## Seminar information archive

Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～

### 2020/12/14

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

On Levi flat hypersurfaces with transversely affine foliation

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**ADACHI Masanori**(Shizuoka University)On Levi flat hypersurfaces with transversely affine foliation

[ Abstract ]

In this talk, we discuss the classification problem of Levi flat hypersurfaces in complex surfaces by restricting ourselves to the case that the Levi foliation is transversely affine. After presenting known examples, we give a proof for the non-existence of real analytic Levi flat hypersurface whose complement is 1-convex and Levi foliation is transversely affine in a compact Kähler surface. This is a joint work with Severine Biard (arXiv:2011.06379).

[ Reference URL ]In this talk, we discuss the classification problem of Levi flat hypersurfaces in complex surfaces by restricting ourselves to the case that the Levi foliation is transversely affine. After presenting known examples, we give a proof for the non-existence of real analytic Levi flat hypersurface whose complement is 1-convex and Levi foliation is transversely affine in a compact Kähler surface. This is a joint work with Severine Biard (arXiv:2011.06379).

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2020/12/10

#### Operator Algebra Seminars

16:45-18:15 Online

Towards an equivariant Kirchberg-Phillips theorem (English)

[ Reference URL ]

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

**Gabor Szabo**(KU Leuven)Towards an equivariant Kirchberg-Phillips theorem (English)

[ Reference URL ]

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

#### Tokyo-Nagoya Algebra Seminar

16:30-18:00 Online

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

Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)

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

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

**Hiroki Matsui**(University of Tokyo)Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)

[ Abstract ]

The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.

[ Reference URL ]The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.

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

#### Information Mathematics Seminar

16:50-18:35 Online

The cyber attack to a car company supply chain network and Zero trust by the Cisco Systems (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The cyber attack to a car company supply chain network and Zero trust by the Cisco Systems (Japanese)

[ Abstract ]

Explanation on the cyber attack to a car company supply chain network and zero trust by the Cisco Systems

[ Reference URL ]Explanation on the cyber attack to a car company supply chain network and zero trust by the Cisco Systems

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/12/09

#### Discrete mathematical modelling seminar

17:00-18:30 Online

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

Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations (English)

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

**Anton DZHAMAY**(University of Northern Colorado)Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations (English)

[ Abstract ]

We use Sakai’s geometric theory of discrete Painlevé equations to study a recurrence relation that can be used to generate ladder operators for the Laguerre unitary ensemble. Using a recently proposed identification procedure for discrete Painlevé equations we show how this recurrence can be transformed into one of the standard equations on the affine D5-algebraic surface. This is a joint work with Yang Chen and Jie Hu.

We use Sakai’s geometric theory of discrete Painlevé equations to study a recurrence relation that can be used to generate ladder operators for the Laguerre unitary ensemble. Using a recently proposed identification procedure for discrete Painlevé equations we show how this recurrence can be transformed into one of the standard equations on the affine D5-algebraic surface. This is a joint work with Yang Chen and Jie Hu.

### 2020/12/08

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

The intersection polynomials of a virtual knot (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shin Satoh**(Kobe University)The intersection polynomials of a virtual knot (JAPANESE)

[ Abstract ]

We define two kinds of invariants of a virtual knot called the first and second intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study several properties of the polynomials. By introducing invariants of long virtual knots, we give connected sum formulae of the intersection polynomials, and prove that there are infinitely many connected sums of any two virtual knots as an application. Furthermore, by studying the behavior under a crossing change, we show that the intersection polynomials are finite type invariants of order two, and find an invariant of a flat virtual knot derived from the the intersection polynomials. This is a joint work with R. Higa, T. Nakamura, and Y. Nakanishi.

[ Reference URL ]We define two kinds of invariants of a virtual knot called the first and second intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study several properties of the polynomials. By introducing invariants of long virtual knots, we give connected sum formulae of the intersection polynomials, and prove that there are infinitely many connected sums of any two virtual knots as an application. Furthermore, by studying the behavior under a crossing change, we show that the intersection polynomials are finite type invariants of order two, and find an invariant of a flat virtual knot derived from the the intersection polynomials. This is a joint work with R. Higa, T. Nakamura, and Y. Nakanishi.

