【04-11】Existence results for Toda system with sign-changing prescribed functions-Xiaobao Zhu
Abstract:
In this talk, we shall introduce some existence results for Toda system with sign-changing prescribed functions.
This is a joint work with Prof. Linlin Sun.
【04-11】Stability of the area preserving mean curvature flow-Jun Sun
Abstract:
In this talk, we consider the long-time existence and convergence of the area preserving mean curvature flow of hypersurfaces in space forms under some initial integral pinching conditions. More precisely, we prove that the flow exists for all time and converges exponentially fast to a totally umbilical sphere if the integral of the traceless second fundamental form is sufficiently small.
Moreover, we show that starting from a sufficiently large coordinate sphere, the area preserving
【04-09】The phenomena of rigidity and flexibility for skew product systems-Changguang Dong
Abstract: We will discuss old and new properties of skew product systems. In particular, we will talk about the rigidity phenomenon on fibers, and limit theorems on the product systems. Based on joint works with Dolgopyat, Kanigowski, Nandori etc.
【04-07】Formality of the de Rham complexes of smooth varieties in positive Characteristic-Zebao Zhang
Abstract：Deligne and Illusie showed that the de Rham complex of a W₂ - liftable smooth variety over a perfect field of characteristic p>0 is formal if its dimension is less than p. However, if the dimension exceeds p, the W₂ - lifting condition is not sufficient to guarantee the formality of the de Rham complex. Nevertheless, Petrov recently demonstrated that the de Rham complex of a quasi - F - split smooth variety is formal. In this talk, we present another class of smooth varieties, called ℓ
【04-03】De Bruijn-Newman constant, Riemann zeta function, and statistical mechanics-Wei Wu
Abstract: The Riemann hypothesis can be formulated as the Fourier transform of a special function having only real zeros. Polya introduced a one-parameter family of the zeta functions associated with the Fourier transform, and the work of De Bruijn and Newman implies that there is a phase transition of the behavior of zeros, marked by the now known De Bruijn-Newman constant. Such behavior of zeros also arises in a different field in statistical mechanics known as the Lee-Yang theorem. In this ta
【04-03】An introduction to noncommutative real analysis: square and maximal inequalities-Guixiang Hong
Abstract：The main aim of this talk is to present the two fundamental research objects---square and maximal inequalities---in noncommutative setting. For this, I shall introduce noncommutative integration theory, which should be viewed as the quantized analogue of Lebesgue integral theory, just as relationship between quantum mechanics and Newtonian mechanics.
【04-02】On best constants in Poincare - type inequalities-Yacine CHITOUR
Abstract：In this talk I will present techniques stemming from optimal control which enable to in establishing classical and less classical Poincare - type inequalities, as well as determining the best constants and the functions realizing the equality cases.
【04-11】Counting Minimal Surfaces in Quasi - Fuchsian 3 - Manifolds and Beyond-Zheng Huang
Abstract：quasi - Fuchsian is an important class of hyperbolic 3 - manifolds whose fundamental groups are of closed surfaces. I will discuss some old and new counting results on minimal surfaces in such a hyperbolic 3 - manifold. Then I will present results towards some degeneration.
【04-21】Kuznetsov trace formula for GSp(4) and applications-Didier Lesesvre
Abstract:
Trace formulas relate statistics on automorphic forms, which often remain mysterious yet central in number theory, with statistics on geometric or arithmetic quantities, which one hopes to be more explicit and better understood.
We will discuss how to establish such a Kuznetsov-type trace formula in the case of the symplectic group GSp(4), and will study the precise analytic behaviour of both the spectral and the arithmetic transforms arising in the formula.
These fundamental propert
【03-31】The n/d conjecture for nonresonant hyperplane arrangements-Baiting Xie
Abstract:
Given a polynomial f, it is difficult to determine the roots of its b-function b_f explicitly. In particular, when f is a homogeneous polynomial of degree d with n variables, it is open to know when -n/d is a root of b_f. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur, Musta\c{t}\u{a} and Teitler and implies the strong monodromy conjecture for arrangements. In this talk, I will introduce a cohomological sufficient condition given by Walther and use
【03-31】Periods of algebraic varieties-Mingmin Shen
Abstract:
Algebraic varieties are spaces defined by polynomial equations. Calculus on such spaces easily leads to integrals of algebraic differential forms along topological cycles; such integrals give an interesting class of numbers, called periods. One example is the elliptic integral, which has played an important role in the development of mathematics.
Periods are very important, but they are also very difficult to calculate. In this talk, I will describe a modern framework for the study of
【03-26】Chaos on the surface-Jérôme BUZZI
Abstract:
It was noticed by Newhouse that surface diffeomorphisms in positive entropy share some of the chaotic flavor of the uniform hyperbolicity of Anosov-Smale.
In a joint project with Sylvain CROVISIER and Omri SARIG, we have indeed generalized many properties of the Anosov-Smale dynamics to arbitrary smooth surface diffeomorphisms with positive entropy: finite multiplicity of the measures maximizing the entropy, exponential mixing, almost sure invariance principle, and many other statist