I will tell two interrelated stories illustrating fruitful interactions between combinatorics and Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter Brändén. They link continuous convex...
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...
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 ...
Category특별강연소속Stanford University강연자Gunnar E. Carlsson
Structures on Persistence Barcodes and Generalized Persistence
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...
Category특별강연소속Stanford University강연자Gunnar E. Carlsson
Homology is a method for assigning signatures to geometric objects which re ects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology...
Category특별강연소속Stanford University강연자Gunnar E. Carlsson
It is very interesting to study what problems can be computed in irreducible plane curve singularities in algebraicgeometry? Then, the aim of this talk is to compute the explicit algorithm for finding the correspondence between the family of...
Despite of the fact that 4-dimensional manifolds together with 3-dimensional manifolds are the most fundamental and important objects in geometry and topology and topologists had great achievements in 1960's, there has been little known on 4...
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...
Category특별강연소속Univ. of Texas, Arlington강연자Dimitar Grantcharov
Regularization by noise in nonlinear evolution equations
There are some phenomena called "regularization by noise" in nonlinear evolution equations. This means that if you add a noise to the system, the system would have a better property than without noise. As one of examples, I will explain this...
A New Approach to Discrete Logarithm with Auxiliary Inputs
Let be a cyclic group with generator . The discrete logarithm problem with auxiliary inputs (DLPwAI) is asked to find with auxiliary inputs , ,…, . In Eurocrypt 2006, an algorithm is proposed to solve DLPwAI in when . In this paper, we reduc...
In this talk, we discuss recent work with Albers, Cieliebak, Fish, Frauenfelder, Hofer and Paternain on several aspects of the three body problem. The ultimate goal of this project is to use modern, holomorphic curve techniques to investigat...
Harmonic bundles and Toda lattices with opposite sign
In this talk, we shall discuss the semi-infinite variation of Hodge structure associated to real valued solutions of a Toda equation. First, we describe a classification of the real valued solutions of the Toda equation in terms of their par...
In this talk, we shall first present several examples of numerical simulations of complex industrial systems. All these simulations rely upon some mathematical models involving Partial Differential Equations and we shall briefly explain the ...
Category특별강연소속Collège de France강연자Pierre-Louis Lions
