## Seminar information archive

Seminar information archive ～02/15｜Today's seminar 02/16 | Future seminars 02/17～

### 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.)

#### thesis presentations

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

#### thesis presentations

15:45-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

17:15-18:30 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

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

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