This talk discusses modern cryptographic techniques, such as zero-knowledge proof, multi-party computation and homomorphic encryption, which provide advanced functionality and security guarantees beyond data privacy and authenticity. I will...

150902_HYKE.pdf

The goal of this lecture is to explain and motivate the connection between AubryMather theory (Dynamical Systems), and viscosity solutions of the Hamilton-Jacobi equation (PDE). This connection is the content of weak KAM Theory. The talk sho...

Fano manifolds of Calabi-Yau Type

It is usually a difficult problem to characterize precisely which elements of a given integral domain can be written as a sum of squares of elements from the integral domain. Let R denote the ring of integers in a quadratic number field. Thi...

The Lie superalgebra q(n) is the second super-analogue of the general Lie algebra gl(n). Due to its complicated structure, q(n) is usually called “the queer superalgebra”. In this talk we will discuss certain old and new results related to t...

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...

The talk will review a new approach to the limits of the quantum N-body dynamics leading to the Hartree equation (in the large N limit) and to the Liouville equation (in the small Planck constant limit). This new strategy for studying both l...

Given a group of isometries of a metric space, one can draw a random sequence of group elements, and look at its action on the space.  What are the asymptotic properties of such a random walk?  The answer depends on the geometry of the space...

The field of operator algebras deals with suitable closed subalgebras of the algebra of bounded linear operators on a Hilbert space. There are two types of operator algebras: C*-algebras and von Neumann algebras. In the 1970s A. Connes obtai...

Homology is a method for assigning signatures to geometric objects which reects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology...

Persistent homology produces invariants which take the form of barcodes, or nite collections of intervals. There are various structures one can imposed on them to yield a useful organization of the space of all barcodes. In addition, there...

One of the important problems in understanding large and complex data sets is how to provide useful representations of a data set. We will discuss some existing methods, as well as topological mapping methods which use simplicial complexes ...

Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline cal...

The significance of dimensions in mathematics

After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finit...

Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one...

Conformal field theory and noncommutative geometry

초록 첨부: Void.pdf