Probabilistic approach to discrete integrable systems

January 17 (Fri) at 15:30 - 17:30, 2025

Makiko Sasada (Professor, Graduate School of Mathematical Sciences, The University of Tokyo)

The KdV equation and the Toda lattice are two central and widely studied examples of classical integrable systems, and many of their variations have been introduced to the present. In particular, the box-ball system (BBS) is a basic example of a discrete integrable system, which has been revealed to be an ultra-discrete version of the KdV equation and the Toda lattice. The BBS has been studied from various viewpoints such as tropical geometry, combinatorics, and cellular-automaton. As a new perspective, research on probabilistic approaches to this system has been rapidly expanding in recent years, including the application of the Pitman transform, analysis of invariant measures and its generalized hydrodynamics. More recently, we find that the application of the Pitman transform and the study of invariant measures of i.i.d.-type also work in the same manner for the discrete KdV equation and the discrete Toda lattice. Further research has begun on the relationship between the Yang-baxter maps and the existence of i.i.d.-type invariant measures for the discrete integrable systems. In this talk, I will introduce these new research topics that have been spreading over the past several years from the basics. This talk is based on several joint works with David Croydon, Tsuyoshi Kato, Satoshi Tsujimoto, Ryosuke Uozumi, Matteo Mucciconi, Tomohiro Sasamoto, Hayate Suda and Stefano Olla.

Venue: Seminar Room #359

Event Official Language: English

Principles of the evolution of human social structures: kinship and gift-giving

January 16 (Thu) at 16:00 - 17:15, 2025

Kenji Itao (Special Postdoctoral Researcher, Computational Group Dynamics Collaboration Unit, RIKEN Center for Brain Science (CBS))

Anthropologists have long noted structural similarities among geographically distant societies. To investigate the origins of these patterns, I develop simple models of human interactions based on field observations, simulating the emergence of social structures. This talk focuses on two key topics. The first examines the evolution of kinship structures in clan societies [1, 2, 3]. By modeling kin and in-law cooperation alongside mating competition, I show how cultural groups with specific marriage rules spontaneously emerge. The second explores the transition of social organizations through competitive gift-giving [4, 5]. By modeling how gifts deliver material goods to recipients and confer social reputation upon donors, I demonstrate transitions across four phases—band, tribe, chiefdom, and kingdom—each characterized by distinct social networks and distributions of wealth and reputation. In both cases, I highlight the alignment between theoretical predictions and empirical observations, offering quantitative criteria and empirically measurable explanatory parameters for classifying social structures.

Venue: via Zoom / Hybrid Format (3F #359 and Zoom), Main Research Building

Event Official Language: English

Visit by ASCENT-6E high school students

January 13 (Mon) at 10:40 - 16:00, 2025

PROGRAMME Visit of students enrolled in the ASCENT Program at Chiba University Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS): RIKEN Wako Campus (Wako City, Saitama) Event date: Monday, January 13th, 2025 ASCENT-6E Program: iTHEMS members: Schedule 10:30-10:40 (10 min): Arriving procedure 10:40-11:00 (20 min) at meeting room on the 4th floor, Main Research Building Introduction of students (to hear their names and scientific fields of interest). We will provide colour-coded badges to write their names and the colour would represent their field of interest (e.g., blue for biology, green for math, red for physics). 11:00-11:10 (10 min) Bathroom break 11:10-12:00 (50 min) at meeting room on the 4th floor, Main Research Building First set of talks by iTHEMS members (10 min each) Tetsuo Hatsuda (Physics, mathematics) Catherine Beauchemin (Physics, biology) Tsukasa Tada (Physics, mathematics) Gen Kurosawa (Biology) Misako Tatsuuma (Physics) 12:00-12:50 (50 min) at Common Space in the 4th floor of Main Research Building (tentative) Discussion Lunch with students 12:50-13:40 (50 min) at meeting room on the 4th floor, Main Research Building Second set of talks by iTHEMS members (10 min each) Akihisa Yamamoto (Physics, biology) Ryo Namba (Physics) Christy Kelly (Mathematics, physics) Rumi Hasegawa (Physics) Jose Gutierrez (Biology) 13:40-13:50 (10 min) at meeting room on the 4th floor, Main Research Building Brief overview of iTHEMS and RIKEN programmes (T.Hatsuda, C.Beauchemin, or T. Tada) (e.g., JRA, IPA, SPDR, RS/SRS) 13:50-14:00 (10 min) Bathroom break 14:00-14:15 (15 min) at meeting room on the 4th floor, Main Research Building (tentative) Short statements by Prof. Jun Nomura and ASCENT program coordinators Qian Wang and Hina Morishige 14:15-16:00 (105 min) at Common Space in the 4th floor of Main Research Building (tentative) Informal discussions among ASCENT program students and iTHEMS members over some snacks and coffee. iTHEMS members will spread at different areas in the common space of 3rd floor and will display posters or conduct activities that can facilitate discussion. If posters are used, they may be the ones used in the Now & Next or new ones.

Venue: #435-437, 4F, Main Research Building

Event Official Language: English

Search for BSM particles from high energy supernova neutrinos

January 10 (Fri) at 14:00 - 15:15, 2025

Kensuke Akita (JSPS Research Fellow, Graduate School of Science, The University of Tokyo)

Light hypothetical particles with masses up to O(100) MeV can be produced in the core of supernovae. Their subsequent decays to neutrinos can produce a flux component with higher energies than the standard flux. We study the impact of heavy neutral leptons, Z′ bosons, in particular U(1)Lμ−Lτ and U(1)B−L gauge bosons, and majorons coupled to neutrinos flavor-dependently. We obtain new strong limits on these particles from no events of high-energy SN 1987A neutrinos and their future sensitivities from observations of galactic supernova neutrinos.

Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359

Event Official Language: English