## Seminar information archive

Seminar information archive ～08/07｜Today's seminar 08/08 | Future seminars 08/09～

### 2019/03/27

#### Tuesday Seminar on Topology

17:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)

On a moduli space interpretation of the Turaev cobracket (ENGLISH)

**Florian Naef**(Université de Genève)On a moduli space interpretation of the Turaev cobracket (ENGLISH)

[ Abstract ]

Given an oriented surface, Goldman defines a Lie bracket on the vector space spanned by free homotopy classes of loops in terms of intersections. This Lie bracket is the universal version of the Atiyah-Bott Poisson structure on the moduli space of flat connections. Using self-intersections Turaev defines a Lie cobracket on loops. We give a possible interpretation of this structure on moduli spaces of flat connections in the form of a natural BV operator on the moduli space of flat connection with values in a super Lie algebra equipped with an odd pairing. This is joint work with A. Alekseev, J. Pulmann and P. Ševera.

Given an oriented surface, Goldman defines a Lie bracket on the vector space spanned by free homotopy classes of loops in terms of intersections. This Lie bracket is the universal version of the Atiyah-Bott Poisson structure on the moduli space of flat connections. Using self-intersections Turaev defines a Lie cobracket on loops. We give a possible interpretation of this structure on moduli spaces of flat connections in the form of a natural BV operator on the moduli space of flat connection with values in a super Lie algebra equipped with an odd pairing. This is joint work with A. Alekseev, J. Pulmann and P. Ševera.

### 2019/03/26

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Cube capacities (ENGLISH)

**Michael Hutchings**(University of California, Berkeley)Cube capacities (ENGLISH)

[ Abstract ]

We define a new series of symplectic capacities using equivariant symplectic homology. These capacities are conjecturally equal to the Ekeland-Hofer capacities, but can be computed in many more examples. In particular, we use these capacities to find many examples of symplectic embeddings of cubes where the cube is as large as possible. This is joint work with Jean Gutt.

We define a new series of symplectic capacities using equivariant symplectic homology. These capacities are conjecturally equal to the Ekeland-Hofer capacities, but can be computed in many more examples. In particular, we use these capacities to find many examples of symplectic embeddings of cubes where the cube is as large as possible. This is joint work with Jean Gutt.

### 2019/03/22

#### Colloquium

13:00-17:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

Mathematical structures of quantum mechanics and classical mechanics (日本語)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~shu/

Algebraic cyles, Periods and Motives (日本語)

[ Reference URL ]

http://gauss.ms.u-tokyo.ac.jp/index-j.html

Research on groups of homeomorphisms (日本語)

https://www.ms.u-tokyo.ac.jp/~tsuboi/

**Shu NAKAMURA**(The University of Tokyo) 13：00-14：00Mathematical structures of quantum mechanics and classical mechanics (日本語)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~shu/

**Tomohide TERASOMA**(The University of Tokyo) 14:30-15:30Algebraic cyles, Periods and Motives (日本語)

[ Reference URL ]

http://gauss.ms.u-tokyo.ac.jp/index-j.html

**Takashi TSUBOI**(The University of Tokyo) 16:00-17:00Research on groups of homeomorphisms (日本語)

[ Abstract ]

The homeomorphisms of a topological space form a group. The group seems to be too wild to be considered. In some cases it becomes a countable group but it is usually uncountable group. I have studied groups of homeomorphisms of topological spaces or groups of diffeomorphisms of manifolds which are related to invariants of foliations. I found several relationship between dynamical properties of group actions and homology of groups. There are many unsolved problems on the group of

homeomorphisms. I also intend to investigate more on the shape of groups. I would like to talk on such topics around groups of homeomorphisms.

[ Reference URL ]The homeomorphisms of a topological space form a group. The group seems to be too wild to be considered. In some cases it becomes a countable group but it is usually uncountable group. I have studied groups of homeomorphisms of topological spaces or groups of diffeomorphisms of manifolds which are related to invariants of foliations. I found several relationship between dynamical properties of group actions and homology of groups. There are many unsolved problems on the group of

homeomorphisms. I also intend to investigate more on the shape of groups. I would like to talk on such topics around groups of homeomorphisms.

https://www.ms.u-tokyo.ac.jp/~tsuboi/

### 2019/03/13

#### Seminar on Probability and Statistics

14:00-15:10 Room #052 (Graduate School of Math. Sci. Bldg.)

On parameter estimation of hidden Markov processes

**Yury A. Kutoyants**(Laboratoire Manceau de Mathématiques, Le Mans University)On parameter estimation of hidden Markov processes

[ Abstract ]

We present a survey of several results devoted to parameter estimation of partially observed models. The hidden processes are Ornstein-Uhlenbeck process and Telegraph process. We describe the asymptotic behavior of the MLE and BE of the unknown parameters of hidden processes and special attention is paid to a new class of estimators called Multi-step MLE-processes, which have the same asymptotic properties as the MLE but can be calculated much easier than MLE.

