Volume 84

iTHEMS Weekly News Letter

Featured Paper of the Week

Kenta Sato thumbnail

Akizuki-Nakano vanishing theorem and its application for globally F-split 3-folds

2020-01-09

In algebraic geometry, it is important to study spaces (=varieties) which may admit singular points. "Smoothing" is an effective way to deal with singularities. Roughly speaking, a smoothing of a (singular) variety helps us to find another variety which is non-singular and is "similar" to the original variety. Namikawa proved that a complex Fano 3-fold whose singular points are at worst ordinary double points admits a smoothing. In this paper, we give an analogy of this result in the case where the Fano variety is not complex, but is defined over a field of positive characteristic. The key ingredient of the proof is the vanishing of the second cohomology of the tangent space, which is a vector space containing an obstruction to construct a smoothing. We prove a positive characteristic analogue of the Akizuki-Nakano type vanishing for 3-dimensional varieties and as a corollary, we conclude the result about a smoothing.

Reference:
Kenta Sato, Shunsuke Takagi
"Weak Akizuki-Nakano vanishing theorem for globally $F$-split 3-folds"
arXiv: 1912.12074

Upcoming Events

Seminar

Tipping point detection of nonlinear dynamics by dynamic network biomarkers, and short-term time-series data prediction by randomly distributed embedding

January 15 (Wed) at 14:00 - 16:30, 2020

Luonan Chen (Professor, Excutive director, Chinese Academy of Sciences, China)

He will talk about theoretical study on complex network data, including clinical data.

His talk consists of two parts:
14:00-15:00: Detecting the tipping points of dynamic processes by dynamic network biomarkers
15:00-15:30: Coffee break
15:30-16:30: Predicting future dynamics of short-term time-series data by randomly distributed embedding

First part of his talk is for general audience.
In second part of his talk, he will explain mathematical basis of his study in detail.

Venue: Large Meeting Room, 2F Welfare and Conference Building (Cafeteria), RIKEN

Event Official Language: English

Colloquium

iTHEMS Colloquium

Exploring the learning principle in the brain

January 16 (Thu) at 15:30 - 17:00, 2020

Taro Toyoizumi (Team Leader, RIKEN Center for Brain Science (CBS))

Animals adapt to the environment for survival. Synaptic plasticity is considered a major mechanism underlying this process. However, the best-known form of synaptic plasticity, i.e., Hebbian plasticity that depends on pre- and post-synaptic activity, can surge coincident activity in model neurons beyond a physiological range. Our lab has explored how neural circuits learn about the environment by synaptic plasticity. The instability of Hebbian plasticity could be mitigated by a global factor that modulates its outcome. For example, TNF-alpha that mediates homeostatic synaptic scaling is released by glia, reflecting the activity level of surrounding neurons. I show that a specific interaction of Hebbian plasticity with this global factor accounts for the time course of adaptation to the altered environment (Toyoizumi et al. 2015). At a more theoretical level, I ask what is the optimal synaptic plasticity rule for achieving an efficient representation of the environment. A solution is the error-gated Hebbian rule, whose update is proportional to the product of Hebbian change and a specific global factor. I show that this rule, suitable also in neuromorphic devices, robustly extracts hidden independent sources in the environment (Isomura and Toyoizumi 2016, 2018, 2019). Finally, I introduce that synapses change by intrinsic spine dynamics, even in the absence of synaptic plasticity. I show that physiological spine-volume distribution and stable cell assemblies are both achieved when intrinsic spine dynamics are augmented in a model (Humble et al.2019).

Venue: Large Meeting Room, 2F Welfare and Conference Building (Cafeteria), RIKEN

Broadcast: R311, Computational Science Research Building, R-CCS, Kobe Campus, RIKEN / SUURI-COOL (Kyoto), #204-205, 2F Maskawa Building for Education and Research, North Campus, Kyoto University / SUURI-COOL (Sendai), #303, 3F AIMR Main Building, Advanced Institute for Materials Research (AIMR), Tohoku University

Event Official Language: English

Seminar

iTHEMS Math Seminar

Semiclassical methods in mathematical quantum mechanics

January 23 (Thu) at 16:00 - 18:10, 2020

Shu Nakamura (Professor, Gakushuin University)

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.

Talk 1: Semiclassical analysis, microlocal analysis and scattering theory.
I plan to talk about overview on the semiclassical analysis and related topics, especially its intrinsic relationship with microlocal analysis and (microlocal) scattering theory. Roughly speaking, the microlocal analysis is an application of semiclassical idea to the analysis of singularities, and its analogue in momentum space is the microlocal scattering theory. We discuss basic notions of these, and mention several recent results.

Talk 2: Microlocal structure of the scattering matrix with long-range perturbations.
As an example of topics discussed in Talk 1, we discuss recent results on the scattering matrix with long-range perturbations. In particular, we show that the scattering matrix is expressed as a Fourier integral operator, and in some cases we can decide its spectral properties. Our approach is fairly geometric and abstract, and thus applies not only to usual Schrödinger operators but also to higher order operators and discrete Schrödinger operators.

Venue: #435-437, Main Research Building, RIKEN

Event Official Language: English

Upcoming Visitors

January 22 (Wed) - 24 (Fri), 2020

Hiroyuki Fuji

Associate Professor, Faculty of Education, Kagawa University

Visiting Place: Main Research Building

Yuki Koyanagi thumbnail

January 22 (Wed) - 24 (Fri), 2020

Yuki Koyanagi

Student Trainee, iTHEMS / Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark

Research fields: Mathematical Biology

Visiting Place: Main Research Building

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