The notion of essential dimension was introduced by Buhler and Reichstein in the late 90s. Roughly speaking, the essential dimension of an algebraic object is the minimal number of algebraically independent parameters one needs to define the...
Equations defining algebraic curves and their tangent and secant varieties
It is a fundamental problem in algebraic geometry to study equations defining algebraic curves. In 1984, Mark Green formulated a famous conjecture on equations defining canonical curves and their syzygies. In early 2000's, Claire Voisin...
※ 강연 뒷부분이 녹화되지 않았습니다. A symplectic manifold is a space with a global structure on which Hamiltonian equations are defined. A classical result by Darboux says that every symplectic manifold locally looks standard, so it has be...
We consider different growth rates associated with the geometry (distance, volume, heat kernel) on a cover of a compact Riemannian manifold. We present general inequalities. We discuss the rigidity results and questions in the case of negati...
Diophantine equations and moduli spaces with nonlinear symmetry
A fundamental result in number theory is that, under certain linear actions of arithmetic groups on homogeneous varieties, the integral points of the varieties decompose into finitely many orbits. For a classical example, the set of integra...
Among many different ways to introduce derived algebraic geometry is an interplay between ordinary algebraic geometry and homotopy theory. The infinity-category theory, as a manifestation of homotopy theory, supplies better descent results ...
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...
Creation of concepts for prediction models and quantitative trading
Modern mathematics with axiomatic systems has been developed to create a complete reasoning system. This was one of the most exciting mathematical experiments. However, even after the failure of the experiment, mathematical research is still...
It is a fascinating and challenging problem to count number fields with bounded discriminant. It has so many applications in number theory. We give two examples. First, we compute the average of the smallest primes belonging to a conjugacy ...
Convex and non-convex optimization methods in image processing
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...
CategoryMath ColloquiaDept.Hong Kong Baptist UniversityLecturerMichael Ng
Contact topology of singularities and symplectic fillings
For an isolated singularity, the intersection with a small sphere forms a smooth manifold, called the link of a singularity. It admits a canonical contact structure, and this turns out to be a fine invariant of singularities and provides an...
Contact instantons and entanglement of Legendrian links
We introduce a conformally invariant nonlinear sigma model on the bulk of contact manifolds with boundary condition on the Legendrian links in any odd dimension. We call any finite energy solution a contact instanton. We also explain its Ha...
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 ...
CategoryMath ColloquiaDept.Univ. of WisconsinLecturerMarshall Slemrod
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...
Connectedness of a zero-level set as a geometric estimate for parabolic PDEs
Studies on PDEs are mostly focused on ?nding properties of PDEs within a speci?c discipline and on developing a technique specialized to them. However, ?nding a common structure over di?erent disciplines and unifying theories from di?erent s...