The corresponding articles are

1.Kutoyants Yu. A., " On the multi-step MLE-process for ergodic

diffusion", (arXiv 1504.01869) Stochastic Processes and their

Applications, 2017, 127, 2243-2261.

2.Khasminskii, R. Z. and Kutoyants, Yu. A. "On parameter estimation of

hidden telegraph process". (arXiv:1509.02704 ) Bernoulli, 2018, 24, 3,

2064-2090.

3.Kutoyants, Yu. A. "On parameter estimation of hidden

Ornstein-Uhlenbeck process", Journal of Multivariate Analysis. 2019,

169, 1, 248-263.

4.Kutoyants, Yu. A. "On parameter estimation of hidden ergodic

Ornstein-Uhlenbeck process", 2019, submitted (arXiv:1902.08500)

We present a survey of several results devoted to parameter estimation of partially observed models. The hidden processes are Ornstein-Uhlenbeck process and Telegraph process. We describe the asymptotic behavior of the MLE and BE of the unknown parameters of hidden processes and special attention is paid to a new class of estimators called Multi-step MLE-processes, which have the same asymptotic properties as the MLE but can be calculated much easier than MLE.

The corresponding articles are

1.Kutoyants Yu. A., " On the multi-step MLE-process for ergodic

diffusion", (arXiv 1504.01869) Stochastic Processes and their

Applications, 2017, 127, 2243-2261.

2.Khasminskii, R. Z. and Kutoyants, Yu. A. "On parameter estimation of

hidden telegraph process". (arXiv:1509.02704 ) Bernoulli, 2018, 24, 3,

2064-2090.

3.Kutoyants, Yu. A. "On parameter estimation of hidden

Ornstein-Uhlenbeck process", Journal of Multivariate Analysis. 2019,

169, 1, 248-263.

4.Kutoyants, Yu. A. "On parameter estimation of hidden ergodic

Ornstein-Uhlenbeck process", 2019, submitted (arXiv:1902.08500)

### 2019/03/05

#### Tuesday Seminar of Analysis

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

The structure of minimal surfaces near polyhedral cones (English)

**Nicholas Edelen**(Massachusetts Institute of Technology)The structure of minimal surfaces near polyhedral cones (English)

[ Abstract ]

We prove a regularity theorem for minimal varifolds which resemble a cone $C_0$ over an equiangular geodesic net. For varifold classes admitting a ``no-hole'' condition on the singular set, we additionally establish regularity near the cone $C_0 \times R^m$. Our result implies the following generalization of Taylor's structure theorem for soap bubbles: given an $n$-dimensional soap bubble $M$ in $R^{n+1}$, then away from an $(n-3)$-dimensional set, $M$ is locally $C^{1,\alpha}$ equivalent to $R^n$, a union of three half-$n$-planes meeting at $120$ degrees, or an $(n-2)$-line of tetrahedral junctions. This is joint work with Maria Colombo and Luca Spolaor.

We prove a regularity theorem for minimal varifolds which resemble a cone $C_0$ over an equiangular geodesic net. For varifold classes admitting a ``no-hole'' condition on the singular set, we additionally establish regularity near the cone $C_0 \times R^m$. Our result implies the following generalization of Taylor's structure theorem for soap bubbles: given an $n$-dimensional soap bubble $M$ in $R^{n+1}$, then away from an $(n-3)$-dimensional set, $M$ is locally $C^{1,\alpha}$ equivalent to $R^n$, a union of three half-$n$-planes meeting at $120$ degrees, or an $(n-2)$-line of tetrahedral junctions. This is joint work with Maria Colombo and Luca Spolaor.

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

### 2019/02/12

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representations of knot groups (ENGLISH)

**Anastasiia Tsvietkova**(Okinawa Institute of Science and Technology, Rutgers University)Representations of knot groups (ENGLISH)

[ Abstract ]

We describe a new method of producing equations for the representation variety of a knot group into (P)SL(2,C). Unlike known methods, this does not involve any polyhedral decomposition or triangulation of the link complement, and uses only a link diagram satisfying a few mild restrictions. This results in a simple algorithm that can often be performed by hand, and in many cases, for an infinite family of knots at once. This is a joint work with Kathleen Peterson (Florida State University).

We describe a new method of producing equations for the representation variety of a knot group into (P)SL(2,C). Unlike known methods, this does not involve any polyhedral decomposition or triangulation of the link complement, and uses only a link diagram satisfying a few mild restrictions. This results in a simple algorithm that can often be performed by hand, and in many cases, for an infinite family of knots at once. This is a joint work with Kathleen Peterson (Florida State University).

### 2019/02/06

#### Seminar on Probability and Statistics

16:30-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Testing the causality of Hawkes processes with time reversal

**Ioane Muni Toke**(Centrale Supelec Paris)Testing the causality of Hawkes processes with time reversal

[ Abstract ]

We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.

We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.

### 2019/02/01

#### thesis presentations

9:15-10:30 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

10:45-12:00 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

9:15-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

10:45-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

9:15-10:30 Room #126 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

10:45-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #126 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)

### 2019/01/31

#### thesis presentations

12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

15:45-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

17:15-18:30 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)

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