Conferences and lectures

FMSP Student Session

2013/03/28 -- 03/29
Room 056, Graduate School of Mathematical Sciences, the University of Tokyo (Komaba Campus)

Schedule

Thursday, March 28
10:00 - 11:00 Koichi Shimada
11:10 - 12:10 Shou Yoshikawa
13:30 - 14:30 Takafumi Mase
14:40 - 15:40 Takahiro Matsushita
16:00 - 17:00 Yuichiro Tanaka

Friday, March 29
10:00 - 11:00 Morimichi Kawasaki
11:10 - 12:10 Ryosuke Nomura
13:30 - 14:30 Ryuichi Nishiyama
14:40 - 15:40 Tomoki Ohtsuki
16:00 - 17:00 Chen Jiang

Koichi Shimada (Graduate School of Mathematical Sciences)

Title: "Rohlin Flows on Amalgamated Free Products."

Abstract: A von Neumann algebra is a kind of rings with a topology. We are interested in R-actions (flows) of von Neumann algebras. Here we focus our attention to so-called Rohlin flows, which are "very outer" flows. Recently, Masuda and Tomatsu have established a classification theorem for Rohlin flows. By their theorem, Rohlin flows on so-called McDuff factors are well-understood. Then how about flows on non-McDuff factors? Masuda and Tomatsu's theorem is also applicable to flows on non-MacDuff factors. However, there have been no known examples of Rohlin flows on non-McDuff factors. So it is important to construct Rohlin flows on non-McDuff factors and to classify them by using the classification theorem. Here we do this by considering flows on so-called amalgamated free product factors, which are non-McDuff.

Shou Yoshikawa (Graduate School of Mathematical Sciences)

Title: "A relation between the discriminant of an elliptic curve and its torsion points."

Abstract: We give an explicit description of the discriminant of an elliptic curve in terms of the 12-torsion points of the elliptic curve. This description involves the Weil-pairing in a crucial way. This is a joint work with K. Fukuda.

Takafumi Mase (Graduate School of Mathematical Sciences)

Title: "The Laurent phenomenon and discrete integrable systems."

Abstract: The Laurent phenomenon is the property that the solution to an initial value problem of a discrete equation is expressed as a Laurent polynomial of the initial values. This concept has arisen from the study of cluster algebras, for which it is known that any cluster variable is a Laurent polynomial of the initial cluster variables. In this talk, we leave the connection with cluster algebras aside and study the Laurent phenomenon for its own sake. We explain that most of the discrete bilinear equations that appear in the field of integrable systems exhibit this phenomenon and we discuss its relation to integrability.

Takahiro Matsushita (Graduate School of Mathematical Sciences)

Title: "Covering map theory for graphs."

Abstract: For a positive integer r, we introduce the notions of r -covering maps and r-fundamental groups of graphs. We show that there is a natural correspondence between r-covering maps and r- fundamental groups, as is the covering space theory in topology. We show that the r-fundamental group gives some obstructions of the existence of graph maps, and is related to the graph coloring problem. Finally, we would like to mention that 2-fundamental groups are closely related to the fundamental groups of Lovász' neighborhood complexes.

Yuichiro Tanaka (Graduate School of Mathematical Sciences)

Title: "Visible actions on flag varieties and a generalization of the Cartan decomposition."

Abstract: With the aim of uniform treatment of multiplicity-free representations of Lie groups, T. Kobayashi introduced a notion of visible actions on complex manifolds. Thanks to this notion, we can not only obtain multiplicity-free theorems but also find some (complex) geometric properties of Lie groups.

In this talk, I will explain visible actions and introduce a generalization of the Cartan decomposition for compact Lie groups, which gives rise to (three) visible actions on flag varieties and leads us to (three) multiplicity-free theorems.

Morimichi Kawasaki (Graduate School of Mathematical Sciences)

Title: "Superheavy Lagrangian immersion in the 2-torus."

Abstract: To solve the problem of displaceability by symplectomorphisms, M. Entov and L. Polterovich defined the "superheaviness" of closed subsets in closed symplectic manifolds. We give an example of a superheavy subset and its application. To prove them, we use a Hamiltonian circle action with noncontractible orbits.

Ryosuke Nomura (Graduate School of Mathematical Sciences)

Title: "Predictability of Approximate Accuracy for Asymptotic Expansion."

Abstract: The pricing of derivatives is an important problem in finance. Compared to Monte Carlo method, which is high accuracy but computationally expensive, asymptotic expansion which approximates probability distributions is a hopeful method. In this presentation, it is aimed to evaluate the availability of asymptotic expansion for various stochastic differential equation models. We use random forests to estimate error rate between asymptotic expansion and Monte Carlo method, and experimentally show that it is possible to determine the criterion to use asymptotic expansion for the pricing of derivatives.

Ryuichi Nishiyama (Department of Earth and Planetary Science, School of Science)

Title: "Simultaneous inversion of gravity and muon radiography data to probe 3D internal density structure of volcanoes."

Abstract: We have developed an integrated processing of gravity anomaly and muon radiography data to determine 3D internal density structure of volcanoes with an unprecedented spatial resolution. This technique will be useful for monitoring volcanic activities. My talk consists of two parts. In the former part, I review the principle of gravity survey and cosmic-ray muon radiography. In the latter part, I show the results of a case study at a small volcano, Showa-Shinzan Lava Dome in Usu volcanic region, Hokkaido, Japan.

Tomoki Ohtsuki (Department of Physics, School of Science)

Title: "Axiomatic approach to Conformal Field Theories?"

Abstract: Conformal Field Theory (CFT) has been playing a significant role in various branches of theoretical physics. Recently an approach to CFT "Conformal Bootstrap Program" has been proposed. In this approach we don't consider each models separately - instead we look at the very basic principles in CFT such as unitarity, conformal symmetry, and some associativity of particular operation. Although we have to truncate the problem into numerical algorithm at this stage, very illuminating results have been reported such as critical exponents of 3d Ising model and existence of 4d superconformal "minimal model". My aim in this talk is to argue that the proper axiomatization of these CFT principles will lead to a mathematical understanding of those nontrivial problem in physics (such as 3d Ising model).

Chen Jiang (Graduate School of Mathematical Sciences)

Title: "Bounding the volumes of singular weak log del Pezzo surfaces."

Abstract: We give an optimal upper bound for the anti-canonical volume of an ε-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface.