## Seminar information archive

Seminar information archive ～05/28｜Today's seminar 05/29 | Future seminars 05/30～

### 2023/01/04

#### Number Theory Seminar

17:00-18:00 Hybrid

G-displays over prisms and deformation theory (Japanese)

**Kazuhiro Ito**(The University of Tokyo, Kavli IPMU)G-displays over prisms and deformation theory (Japanese)

[ Abstract ]

The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.

The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.

#### Lectures

17:00-18:00 Online

On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09

**Professor Debora Presti**(Messina University)On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09

### 2022/12/27

#### Lectures

16:00-17:00 Online

Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09

**Professor Salah-Eddine CHORFI**(Cadi Ayyad University, Faculty of Sciences, Morocco)Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09

### 2022/12/22

#### Information Mathematics Seminar

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

Theory of fault-tolerant quantum computing I (Japanese)

**Yasunari Suzuki**(NTT)Theory of fault-tolerant quantum computing I (Japanese)

[ Abstract ]

To demonstrate reliable quantum computing, we need to integrate quantum error correction techniques and achieve fault-tolerant quantum computing. In this seminar, I will explain the basic of fault-tolerant quantum computing and recent progress towards its experimental realization.

To demonstrate reliable quantum computing, we need to integrate quantum error correction techniques and achieve fault-tolerant quantum computing. In this seminar, I will explain the basic of fault-tolerant quantum computing and recent progress towards its experimental realization.

### 2022/12/21

#### Algebraic Geometry Seminar

13:00-14:00 or 14:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

The room is different from the usual place. This is a joint seminar with Kyoto University.

Towards a geometric origin of the dynamical filtrations (English)

The room is different from the usual place. This is a joint seminar with Kyoto University.

**Hsueh-Yung Lin**(NTU)Towards a geometric origin of the dynamical filtrations (English)

[ Abstract ]

Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.

If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.

Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.

If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.

### 2022/12/20

#### Algebraic Geometry Seminar

9:30-10:30 Room #オンラインZoom (Graduate School of Math. Sci. Bldg.)

The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)

**Takumi Murayama**(Purdue)The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)

[ Abstract ]

In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.

In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.

In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.

In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.

#### Tuesday Seminar of Analysis

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

A commentary on J. Boman's recent two related results about the support of a distribution and its analyticity, and a special relationship between Radon transformations and ellipsoidal regions (Japanese)

https://forms.gle/BpciRTzKh9FPUV8D7

**KATAOKA Kiyoomi**(The University of Tokyo)A commentary on J. Boman's recent two related results about the support of a distribution and its analyticity, and a special relationship between Radon transformations and ellipsoidal regions (Japanese)

[ Abstract ]

Jan Boman's (Stockholm Univ.) recent two papers:

[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).

[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.

In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.

[ Reference URL ]Jan Boman's (Stockholm Univ.) recent two papers:

[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).

[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.

In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.

https://forms.gle/BpciRTzKh9FPUV8D7

#### Operator Algebra Seminars

16:45-18:15 Online

Band width and the Rosenberg index

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

**Yosuke Kubota**(Shinshu Univ.)Band width and the Rosenberg index

[ Abstract ]

Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.

In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.

[ Reference URL ]Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.

In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.

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

### 2022/12/13

#### Algebraic Geometry Seminar

10:30-11:30 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)

The speaker will give his talk by Zoom

Moduli of G-constellations and crepant resolutions (日本語)

The speaker will give his talk by Zoom

**山岸亮**(NTU)Moduli of G-constellations and crepant resolutions (日本語)

[ Abstract ]

For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.

For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.

#### Operator Algebra Seminars

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

Entropy in QFT

[ Reference URL ]

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

**Feng Xu**(UC Riverside)Entropy in QFT

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Kota Hattori**(Keio University)Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)

[ Abstract ]

In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.

[ Reference URL ]In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.

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.)

Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)

https://forms.gle/CRha8hydEuXzh71S7

**TADANO Yukihide**(Tokyo University of Science)Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)

[ Abstract ]

We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).

[ Reference URL ]We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).

https://forms.gle/CRha8hydEuXzh71S7

### 2022/12/12

#### Seminar on Geometric Complex Analysis

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

$L^2$-extension index and its applications (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Takahiro Inayama**(Tokyo University of Science)$L^2$-extension index and its applications (Japanese)

[ Abstract ]

In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.

