## Seminar information archive

Seminar information archive ～02/26｜Today's seminar 02/27 | Future seminars 02/28～

### 2021/08/18

#### Seminar on Probability and Statistics

14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)

Dependence, Sklar's copulas and discreteness

https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform

**Gery Geenens**(The University of New South Wales (UNSW Sydney))Dependence, Sklar's copulas and discreteness

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.

https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform

### 2021/07/30

#### Colloquium

15:30-16:30 Online

Registration is closed (12:00, July 30).

Toda equations and harmonic bundles (JAPANESE)

Registration is closed (12:00, July 30).

**Takuro Mochizuki**(RIMS, Kyoto University)Toda equations and harmonic bundles (JAPANESE)

### 2021/07/29

#### Applied Analysis

16:00-17:00 Online

Lotka-Volterra competition-diffusion system: the critical case

https://forms.gle/LHj5mVUdpQ3Jxkrd6

**Dongyuan Xiao**( )Lotka-Volterra competition-diffusion system: the critical case

[ Abstract ]

We consider the reaction-diffusion competition system u_t=u_{xx}+u(1-u-v), v_t=dv_{xx}+rv(1-v-u), which is the so-called critical case. The associated ODE system then admits infinitely many equilibria, which makes the analysis quite intricate. We first prove the non-existence of monotone traveling waves by applying the phase plane analysis. Next, we study the long time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the ''faster'' species excludes the ''slower'' species (with an identified ''spreading speed''), but also provide a sharp description of the profile of the solution, thus shedding light on a new ''bump phenomenon''.

[ Reference URL ]We consider the reaction-diffusion competition system u_t=u_{xx}+u(1-u-v), v_t=dv_{xx}+rv(1-v-u), which is the so-called critical case. The associated ODE system then admits infinitely many equilibria, which makes the analysis quite intricate. We first prove the non-existence of monotone traveling waves by applying the phase plane analysis. Next, we study the long time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the ''faster'' species excludes the ''slower'' species (with an identified ''spreading speed''), but also provide a sharp description of the profile of the solution, thus shedding light on a new ''bump phenomenon''.

https://forms.gle/LHj5mVUdpQ3Jxkrd6

#### Information Mathematics Seminar

16:50-18:35 Online

Think about a zero trust from information security 10 size menace 2021 (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Think about a zero trust from information security 10 size menace 2021 (Japanese)

[ Abstract ]

Consideration on a zero trust from information security 10 size menace 2021

[ Reference URL ]Consideration on a zero trust from information security 10 size menace 2021

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/07/28

#### Lie Groups and Representation Theory

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

Collapsing Ricci-flat metrics and a priori estimate for the Monge-Ampere equation

(Japanese)

**Yoshiki Oshima**(Osaka University, Graduate School of Information Science and Technology)Collapsing Ricci-flat metrics and a priori estimate for the Monge-Ampere equation

(Japanese)

[ Abstract ]

Yau proved the Calabi conjecture by using a priori estimate for the Monge-Ampere equation. Recently, for a Calabi-Yau manifold with a fiber space structure, the behavior of Ricci-flat metrics collapsing to a Kahler class of the base space was studied by Gross-Tosatti-Zhang, etc. The Gromov-Hausdorff convergence of K3 surfaces to spheres obtained by a joint work with Yuji Odaka (arXiv:1810.07685) is also based on those estimates for solutions to the Monge-Ampere equation. In this talk, I would like to discuss how an estimate of solutions to differential equations deduces the existence of canonical metrics and the Gromov-

Hausdorff convergence.

Yau proved the Calabi conjecture by using a priori estimate for the Monge-Ampere equation. Recently, for a Calabi-Yau manifold with a fiber space structure, the behavior of Ricci-flat metrics collapsing to a Kahler class of the base space was studied by Gross-Tosatti-Zhang, etc. The Gromov-Hausdorff convergence of K3 surfaces to spheres obtained by a joint work with Yuji Odaka (arXiv:1810.07685) is also based on those estimates for solutions to the Monge-Ampere equation. In this talk, I would like to discuss how an estimate of solutions to differential equations deduces the existence of canonical metrics and the Gromov-

Hausdorff convergence.

### 2021/07/26

#### thesis presentations

13:15-14:30 Online

Studies on algebraic varieties admitting a polarized endomorphism and the minimal model program in mixed characteristic

[ Reference URL ]

https://forms.gle/3TjbHdBRZfmctfTAA

**Sho Yoshikawa**(Graduate School of Mathematical Sciences University of Tokyo)Studies on algebraic varieties admitting a polarized endomorphism and the minimal model program in mixed characteristic

[ Reference URL ]

https://forms.gle/3TjbHdBRZfmctfTAA

### 2021/07/21

#### Algebraic Geometry Seminar

15:00-16:00 Room #zoom (Graduate School of Math. Sci. Bldg.)