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

### 2020/12/03

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

Full strong exceptional collections for invertible polynomials of chain type

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

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

**Yuki Hirano**(Kyoto University)Full strong exceptional collections for invertible polynomials of chain type

[ Abstract ]

Constructing a tilting object in the stable category of graded maximal Cohen-Macaulay modules over a given graded Gorenstein ring is an important problem in the representation theory of graded Gorenstein rings. For a hypersurface S/f in a graded regular ring S, this problem is equivalent to constructing a tilting object in the homotopy category of graded matrix factorizations of f. In this talk, we discuss this problem in the case when S is a polynomial ring, f is an invertible polynomial of chain type and S has a rank one abelian group grading (called the maximal grading of f), and in this case we show the existence of a tilting object arising from a full strong exceptional collection. This is a joint work with Genki Ouchi.

[ Reference URL ]Constructing a tilting object in the stable category of graded maximal Cohen-Macaulay modules over a given graded Gorenstein ring is an important problem in the representation theory of graded Gorenstein rings. For a hypersurface S/f in a graded regular ring S, this problem is equivalent to constructing a tilting object in the homotopy category of graded matrix factorizations of f. In this talk, we discuss this problem in the case when S is a polynomial ring, f is an invertible polynomial of chain type and S has a rank one abelian group grading (called the maximal grading of f), and in this case we show the existence of a tilting object arising from a full strong exceptional collection. This is a joint work with Genki Ouchi.

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

#### Information Mathematics Seminar

16:50-18:35 Online

History of PC-LAN offense and defense/Classification of Flynn/Quantum gate, Actual Quantum Gate (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)History of PC-LAN offense and defense/Classification of Flynn/Quantum gate, Actual Quantum Gate (Japanese)

[ Abstract ]

Explanation on the history of PC-LAN offense and defense/Classification of Flynn/Quantum Gate, Actual Quantum Gate

[ Reference URL ]Explanation on the history of PC-LAN offense and defense/Classification of Flynn/Quantum Gate, Actual Quantum Gate

https://forms.gle/Uhy8uBujZatjNMsGA

#### Operator Algebra Seminars

16:45-18:15 Online

Generalized strong asymptotic freeness (English)

[ Reference URL ]

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

**Benoit Collins**(Kyoto Univ.)Generalized strong asymptotic freeness (English)

[ Reference URL ]

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

### 2020/12/01

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Goeritz groups of bridge decompositions (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yuya Koda**(Hiroshima University)Goeritz groups of bridge decompositions (JAPANESE)

[ Abstract ]

For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. The Birman-Hilden theory tells us that this is a $\mathbb{Z} / 2 \mathbb{Z}$-quotient of a "hyperelliptic Goeritz group". In this talk, we discuss properties, mainly of dynamical nature, of this group using a measure of complexity called the distance of the decomposition. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings. This talk is based on a joint work with Susumu Hirose, Daiki Iguchi and Eiko Kin.

[ Reference URL ]For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. The Birman-Hilden theory tells us that this is a $\mathbb{Z} / 2 \mathbb{Z}$-quotient of a "hyperelliptic Goeritz group". In this talk, we discuss properties, mainly of dynamical nature, of this group using a measure of complexity called the distance of the decomposition. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings. This talk is based on a joint work with Susumu Hirose, Daiki Iguchi and Eiko Kin.

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

#### Numerical Analysis Seminar

16:30-18:00 Online

Conjugate gradient methods for optimization problems on manifolds (Japanese)

[ Reference URL ]

https://forms.gle/Ubeccm8neLkacjbk8

**Hiroyuki Sato**(Kyoto University)Conjugate gradient methods for optimization problems on manifolds (Japanese)

[ Reference URL ]

https://forms.gle/Ubeccm8neLkacjbk8

#### PDE Real Analysis Seminar

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

Existence of the $1$-harmonic map flow (English)

**Michał Łasica**(Institute of Mathematics of the Polish Academy of Sciences / University of Tokyo)Existence of the $1$-harmonic map flow (English)

[ Abstract ]

Similarly as in the real-valued case, the total variation of maps taking values in a Riemannian manifold extends to a lower semicontinuous functional on $L^2$. However, in general this functional is not geodesically semiconvex, so the existence of its gradient flow is not provided by general variational theory. Alternatively, one can try to apply the theory of parabolic PDE systems, mimicking the approach used for $p$-harmonic map flows, $p>1$. This poses some difficulties, because the PDE system corresponding to the flow is strongly nonlinear, singular and degenerate. However, in some cases, this approach was successful. In this talk, I will describe known results on the existence of the flow, focusing on my work with Lorenzo Giacomelli and Salvador Moll.

