【04-15】Structure, cohomology and deformations of local homogeneous Poisson brackets of arbitrary degree-Guido Carlet
Abstract: Dubrovin and Novikov initiated the study of local homogeneous differential-geometric Poisson brackets of arbitrary degree k in their seminal 1984 paper. Despite many efforts, and several results in low degree, very little is known about their structure for arbitrary k. After an introduction to the topic, we first report on our recent results on the structure of DN brackets of degree k. By applying homological algebra methods to the computation of their Poisson cohomology (or rather of
【04-15】KP integrability in topological recursion through the x-y swap relation - Alexander Alexandrov
Abstract:
I will discuss KP integrability of topological recursion which is very natural in the context of the x-y swap relation. It can be described by certain integral transforms, leading to the Kontsevich-like matrix models.
This allows us to establish general KP integrability properties of the topological recursion differentials for genus zero spectral curves.
This talk is based on a joint work with Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, and Sergey Shadrin.
【04-10】Chromatic, homomorphism and blowup thresholds-Hong Liu
Abstract:
I will talk about the classical chromatic/homomorphism thresholds problems which studies density conditions that guarantee an H-free graph to have bounded complexity. I will survey some recent developments, including an unexpected connection to the theory of VC dimension and also discrete geometry, a novel asymmetric version that we introduce to interpolate these two problems. If time permits, I will discuss two related problems, blowup and VC thresholds.
【04-14】Coupling between Brownian motion and random walks on the infinite percolation cluster-Chenlin Gu
Abstract: For the supercritical \(\mathbb{Z}^d\) - Bernoulli percolation (\(d \geq 2\)), we give a coupling between the random walk on the infinite cluster and its limit Brownian motion, such that the typical distance between the paths during \([0, T ]\) is of order \(T^{1/3 +o(1)}\). This partially answers an open question posed by Biskup [Probab. Surv., 8:294 - 373, 2011]. The construction of the coupling utilizes the optimal transport tool, and the analysis relies on local CLT and percolation
【04-10】The critical mass problem - Emanuel Indrei
Abstract: Gamow developed his model of atomic nuclei with a 1930 paper and it successfully predicts the spherical shape of nuclei and the non-existence of nuclei with a large atomic number. More specifically, assuming E to be a (three-dimensional) nucleus with constant density one, the number of nucleons corresponds approximately to the Lebesgue measure of the nucleus, |E|=m. In the surface energy, the surface tension keeps the nucleus together and the repulsion energy encodes the repulsion amon
【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.