## Seminar information archive

Seminar information archive ～09/28｜Today's seminar 09/29 | Future seminars 09/30～

### 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

### 2021/07/13

#### 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

#### Algebraic Geometry Seminar

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

Birational geometry of foliations (English)

**Paolo Cascini**(Imperial College London)Birational geometry of foliations (English)

[ Abstract ]

I will survey about some recent progress towards the Minimal Model Program for foliations on complex varieties, focusing mainly on the case of threefolds and the case of algebraically integrable foliations.

I will survey about some recent progress towards the Minimal Model Program for foliations on complex varieties, focusing mainly on the case of threefolds and the case of algebraically integrable foliations.

### 2021/07/01

#### Algebraic Geometry Seminar

10:00-11:00 Room # (Graduate School of Math. Sci. Bldg.)

An O-acyclic variety of even index

**Fumiaki Suzuki**(UCLA)An O-acyclic variety of even index

[ Abstract ]

I will construct a family of Enriques surfaces parametrized by P^1 such that any multi-section has even degree over the base P^1. Over the function field of a complex curve, this gives the first example of an O-acyclic variety (H^i(X,O)=0 for i>0) whose index is not equal to one, and an affirmative answer to a question of Colliot-Thélène and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre’s question on universality of the Abel-Jacobi maps. This is joint work with John Christian Ottem.

I will construct a family of Enriques surfaces parametrized by P^1 such that any multi-section has even degree over the base P^1. Over the function field of a complex curve, this gives the first example of an O-acyclic variety (H^i(X,O)=0 for i>0) whose index is not equal to one, and an affirmative answer to a question of Colliot-Thélène and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre’s question on universality of the Abel-Jacobi maps. This is joint work with John Christian Ottem.

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