Similarly as in the real-valued case, the total variation of maps taking values in a Riemannian manifold extends to a lower semicontinuous functional on $L^2$. However, in general this functional is not geodesically semiconvex, so the existence of its gradient flow is not provided by general variational theory. Alternatively, one can try to apply the theory of parabolic PDE systems, mimicking the approach used for $p$-harmonic map flows, $p>1$. This poses some difficulties, because the PDE system corresponding to the flow is strongly nonlinear, singular and degenerate. However, in some cases, this approach was successful. In this talk, I will describe known results on the existence of the flow, focusing on my work with Lorenzo Giacomelli and Salvador Moll.

### 2020/11/30

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

On asymptotic base loci of relative anti-canonical divisors

[ Reference URL ]

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**IWAI Masataka**(Osaka City Univ. and Kyoto Univ.)On asymptotic base loci of relative anti-canonical divisors

[ Reference URL ]

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2020/11/27

#### Seminar on Probability and Statistics

17:00-18:10 Room #on-line (Graduate School of Math. Sci. Bldg.)

Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.

Processes with small ball estimate: properties, examples, statistical inference (ENGLISH)

https://docs.google.com/forms/d/e/1FAIpQLSeYCDQS9c9i0gy-Y0YY-q5TPJlwGmWhCYnkKRE7udvMOoy0mw/viewform

Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.

**Yuliya Mishura**(Taras Shevchenko National University of Kyiv)Processes with small ball estimate: properties, examples, statistical inference (ENGLISH)

[ Abstract ]

The notion of a process with small ball estimate is introduced and studied. In particular, divergence of integral functional of such process is established and applied to statistical estimation. Several interesting examples are provided, and various modifications of the main group of properties are considered. The talk is based on the common research with Prof. Nakahiro Yoshida.

[ Reference URL ]The notion of a process with small ball estimate is introduced and studied. In particular, divergence of integral functional of such process is established and applied to statistical estimation. Several interesting examples are provided, and various modifications of the main group of properties are considered. The talk is based on the common research with Prof. Nakahiro Yoshida.

https://docs.google.com/forms/d/e/1FAIpQLSeYCDQS9c9i0gy-Y0YY-q5TPJlwGmWhCYnkKRE7udvMOoy0mw/viewform

### 2020/11/26

#### Information Mathematics Seminar

16:50-18:35 Online

Reinforcement learning and Regression algorithm to support AI (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Reinforcement learning and Regression algorithm to support AI (Japanese)

[ Abstract ]

Explanation on the reinforcement learning and regression algorithm to support AI

[ Reference URL ]Explanation on the reinforcement learning and regression algorithm to support AI

https://forms.gle/Uhy8uBujZatjNMsGA

#### Mathematical Biology Seminar

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

Some reinfection models (Japanese)

**Yukihiko Nakata**(Department of Physics and Mathematics, Aoyama Gakuin University)Some reinfection models (Japanese)

### 2020/11/24

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

Intersection of Poincare holonomy varieties and Bers' simultaneous uniformization theorem (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shinpei Baba**(Osaka University)Intersection of Poincare holonomy varieties and Bers' simultaneous uniformization theorem (JAPANESE)

[ Abstract ]

Given a marked compact Riemann surface X, the vector space of holomorphic quadratic differentials on X is identified with the space of CP

In this manner, different Riemann surfaces structures yield different half-dimensional smooth analytic subvarieties in the character variety. In this talk, we discuss some properties of their intersection. To do so, we utilize a cut-and-paste operation, called grafting, of CP

[ Reference URL ]Given a marked compact Riemann surface X, the vector space of holomorphic quadratic differentials on X is identified with the space of CP

^{1}-structures on X. Then, by the holonomy representations of CP^{1}-structures, this vector space properly embeds into the PSL(2, C)-character variety, the space of representations of the fundamental group of X into PSL(2,C).In this manner, different Riemann surfaces structures yield different half-dimensional smooth analytic subvarieties in the character variety. In this talk, we discuss some properties of their intersection. To do so, we utilize a cut-and-paste operation, called grafting, of CP

^{1}-structures.https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2020/11/20

#### Colloquium

15:30-16:30 Online

Please register at the link below to attend this online colloquium

Tilting theory and its companions (JAPANESE)

