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We report the work “Duality between the pseudoeffective and the movable cone of a projective manifold” of Witt Nystrom, where he proved the transcendental Morse inequality for projective manifolds.
The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I wi...
In this series of work, we aim at improving the bootstrapping paradigm for fully homomorphic encryption (FHE). Our main goal is to show that the amortized cost of bootstrapping within a polynomial mod...
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
We'll start with reviewing Quillen and Lurie's theory of non-abelian derived categories (also known as the "animation" theory). Following that, we will apply this theory to generalize the classical Sc...
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
In this talk I will introduce some basic concepts in higher category and some details of the construction in the first talk. I will introduce crossed modules and the example of strict 2-representation...
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
In this talk, we address on the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with s...
I will talk about affine Grassmannians for the exceptional group of type G_2. This group can be given as automorphisms of octonion algebras. I consider all maximal parahoric subgroups in G_2, and give...
The motivic Chern classes of the Schubert cells are the K-theoretic generalizations of the Chern-Schwartz-MacPherson classes in homology. I will report some joint work in progress with L. Mihalcea and...
We introduce the notion of expanding cone of a noncompact simple Lie group. This allows us to extend several results in homogeneous dynamics to more general settings. We show how this notion is used i...
We will construct some new examples of steady gradient Ricci solitons with positive curvature operator. Moreover, for any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic ...
A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...

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