of the Kontsevich integral to tangles in handlebodies, Habiro and Massuyeau construct a functor from the category of bottom tangles in handlebodies to the linear category A of Jacobi diagrams in handlebodies. The category A has a subcategory equivalent to the linearization of the opposite of the category of finitely generated free groups, denoted by $\textbf{gr}^{op}$. By restriction to this subcategory, morphisms in the linear category $\textbf{A}$ give rise to interesting contravariant functors on the category $\textbf{gr}$, encoding part of the composition structure of the category A.

In recent papers, Katada studies the functor given by the morphisms in the category A from 0. In particular, she obtains a family of polynomial functors on $\textbf{gr}^{op}$ which are outer functors, in the sense that inner automorphisms act trivially.

In this talk, I will explain these results and give extensions of Katada’s results concerning the functors given by the morphisms in the category A from any integer k. These functors give rise to families of polynomial functors on $\textbf{gr}^{op}$ which are no more outer functors. Our approach is based on an equivalence of categories given by Powell. Through this equivalence the previous polynomial functors correspond to functors given by beaded open Jacobi diagrams.

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

### 2022/05/20

#### Colloquium

15:30-16:30 Hybrid

The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.

Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.

**Ryo Takada**(Graduate School of Mathematical Sciences, the University of Tokyo)Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

[ Abstract ]

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

### 2022/05/19

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computersVI (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computersVI (Japanese)

### 2022/05/18

#### Number Theory Seminar

17:00-18:00 Hybrid

Local Langlands correspondence for non-quasi-split odd special orthogonal groups (JAPANESE)

**Hiroshi Ishimoto**(University of Tokyo)Local Langlands correspondence for non-quasi-split odd special orthogonal groups (JAPANESE)

[ Abstract ]

In 2013, Arthur established the endoscopic classification of representations of quasi-split symplectic and orthogonal groups, and Mok analogously proved the similar classification for quasi-split unitary groups. In 2014, Kaletha-Minguez-Shin-White established the classification for non-quasi-spilt unitary groups assuming Mok's results. Similarly, we can prove that for non-quasi-split odd orthogonal groups assuming Arthur's results. In this talk, I will explain the local Langlands correspondence for non-quasi-split odd special orthogonal groups, which is a part of the classification of representations.

In 2013, Arthur established the endoscopic classification of representations of quasi-split symplectic and orthogonal groups, and Mok analogously proved the similar classification for quasi-split unitary groups. In 2014, Kaletha-Minguez-Shin-White established the classification for non-quasi-spilt unitary groups assuming Mok's results. Similarly, we can prove that for non-quasi-split odd orthogonal groups assuming Arthur's results. In this talk, I will explain the local Langlands correspondence for non-quasi-split odd special orthogonal groups, which is a part of the classification of representations.

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