[ Reference URL ]

https://zoom.us/meeting/register/tJIrcu-prjoiGdNRSs0z3a5rl1SiuVgk0W8K

Please register at the link below to attend this online colloquium

**Osamu Iyama**(University of Tokyo)Tilting theory and its companions (JAPANESE)

[ Reference URL ]

https://zoom.us/meeting/register/tJIrcu-prjoiGdNRSs0z3a5rl1SiuVgk0W8K

### 2020/11/19

#### Operator Algebra Seminars

16:45-18:15 Online

Covariant homogeneous nets of standard subspaces (English)

[ Reference URL ]

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

**Vincenzo Morinelli**(University of Rome, Tor Vergata)Covariant homogeneous nets of standard subspaces (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

The consideration of the account injustice access case and zero trust by Microsoft (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The consideration of the account injustice access case and zero trust by Microsoft (Japanese)

[ Abstract ]

We give a consideration of the account injustice access case and zero trust by Microsoft

[ Reference URL ]We give a consideration of the account injustice access case and zero trust by Microsoft

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/11/18

#### Discrete mathematical modelling seminar

17:00-18:00 Online

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

Recent developments on variational difference equations and their classification (English)

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

**Giorgio GUBBIOTTI**(The University of Sydney, School of Mathematics and Statistics)Recent developments on variational difference equations and their classification (English)

[ Abstract ]

We review some recent development in the theory of variational difference equations of order higher than two. In particular we present our recent solution of the inverse problem of calculus variations. Then, we present the application of such solution in the classification of variational fourth-order difference equations. To be more specific, we will present the most general form of variational additive and multiplicative fourth-order difference equations.

We review some recent development in the theory of variational difference equations of order higher than two. In particular we present our recent solution of the inverse problem of calculus variations. Then, we present the application of such solution in the classification of variational fourth-order difference equations. To be more specific, we will present the most general form of variational additive and multiplicative fourth-order difference equations.

#### Number Theory Seminar

17:00-18:00 Online

Symmetric bilinear forms and local epsilon factors of isolated singularities in positive characteristic (Japanese)

**Daichi Takeuchi**(University of Tokyo)Symmetric bilinear forms and local epsilon factors of isolated singularities in positive characteristic (Japanese)

[ Abstract ]

For a function on a smooth variety with an isolated singular point, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other is the vanishing cycles complex (\'etale). The latter is a Galois representation of a local field measuring a complexity of the singularity.

In this talk, I will give a formula which expresses the local epsilon factor of the vanishing cycles complex in terms of the bilinear form. In particular, the sign of the local epsilon factor is determined by the discriminant of the bilinear form. This can be regarded as a refinement of Milnor formula in SGA 7, which compares the rank of the bilinear form and the total dimension of the vanishing cycles.

In characteristic 2, we find a generalization of Arf invariant, which can be regarded as an invariant for a non-degenerate quadratic singularity, to a general isolated singularity.

For a function on a smooth variety with an isolated singular point, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other is the vanishing cycles complex (\'etale). The latter is a Galois representation of a local field measuring a complexity of the singularity.

In this talk, I will give a formula which expresses the local epsilon factor of the vanishing cycles complex in terms of the bilinear form. In particular, the sign of the local epsilon factor is determined by the discriminant of the bilinear form. This can be regarded as a refinement of Milnor formula in SGA 7, which compares the rank of the bilinear form and the total dimension of the vanishing cycles.

In characteristic 2, we find a generalization of Arf invariant, which can be regarded as an invariant for a non-degenerate quadratic singularity, to a general isolated singularity.

#### Seminar on Probability and Statistics

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

Please register at least 3 days before at the reference URL. The URL for participation will be sent before the seminar.

Hamiltonian Monte Carlo In Bayesian Empirical Likelihood Computation (English)

https://docs.google.com/forms/d/e/1FAIpQLSfbk6GTAzQuj0__YUtUMiAgbPWabT-M1vmbgldohiwPxPltuw/viewform

Please register at least 3 days before at the reference URL. The URL for participation will be sent before the seminar.