Cancelled

TBA (日本語)

Cancelled

**Keisuke Miyamoto**(Osaka)TBA (日本語)

[ Abstract ]

TBA

TBA

### 2021/07/20

#### Operator Algebra Seminars

16:45-18:15 Online

Spectra of principal minors of random matrices invariant by unitary conjugacy

[ Reference URL ]

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

**Takahiro Hasebe**(Hokkaido University)Spectra of principal minors of random matrices invariant by unitary conjugacy

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

On the existence of a nonzero linear period (Japanese)

**Hiroyoshi Tamori**(Hokkaido University)On the existence of a nonzero linear period (Japanese)

[ Abstract ]

Let $(G,H)$ be a symmetric pair $(\mathrm{GL}(n,\mathbb{H}),\mathrm{GL}(n,\mathbb{C}))$ or $(\mathrm{GL}(2n,\mathbb{R}),\mathrm{GL}(n,\mathbb{C}))$. It was proved by Broussous-Matringe that for an irreducible smooth admissible Fr\'{e}chet representation $\pi$ of $G$ of moderate growth, the dimension of the space of $H$-linear period of $\pi$ is not greater then one. We give some necessary condition for the existence of a nonzero $H$-linear period of $\pi$, which proves the archimedean case of a conjecture by Prasad and Takloo-Bighash. Our approach is based on the $H$-orbit decomposition of the flag variety of $G$, and homology of principal series representations. This is a joint work with Miyu Suzuki (Kanazawa University).

Let $(G,H)$ be a symmetric pair $(\mathrm{GL}(n,\mathbb{H}),\mathrm{GL}(n,\mathbb{C}))$ or $(\mathrm{GL}(2n,\mathbb{R}),\mathrm{GL}(n,\mathbb{C}))$. It was proved by Broussous-Matringe that for an irreducible smooth admissible Fr\'{e}chet representation $\pi$ of $G$ of moderate growth, the dimension of the space of $H$-linear period of $\pi$ is not greater then one. We give some necessary condition for the existence of a nonzero $H$-linear period of $\pi$, which proves the archimedean case of a conjecture by Prasad and Takloo-Bighash. Our approach is based on the $H$-orbit decomposition of the flag variety of $G$, and homology of principal series representations. This is a joint work with Miyu Suzuki (Kanazawa University).

### 2021/07/19

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

$\mathbb{C}^n$上の不分岐Riemann領域に対する中間的擬凸性 (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Makoto Abe**(Hiroshima University)$\mathbb{C}^n$上の不分岐Riemann領域に対する中間的擬凸性 (Japanese)

[ Abstract ]

The talk is based on a joint work with T. Shima and S. Sugiyama.

We characterize the intermediate pseudoconvexity for unramified Riemann domains over $\mathbb{C}^n$ by the continuity property which holds for a class of maps whose projections to $\mathbb{C}^n$ are families of unidirectionally parameterized intermediate dimensional analytic balls written by polynomials of degree $\le 2$.

[ Reference URL ]The talk is based on a joint work with T. Shima and S. Sugiyama.

We characterize the intermediate pseudoconvexity for unramified Riemann domains over $\mathbb{C}^n$ by the continuity property which holds for a class of maps whose projections to $\mathbb{C}^n$ are families of unidirectionally parameterized intermediate dimensional analytic balls written by polynomials of degree $\le 2$.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/07/15

#### Information Mathematics Seminar

16:50-18:35 Online

From the Cyber Attack by the malware to the Zero Trust Network

(Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)From the Cyber Attack by the malware to the Zero Trust Network

(Japanese)

[ Abstract ]

Explanation on the Cyber Attack by the malware and the Zero Trust Network

[ Reference URL ]Explanation on the Cyber Attack by the malware and the Zero Trust Network

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/07/14

#### Seminar on Probability and Statistics

14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)

Statistics for Functional Data

https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform

**Anirvan Chakraborty**( IISER Kolkata, India)Statistics for Functional Data

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

With the advancement in technology, statisticians often have to analyze data which are curves or functions observed over a domain. Data of this type is usually called functional data and is very common these days in various fields of science. Statistical modelling of this type of data is usually done by viewing the data as a random sample from a probability distribution on some infinite dimensional function space. This formulation, however, implies that one has to delve into the mathematical rigour and complexity of dealing with infinite dimensional objects and probability distributions in function spaces. As such, standard multivariate statistical methods are far from useful in analyzing such data. We will discuss some statistical techniques for analyzing functional data as well as outline some of the unique challenges faced and also discuss some interesting open problems in this frontline research area.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

