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In this talk, we will discuss some of our recent work on the master equation involving the fully fractional heat operator. Specifically, we will present two main results. The first one pertains to a g...
We are motivated to study this problem so that the proof of Arnold Diffusion of many degrees of freedom can be significantly simplified.
In 1960s, Arnold conjectured that the number of fixed points of a Hamiltonian diffeomorphism of a symplectic manifold should be (much) greater than its counterpart for a general diffeomorphism. This c...
In this talk, we will talk about Fernandez-Molina’s paper”Futaki invariants and Yau’s conjecture on the Hull-Strominger system”. We will introduce a new obstruction to the existence of solutions of th...
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
Bloch's conjecture for a surface X over an algebraically closed field k states that every homologically trivial correspondence acts as 0 on the Albanese kernel. When X is a K3 surface, this conjecture...
In this talk, I'll make a discussion on recent progress in the research of scalar curvature. I'll review the backgrounds from Gauss-Bonnet formula to the aspherical conjecture, and then focus on the f...
In this talk, I will explain the relationship between the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces and the existence of Shokurov polytopes. For K3 fibrations, this enables us to e...
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
The Borel conjecture considers the obstruction from homotopy equivalence to homeomorphism for aspherical manifolds. The torus is the first computed case of Borel conjecture with the idea of splitting ...
Past Member (2020–21) Jinyoung Park, a Szegö Assistant Professor at Stanford University, and Huy Tuan Pham, a Stanford Ph.D. student, proved the Kahn-Kalai Conjecture, a central problem in probab...
Lightweight cryptography is an important tool for building strong security solutions for pervasive devices with limited resources. Due to the stringent cost constraints inherent in extremely large app...
In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conjecture on properties of the solutions of a type of quadratic equation over the binary extension fields, which had been convinced ...
The purpose of this workshop is to bring focused attention on a recent breakthrough by Brown, Fisher and ZIM2018_imageHurtado on Zimmer’s Conjecture. The conjecture concerns low dimensional actions of...

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