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Seminar information archive ～02/05｜Today's seminar 02/06 | Future seminars 02/07～

2017/02/20

Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Jørgen Ellegaard Andersen (Aarhus University)
The Verlinde formula for Higgs bundles (ENGLISH)

[ Abstract ]
In this talk we will present a Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. We further present a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. We will explain how all these dimensions fit into a one parameter family of 2D TQFT's, encoded in a one parameter family of Frobenius algebras, which we will construct.

2017/02/16

Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / University of Paris-Sud)
Diffusive and inviscid traveling wave solution of the Fisher-KPP equation
(ENGLISH)

[ Abstract ]
Our purpose is to study the limit of traveling wave solutions of the Fisher-KPP equation as the diffusion coefficient tends to zero. More precisely, we consider monotone traveling waves which connect the stable steady state to the unstable one. It is well known that there exists a positive constant c* such that there does not exist any traveling wave solution if c < c* and a unique (up to translation) monotone traveling wave solution of wave speed c for each c > c*.

We consider the corresponding inviscid ordinary differential equation where the diffusion coefficient is equal to zero and show that it possesses a unique traveling wave solution. We then fix c > 0 arbitrary and prove the convergence of the travelling wave of the parabolic equation with velocity c to that of the corresponding traveling wave solution of the inviscid problem.

Further research should involve a similar problem for monostable systems.

This is joint work with Yong Jung Kim.

2017/02/13

Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Qi'an Guan (Peking University)
A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)

[ Abstract ]
In this talk, we will present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa-Takegoshi extension theorem holds. We also present a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.
This is joint work with Dr. Zhenqian Li.

Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Yokoyama (Graduate school of mathematical sciences, the university of Tokyo)
Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation

2017/02/10

Algebraic Geometry Seminar

14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Chenyang Xu (Beijing International Center of Mathematics Research)
Stability theory of a klt singularity II (English)

[ Abstract ]
In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

2017/02/09

Discrete mathematical modelling seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Dinh Tran (University of New South Wales, Sydney, Australia)
Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)

[ Abstract ]
We study growth of degrees of autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps us to prove polynomial growth of a certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic reductions of integrable lattice equations. We also study signatures of growth of degrees of lattice equations over finite fields.

2017/02/07

Algebraic Geometry Seminar

15:30-17:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Chenyang Xu ( Beijing International Center of Mathematics Research)
Stability theory of a klt singularity I (English)