With the advancement in technology, statisticians often have to analyze data which are curves or functions observed over a domain. Data of this type is usually called functional data and is very common these days in various fields of science. Statistical modelling of this type of data is usually done by viewing the data as a random sample from a probability distribution on some infinite dimensional function space. This formulation, however, implies that one has to delve into the mathematical rigour and complexity of dealing with infinite dimensional objects and probability distributions in function spaces. As such, standard multivariate statistical methods are far from useful in analyzing such data. We will discuss some statistical techniques for analyzing functional data as well as outline some of the unique challenges faced and also discuss some interesting open problems in this frontline research area.

https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform

### 2021/07/13

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Li-Yau type inequality for curves and applications (Japanese)

https://forms.gle/gR4gfn8v59LEoqp38

**MIURA Tatsuya**(Tokyo Institute of Technology)Li-Yau type inequality for curves and applications (Japanese)

[ Abstract ]

A classical result of Li and Yau asserts an optimal relation between the bending energy and multiplicity of a closed surface in Euclidean space. Here we establish an analogue for curves in a completely general form, and observe new phenomena due to low dimensionality. We also discuss its applications to elastic flows, networks, and knots.

[ Reference URL ]A classical result of Li and Yau asserts an optimal relation between the bending energy and multiplicity of a closed surface in Euclidean space. Here we establish an analogue for curves in a completely general form, and observe new phenomena due to low dimensionality. We also discuss its applications to elastic flows, networks, and knots.

https://forms.gle/gR4gfn8v59LEoqp38

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Homotopy motions of surfaces in 3-manifolds (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Makoto Sakuma**(Osaka City University Advanced Mathematical Institute)Homotopy motions of surfaces in 3-manifolds (JAPANESE)

[ Abstract ]

We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).

[ Reference URL ]We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).

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

#### Operator Algebra Seminars

16:45-18:15 Online

Quantization of locally compact groups from matched pairs

[ Reference URL ]

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

**Makoto Yamashita**(Univ. Oslo)Quantization of locally compact groups from matched pairs

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Compactification of locally symmetric spaces and collapsing of canonical Kahler metrics (Japanese)

**Yoshiki Oshima**(Osaka University, Graduate School of Information Science and Technology)Compactification of locally symmetric spaces and collapsing of canonical Kahler metrics (Japanese)

[ Abstract ]

The moduli spaces of Abelian varieties and K3 surfaces are known to have a structure of locally symmetric spaces. Around 1960, a finite number of compactifications of locally symmetric spaces are constructed by Ichiro Satake. In this talk, based on a joint work with Yuji Odaka (arXiv:1810:07685), we will see that one of Satake compactifications parametrizes limits of canonical (Ricci-flat) Kahler metrics on Abelian varieties and K3 surfaces.

The moduli spaces of Abelian varieties and K3 surfaces are known to have a structure of locally symmetric spaces. Around 1960, a finite number of compactifications of locally symmetric spaces are constructed by Ichiro Satake. In this talk, based on a joint work with Yuji Odaka (arXiv:1810:07685), we will see that one of Satake compactifications parametrizes limits of canonical (Ricci-flat) Kahler metrics on Abelian varieties and K3 surfaces.

### 2021/07/12

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Parametrization of Weil-Petersson curves on the plane (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Katsuhiko Matsuzaki**(Waseda University)Parametrization of Weil-Petersson curves on the plane (Japanese)

[ Abstract ]

A Weil-Petersson curve is the image of the real line by a quasiconformal homeomorphism of the plane whose complex dilatation is square integrable with respect to the hyperbolic metrics on the upper and the lower half-planes. We consider two parameter spaces of all such curves and show that they are biholomorphically equivalent. As a consequence, we prove that the variant of the Beurling-Ahlfors quasiconformal extension defined by using the heat kernel for the convolution yields a global real-analytic section for the Teichmueller projection to the Weil-Petersson Teichmueller space. This is a joint work with Huaying Wei.

[ Reference URL ]A Weil-Petersson curve is the image of the real line by a quasiconformal homeomorphism of the plane whose complex dilatation is square integrable with respect to the hyperbolic metrics on the upper and the lower half-planes. We consider two parameter spaces of all such curves and show that they are biholomorphically equivalent. As a consequence, we prove that the variant of the Beurling-Ahlfors quasiconformal extension defined by using the heat kernel for the convolution yields a global real-analytic section for the Teichmueller projection to the Weil-Petersson Teichmueller space. This is a joint work with Huaying Wei.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/07/08

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

Sign-stable mutation loops and pseudo-Anosov mapping classes (Japanese)

[ Reference URL ]

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

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

**Tsukasa Ishibashi**(RIMS, Kyoto University)Sign-stable mutation loops and pseudo-Anosov mapping classes (Japanese)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

Telework society and menace of the cyber attack (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Telework society and menace of the cyber attack (Japanese)

[ Abstract ]

Explanation on the telework society and the menace of cyber attack.

