Adam Kanigowski (University of Maryland)
Sparse Equidistribution Problems in Dynamics
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Konstantin Andritsch (ETHZ)
Joined Equidistribution of Arithmetic Objects associated to Planes in Indefinite Quaternary Quadratic Space abstract
Abstract:
Recent advances in the understanding of higher-rank diagonalizable actions on homogeneous spaces by Einsiedler and Lindenstrauss have opened the door to natural couplings of distributions of objects like periodic geodesics or complex multiplication points on the modular surface, or the distribution of integer points on large spheres. In this talk we will discuss such a natural coupling by considering an indefinite quaternary quadratic vector space (V, Q). To each rational plane in V one can naturally attach three arithmetic objects which are associated to quadratic forms. The first two objects arise from the plane and its orthogonal complements with respect to Q, the third (accidental) object is constructed via the Clifford algebra of (V, Q). These arithmetic objects lead to tuples consisting of three geodesics and a point. We discuss their constructions and simultaneous equidistribution using the joining classification result of Einsiedler and Lindenstrauss under a splitting condition. This is joint work with Menny Aka and Andreas Wieser.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Michel van Garrel (University of Birmingham)
Geometric generating functions of punctured Gromov-Witten invariants and enumerative mirror symmetry abstract
Abstract:
Intrinsic Mirror Symmetry (Gross, Siebert) associates to a log Calabi-Yau variety (Y,D) a geometric generating function with support the tropicalisation of (Y,D), and with invariants the corresponding punctured Gromov-Witten invariants. This construction defines a ring and a mirror family. The enumerative mirror conjecture then states that various period integrals on the mirror family compute various Gromov-Witten invariants of (Y,D), not necessarily punctured. I will describe some examples, where this is realized, and where one obtains some new relations for Gromov-Witten invariants. Joint work with Siebert and Ruddat.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Wojciech Ozanski (Florida State University)
Abstract:
We are concerned with the ideal magneto-hydrodynamic system of PDEs posed on a domain in $\\mathbb{R}^2$ or $\\mathbb{R}^3$, such that a part $\\Gamma $ of the boundary of the domain is controlled in the sense that $v\\cdot n = k, b\\cdot n =l$ on $\\Gamma$, where $k,l$ are controls, and $v$ and $b$ denote the velocity field and the magnetic field of the system, respectively. The aim of the control is to bring the system from a given initial state $(v_0,b_0)$ into a given final state $(v_1,b_1)$ in finite time. Such a controllability problem was resolved for the 2D and 3D incompressible Euler equation in the 1990\'s by Coron and Glass. The case of the ideal MHD system is much harder due to the lack of the pressure function in the equation for $b$. Very recently, exact boundary controllability of the 2D MHD system was achieved in the case of a flat channel by Kukavica, Novack, Vicol. In the talk we will discuss the main difficulties of the problem and present a recent result (joint with Kukavica), which completely resolves the case of any domain in both 2D and 3D incompressible ideal MHD system.
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Stephan Stadler (MPIM Bonn)
Isoperimetric gaps in CAT(0) spaces abstract
Abstract:
A metric space X satisfies a Euclidean isoperimetric inequality for n-spheres, if every n-sphere S ⊂ X bounds a ball B ⊂ X with voln+1(B)≤ C · voln(S)(n+1)/n. Every CAT(0) space X satisfies Euclidean isoperimetric inequalities for 1-spheres with the sharp constant C=1/4π. Moreover, if such inequalities hold with a constant strictly smaller than 1/4π, then X has to be Gromov hyperbolic. In particular, a sharp isoperimetric gap appears. In the talk I will focus on the case n=2, namely fillings of 2-spheres by 3-balls. This is based on joint work with Drutu, Lang and Papasoglu.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Xiaoyu Yang (Kyushu University)
Large deviation principle for slow-fast rough differential equations via controlled rough paths abstract
Abstract:
We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter 1/3<H<1/2. Our approach is based on the continuity of the solution mapping and the variational framework for mixed fractional Brownian motion. By utilizing the variational representation, our problem is transformed into a qualitative property of the controlled system. In particular, the fast rough differential equation coincides with Itô SDE almost surely, which possesses a unique invariant probability measure with frozen slow component. We then demonstrate the weak convergence of the controlled slow component by averaging with respect to the invariant measure of the fast equation and exploiting the continuity of the solution mapping.
16:00 • EPF Lausanne, CM1 517
Daniela Portillo del Valle (Universität Zürich, Switzerland)
CANCELLED: Graduate Workshop Reinforcement
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12