**Sanjay Chaudhuri**(National University of Singapore)Hamiltonian Monte Carlo In Bayesian Empirical Likelihood Computation (English)

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home

Abstract: We consider Bayesian empirical likelihood estimation and develop an efficient Hamiltonian Monte Carlo method for sampling from the posterior distribution of the parameters of interest. The proposed method uses hitherto unknown properties of the gradient of the underlying log-empirical likelihood function. It is seen that these properties hold under minimal assumptions on the parameter space, prior density and the functions used in the estimating equations determining the empirical likelihood. We overcome major challenges posed by complex, non-convex boundaries of the support routinely observed for empirical likelihood which prevents efficient implementation of traditional Markov chain Monte Carlo methods like random walk Metropolis-Hastings etc. with or without parallel tempering. Our method employs finite number of estimating equations and observations but produces valid semi-parametric inference for a large class of statistical models including mixed effects models, generalised linear models, hierarchical Bayes models etc. A simulation study confirms that our proposed method converges quickly and draws samples from the posterior support efficiently. We further illustrate its utility through an analysis of a discrete data-set in small area estimation.

Keywords: Constrained convex optimisation; Empirical likelihood; Generalised linear models; Hamiltonian Monte Carlo; Mixed effect models; Score equations; Small area estimation; Unbiased estimating equations.

This is a joint work with Debashis Mondal, Oregon State University and Yin Teng, E&Y, Singapore.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home

Abstract: We consider Bayesian empirical likelihood estimation and develop an efficient Hamiltonian Monte Carlo method for sampling from the posterior distribution of the parameters of interest. The proposed method uses hitherto unknown properties of the gradient of the underlying log-empirical likelihood function. It is seen that these properties hold under minimal assumptions on the parameter space, prior density and the functions used in the estimating equations determining the empirical likelihood. We overcome major challenges posed by complex, non-convex boundaries of the support routinely observed for empirical likelihood which prevents efficient implementation of traditional Markov chain Monte Carlo methods like random walk Metropolis-Hastings etc. with or without parallel tempering. Our method employs finite number of estimating equations and observations but produces valid semi-parametric inference for a large class of statistical models including mixed effects models, generalised linear models, hierarchical Bayes models etc. A simulation study confirms that our proposed method converges quickly and draws samples from the posterior support efficiently. We further illustrate its utility through an analysis of a discrete data-set in small area estimation.

Keywords: Constrained convex optimisation; Empirical likelihood; Generalised linear models; Hamiltonian Monte Carlo; Mixed effect models; Score equations; Small area estimation; Unbiased estimating equations.

This is a joint work with Debashis Mondal, Oregon State University and Yin Teng, E&Y, Singapore.

https://docs.google.com/forms/d/e/1FAIpQLSfbk6GTAzQuj0__YUtUMiAgbPWabT-M1vmbgldohiwPxPltuw/viewform

### 2020/11/17

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yoshihiko Mitsumatsu**(Chuo University)Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (JAPANESE)

[ Abstract ]

In this talk a joint work with Naohiko Kasuya(Kyoto Sangyo U.), Hiroki Kodama(Tohoku U.), and Atsuhide Mori(Osaka Dental U.) is reported. The main result is the following.

There exist a Lefschetz fibration of the Milnor fiber of T_{pqr}-singularity (1/p + 1/q + 1/r ≦ 1) to the unit disk with regular fiber diffeomorphic to T^2.

An outline of the construction will be explained, through which, the space of 2-jets of (R^4, 0) to (R^2, 0) is analysed. This is motivated by F. Presas' suggestion that the speaker's construction of regular Poisson structures(=leafwise symplectic foliations) on S^5 might be interpreted by ``leafwise Lefschetz fibration''. These Lefschetz fibrations give a way to look at K3 surfaces through an extended class of Arnol'd's strange duality. These applications are introduced as well.

[ Reference URL ]In this talk a joint work with Naohiko Kasuya(Kyoto Sangyo U.), Hiroki Kodama(Tohoku U.), and Atsuhide Mori(Osaka Dental U.) is reported. The main result is the following.

There exist a Lefschetz fibration of the Milnor fiber of T_{pqr}-singularity (1/p + 1/q + 1/r ≦ 1) to the unit disk with regular fiber diffeomorphic to T^2.

An outline of the construction will be explained, through which, the space of 2-jets of (R^4, 0) to (R^2, 0) is analysed. This is motivated by F. Presas' suggestion that the speaker's construction of regular Poisson structures(=leafwise symplectic foliations) on S^5 might be interpreted by ``leafwise Lefschetz fibration''. These Lefschetz fibrations give a way to look at K3 surfaces through an extended class of Arnol'd's strange duality. These applications are introduced as well.

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

### 2020/11/12

#### Operator Algebra Seminars

16:45-18:15 Online

Contraction and bosonisation (English)

[ Reference URL ]

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

**Sutanu Roy**(NISER)Contraction and bosonisation (English)

[ Reference URL ]

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

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