[ Reference URL ]Explanation on the telework society and the menace of cyber attack.

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/07/07

#### Discrete mathematical modelling seminar

17:15-19:00 Online

This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.

Combinatorics of K-theoretic special polynomials -- free fermion representation and integrable systems (Japanese)

This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.

**Iwao Shinsuke**(Tokai University)Combinatorics of K-theoretic special polynomials -- free fermion representation and integrable systems (Japanese)

#### Number Theory Seminar

17:00-18:00 Online

On the BSD conjecture for the quadratic twists of the elliptic curve $X_0(49)$ (Japanese)

**Takumi Yoshida**(Keio University)On the BSD conjecture for the quadratic twists of the elliptic curve $X_0(49)$ (Japanese)

[ Abstract ]

The full BSD conjecture (the full Birch-Swinnerton-Dyer conjecture) is the important conjecture, which connects the algebraic invariants and analytic invariants of elliptic curves. When the elliptic curve is defined over $\mathbb{Q}$, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over $\mathbb{Q}$ and the $L$-function is not $0$ at $s=1$, it is not shown that the $2$-orders of these invariants are equal. Coates, Kim, Liang and Zhao proved the full BSD conjecture for some quadratic twists of $X_0(49)$, by proving that these $2$-orders are same. We extends this result, and prove the full BSD conjecture for more twists.

The full BSD conjecture (the full Birch-Swinnerton-Dyer conjecture) is the important conjecture, which connects the algebraic invariants and analytic invariants of elliptic curves. When the elliptic curve is defined over $\mathbb{Q}$, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over $\mathbb{Q}$ and the $L$-function is not $0$ at $s=1$, it is not shown that the $2$-orders of these invariants are equal. Coates, Kim, Liang and Zhao proved the full BSD conjecture for some quadratic twists of $X_0(49)$, by proving that these $2$-orders are same. We extends this result, and prove the full BSD conjecture for more twists.

### 2021/07/06

#### Numerical Analysis Seminar

16:30-18:00 Online

Iterative solution methods for least squares problems and their applications

(Japanese)

[ Reference URL ]

https://forms.gle/B5Hwxa7o8F36hZKr7

**Ken Hayami**(National Institute of Informatics (Professor Emeritus))Iterative solution methods for least squares problems and their applications

(Japanese)

[ Reference URL ]

https://forms.gle/B5Hwxa7o8F36hZKr7

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

Codimension 2 transfer map in higher index theory (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yosuke Kubota**(Shinshu University)Codimension 2 transfer map in higher index theory (JAPANESE)

[ Abstract ]

The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.

[ Reference URL ]The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.

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

#### Lie Groups and Representation Theory

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

A counterexample to a Q-series analogue of Casselman's subrepresentation theorem (Japanese)

**Taito Tauchi**(Kyushu University )A counterexample to a Q-series analogue of Casselman's subrepresentation theorem (Japanese)

[ Abstract ]

Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a

subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate

principal series representation induced from Q.

Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a

subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate

principal series representation induced from Q.

### 2021/07/05

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Several stronger concepts of relative K-stability for polarized toric manifolds (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Nitta Yasufumi**(Tokyo University of Science)Several stronger concepts of relative K-stability for polarized toric manifolds (Japanese)

[ Abstract ]

We study relations between algebro-geometric stabilities for polarized toric manifolds. In this talk, we introduce several strengthenings of relative K-stability such as uniform stability and K-stability tested by more objects than test configurations, and show that these approaches are all equivalent. As a consequence, we solve a uniform version of the Yau-Tian-Donaldson conjecture for Calabi's extremal Kähler metrics in the toric setting. This talk is based on a joint work with Shunsuke Saito.

[ Reference URL ]We study relations between algebro-geometric stabilities for polarized toric manifolds. In this talk, we introduce several strengthenings of relative K-stability such as uniform stability and K-stability tested by more objects than test configurations, and show that these approaches are all equivalent. As a consequence, we solve a uniform version of the Yau-Tian-Donaldson conjecture for Calabi's extremal Kähler metrics in the toric setting. This talk is based on a joint work with Shunsuke Saito.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

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