<학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
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...
Category수학강연회소속송용수강연자<학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
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...
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...
Quantum Dynamics in the Mean-Field and Semiclassical Regime
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...
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...
Category수학강연회소속Stanford University강연자Gunnar E. Carlsson
Topological aspects in the theory of aperiodic solids and tiling spaces
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...
Category수학강연회소속Georgia Institute of Technology, School of Mathematics and School of Physics강연자Jean V. Bellissard
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...
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...
Category수학강연회소속Simons Center for Geometry and Physics강연자Kenji Fukaya
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...
Category수학강연회소속Univ. of Toronto / KIAS강연자Kim, Henry
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 ...
Category수학강연회소속Univ. of Wisconsin강연자Marshall Slemrod