[ Reference URL ]In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/12/08

#### Information Mathematics Seminar

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

Near-term quantum algorithms and quantum error mitigation (Japanese)

**Suguru Endo**(NTT)Near-term quantum algorithms and quantum error mitigation (Japanese)

[ Abstract ]

The current or near-term quantum computing devices are still small and noisy. In this talk, I will near-term quantum algorithms and quantum error mitigation for improving computation accuracy.

The current or near-term quantum computing devices are still small and noisy. In this talk, I will near-term quantum algorithms and quantum error mitigation for improving computation accuracy.

### 2022/12/06

#### Operator Algebra Seminars

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

Equivariant covering spaces of quantum homogeneous spaces

[ Reference URL ]

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

**Mao Hoshino**(Univ. Tokyo)Equivariant covering spaces of quantum homogeneous spaces

[ 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.

Torsion in the abelianization of the Johnson kernel (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Quentin Faes**(The Univesity of Tokyo)Torsion in the abelianization of the Johnson kernel (ENGLISH)

[ Abstract ]

The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.

[ Reference URL ]The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.

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

### 2022/12/05

#### Seminar on Geometric Complex Analysis

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

On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Shota Kikuchi**(National Institute of Technology, Suzuka College)On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (Japanese)

[ Abstract ]

Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.

In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.

[ Reference URL ]Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.

In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.

https://forms.gle/hYT2hVhDE3q1wDSh6

#### Seminar on Probability and Statistics

14:40-15:50 Room # (Graduate School of Math. Sci. Bldg.)

A binary branching model with Moran-type interactions (English)

(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5

**Michael Choi**(National University of Singapore and Yale-NUS College)A binary branching model with Moran-type interactions (English)

[ Abstract ]

Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).

[ Reference URL ]Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).

(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5

### 2022/12/01

#### Information Mathematics Seminar

16:50-18:35 Room #123 (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 Shor’s algorithm for factoring and discrete logarithm, quantum money, and verification of quantum computation based on cryptography.

I explain several topics on quantum computing and cryptography including Shor’s algorithm for factoring and discrete logarithm, quantum money, and verification of quantum computation based on cryptography.

### 2022/11/30

#### Number Theory Seminar

17:00-18:00 Hybrid

The modularity of elliptic curves over some number fields (English)

**Xinyao Zhang**(University of Tokyo)The modularity of elliptic curves over some number fields (English)

[ Abstract ]

As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.

As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.

#### Discrete mathematical modelling seminar

15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Folding transformations for q-Painleve equations (English)

**Mikhail Bershtein**(Skoltech・HSE / IPMU)Folding transformations for q-Painleve equations (English)

[ Abstract ]

Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.

Based on joint work with A. Shchechkin [arXiv:2110.15320]

Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.

Based on joint work with A. Shchechkin [arXiv:2110.15320]

### 2022/11/29

#### Tuesday Seminar of Analysis

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

Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)

https://forms.gle/93YQ9C6DGYt5Vjuf7

**TAKIMOTO Kazuhiro**(Hiroshima University)Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)

[ Abstract ]

In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.

[ Reference URL ]In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.

https://forms.gle/93YQ9C6DGYt5Vjuf7

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

GKM graph with legs and graph equivariant cohomology (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shintaro Kuroki**(Okayama University of Science)GKM graph with legs and graph equivariant cohomology (JAPANESE)

[ Abstract ]

A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).

[ Reference URL ]A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).

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

#### Operator Algebra Seminars

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

Actions of tensor categories on $C^*$-algebras

[ Reference URL ]

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

**Yuki Arano**(Kyoto Univ.)Actions of tensor categories on $C^*$-algebras

[ Reference URL ]

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

#### Algebraic Geometry Seminar

10:30-11:30 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)

The behaviour of Kahler-Einstein polygons under combinatorial mutation

(English)

**Thomas Hall**(University of Nottingham)The behaviour of Kahler-Einstein polygons under combinatorial mutation

(English)

[ Abstract ]

Combinatorial mutations play an important role in the mirror symmetry approach to the classification of Fano varieties. Another important notion for Fano varieties is that of K-polystability, which turns out to have a nice combinatorial characterisation in the toric case. In this talk, I will give an overview of how mutations work and sketch the key ideas used to explore its interaction with Kahler-Einstein polygons (i.e. the Fano polygons whose associated toric variety is K-polystable).

Combinatorial mutations play an important role in the mirror symmetry approach to the classification of Fano varieties. Another important notion for Fano varieties is that of K-polystability, which turns out to have a nice combinatorial characterisation in the toric case. In this talk, I will give an overview of how mutations work and sketch the key ideas used to explore its interaction with Kahler-Einstein polygons (i.e. the Fano polygons whose associated toric variety is K-polystable).

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