In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...

From 1980’s, the study of Kleinian groups has been carried out in the framework of the paradigm of “Thurston’s problems”. Now they are all solved, and we can tackle deeper problems; for instance to determine the topological types of the defo...

Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself...

Unconditional results without an unproved hypothesis such as the generalized Riemann hypothesis (GRH) are very weak for an individual number field. But if we consider a family of number fields, one can prove just as strong results as we woul...

A function from a group G to integers Z is called a quasi-morphism if there is a constant C such that for all g and h in G, |f(gh)-f(g)-f(h)| < C. Surprisingly, this idea has been useful. I will overview the theory of quasi-morphisms includi...

A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold M2 which can be realized as isometric immersions into R3. This problem can be formulated as initial and/or boundary ...

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Sheaf quantization of Hamiltonian isotopies and non-displacability problems

We proved the codimension three conjecture that says the micro-local perverse sheaves extend if it is defined outside odimension three (counting from Lagrangian subvarity). It is a joint work with Kari Vilonen.

Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector spac...

The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular...

In this talk, we discuss some results of convex and non-convex optimization methods in image processing. Examples including image colorization, blind decovolution and impulse noise removal are presented to demonstrate these methods. Their a...

Fokker-Planck and Kolmogorov (backward) equations can be interpreted as linearisations of the underlying stochastic differential equations (SDE). It turns out that, in particular, on infinite dimensional spaces (i.e. for example if the SDE i...

Unprojection or "constructing bigger Gorenstein ideals from smaller one" is an algebraic device for constructing Gorenstein varieties in codimension 4, 5, ..., beyond the range of standard structure theorems; it has a large number of fairly ...

I will talk about arithmetic topology, in particular, some issues related to class field theory for 3-dimensional foliated dynamical systems.

I will talk on Cannes's Embedding Conjecture, which is considered as one of the most important open problems in the field of operator algebras. It asserts that every finite von Neumann algebra is approximable by matrix algebras in suitable s...

In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...

A classical theorem of Jacobs, de Leeuw and Glicksberg shows that a representation of a group on a reflexive Banach space may be decomposed into a returning subspace and a weakly mixing subspace. This may be realized as arising from the idem...

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